Machines | An Open Access Journal from MDPI

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Research and Public Health (IJERPH) </option> <option value="ijfs" > International Journal of Financial Studies (IJFS) </option> <option value="ijms" > International Journal of Molecular Sciences (IJMS) </option> <option value="IJNS" > International Journal of Neonatal Screening (IJNS) </option> <option value="ijom" > International Journal of Orofacial Myology and Myofunctional Therapy (IJOM) </option> <option value="ijpb" > International Journal of Plant Biology (IJPB) </option> <option value="ijt" > International Journal of Topology </option> <option value="ijtm" > International Journal of Translational Medicine (IJTM) </option> <option value="ijtpp" > International Journal of Turbomachinery, Propulsion and Power (IJTPP) </option> <option value="ime" > International Medical Education (IME) </option> <option value="inventions" > Inventions </option> <option value="IoT" > IoT </option> <option value="ijgi" > ISPRS International Journal of Geo-Information (IJGI) </option> <option value="J" > J </option> <option value="jal" > Journal of Ageing and Longevity (JAL) </option> <option value="jcdd" > Journal of Cardiovascular Development and Disease (JCDD) </option> <option value="jcto" > Journal of Clinical & Translational Ophthalmology (JCTO) </option> <option value="jcm" > Journal of Clinical Medicine (JCM) </option> <option value="jcs" > Journal of Composites Science (J. Compos. Sci.) </option> <option value="jcp" > Journal of Cybersecurity and Privacy (JCP) </option> <option value="jdad" > Journal of Dementia and Alzheimer's Disease (JDAD) </option> <option value="jdb" > Journal of Developmental Biology (JDB) </option> <option value="jeta" > Journal of Experimental and Theoretical Analyses (JETA) </option> <option value="jemr" > Journal of Eye Movement Research (JEMR) </option> <option value="jfb" > Journal of Functional Biomaterials (JFB) </option> <option value="jfmk" > Journal of Functional Morphology and Kinesiology (JFMK) </option> <option value="jof" > Journal of Fungi (JoF) </option> <option value="jimaging" > Journal of Imaging (J. Imaging) </option> <option value="jintelligence" > Journal of Intelligence (J. Intell.) </option> <option value="jlpea" > Journal of Low Power Electronics and Applications (JLPEA) </option> <option value="jmmp" > Journal of Manufacturing and Materials Processing (JMMP) </option> <option value="jmse" > Journal of Marine Science and Engineering (JMSE) </option> <option value="jmahp" > Journal of Market Access & Health Policy (JMAHP) </option> <option value="jmms" > Journal of Mind and Medical Sciences (JMMS) </option> <option value="jmp" > Journal of Molecular Pathology (JMP) </option> <option value="jnt" > Journal of Nanotheranostics (JNT) </option> <option value="jne" > Journal of Nuclear Engineering (JNE) </option> <option value="ohbm" > Journal of Otorhinolaryngology, Hearing and Balance Medicine (JOHBM) </option> <option value="jop" > Journal of Parks </option> <option value="jpm" > Journal of Personalized Medicine (JPM) </option> <option value="jpbi" > Journal of Pharmaceutical and BioTech Industry (JPBI) </option> <option value="jor" > Journal of Respiration 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<option value="laws" > Laws </option> <option value="life" > Life </option> <option value="limnolrev" > Limnological Review </option> <option value="lipidology" > Lipidology </option> <option value="liquids" > Liquids </option> <option value="literature" > Literature </option> <option value="livers" > Livers </option> <option value="logics" > Logics </option> <option value="logistics" > Logistics </option> <option value="lubricants" > Lubricants </option> <option value="lymphatics" > Lymphatics </option> <option value="make" > Machine Learning and Knowledge Extraction (MAKE) </option> <option value="machines" selected='selected'> Machines </option> <option value="macromol" > Macromol </option> <option value="magnetism" > Magnetism </option> <option value="magnetochemistry" > Magnetochemistry </option> <option value="marinedrugs" > Marine Drugs </option> <option value="materials" > Materials </option> <option value="materproc" > Materials Proceedings </option> <option value="mca" > Mathematical and Computational Applications (MCA) </option> <option value="mathematics" > Mathematics </option> <option value="medsci" > Medical Sciences </option> <option value="msf" > Medical Sciences Forum </option> <option value="medicina" > Medicina </option> <option value="medicines" > Medicines </option> <option value="membranes" > Membranes </option> <option value="merits" > Merits </option> <option value="metabolites" > Metabolites </option> <option value="metals" > Metals </option> <option value="meteorology" > Meteorology </option> <option value="methane" > Methane </option> <option value="mps" > Methods and Protocols (MPs) </option> <option value="metrics" > Metrics </option> <option value="metrology" > Metrology </option> <option value="micro" > Micro </option> <option value="microbiolres" > Microbiology Research </option> <option value="micromachines" > Micromachines </option> <option value="microorganisms" > Microorganisms </option> <option value="microplastics" > Microplastics </option> <option value="microwave" > Microwave </option> <option value="minerals" > Minerals </option> <option value="mining" > Mining </option> <option value="modelling" > Modelling </option> <option value="mmphys" > Modern Mathematical Physics </option> <option value="molbank" > Molbank </option> <option value="molecules" > Molecules </option> <option value="mti" > Multimodal Technologies and Interaction (MTI) </option> <option value="muscles" > Muscles </option> <option value="nanoenergyadv" > Nanoenergy Advances </option> <option value="nanomanufacturing" > Nanomanufacturing </option> <option value="nanomaterials" > Nanomaterials </option> <option value="ndt" > NDT </option> <option value="network" > Network </option> <option value="neuroglia" > Neuroglia </option> <option value="neurolint" > Neurology International </option> <option value="neurosci" > NeuroSci </option> <option value="nitrogen" > Nitrogen </option> <option value="ncrna" > Non-Coding RNA (ncRNA) 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value="pharmacoepidemiology" > Pharmacoepidemiology </option> <option value="pharmacy" > Pharmacy </option> <option value="philosophies" > Philosophies </option> <option value="photochem" > Photochem </option> <option value="photonics" > Photonics </option> <option value="phycology" > Phycology </option> <option value="physchem" > Physchem </option> <option value="psf" > Physical Sciences Forum </option> <option value="physics" > Physics </option> <option value="physiologia" > Physiologia </option> <option value="plants" > Plants </option> <option value="plasma" > Plasma </option> <option value="platforms" > Platforms </option> <option value="pollutants" > Pollutants </option> <option value="polymers" > Polymers </option> <option value="polysaccharides" > Polysaccharides </option> <option value="populations" > Populations </option> <option value="poultry" > Poultry </option> <option value="powders" > Powders </option> <option value="proceedings" > Proceedings </option> <option 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value="reports" > Reports </option> <option value="reprodmed" > Reproductive Medicine (Reprod. Med.) </option> <option value="resources" > Resources </option> <option value="rheumato" > Rheumato </option> <option value="risks" > Risks </option> <option value="robotics" > Robotics </option> <option value="ruminants" > Ruminants </option> <option value="safety" > Safety </option> <option value="sci" > Sci </option> <option value="scipharm" > Scientia Pharmaceutica (Sci. Pharm.) </option> <option value="sclerosis" > Sclerosis </option> <option value="seeds" > Seeds </option> <option value="sensors" > Sensors </option> <option value="separations" > Separations </option> <option value="sexes" > Sexes </option> <option value="signals" > Signals </option> <option value="sinusitis" > Sinusitis </option> <option value="smartcities" > Smart Cities </option> <option value="socsci" > Social Sciences </option> <option value="siuj" > Société Internationale d’Urologie Journal (SIUJ) </option> <option value="societies" > Societies </option> <option value="software" > Software </option> <option value="soilsystems" > Soil Systems </option> <option value="solar" > Solar </option> <option value="solids" > Solids </option> <option value="spectroscj" > Spectroscopy Journal </option> <option value="sports" > Sports </option> <option value="standards" > Standards </option> <option value="stats" > Stats </option> <option value="stresses" > Stresses </option> <option value="surfaces" > Surfaces </option> <option value="surgeries" > Surgeries </option> <option value="std" > Surgical Techniques Development </option> <option value="sustainability" > Sustainability </option> <option value="suschem" > Sustainable Chemistry </option> <option value="symmetry" > Symmetry </option> <option value="synbio" > SynBio </option> <option value="systems" > Systems </option> <option value="targets" > Targets </option> <option value="taxonomy" > Taxonomy </option> <option value="technologies" > Technologies </option> <option value="telecom" > Telecom </option> <option value="textiles" > Textiles </option> <option value="thalassrep" > Thalassemia Reports </option> <option value="therapeutics" > Therapeutics </option> <option value="thermo" > Thermo </option> <option value="timespace" > Time and Space </option> <option value="tomography" > Tomography </option> <option value="tourismhosp" > Tourism and Hospitality </option> <option value="toxics" > Toxics </option> 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The <a href="https://iftomm-world.org/">IFToMM</a> is affiliated with <em>Machines</em> and its members receive a discount on the article processing charges. <ul> <li><span class="label openaccess"><a title="Open Access" href="https://www.mdpi.com/openaccess">Open Access</a></span>— free for readers, with <a href="https://www.mdpi.com/journal/machines/apc">article processing charges (APC)</a> paid by authors or their institutions.</li> <li><strong>High Visibility:</strong> indexed within <a href="https://www.scopus.com/sourceid/21100838145#tabs=0">Scopus</a>, <a href="https://mjl.clarivate.com/search-results?issn=2075-1702&hide_exact_match_fl=true&utm_source=mjl&utm_medium=share-by-link&utm_campaign=search-results-share-this-journal">SCIE (Web of Science)</a>, <a href="https://inspec-direct-app.theiet.org/">Inspec</a>, and <a href="https://www.mdpi.com/journal/machines/indexing">other databases</a>.</li> <li><strong><strong>Journal Rank:</strong></strong> JCR - Q2 (Engineering, Mechanical) / CiteScore - Q2 (Control and Optimization)</li> <li><strong>Rapid Publication:</strong> manuscripts are peer-reviewed and a first decision is provided to authors approximately 15.5 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2024).</li> <li><strong>Recognition of Reviewers:</strong> reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.</li> </ul> </div> <div style="margin-bottom: 15px;"> <strong>Impact Factor:</strong> 2.1 (2023); 5-Year Impact Factor: 2.2 (2023) </div> <div> <a href="/journal/machines/imprint" class="UI_JournalImprintsInfoButton"> <i class="material-icons spaced-link">subject</i> Imprint Information </a>    <a href="/journal/machines/machines_flyer.pdf" class="UD_JournalFlyer"> <i class="material-icons spaced-link">get_app</i> Journal Flyer </a>     <a class="oa-link" href="https://www.mdpi.com/about/openaccess"> <i class="material icons spaced-link"></i> Open Access </a>     <strong> ISSN: 2075-1702 </strong> </div> <div style="clear: both;"></div> </div> </div> </div> <div class="content__container content__container--overflow-initial"> <div class="custom-accordion-for-small-screen-link active"> <h2 class="no-padding-left">Latest Articles</h2> </div> <div class="custom-accordion-for-small-screen-content"> <div class="expanding-div collapsed"> <div class="generic-item article-item no-border"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 26 pages, 6335 KiB   </span> <a href="/2075-1702/13/2/155/pdf?version=1739777806" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Analysis of Nonlinear Dynamics of a Gear Transmission System Considering Effects of the Extended Tooth Contact" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/155">Analysis of Nonlinear Dynamics of a Gear Transmission System Considering Effects of the Extended Tooth Contact</a> <div class="authors"> by <span class="inlineblock "><strong>Fulin Liao</strong>, </span><span class="inlineblock "><strong>Xingyuan Zheng</strong>, </span><span class="inlineblock "><strong>Jianliang Huang</strong> and </span><span class="inlineblock "><strong>Weidong Zhu</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 155; https://doi.org/10.3390/machines13020155 (registering DOI) - 17 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/155/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Considering the elasticity of gear solid bodies, the load applied to gear teeth will force theoretically separated gear teeth to get into engaging state in advance. This phenomenon is named as the extended tooth contact (ETC). Effects of the ETC directly influence the time-varying mesh stiffness of gear pairs and subsequently alter nonlinear dynamic characteristics of gear transmission systems. Time-vary mesh stiffness, considering effects of the ETC, is thus introduced into the dynamic model of the gear transmission system. Periodic motions of a gear transmission system are discussed in detail in this work. The analytical model of time-varying mesh stiffness with effects of the ETC is proposed, and the effectiveness of the analytical model is demonstrated in comparison with finite element (FE) results. The gear transmission system is simplified as a single degree-of-freedom (DOF) model system by employing the lumped mass method. The correctness of the dynamic model is verified in comparison with experimental results. An incremental harmonic balance (IHB) method is modified to obtain periodic responses of the gear transmission system. The improved Floquet theory is employed to determine the stability and bifurcation of the periodic responses of the gear transmission system. Some interesting phenomena exist in the periodic responses consisting of “softening-spring” behaviors, jump phenomena, primary resonances (PRs), and super-harmonic resonances (SP-HRs), and saddle-node bifurcations are observed. Especially, effects of loads on unstable regions, amplitudes, and positions of bifurcation points of frequency response curves are revealed. Analytical results obtained by the IHB method match very well with those from numerical integration. <a href="/2075-1702/13/2/155">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/3OW18A1VD8 ">Advancements in Mechanical Power Transmission and Its Elements</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/155/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592702"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592702"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592702" data-cycle-prev="#prev1592702" data-cycle-progressive="#images1592702" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592702-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g001-550.jpg?1739777972" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592702" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g002-550.jpg?1739777974'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g003a-550.jpg?1739777976'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g003b-550.jpg?1739777978'><p>Figure 3 Cont.</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g004-550.jpg?1739777980'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g005-550.jpg?1739777981'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g006-550.jpg?1739777982'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g007-550.jpg?1739777984'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g008-550.jpg?1739777990'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g009-550.jpg?1739777991'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1592702-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g0A1-550.jpg?1739777992'><p>Figure A1</p></div></script></div></div><div id="article-1592702-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g001-550.jpg?1739777972" title=" <strong>Figure 1</strong><br/> <p>The single-DOF dynamic model of the gear transmission system considering time-varying mesh stiffness.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g002-550.jpg?1739777974" title=" <strong>Figure 2</strong><br/> <p>A logic diagram the IHB method.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g003a-550.jpg?1739777976" title=" <strong>Figure 3</strong><br/> <p>Comparisons between analytical results and FE results of the time-varying mesh stiffness of the gear transmission system for loads of 100 Nm and 180 Nm: (<b>a</b>) the gear transmission system neglecting effects of the ETC for a load of 100 Nm, (<b>b</b>) the gear transmission system considering effects of the ETC for a load of 100 Nm, (<b>c</b>) the gear transmission system neglecting effects of the ETC for a load of 180 Nm, and (<b>d</b>) the gear transmission system considering effects of the ETC for a load of 180 Nm.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g003b-550.jpg?1739777978" title=" <strong>Figure 3 Cont.</strong><br/> <p>Comparisons between analytical results and FE results of the time-varying mesh stiffness of the gear transmission system for loads of 100 Nm and 180 Nm: (<b>a</b>) the gear transmission system neglecting effects of the ETC for a load of 100 Nm, (<b>b</b>) the gear transmission system considering effects of the ETC for a load of 100 Nm, (<b>c</b>) the gear transmission system neglecting effects of the ETC for a load of 180 Nm, and (<b>d</b>) the gear transmission system considering effects of the ETC for a load of 180 Nm.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g004-550.jpg?1739777980" title=" <strong>Figure 4</strong><br/> <p>Effects of loads on the time-varying mesh stiffness of the gear transmission system: (<b>a</b>) the gear transmission system neglecting effects of the ETC and (<b>b</b>) the gear transmission system considering effects of the ETC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g005-550.jpg?1739777981" title=" <strong>Figure 5</strong><br/> <p>Flowchart of collecting and analyzing experimental data.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g006-550.jpg?1739777982" title=" <strong>Figure 6</strong><br/> <p>Equivalent root-mean-square (rms) amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </semantics></math> from experimental results [<a href="#B49-machines-13-00155" class="html-bibr">49</a>], numerical results [<a href="#B35-machines-13-00155" class="html-bibr">35</a>], and the IHB method results.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g007-550.jpg?1739777984" title=" <strong>Figure 7</strong><br/> <p>Time history map and phase plane diagram of the periodic response when <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.5990</mn> </mrow> </semantics></math>: (<b>a</b>) time history map and (<b>b</b>) phase plane diagram.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g008-550.jpg?1739777990" title=" <strong>Figure 8</strong><br/> <p>Nonlinear dynamic responses of the gear transmission system under different loads: (<b>a</b>) the equivalent root-mean-square amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </semantics></math> of the gear transmission system neglecting effects of the ETC and (<b>b</b>) the equivalent root-mean-square amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mrow> <mi>r</mi> <mi>m</mi> <mi>s</mi> </mrow> </msub> </semantics></math> of the gear transmission system considering effects of the ETC; (<b>c</b>) the first-order harmonic amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mn>1</mn> </msub> </semantics></math> of the gear transmission system neglecting effects of the ETC and (<b>d</b>) the first-order harmonic amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mn>1</mn> </msub> </semantics></math> of the gear transmission system considering effects of the ETC; and (<b>e</b>) the second-order harmonic amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mn>2</mn> </msub> </semantics></math> of the gear transmission system neglecting effects of the ETC and (<b>f</b>) the second-order harmonic amplitude <math display="inline"><semantics> <msub> <mi>A</mi> <mn>2</mn> </msub> </semantics></math> of the gear transmission system considering effects of the ETC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g009-550.jpg?1739777991" title=" <strong>Figure 9</strong><br/> <p>Effects of loads on the bifurcation characteristics of the gear transmission system: (<b>a</b>) bifurcation characteristics of the gear transmission system neglecting the effects of the ETC and (<b>b</b>) bifurcation characteristics of the gear transmission system considering the effects of the ETC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00155/article_deploy/html/images/machines-13-00155-g0A1-550.jpg?1739777992" title=" <strong>Figure A1</strong><br/> <p>Zeros of the equation <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mover accent="true"> <mi>x</mi> <mo>¯</mo> </mover> <mn>0</mn> </msub> <mrow> <mo>|</mo> <mo>=</mo> <mi>b</mi> <mo>/</mo> </mrow> <msub> <mi>b</mi> <mi>c</mi> </msub> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/155'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="extending-content content-ready"> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 25 pages, 43246 KiB   </span> <a href="/2075-1702/13/2/154/pdf?version=1739778115" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Benchmark Feature Detection Method for Mobile Robot Automatic Drilling System Integrated with Deep Learning" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/154">Benchmark Feature Detection Method for Mobile Robot Automatic Drilling System Integrated with Deep Learning</a> <div class="authors"> by <span class="inlineblock "><strong>Jialong Dai</strong>, </span><span class="inlineblock "><strong>Jianxin Shen</strong>, </span><span class="inlineblock "><strong>Wei Tian</strong>, </span><span class="inlineblock "><strong>Pengcheng Li</strong>, </span><span class="inlineblock "><strong>He Liu</strong> and </span><span class="inlineblock "><strong>Xiangshun Cui</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 154; https://doi.org/10.3390/machines13020154 (registering DOI) - 17 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Benchmark feature detection is critical in mobile robot automatic drilling systems for compensating robot accuracy and assembly errors in aerospace manufacturing. System accuracy is influenced by reference feature recognition, which is often hindered by material interference and background noise. To address these issues, <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/154/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Benchmark feature detection is critical in mobile robot automatic drilling systems for compensating robot accuracy and assembly errors in aerospace manufacturing. System accuracy is influenced by reference feature recognition, which is often hindered by material interference and background noise. To address these issues, this paper proposes a method that uses a 2D industrial camera for image capture, applies deep learning for initial target recognition and positioning, and then determines the feature extraction location based on the initial recognition. The extracted benchmark positions are accurately fitted using an improved Huber algorithm. Experimental results demonstrate that this approach improves the benchmark feature detection recognition rate by 43.8%, center recognition accuracy by 78.26%, and overall hole processing accuracy by 54.69%. <a href="/2075-1702/13/2/154">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/54H69MZABE ">Interactive Manipulation of Mobile Manipulators</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/154/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592714"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592714"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592714" data-cycle-prev="#prev1592714" data-cycle-progressive="#images1592714" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592714-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g001-550.jpg?1739778189" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592714" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g002-550.jpg?1739778190'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g003-550.jpg?1739778193'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g004-550.jpg?1739778194'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g005-550.jpg?1739778195'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g006-550.jpg?1739778196'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g007-550.jpg?1739778197'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g008-550.jpg?1739778200'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g009-550.jpg?1739778201'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g010-550.jpg?1739778202'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g011-550.jpg?1739778204'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g012-550.jpg?1739778206'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g013-550.jpg?1739778207'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g014-550.jpg?1739778208'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1592714-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g015-550.jpg?1739778210'><p>Figure 15</p></div></script></div></div><div id="article-1592714-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g001-550.jpg?1739778189" title=" <strong>Figure 1</strong><br/> <p>Mobile robot automatic drilling system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g002-550.jpg?1739778190" title=" <strong>Figure 2</strong><br/> <p>Benchmark detection module.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g003-550.jpg?1739778193" title=" <strong>Figure 3</strong><br/> <p>Coordinate system of the benchmark detection process.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g004-550.jpg?1739778194" title=" <strong>Figure 4</strong><br/> <p>Overall flow chart of deep learning-based benchmark feature detection.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g005-550.jpg?1739778195" title=" <strong>Figure 5</strong><br/> <p>Sampling diagram.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g006-550.jpg?1739778196" title=" <strong>Figure 6</strong><br/> <p>Edge intensity waveform.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g007-550.jpg?1739778197" title=" <strong>Figure 7</strong><br/> <p>Polarity and threshold screening.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g008-550.jpg?1739778200" title=" <strong>Figure 8</strong><br/> <p>Mobile robot automatic drilling test system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g009-550.jpg?1739778201" title=" <strong>Figure 9</strong><br/> <p>mAP average precision mean graph. (<b>a</b>) mAP_0.5 Mean average precision. (<b>b</b>) mAP _0.5:0.95 Mean average precision.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g010-550.jpg?1739778202" title=" <strong>Figure 10</strong><br/> <p>Precision and recall graph. (<b>a</b>) Precision. (<b>b</b>) Recall.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g011-550.jpg?1739778204" title=" <strong>Figure 11</strong><br/> <p>Validation set test diagram.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g012-550.jpg?1739778206" title=" <strong>Figure 12</strong><br/> <p>Statistics on the effectiveness of seven types of benchmark recognition.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g013-550.jpg?1739778207" title=" <strong>Figure 13</strong><br/> <p>Algorithm error comparison.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g014-550.jpg?1739778208" title=" <strong>Figure 14</strong><br/> <p>Experimental drilling process diagram. (<b>a</b>) Experimental drilling process. (<b>b</b>) Experimental drilling results.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00154/article_deploy/html/images/machines-13-00154-g015-550.jpg?1739778210" title=" <strong>Figure 15</strong><br/> <p>Comparison of actual hole spacing differences of the mobile robot automatic drilling system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/154'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 4376 KiB   </span> <a href="/2075-1702/13/2/153/pdf?version=1739773538" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="A Review of Machine Learning-Based Thermal Error Modeling Methods for CNC Machine Tools" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2075-1702/13/2/153">A Review of Machine Learning-Based Thermal Error Modeling Methods for CNC Machine Tools</a> <div class="authors"> by <span class="inlineblock "><strong>Sen Mu</strong>, </span><span class="inlineblock "><strong>Chunping Yu</strong>, </span><span class="inlineblock "><strong>Kunlong Lin</strong>, </span><span class="inlineblock "><strong>Caijiang Lu</strong>, </span><span class="inlineblock "><strong>Xi Wang</strong>, </span><span class="inlineblock "><strong>Tao Wang</strong> and </span><span class="inlineblock "><strong>Guoqiang Fu</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 153; https://doi.org/10.3390/machines13020153 (registering DOI) - 17 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Heat source-induced thermal error is a primary element influencing the precision of CNC machine tools. A practical and economical approach to mitigating thermal errors is through thermal error compensation. To provide a comprehensive understanding of thermal error modeling and its advancements, this paper <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/153/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Heat source-induced thermal error is a primary element influencing the precision of CNC machine tools. A practical and economical approach to mitigating thermal errors is through thermal error compensation. To provide a comprehensive understanding of thermal error modeling and its advancements, this paper systematically reviews machine learning-based methods for thermal error compensation. Thermal error modeling is the most critical step in thermal error compensation, as it directly influences the effectiveness of the compensation due to its accuracy and robustness. With the rapid development of big data and artificial intelligence, machine learning has emerged as a powerful tool in thermal error modeling, leading to significant research progress in recent years. In this paper, an overview of the thermal error modeling methods based on deep learning that have been researched and applied in recent years is presented. Specifically, two methods for reducing thermal errors, namely, thermal error suppression and thermal error compensation, are introduced and analyzed. Second, machine learning-based thermal error modeling methods are categorized into traditional machine learning-driven and deep learning-driven approaches. The application of these two methods in thermal error modeling and compensation is reviewed and summarized in detail. By synthesizing these studies, this paper identifies key challenges and trends in machine learning-based thermal error modeling. Finally, the thermal error modeling methods discussed in this paper are summarized, and future research directions are proposed to further enhance modeling accuracy and robustness. <a href="/2075-1702/13/2/153">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Machines_Testing_and_Maintenance">Machines Testing and Maintenance</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/153/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592647"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592647"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592647" data-cycle-prev="#prev1592647" data-cycle-progressive="#images1592647" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592647-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g001-550.jpg?1739773643" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592647" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592647-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g002a-550.jpg?1739773645'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592647-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g002b-550.jpg?1739773646'><p>Figure 2 Cont.</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592647-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g003-550.jpg?1739773649'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592647-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g004-550.jpg?1739773651'><p>Figure 4</p></div></script></div></div><div id="article-1592647-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g001-550.jpg?1739773643" title=" <strong>Figure 1</strong><br/> <p>Basic structure of ANFIS with FCM clustering [<a href="#B24-machines-13-00153" class="html-bibr">24</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/153'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g002a-550.jpg?1739773645" title=" <strong>Figure 2</strong><br/> <p>Prediction results’ comparison and performance [<a href="#B41-machines-13-00153" class="html-bibr">41</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/153'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g002b-550.jpg?1739773646" title=" <strong>Figure 2 Cont.</strong><br/> <p>Prediction results’ comparison and performance [<a href="#B41-machines-13-00153" class="html-bibr">41</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/153'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g003-550.jpg?1739773649" title=" <strong>Figure 3</strong><br/> <p>Structure schematic of ViT [<a href="#B28-machines-13-00153" class="html-bibr">28</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/153'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00153/article_deploy/html/images/machines-13-00153-g004-550.jpg?1739773651" title=" <strong>Figure 4</strong><br/> <p>Thermal error modeling based on CNN [<a href="#B59-machines-13-00153" class="html-bibr">59</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/153'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 28 pages, 34209 KiB   </span> <a href="/2075-1702/13/2/152/pdf?version=1739778209" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Autonomous Non-Communicative Navigation Assistance to the Ground Vehicle by an Aerial Vehicle" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/152">Autonomous Non-Communicative Navigation Assistance to the Ground Vehicle by an Aerial Vehicle</a> <div class="authors"> by <span class="inlineblock "><strong>Ashok Kumar Sivarathri</strong> and </span><span class="inlineblock "><strong>Amit Shukla</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 152; https://doi.org/10.3390/machines13020152 (registering DOI) - 17 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Vision-based UAV-AGV (Unmanned Aerial Vehicle–Autonomous Ground Vehicle) systems are prominent for executing tasks in GPS (Global Positioning System)-inaccessible areas. One of the roles of the UAV is guiding the navigation of the AGV. Reactive/mapless navigation assistance to an AGV from a UAV is <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/152/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Vision-based UAV-AGV (Unmanned Aerial Vehicle–Autonomous Ground Vehicle) systems are prominent for executing tasks in GPS (Global Positioning System)-inaccessible areas. One of the roles of the UAV is guiding the navigation of the AGV. Reactive/mapless navigation assistance to an AGV from a UAV is well known and suitable for computationally less powerful systems. This method requires communication between both agents during navigation as per state of the art. However, communication delays and failures will cause failures in tasks, especially during outdoor missions. In the present work, we propose a mapless technique for the navigation of AGVs assisted by UAVs without communication of obstacles to AGVs. The considered scenario is that the AGV is undergoing sensor and communication module failure and is completely dependent on the UAV for its safe navigation. The goal of the UAV is to take AGV to the destination while guiding it to avoid obstacles. We exploit the autonomous tracking task between the UAV and AGV for obstacle avoidance. In particular, AGV tracking the motion of the UAV is exploited for the navigation of the AGV. YOLO (You Only Look Once) v8 has been implemented to detect the drone by AGV camera. The sliding mode control method is implemented for the tracking motion of the AGV and obstacle avoidance control. The job of the UAV is to localize obstacles in the image plane and guide the AGV without communicating with it. Experimental results are presented to validate the proposed method. This proves to be a significant technique for the safe navigation of the AGV when it is non-communicating and experiencing sudden sensor failure. <a href="/2075-1702/13/2/152">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/2O6C5YZEO9 ">Guidance, Navigation and Control of Mobile Robots</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/152/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592715"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592715"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592715" data-cycle-prev="#prev1592715" data-cycle-progressive="#images1592715" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592715-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g001-550.jpg?1739778329" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592715" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g002-550.jpg?1739778331'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g003-550.jpg?1739778334'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g004-550.jpg?1739778337'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g005-550.jpg?1739778338'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g006-550.jpg?1739778339'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g007-550.jpg?1739778340'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g008-550.jpg?1739778341'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g009-550.jpg?1739778342'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g010-550.jpg?1739778343'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g011-550.jpg?1739778345'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g012-550.jpg?1739778348'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g013-550.jpg?1739778350'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g014-550.jpg?1739778351'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g015-550.jpg?1739778353'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g016-550.jpg?1739778354'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g017-550.jpg?1739778355'><p>Figure 17</p></div> --- <div class='openpopupgallery' data-imgindex='17' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g018-550.jpg?1739778357'><p>Figure 18</p></div> --- <div class='openpopupgallery' data-imgindex='18' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g019-550.jpg?1739778360'><p>Figure 19</p></div> --- <div class='openpopupgallery' data-imgindex='19' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g020-550.jpg?1739778366'><p>Figure 20</p></div> --- <div class='openpopupgallery' data-imgindex='20' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g021-550.jpg?1739778367'><p>Figure 21</p></div> --- <div class='openpopupgallery' data-imgindex='21' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g022-550.jpg?1739778369'><p>Figure 22</p></div> --- <div class='openpopupgallery' data-imgindex='22' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g023-550.jpg?1739778370'><p>Figure 23</p></div> --- <div class='openpopupgallery' data-imgindex='23' data-target='article-1592715-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g024-550.jpg?1739778371'><p>Figure 24</p></div></script></div></div><div id="article-1592715-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g001-550.jpg?1739778329" title=" <strong>Figure 1</strong><br/> <p>Illustration of obstacle avoidance problem.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g002-550.jpg?1739778331" title=" <strong>Figure 2</strong><br/> <p>Methodology of proposed technique.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g003-550.jpg?1739778334" title=" <strong>Figure 3</strong><br/> <p>Image processing operations in both vehicles for relative localization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g004-550.jpg?1739778337" title=" <strong>Figure 4</strong><br/> <p>Sample test images.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g005-550.jpg?1739778338" title=" <strong>Figure 5</strong><br/> <p>Localization of UAV in AGV camera.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g006-550.jpg?1739778339" title=" <strong>Figure 6</strong><br/> <p>Detection and localization of ArUco marker in image plane of UAV camera.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g007-550.jpg?1739778340" title=" <strong>Figure 7</strong><br/> <p>(<b>a</b>) Localization of AGV and obstacle in UAV camera and (<b>b</b>) localization of UAV and obstacle in virtual plane of AGV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g008-550.jpg?1739778341" title=" <strong>Figure 8</strong><br/> <p>Control architecture for AGV to track UAV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g009-550.jpg?1739778342" title=" <strong>Figure 9</strong><br/> <p>Reaching law.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g010-550.jpg?1739778343" title=" <strong>Figure 10</strong><br/> <p>Variation in position of obstacle in VP and controller output.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g011-550.jpg?1739778345" title=" <strong>Figure 11</strong><br/> <p>Variation in position of obstacle in VP and virtual velocity of AGV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g012-550.jpg?1739778348" title=" <strong>Figure 12</strong><br/> <p>Hardware.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g013-550.jpg?1739778350" title=" <strong>Figure 13</strong><br/> <p>ROS node commutation in both agents.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g014-550.jpg?1739778351" title=" <strong>Figure 14</strong><br/> <p>Overall non-communicative tracking strategy for AGV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g015-550.jpg?1739778353" title=" <strong>Figure 15</strong><br/> <p>Image taken during tracking experiment.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g016-550.jpg?1739778354" title=" <strong>Figure 16</strong><br/> <p>(<b>a</b>) Apparent position of UAV and linear velocity of AGV and (<b>b</b>) variation in velocity of UAV and AGV during tracking.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g017-550.jpg?1739778355" title=" <strong>Figure 17</strong><br/> <p>(<b>a</b>) Apparent position of UAV and linear velocity of AGV and (<b>b</b>) variation in velocity of UAV and AGV during tracking.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g018-550.jpg?1739778357" title=" <strong>Figure 18</strong><br/> <p>Overall strategy for non-communicative navigation of AGV assisted by UAV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g019-550.jpg?1739778360" title=" <strong>Figure 19</strong><br/> <p>(<b>a</b>) UAV with down-facing camera and (<b>b</b>) obstacle avoidance experimentation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g020-550.jpg?1739778366" title=" <strong>Figure 20</strong><br/> <p>Aerial image instances during obstacle avoidance.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g021-550.jpg?1739778367" title=" <strong>Figure 21</strong><br/> <p>(<b>a</b>) Velocity of the UAV and AGV in the body frame of the AGV and (<b>b</b>) linear velocity of the UAV and AGV in the body frame of the AGV during the obstacle avoidance experiment.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g022-550.jpg?1739778369" title=" <strong>Figure 22</strong><br/> <p>(<b>a</b>) Variation in apparent pose of AGV in UAV image frame and (<b>b</b>) variation in apparent position of UAV in AGV image frame.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g023-550.jpg?1739778370" title=" <strong>Figure 23</strong><br/> <p>(<b>a</b>) Apparent position of obstacle in UAV image frame and (<b>b</b>) apparent position of obstacle in AGV virtual plane during obstacle avoidance.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00152/article_deploy/html/images/machines-13-00152-g024-550.jpg?1739778371" title=" <strong>Figure 24</strong><br/> <p>Multiple static/dynamic obstacles in FOV of UAV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/152'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 5829 KiB   </span> <a href="/2075-1702/13/2/151/pdf?version=1739687462" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Research on Remote Operation and Maintenance Based on Digital Twin Technology" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/151">Research on Remote Operation and Maintenance Based on Digital Twin Technology</a> <div class="authors"> by <span class="inlineblock "><strong>Peilu Sun</strong> and </span><span class="inlineblock "><strong>Xin Liu</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 151; https://doi.org/10.3390/machines13020151 (registering DOI) - 16 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> With the wide application of a new generation of information technology, remote technical services are receiving an increasing amount of attention in the manufacturing field. In view of the fact that most mechanical and electrical equipment manufacturing enterprises still need to send a <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/151/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> With the wide application of a new generation of information technology, remote technical services are receiving an increasing amount of attention in the manufacturing field. In view of the fact that most mechanical and electrical equipment manufacturing enterprises still need to send a substantial number of employees to the site to provide operation and maintenance services for customers, and the operation and maintenance costs of enterprises remain high, a remote operation and maintenance method of mechanical and electrical equipment based on digital twin technology is proposed. A digital twin remote operation and maintenance services model is constructed, and digital twin remote operation and maintenance technology is divided into four basic levels: virtual simulation, software/hardware-in-the-loop virtual commissioning, virtual and real synchronization, and cloud–end interconnection. With this, we conduct in-depth research on the key technologies involved in these four levels. The digital twin remote operation and maintenance service platform has been built; this platform can provide maintenance, repair, overhaul, and operation services for enterprise equipment. The feasibility of both the digital twin remote operation and maintenance services model and the digital twin remote operation and maintenance service platform was verified through cases, which provided an efficient and feasible solution for enterprises to improve service efficiency and reduce labor costs. <a href="/2075-1702/13/2/151">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Topic <a href="/topics/378CG0EQYT">Smart Product Design and Manufacturing on Industrial Internet</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/151/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592263"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592263"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592263" data-cycle-prev="#prev1592263" data-cycle-progressive="#images1592263" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592263-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g001-550.jpg?1739687531" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592263" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g002-550.jpg?1739687532'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g003-550.jpg?1739687533'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g004-550.jpg?1739687534'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g005-550.jpg?1739687535'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g006-550.jpg?1739687536'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g007-550.jpg?1739687537'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g008-550.jpg?1739687537'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g009-550.jpg?1739687538'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g010-550.jpg?1739687539'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g011-550.jpg?1739687541'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g012-550.jpg?1739687542'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g013-550.jpg?1739687543'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g014-550.jpg?1739687544'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g015-550.jpg?1739687545'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g016-550.jpg?1739687547'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1592263-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g017-550.jpg?1739687548'><p>Figure 17</p></div></script></div></div><div id="article-1592263-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g001-550.jpg?1739687531" title=" <strong>Figure 1</strong><br/> <p>Conceptual model of the digital twin remote operation and maintenance service.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g002-550.jpg?1739687532" title=" <strong>Figure 2</strong><br/> <p>Four levels of digital twin remote operation and maintenance service technology.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g003-550.jpg?1739687533" title=" <strong>Figure 3</strong><br/> <p>The relationship between the four levels of digital twin remote operation and maintenance service technology and digital twins.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g004-550.jpg?1739687534" title=" <strong>Figure 4</strong><br/> <p>Virtual simulation schematics.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g005-550.jpg?1739687535" title=" <strong>Figure 5</strong><br/> <p>The relationship between the whole life cycle of the product and the period and stage of the manufacturing industry.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g006-550.jpg?1739687536" title=" <strong>Figure 6</strong><br/> <p>Schematic diagram of software/hardware-in-the-loop virtual commissioning technology.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g007-550.jpg?1739687537" title=" <strong>Figure 7</strong><br/> <p>Schematic diagram of virtual–real synchronization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g008-550.jpg?1739687537" title=" <strong>Figure 8</strong><br/> <p>Simulate the schematic diagram of virtual and real synchronization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g009-550.jpg?1739687538" title=" <strong>Figure 9</strong><br/> <p>Location curve of cylinder rod movement position.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g010-550.jpg?1739687539" title=" <strong>Figure 10</strong><br/> <p>Schematic diagram of cloud–end interconnection.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g011-550.jpg?1739687541" title=" <strong>Figure 11</strong><br/> <p>Process and results of cloud–end interconnection experiment. (<b>a</b>) Initial diagram of cylinder control; (<b>b</b>) result diagram of cylinder control; (<b>c</b>) cylinder location graph after control.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g012-550.jpg?1739687542" title=" <strong>Figure 12</strong><br/> <p>Digital twin remote operation and maintenance service platform.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g013-550.jpg?1739687543" title=" <strong>Figure 13</strong><br/> <p>Conveyor equipment.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g014-550.jpg?1739687544" title=" <strong>Figure 14</strong><br/> <p>PLC control box.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g015-550.jpg?1739687545" title=" <strong>Figure 15</strong><br/> <p>The process of establishing virtual–real synchronization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g016-550.jpg?1739687547" title=" <strong>Figure 16</strong><br/> <p>Experimental process.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00151/article_deploy/html/images/machines-13-00151-g017-550.jpg?1739687548" title=" <strong>Figure 17</strong><br/> <p>Comparison chart of local equipment and twin model running data.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/151'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 12 pages, 955 KiB   </span> <a href="/2075-1702/13/2/150/pdf?version=1739613089" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Pareto Analysis of Electro-Mechanical Variables in Predictive Control of Drives" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/150">Pareto Analysis of Electro-Mechanical Variables in Predictive Control of Drives</a> <div class="authors"> by <span class="inlineblock "><strong>Manuel G. Satué</strong>, </span><span class="inlineblock "><strong>Manuel R. Arahal</strong> and </span><span class="inlineblock "><strong>Manuel G. Ortega</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 150; https://doi.org/10.3390/machines13020150 (registering DOI) - 15 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Variable speed drives are often controlled by a double-loop scheme in which a proportional integral controller takes on the speed loop. The tuning of this loop is a complex job. In most cases just mechanical variables are considered for tuning. This paper presents <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/150/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Variable speed drives are often controlled by a double-loop scheme in which a proportional integral controller takes on the speed loop. The tuning of this loop is a complex job. In most cases just mechanical variables are considered for tuning. This paper presents a new Pareto analysis incorporating mechanical and electrical variables. A state of the art finite state model predictive controller is used for stator current control. The analysis is performed using experimental data from a five-phase induction motor and considers considering commonly found performance indicators derived from experimental data. The results show undocumented connections between those performance indicators. The analysis not only helps in PI tuning but, more importantly, prompts for a revision of the methods usually utilized to report performance enhancements of new methods. <a href="/2075-1702/13/2/150">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/111Y969J29 ">Recent Progress in Electrical Machines and Motor Drives</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/150/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1592010"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1592010"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1592010" data-cycle-prev="#prev1592010" data-cycle-progressive="#images1592010" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1592010-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g001-550.jpg?1739613216" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1592010" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1592010-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g002-550.jpg?1739613217'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1592010-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g003-550.jpg?1739613218'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1592010-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g004-550.jpg?1739613219'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1592010-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g005-550.jpg?1739613221'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1592010-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g006-550.jpg?1739613224'><p>Figure 6</p></div></script></div></div><div id="article-1592010-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g001-550.jpg?1739613216" title=" <strong>Figure 1</strong><br/> <p>Diagram and photographs of the laboratory setup used in the experiments.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g002-550.jpg?1739613217" title=" <strong>Figure 2</strong><br/> <p>Diagram of the control scheme for a multi-phase motor.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g003-550.jpg?1739613218" title=" <strong>Figure 3</strong><br/> <p>Steady state evolution of currents.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g004-550.jpg?1739613219" title=" <strong>Figure 4</strong><br/> <p>Electrical torque (<b>left</b> column) and speed (<b>right</b> column) in a step test.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g005-550.jpg?1739613221" title=" <strong>Figure 5</strong><br/> <p>Projections of set <math display="inline"><semantics> <mi mathvariant="bold-italic">P</mi> </semantics></math> for <math display="inline"><semantics> <mrow> <msup> <mi>ω</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>400</mn> </mrow> </semantics></math> (rpm). Different hues correspond to different <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>3</mn> </msub> </semantics></math> values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00150/article_deploy/html/images/machines-13-00150-g006-550.jpg?1739613224" title=" <strong>Figure 6</strong><br/> <p>Projections of set <math display="inline"><semantics> <mi mathvariant="bold-italic">P</mi> </semantics></math> for <math display="inline"><semantics> <mrow> <msup> <mi>ω</mi> <mo>∗</mo> </msup> <mo>=</mo> <mn>120</mn> </mrow> </semantics></math> (rpm). Different hues correspond to different <math display="inline"><semantics> <msub> <mi>γ</mi> <mn>3</mn> </msub> </semantics></math> values.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/150'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 15 pages, 2872 KiB   </span> <a href="/2075-1702/13/2/149/pdf?version=1739544252" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="The Design and Research of a Cup Body Weld Seam Polishing Positioning System Based on Machine Vision" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/149">The Design and Research of a Cup Body Weld Seam Polishing Positioning System Based on Machine Vision</a> <div class="authors"> by <span class="inlineblock "><strong>Yanqing Qiu</strong>, </span><span class="inlineblock "><strong>Zhinan Zhao</strong>, </span><span class="inlineblock "><strong>Tingting Lang</strong> and </span><span class="inlineblock "><strong>Wei Liu</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 149; <a href="https://doi.org/10.3390/machines13020149">https://doi.org/10.3390/machines13020149</a> - 14 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> A machine vision-based weld seam positioning system for thermos cups is proposed. The system’s operational flow and image algorithms are designed to achieve automatic calibration of the weld seam orientation. Experimental results show a qualification rate of 97.8%, demonstrating robust performance across various <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/149/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> A machine vision-based weld seam positioning system for thermos cups is proposed. The system’s operational flow and image algorithms are designed to achieve automatic calibration of the weld seam orientation. Experimental results show a qualification rate of 97.8%, demonstrating robust performance across various cup models. The average positioning error is 45 pixels, with a maximum error of 153 pixels, corresponding to angular deviations of 0.68° and 2.30°, respectively. The average processing time of a single algorithm run is 128 ms, ensuring efficient operation in non-high-speed production scenarios. The results of this study have good application value and also provide some insights for the position calibration of other rotational objects. <a href="/2075-1702/13/2/149">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Automation_Systems">Automation and Control Systems</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 20 pages, 11911 KiB   </span> <a href="/2075-1702/13/2/148/pdf?version=1739529054" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Comparison of Automation-Supported and Conventional Methods for Measuring Energy Consumption in Computer Numerical Control Machining" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/148">Comparison of Automation-Supported and Conventional Methods for Measuring Energy Consumption in Computer Numerical Control Machining</a> <div class="authors"> by <span class="inlineblock "><strong>Erman Zurnacı</strong>, </span><span class="inlineblock "><strong>Sabri Uzuner</strong> and </span><span class="inlineblock "><strong>Engin Nas</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 148; <a href="https://doi.org/10.3390/machines13020148">https://doi.org/10.3390/machines13020148</a> - 14 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Optimizing energy consumption in machining processes is critical for achieving sustainable manufacturing. This study introduces an Automation-Supported measurement approach that integrates a custom power analyzer with real-time data logging and visualization capabilities to accurately measure energy usage during CNC (computer numerical control) operations. <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/148/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Optimizing energy consumption in machining processes is critical for achieving sustainable manufacturing. This study introduces an Automation-Supported measurement approach that integrates a custom power analyzer with real-time data logging and visualization capabilities to accurately measure energy usage during CNC (computer numerical control) operations. Statistical comparisons were conducted using the independent samples <i>t</i>-test and Taguchi analysis to evaluate the effectiveness of the proposed method against traditional measurement techniques. The results revealed that there is a statistically significant difference (<i>p</i> < 0.05) in the current measurements across X, Z, and spindle motors between the proposed and conventional methods. The advanced method based on automation reduced the error rate in measuring spindle motor power consumption due to the selection of processing parameters from 34.17% to 2.7%. Additionally, Taguchi analysis demonstrated that the measurement method influenced the optimization of machining parameters, with <i>S</i>/<i>N</i> ratio improvements observed. These findings confirm that the proposed method enhances energy efficiency, reduces environmental impact, and supports sustainable manufacturing practices. <a href="/2075-1702/13/2/148">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/industrial_systems">Industrial Systems</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/148/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1591379"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1591379"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1591379" data-cycle-prev="#prev1591379" data-cycle-progressive="#images1591379" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1591379-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g001-550.jpg?1739529173" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1591379" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g002-550.jpg?1739529175'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g003-550.jpg?1739529176'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g004-550.jpg?1739529178'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g005-550.jpg?1739529180'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g006-550.jpg?1739529182'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g007-550.jpg?1739529184'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g008-550.jpg?1739529185'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g009-550.jpg?1739529187'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g010-550.jpg?1739529191'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g011-550.jpg?1739529191'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g012-550.jpg?1739529192'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g013-550.jpg?1739529193'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1591379-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g014-550.jpg?1739529194'><p>Figure 14</p></div></script></div></div><div id="article-1591379-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g001-550.jpg?1739529173" title=" <strong>Figure 1</strong><br/> <p>Electrical power consumption by sector [<a href="#B9-machines-13-00148" class="html-bibr">9</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g002-550.jpg?1739529175" title=" <strong>Figure 2</strong><br/> <p>Power profile of a machine tool during machining [<a href="#B12-machines-13-00148" class="html-bibr">12</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g003-550.jpg?1739529176" title=" <strong>Figure 3</strong><br/> <p>Electrical power consumption of main functions during machining [<a href="#B13-machines-13-00148" class="html-bibr">13</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g004-550.jpg?1739529178" title=" <strong>Figure 4</strong><br/> <p>The framework of different energy measurement methods used in machining operation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g005-550.jpg?1739529180" title=" <strong>Figure 5</strong><br/> <p>Research framework for the comparison of power consumption-measuring methods.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g006-550.jpg?1739529182" title=" <strong>Figure 6</strong><br/> <p>The components of the Automation-Supported energy consumption measurement system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g007-550.jpg?1739529184" title=" <strong>Figure 7</strong><br/> <p>Components of the custom power analyzer: (<b>a</b>) voltage and (<b>b</b>) current measurement board.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g008-550.jpg?1739529185" title=" <strong>Figure 8</strong><br/> <p>Data visualization interface designed for storing and visualizing data.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g009-550.jpg?1739529187" title=" <strong>Figure 9</strong><br/> <p>Real-time electrical and machining data obtained via data visualization interface.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g010-550.jpg?1739529191" title=" <strong>Figure 10</strong><br/> <p>The average current values consumed by motors: (<b>a</b>) spindle, (<b>b</b>) X-axis, and (<b>c</b>) Z-axis motors. Prediction error was calculated using the formula “<span class="html-italic">absolute percentage predicted error (%) = |((Unconsidered − Automation-Supported)/Automation-Supported) × 100)|</span>”.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g011-550.jpg?1739529191" title=" <strong>Figure 11</strong><br/> <p>Average total power values were measured during the cutting phase.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g012-550.jpg?1739529192" title=" <strong>Figure 12</strong><br/> <p>The power consumption in the spindle was measured using (<b>a</b>) Automation-Supported and (<b>b</b>) Unconsidered methods. The black line illustrates the percentage increase in spindle power consumption during the cutting phase compared to the air-cutting phase.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g013-550.jpg?1739529193" title=" <strong>Figure 13</strong><br/> <p>Main effect plot for <span class="html-italic">S</span>/<span class="html-italic">N</span> of spindle power consumption according to measurement method: (<b>a</b>) Unconsidered and (<b>b</b>) Automation-Supported.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00148/article_deploy/html/images/machines-13-00148-g014-550.jpg?1739529194" title=" <strong>Figure 14</strong><br/> <p>Main effect plot for <span class="html-italic">S</span>/<span class="html-italic">N</span> of total power consumption according to measurement method: (<b>a</b>) Indirect and (<b>b</b>) Automation-Supported.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/148'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 20 pages, 8863 KiB   </span> <a href="/2075-1702/13/2/147/pdf?version=1739537393" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Comparative Study of Hydrodynamic Performance of Submerged Water Jet Propeller and Conventional Propeller Under Multiple Operating Conditions" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/147">Comparative Study of Hydrodynamic Performance of Submerged Water Jet Propeller and Conventional Propeller Under Multiple Operating Conditions</a> <div class="authors"> by <span class="inlineblock "><strong>Jiayi Li</strong>, </span><span class="inlineblock "><strong>Lei Ma</strong>, </span><span class="inlineblock "><strong>Dongyang Chen</strong>, </span><span class="inlineblock "><strong>Yunpeng Qi</strong>, </span><span class="inlineblock "><strong>Tiechao Bai</strong> and </span><span class="inlineblock "><strong>Guang Pan</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 147; <a href="https://doi.org/10.3390/machines13020147">https://doi.org/10.3390/machines13020147</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> As global shipping accelerates toward a green and low-carbon transformation, submerged water jet propulsion has emerged as a promising alternative to traditional propellers due to its high speed efficiency, noise reduction, and adaptability. This study establishes a high-fidelity CFD (computational fluid dynamics) model <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/147/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> As global shipping accelerates toward a green and low-carbon transformation, submerged water jet propulsion has emerged as a promising alternative to traditional propellers due to its high speed efficiency, noise reduction, and adaptability. This study establishes a high-fidelity CFD (computational fluid dynamics) model incorporating vehicle body wake characteristics, validated through open-water experiments. A comparative analysis reveals that the vehicle body wake improves propulsion efficiency by 4.66% for conventional propellers and 2.32% for submerged water jet systems in near-surface operations while exacerbating cavitation-induced efficiency losses by 1.7% and 1.0%, respectively. Notably, submerged water jet propulsion demonstrates superior performance under high-velocity conditions, achieving 5–12.27% higher efficiency than conventional propellers across both open-water and vehicle body wake-affected scenarios. These findings substantiate submerged water jet propulsion’s advantages in complex flow fields, offering critical insights for marine propulsion system optimization. <a href="/2075-1702/13/2/147">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/TH8XXN8T10 ">Advancements in Fluid-Structure Interaction Vibration Control Technology</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/147/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1590755"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1590755"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1590755" data-cycle-prev="#prev1590755" data-cycle-progressive="#images1590755" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1590755-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g001-550.jpg?1739537519" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1590755" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g002-550.jpg?1739537520'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g003-550.jpg?1739537522'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g004-550.jpg?1739537524'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g005-550.jpg?1739537526'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g006-550.jpg?1739537527'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g007-550.jpg?1739537528'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g008-550.jpg?1739537529'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g009-550.jpg?1739537531'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g010-550.jpg?1739537533'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g011-550.jpg?1739537534'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g012-550.jpg?1739537536'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g013-550.jpg?1739537537'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g014-550.jpg?1739537539'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g015-550.jpg?1739537540'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1590755-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g016-550.jpg?1739537541'><p>Figure 16</p></div></script></div></div><div id="article-1590755-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g001-550.jpg?1739537519" title=" <strong>Figure 1</strong><br/> <p>Schematic diagram of calculation domain of submerged water jet propeller and conventional propeller.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g002-550.jpg?1739537520" title=" <strong>Figure 2</strong><br/> <p>Schematic diagram of calculation domain of submerged water jet propeller and conventional propeller considering the vehicle body’s wake.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g003-550.jpg?1739537522" title=" <strong>Figure 3</strong><br/> <p>Schematic diagrams of three grids: (<b>a</b>) coarse grids, (<b>b</b>) medium grids, and (<b>c</b>) fine grids.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g004-550.jpg?1739537524" title=" <strong>Figure 4</strong><br/> <p>Schematic diagram of propeller grids and submerged water jet propeller grids.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g005-550.jpg?1739537526" title=" <strong>Figure 5</strong><br/> <p>Schematic of the grids of the hull coupled with the conventional propeller and the grids of the hull coupled with submerged water jet propeller.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g006-550.jpg?1739537527" title=" <strong>Figure 6</strong><br/> <p>Working section of the cavitation tunnel and schematic diagram of the model.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g007-550.jpg?1739537528" title=" <strong>Figure 7</strong><br/> <p>Hydrodynamic coefficient simulation results of the submerged water jet propeller compared with experimental data.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g008-550.jpg?1739537529" title=" <strong>Figure 8</strong><br/> <p>Contour of PPTC propeller cavitation. (<b>a</b>) CFD contour. (<b>b</b>) EFD contour [<a href="#B25-machines-13-00147" class="html-bibr">25</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g009-550.jpg?1739537531" title=" <strong>Figure 9</strong><br/> <p>Comparison curves of open water efficiency, power, and total thrust of submerged jet propellers.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g010-550.jpg?1739537533" title=" <strong>Figure 10</strong><br/> <p>Cavitation contours of submerged water jet propeller and conventional propeller.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g011-550.jpg?1739537534" title=" <strong>Figure 11</strong><br/> <p>Pressure coefficient contours of various components of the submerged water jet propeller and conventional propeller before and after cavitation: (<b>a</b>) before cavitation, (<b>b</b>) after cavitation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g012-550.jpg?1739537536" title=" <strong>Figure 12</strong><br/> <p>Velocity contour of submerged water jet propeller and conventional high-efficiency propeller flow field in X-Y section.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g013-550.jpg?1739537537" title=" <strong>Figure 13</strong><br/> <p>Performance curves of submerged water jet propeller considering effect of vehicle body wake.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g014-550.jpg?1739537539" title=" <strong>Figure 14</strong><br/> <p>Performance curves of propeller considering effect of vehicle body wake.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g015-550.jpg?1739537540" title=" <strong>Figure 15</strong><br/> <p>Cavitation contours of propeller and submerged water jet propeller considering effect of vehicle body wake.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00147/article_deploy/html/images/machines-13-00147-g016-550.jpg?1739537541" title=" <strong>Figure 16</strong><br/> <p>Pressure coefficient contours of various components of the submerged water jet propeller considering the effect of the vehicle body’s wake before and after cavitation: (<b>a</b>) before cavitation, (<b>b</b>) after cavitation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/147'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 15 pages, 1648 KiB   </span> <a href="/2075-1702/13/2/146/pdf?version=1739460066" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="A Real-Time Demanded Current Observation-Based Sliding Mode Control of Permanent Magnet Synchronous Motors" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/146">A Real-Time Demanded Current Observation-Based Sliding Mode Control of Permanent Magnet Synchronous Motors</a> <div class="authors"> by <span class="inlineblock "><strong>Guangping Li</strong>, </span><span class="inlineblock "><strong>Guolong Zhong</strong>, </span><span class="inlineblock "><strong>Likun Hu</strong>, </span><span class="inlineblock "><strong>Pingping Gong</strong> and </span><span class="inlineblock "><strong>Gaoxiang Li</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 146; <a href="https://doi.org/10.3390/machines13020146">https://doi.org/10.3390/machines13020146</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> To improve the dynamic and steady-state performance of permanent magnet synchronous motors (PMSM), this paper proposes a real-time demanded current observation based sliding mode control strategy. Firstly, based on the mechanism between motor speed and current, a real-time demanded current observer is proposed, <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/146/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> To improve the dynamic and steady-state performance of permanent magnet synchronous motors (PMSM), this paper proposes a real-time demanded current observation based sliding mode control strategy. Firstly, based on the mechanism between motor speed and current, a real-time demanded current observer is proposed, which can obtain the demanded current based on the motor speed. Secondly, the demanded current is directly used to calibrate the q-axis current reference in real-time, which can update the current reference value faster than the sliding mode controller. Due to the real-time demanded current feedforward, the anti-interference performance of the PMSM under the proposed control is improved effectively. Compared with the conventional sliding mode control, the proposed control has a better dynamic and steady-state performance. Finally, the effectiveness of the proposed control has been verified through simulation and experiments. <a href="/2075-1702/13/2/146">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Automation_Systems">Automation and Control Systems</a>)<br/> </div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 33 pages, 6763 KiB   </span> <a href="/2075-1702/13/2/145/pdf?version=1739613221" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Modified Dynamic Movement Primitive-Based Closed Ankle Reduction Technique Learning and Variable Impedance Control for a Redundant Parallel Bone-Setting Robot" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/145">Modified Dynamic Movement Primitive-Based Closed Ankle Reduction Technique Learning and Variable Impedance Control for a Redundant Parallel Bone-Setting Robot</a> <div class="authors"> by <span class="inlineblock "><strong>Zhao Tan</strong>, </span><span class="inlineblock "><strong>Yahui Zhang</strong>, </span><span class="inlineblock "><strong>Jiahui Yuan</strong>, </span><span class="inlineblock "><strong>Xu Song</strong>, </span><span class="inlineblock "><strong>Jialong Zhang</strong>, </span><span class="inlineblock "><strong>Guilin Wen</strong>, </span><span class="inlineblock "><strong>Xiaoyan Hu</strong> and </span><span class="inlineblock "><strong>Hanfeng Yin</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 145; <a href="https://doi.org/10.3390/machines13020145">https://doi.org/10.3390/machines13020145</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Traditional fracture reduction relies heavily on the surgeon’s experience, which hinders the transmission of skills. This specialization bottleneck, coupled with the high demands on physical strength, significantly limits the efficiency of daily treatments in trauma orthopedics. Currently, most fracture surgery robots focus on <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/145/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Traditional fracture reduction relies heavily on the surgeon’s experience, which hinders the transmission of skills. This specialization bottleneck, coupled with the high demands on physical strength, significantly limits the efficiency of daily treatments in trauma orthopedics. Currently, most fracture surgery robots focus on open or minimally invasive reduction techniques, which inherently carry the risk of iatrogenic damage due to surgical incisions or bone pin insertions. However, research in closed reduction-oriented robotic systems is remarkably limited. Addressing this gap, our study introduces a novel bone-setting robot for the closed reduction of ankle fractures designed with a redundant parallel platform. The parallel robot’s design incorporates three sliding redundancy actuators that enhance its tilt flexibility while maintaining load performance. Moreover, a singularity-free redundant kinematic solver has been developed, optimizing the robot’s operational efficacy. Building upon the demonstrations from professional closed reduction techniques, we propose the use of a multivariate Student-t process as a multi-output regression model within dynamic movement primitive for accurately learning stable reduction maneuvers. Additionally, we develop an anthropomorphic variable impedance controller based on inverse dynamics. The simulation results demonstrate convincingly that the developed ankle bone-setting robot is proficient in effectively replicating and learning the nuanced closed reduction techniques. <a href="/2075-1702/13/2/145">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Robotics-Mechatronics-Intelligent-Machines">Robotics, Mechatronics and Intelligent Machines</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/145/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1590602"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1590602"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1590602" data-cycle-prev="#prev1590602" data-cycle-progressive="#images1590602" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1590602-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g001-550.jpg?1739613324" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1590602" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g002-550.jpg?1739613325'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g003-550.jpg?1739613326'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g004-550.jpg?1739613327'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g005-550.jpg?1739613328'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g006-550.jpg?1739613329'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g007-550.jpg?1739613330'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g008-550.jpg?1739613332'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g009-550.jpg?1739613333'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g010-550.jpg?1739613334'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g011-550.jpg?1739613336'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g012-550.jpg?1739613337'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g013-550.jpg?1739613339'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g014-550.jpg?1739613340'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g015-550.jpg?1739613342'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g016-550.jpg?1739613343'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1590602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g017-550.jpg?1739613344'><p>Figure 17</p></div></script></div></div><div id="article-1590602-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g001-550.jpg?1739613324" title=" <strong>Figure 1</strong><br/> <p>Framework diagram of the bone-setting robot system. The blue dashed box outlines the experimental setup for the redundant parallel bone-setting robot. The red dashed box represents the learning process for the closed ankle reduction utilizing a modified dynamic movement primitive (DMP) algorithm. The purple dashed box highlights the variable impedance control framework proposed in this study.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g002-550.jpg?1739613325" title=" <strong>Figure 2</strong><br/> <p>Ankle illustration. (<b>a</b>) The anatomical and physiological structure of the ankle complex. (<b>b</b>) The movements of the ankle.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g003-550.jpg?1739613326" title=" <strong>Figure 3</strong><br/> <p>Classic closed reduction maneuvers. (<b>a</b>) Traction. (<b>b</b>) Inversion and lift.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g004-550.jpg?1739613327" title=" <strong>Figure 4</strong><br/> <p>Schematic diagram of the bone-setting robot system. The red arrow points to the core component of the bone-setting robot system, while the blue arrow indicates the core component of the redundant parallel bone-setting robot.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g005-550.jpg?1739613328" title=" <strong>Figure 5</strong><br/> <p>Process of robot bone-setting.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g006-550.jpg?1739613329" title=" <strong>Figure 6</strong><br/> <p>Schematic diagram of redundant parallel platform. (<b>a</b>) Diagram of overall. (<b>b</b>) Moving platform. (<b>c</b>) Base. (<b>d</b>) Three-dimensional model.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g007-550.jpg?1739613330" title=" <strong>Figure 7</strong><br/> <p>Flow chart of MV-TP-DMP.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g008-550.jpg?1739613332" title=" <strong>Figure 8</strong><br/> <p>Effects of different coefficients on the variable stiffness function. (<b>a</b>) <span class="html-italic">c<sub>a</sub></span>. (<b>b</b>) <span class="html-italic">c<sub>b</sub></span>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g009-550.jpg?1739613333" title=" <strong>Figure 9</strong><br/> <p>Process of the bone-setting. (<b>a</b>) Pre-reduction. (<b>b</b>) Traction. (<b>c</b>) Inversion. (<b>d</b>) Lift. (<b>e</b>) End of reduction.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g010-550.jpg?1739613334" title=" <strong>Figure 10</strong><br/> <p>Preoperative simulation for the process of bone-setting. (<b>a</b>) Pre-reduction. (<b>b</b>) Traction. (<b>c</b>) Inversion. (<b>d</b>) Lift. (<b>e</b>) End of reduction.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g011-550.jpg?1739613336" title=" <strong>Figure 11</strong><br/> <p>Reproducing and generalizing tests of position and orientation trajectory for MV-TP-DMP. The gray lines represent the demo trajectories used for training, which are processed by DTW and denoised. The green lines denote the reference trajectories used for the reproduction test. The blue lines indicate the trajectories generated by the MV-TP-DMP algorithm during the reproduction test, while the red lines represent the trajectories produced by the algorithm in the generalization test. The reduction process is divided by using three phases, which correspond to “Traction”, “Inversion”, and “Lift”, respectively. (<b>a</b>–<b>c</b>) represent the position along the X, Y and Z axes, respectively. (<b>d</b>–<b>f</b>) are respectively three Euler angles.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g012-550.jpg?1739613337" title=" <strong>Figure 12</strong><br/> <p>Additional disturbance forces.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g013-550.jpg?1739613339" title=" <strong>Figure 13</strong><br/> <p>End-effector position and orientation trajectory under the control of constant impedance controller and variable impedance controller. The closed reduction process is divided using three phases, which correspond to “Traction”, “Inversion”, and “Lift”, respectively. (<b>a</b>–<b>c</b>) represent the position along the X, Y and Z axes, respectively. (<b>d</b>–<b>f</b>) are respectively three Euler angles.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g014-550.jpg?1739613340" title=" <strong>Figure 14</strong><br/> <p>Variable impedance control test under disturbance. (<b>a</b>) Diagram of variable stiffness coefficient. (<b>b</b>) Tracking error diagram of position trajectory.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g015-550.jpg?1739613342" title=" <strong>Figure 15</strong><br/> <p>Actual contact force <span class="html-italic">F<sub>I</sub></span> and torque <span class="html-italic">M<sub>I</sub></span> between humans and robots. (<b>a</b>) Actual contact force. (<b>b</b>) Actual contact torque.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g016-550.jpg?1739613343" title=" <strong>Figure 16</strong><br/> <p>Trajectories of the actuators. (<b>a</b>) Prismatic actuators. (<b>b</b>) Sliding actuators.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00145/article_deploy/html/images/machines-13-00145-g017-550.jpg?1739613344" title=" <strong>Figure 17</strong><br/> <p>Forces in the actuators. (<b>a</b>) Forces of the prismatic actuators. (<b>b</b>) Forces of the sliding actuators.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/145'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 16 pages, 676 KiB   </span> <a href="/2075-1702/13/2/144/pdf?version=1739438652" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Condition Monitoring of Electric Machines: Modern Frameworks and Data-Driven Methodologies" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2075-1702/13/2/144">Condition Monitoring of Electric Machines: Modern Frameworks and Data-Driven Methodologies</a> <div class="authors"> by <span class="inlineblock "><strong>Wesley Doorsamy</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 144; <a href="https://doi.org/10.3390/machines13020144">https://doi.org/10.3390/machines13020144</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Electrical machines are at the centre of most engineering processes, with rotating electrical machines, in particular, becoming increasingly important in recent history due to their growing applications in electric vehicles and renewable energy. Although the landscape of condition monitoring in electrical machines has <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/144/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Electrical machines are at the centre of most engineering processes, with rotating electrical machines, in particular, becoming increasingly important in recent history due to their growing applications in electric vehicles and renewable energy. Although the landscape of condition monitoring in electrical machines has evolved over the past 50 years, the intensification of engineering efforts towards sustainability, reliability, and efficiency, coupled with breakthroughs in computing, has prompted a data-driven paradigm shift. This paper explores the evolution of condition monitoring of rotating electrical machines in the context of maintenance strategy, focusing on the emergence of this data-driven paradigm. Due to the broad and varying nature of condition monitoring practices, a framework is also offered here, along with other essential terms of reference, to provide a concise overview of recent developments and to highlight the modern challenges and opportunities within this area. The paper is purposefully written as a tutorial-style overview for the benefit of practising engineers and researchers who are new to the field or not familiar with the wider intricacies of modern condition monitoring systems. <a href="/2075-1702/13/2/144">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Machines_Testing_and_Maintenance">Machines Testing and Maintenance</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/144/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1590257"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1590257"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1590257" data-cycle-prev="#prev1590257" data-cycle-progressive="#images1590257" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1590257-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g001-550.jpg?1739438717" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1590257" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1590257-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g002-550.jpg?1739438720'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1590257-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g003-550.jpg?1739438720'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1590257-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g004-550.jpg?1739438721'><p>Figure 4</p></div></script></div></div><div id="article-1590257-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g001-550.jpg?1739438717" title=" <strong>Figure 1</strong><br/> <p>Condition monitoring in the context of maintenance strategies.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/144'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g002-550.jpg?1739438720" title=" <strong>Figure 2</strong><br/> <p>Categorisation of maintenance strategies.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/144'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g003-550.jpg?1739438720" title=" <strong>Figure 3</strong><br/> <p>Generalised framework for condition monitoring.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/144'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00144/article_deploy/html/images/machines-13-00144-g004-550.jpg?1739438721" title=" <strong>Figure 4</strong><br/> <p>Example of modern condition monitoring architecture for exploiting system-level integration.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/144'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 17 pages, 7886 KiB   </span> <a href="/2075-1702/13/2/143/pdf?version=1739495369" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Multi-Objective Lightweight Design Method for Lower Control Arms Based on Multi-Axial Random Vibration Fatigue Life" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/143">Multi-Objective Lightweight Design Method for Lower Control Arms Based on Multi-Axial Random Vibration Fatigue Life</a> <div class="authors"> by <span class="inlineblock "><strong>Yan Zhang</strong>, </span><span class="inlineblock "><strong>Qi Li</strong>, </span><span class="inlineblock "><strong>Jie Wan</strong> and </span><span class="inlineblock "><strong>Haodong Sun</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 143; <a href="https://doi.org/10.3390/machines13020143">https://doi.org/10.3390/machines13020143</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> To reduce the computational cost of the multi-objective optimization process and improve the accuracy of fatigue life prediction for the lower control arm (LCA) of a vehicle under multiaxial random vibration, this paper focuses on the LCA of a MacPherson suspension in a <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/143/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> To reduce the computational cost of the multi-objective optimization process and improve the accuracy of fatigue life prediction for the lower control arm (LCA) of a vehicle under multiaxial random vibration, this paper focuses on the LCA of a MacPherson suspension in a specific vehicle model and proposes a multi-objective lightweight design method based on multiaxial random vibration fatigue. This method combines the Latin hypercube sampling (LHS) technique, Kriging surrogate modeling, and the second-generation non-dominated sorting genetic algorithm (NSGA-II). First, static and dynamic analyses are conducted to extract the design parameters required to meet the design specifications of the reference LCA. Subsequently, the LHS technique is employed to obtain 50 sample points, which are used to construct the sample space. The Kriging method is then applied to build surrogate models that capture the relationship between design variables and various responses. Finally, the NSGA-II multi-objective genetic algorithm is utilized to obtain the optimized solution. Considering 1.2 times the safe driving distance, the optimal solution with the minimum LCA mass is selected from the Pareto frontier. The optimization results show that compared to the initial LCA model, the mass of the optimized model is reduced by 13.06%, the fatigue life is increased by 47.48%, and the maximum displacement and maximum stress are reduced by 1.78% and 4.31%, respectively. Additionally, the first-order modal frequency decreases by 4.60%. <a href="/2075-1702/13/2/143">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Machine_Design_Theory">Machine Design and Theory</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/143/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1589929"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1589929"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1589929" data-cycle-prev="#prev1589929" data-cycle-progressive="#images1589929" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1589929-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g001-550.jpg?1739495514" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1589929" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g002-550.jpg?1739495515'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g003-550.jpg?1739495516'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g004-550.jpg?1739495516'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g005-550.jpg?1739495517'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g006-550.jpg?1739495518'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g007-550.jpg?1739495521'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g008-550.jpg?1739495522'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g009-550.jpg?1739495523'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g010-550.jpg?1739495524'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g011-550.jpg?1739495525'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g012-550.jpg?1739495526'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g013-550.jpg?1739495527'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g014-550.jpg?1739495529'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1589929-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g015-550.jpg?1739495529'><p>Figure 15</p></div></script></div></div><div id="article-1589929-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g001-550.jpg?1739495514" title=" <strong>Figure 1</strong><br/> <p>The multi-objective optimization process for the LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g002-550.jpg?1739495515" title=" <strong>Figure 2</strong><br/> <p>Latin hypercube sampling.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g003-550.jpg?1739495516" title=" <strong>Figure 3</strong><br/> <p>The position of the LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g004-550.jpg?1739495516" title=" <strong>Figure 4</strong><br/> <p>Three-axis random vibration load at point A.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g005-550.jpg?1739495517" title=" <strong>Figure 5</strong><br/> <p>Boundary conditions for static analysis of the LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g006-550.jpg?1739495518" title=" <strong>Figure 6</strong><br/> <p>LCA static analysis: (<b>a</b>) maximum displacement contour plot; (<b>b</b>) maximum stress contour plot.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g007-550.jpg?1739495521" title=" <strong>Figure 7</strong><br/> <p>The first six mode shapes of the LCA: (<b>a</b>) first-order; (<b>b</b>) Second order; (<b>c</b>) Third order; (<b>d</b>) Fourth order; (<b>e</b>) Fifth order; (<b>f</b>) Six order.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g008-550.jpg?1739495522" title=" <strong>Figure 8</strong><br/> <p>Triaxial A-PSD and C-PSD.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g009-550.jpg?1739495523" title=" <strong>Figure 9</strong><br/> <p>The S–N Curve of DP600HR.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g010-550.jpg?1739495524" title=" <strong>Figure 10</strong><br/> <p>Fatigue life contour plot of LCA under random vibration.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g011-550.jpg?1739495525" title=" <strong>Figure 11</strong><br/> <p>Variable of LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g012-550.jpg?1739495526" title=" <strong>Figure 12</strong><br/> <p>Accuracy test of kriging surrogate models: (<b>a</b>) mass; (<b>b</b>) life.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g013-550.jpg?1739495527" title=" <strong>Figure 13</strong><br/> <p>Pareto solution set for multi-objective optimization of LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g014-550.jpg?1739495529" title=" <strong>Figure 14</strong><br/> <p>Static analysis of the optimized LCA: (<b>a</b>) maximum displacement contour plot; (<b>b</b>) maximum stress contour plot.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00143/article_deploy/html/images/machines-13-00143-g015-550.jpg?1739495529" title=" <strong>Figure 15</strong><br/> <p>Fatigue life contour plot of the optimized LCA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/143'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 14 pages, 11249 KiB   </span> <a href="/2075-1702/13/2/142/pdf?version=1739419137" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Loaded Surface Shape Stability Analysis of Short-Focus Off-Axis Aspheres for Stressed Mirror Polishing" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/142">Loaded Surface Shape Stability Analysis of Short-Focus Off-Axis Aspheres for Stressed Mirror Polishing</a> <div class="authors"> by <span class="inlineblock "><strong>Jinfeng Li</strong>, </span><span class="inlineblock "><strong>Haifei Hu</strong>, </span><span class="inlineblock "><strong>Junqing Zhu</strong>, </span><span class="inlineblock "><strong>Han Pei</strong> and </span><span class="inlineblock "><strong>Le Liu</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 142; <a href="https://doi.org/10.3390/machines13020142">https://doi.org/10.3390/machines13020142</a> - 13 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> The Stressed Mirror Polishing method (SMP) enables the high-quality and efficient fabrication of short-focus off-axis aspheres (SFOA) for overcoming difficulties arising from large asphericity, which makes the polishing tool unfitted for the mirror surface shape and produces mid- and high-frequency errors. However, there <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/142/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> The Stressed Mirror Polishing method (SMP) enables the high-quality and efficient fabrication of short-focus off-axis aspheres (SFOA) for overcoming difficulties arising from large asphericity, which makes the polishing tool unfitted for the mirror surface shape and produces mid- and high-frequency errors. However, there remains a lack of precise iterative loading methods and detailed analyses of loaded surface shape stability for processing SFOA through SMP. Therefore, a foundational analysis model for SMP was established, integrating mathematical theoretical modeling with a finite element analysis (FEA). Based on this model, an iterative loading strategy, based on the proportional relationship between the Zernike coefficients and the SMP-type surface shape error, was proposed to achieve a high dynamic range of >100, which is 10 times larger than the reported ones. Moreover, to guide the loading structure design and quantify the surface shape’s sensitivity to design parameters, both design of experiments (DOE) and radial basis function (RBF) methods had been used to ascertain the precision requirement of each force and the corresponding arm length at separated loading points, under the shape precision requirement of PV < 1 μm which coordinates with the ability of the Ion Beam Figuring (IBF) technique. <a href="/2075-1702/13/2/142">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/advanced_manufacturing_1">Advanced Manufacturing</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/142/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1589910"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1589910"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1589910" data-cycle-prev="#prev1589910" data-cycle-progressive="#images1589910" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1589910-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g001-550.jpg?1739419211" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1589910" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g002-550.jpg?1739419211'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g003-550.jpg?1739419212'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g004-550.jpg?1739419214'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g005-550.jpg?1739419217'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g006-550.jpg?1739419217'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g007-550.jpg?1739419218'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g008-550.jpg?1739419218'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g009-550.jpg?1739419219'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g010-550.jpg?1739419220'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g011-550.jpg?1739419221'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g012-550.jpg?1739419222'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g013-550.jpg?1739419224'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g014-550.jpg?1739419226'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g015-550.jpg?1739419227'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1589910-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g016-550.jpg?1739419228'><p>Figure 16</p></div></script></div></div><div id="article-1589910-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g001-550.jpg?1739419211" title=" <strong>Figure 1</strong><br/> <p>The basic technical process of SMP. (<b>a</b>) Initial mirror blank, (<b>b</b>) loading to get inverse asphericity, (<b>c</b>) polishing spherical under load, (<b>d</b>) spherical test, (<b>e</b>) aspherical test, (<b>f</b>) required aspheric mirrors.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g002-550.jpg?1739419211" title=" <strong>Figure 2</strong><br/> <p>Local coordinate system on a single segment.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g003-550.jpg?1739419212" title=" <strong>Figure 3</strong><br/> <p>Schematic flowchart for the simulation of iterative loading of SFOA mirrors.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g004-550.jpg?1739419214" title=" <strong>Figure 4</strong><br/> <p>FE model of SFOA mirror with boundary conditions. (<b>a</b>) Boundary conditions: 12-point loading and center fixation, (<b>b</b>) uniform back pressure.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g005-550.jpg?1739419217" title=" <strong>Figure 5</strong><br/> <p>SFOA aspherical surface shape. (<b>a</b>) Initial asphericity, (<b>b</b>) initial residual surface shape error, (<b>c</b>) ninth iteration asphericity, (<b>d</b>) ninth iteration residual surface shape error.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g006-550.jpg?1739419217" title=" <strong>Figure 6</strong><br/> <p>Iterative history of the residual surface shape error PV through loading optimization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g007-550.jpg?1739419218" title=" <strong>Figure 7</strong><br/> <p>Schematic diagram of force and force arm distribution.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g008-550.jpg?1739419218" title=" <strong>Figure 8</strong><br/> <p>Variable definition diagram. (<b>a</b>) Loading point groupings, (<b>b</b>) force and force arm.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g009-550.jpg?1739419219" title=" <strong>Figure 9</strong><br/> <p>Response surface approximation model optimal solution block diagram.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g010-550.jpg?1739419220" title=" <strong>Figure 10</strong><br/> <p>The complex correlation coefficients <math display="inline"><semantics> <mrow> <msup> <mrow> <mi mathvariant="normal">R</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </semantics></math> index: (<b>a</b>) RSM model, (<b>b</b>) RBF model.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g011-550.jpg?1739419221" title=" <strong>Figure 11</strong><br/> <p>Pareto plot of response for the residual surface shape error PV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g012-550.jpg?1739419222" title=" <strong>Figure 12</strong><br/> <p>The degree of global effect for the residual surface shape error PV. (<b>a</b>) All variables; (<b>b</b>) top 14 variables.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g013-550.jpg?1739419224" title=" <strong>Figure 13</strong><br/> <p>The extreme values of the residual surface shape error for the RBF model correspond to the FEA. (<b>a</b>) Initial PV, (<b>b</b>) PV<sub>max</sub>, (<b>c</b>) PV<sub>min</sub>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g014-550.jpg?1739419226" title=" <strong>Figure 14</strong><br/> <p>Shorter SFOA aspherical surface shape. (<b>a</b>) Initial asphericity, (<b>b</b>) initial residual surface shape error, (<b>c</b>) ninth iteration asphericity, (<b>d</b>) ninth iteration residual surface shape error.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g015-550.jpg?1739419227" title=" <strong>Figure 15</strong><br/> <p>Iterative history of the residual surface shape error PV and RMS through loading optimization.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00142/article_deploy/html/images/machines-13-00142-g016-550.jpg?1739419228" title=" <strong>Figure 16</strong><br/> <p>Surface accuracy of shorter SFOA mirror within two typical hexagonal effective apertures: (<b>a</b>) hexagon aperture located at X-axis; (<b>b</b>) hexagon aperture located at <span class="html-italic">Y</span>-axis.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/142'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 15 pages, 4002 KiB   </span> <a href="/2075-1702/13/2/141/pdf?version=1739439529" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Condition-Based Maintenance for Degradation-Aware Control Systems in Continuous Manufacturing" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/141">Condition-Based Maintenance for Degradation-Aware Control Systems in Continuous Manufacturing</a> <div class="authors"> by <span class="inlineblock "><strong>Faisal Alsaedi</strong> and </span><span class="inlineblock "><strong>Sara Masoud</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 141; <a href="https://doi.org/10.3390/machines13020141">https://doi.org/10.3390/machines13020141</a> - 12 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> To enhance maintenance endeavors, it is imperative to gain a deep understanding of system degradation. In systems with degradation-aware control, observing degradation becomes particularly challenging. Even with sensors, such controllers continuously mitigate deviations to ensure the system operates within optimal limits. Here, we <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/141/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> To enhance maintenance endeavors, it is imperative to gain a deep understanding of system degradation. In systems with degradation-aware control, observing degradation becomes particularly challenging. Even with sensors, such controllers continuously mitigate deviations to ensure the system operates within optimal limits. Here, we propose a framework explicitly tailored for degradation-aware control systems, built upon two main components: (1) degradation modeling to estimate and track hidden degradation over time and (2) a Long Short-Term Memory Autoencoder-Degradation Stage Detector (A-LSTMA-DSD) to define alarm and failure thresholds for enabling condition-based maintenance. In degradation modeling, the framework utilizes actuator measurements to model hidden degradation. Next, an A-LSTMA-DSD model is developed to flag anomalies, based on which alarm and failure thresholds are assigned. These dynamic thresholds are defined to ensure sufficient time for addressing maintenance requirements. Working with real data from a boiler unit in an oil refinery and focusing on steam leakages, our proposed framework successfully identified all failures and on average triggered alarm and failure thresholds 15 and 8 days in advance of failures, respectively. In addition to triggering these thresholds, our system outperforms baseline models, such as CNN, LSTM, ANN, ARIMA, and Facebook Profit, in identifying failures by 60% and 95%, respectively. <a href="/2075-1702/13/2/141">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/QP7LO6RP15 ">Smart Manufacturing and Beyond: Bridging Innovation in Industry 4.0 and 5.0</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/141/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1589665"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1589665"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1589665" data-cycle-prev="#prev1589665" data-cycle-progressive="#images1589665" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1589665-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g001-550.jpg?1739439641" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1589665" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g002-550.jpg?1739439642'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g003-550.jpg?1739439643'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g004-550.jpg?1739439644'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g005-550.jpg?1739439645'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g006-550.jpg?1739439646'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g007-550.jpg?1739439649'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g008-550.jpg?1739439650'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g009-550.jpg?1739439651'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g010-550.jpg?1739439652'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g011-550.jpg?1739439653'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g012-550.jpg?1739439654'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g013-550.jpg?1739439655'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1589665-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g014-550.jpg?1739439655'><p>Figure 14</p></div></script></div></div><div id="article-1589665-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g001-550.jpg?1739439641" title=" <strong>Figure 1</strong><br/> <p>Classification of maintenance methods.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g002-550.jpg?1739439642" title=" <strong>Figure 2</strong><br/> <p>The general structure and flow in a PIC.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g003-550.jpg?1739439643" title=" <strong>Figure 3</strong><br/> <p>Our proposed A-LSTM-DSD framework.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g004-550.jpg?1739439644" title=" <strong>Figure 4</strong><br/> <p>The data pre-processing steps in degradation modeling.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g005-550.jpg?1739439645" title=" <strong>Figure 5</strong><br/> <p>A stacked LSTM architecture.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g006-550.jpg?1739439646" title=" <strong>Figure 6</strong><br/> <p>The trained A-LSTM architecture.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g007-550.jpg?1739439649" title=" <strong>Figure 7</strong><br/> <p>The proposed Alarm Setting Algorithm (Algorithm 1).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g008-550.jpg?1739439650" title=" <strong>Figure 8</strong><br/> <p>Architecture of the boiler under study.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g009-550.jpg?1739439651" title=" <strong>Figure 9</strong><br/> <p>Three years of unit pressure in PSI.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g010-550.jpg?1739439652" title=" <strong>Figure 10</strong><br/> <p>Episode 14’s degradation stages.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g011-550.jpg?1739439653" title=" <strong>Figure 11</strong><br/> <p>Degradation detection using our proposed framework.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g012-550.jpg?1739439654" title=" <strong>Figure 12</strong><br/> <p>Performance comparisons of A-LSTM-DSD, ANN, LSTM, CNN, ARIMA, and FP.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g013-550.jpg?1739439655" title=" <strong>Figure 13</strong><br/> <p>A-LSTM results without implementing degradation path modeling.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00141/article_deploy/html/images/machines-13-00141-g014-550.jpg?1739439655" title=" <strong>Figure 14</strong><br/> <p>A-LSTM-DSD results of the 15th episode.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/141'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 60 pages, 12798 KiB   </span> <a href="/2075-1702/13/2/140/pdf?version=1739438522" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Advances in Computer Numerical Control Geometric Error Compensation: Integrating AI and On-Machine Technologies for Ultra-Precision Manufacturing" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Review</span></div> <a class="title-link" href="/2075-1702/13/2/140">Advances in Computer Numerical Control Geometric Error Compensation: Integrating AI and On-Machine Technologies for Ultra-Precision Manufacturing</a> <div class="authors"> by <span class="inlineblock "><strong>Yassmin Seid Ahmed</strong> and </span><span class="inlineblock "><strong>Fred Lacerda Amorim</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 140; <a href="https://doi.org/10.3390/machines13020140">https://doi.org/10.3390/machines13020140</a> - 12 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Geometric inaccuracies in machine configuration and part specifications are a major source of errors in CNC machining. These discrepancies have long affected the quality of manufactured components and continue to be a key research area in academia and industry. Over the years, significant <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/140/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Geometric inaccuracies in machine configuration and part specifications are a major source of errors in CNC machining. These discrepancies have long affected the quality of manufactured components and continue to be a key research area in academia and industry. Over the years, significant efforts have been made to minimize these errors and enhance machining precision. Researchers have explored various methodologies to identify, measure, and compensate for spatial inaccuracies, improving accuracy in modern machining systems. This paper comprehensively reviews recent advancements in geometric error measurement and compensation techniques, particularly in five-axis machine tools. It examines the latest methods for detecting errors and explores volumetric error modeling approaches designed to enhance machining precision. This review highlights the growing role of emerging technologies, including on-machine measurement systems, machine learning algorithms, and digital twin frameworks, in improving real-time error detection and compensation strategies. Furthermore, advanced tools such as laser interferometry and hybrid software–hardware approaches are discussed for their potential to drive innovation in ultra-precision machining. This paper also addresses key challenges in achieving high volumetric accuracy and outlines future opportunities for improving CNC machining performance. Future research can enhance precision and reliability in modern manufacturing by integrating intelligent systems and advanced measurement techniques. <a href="/2075-1702/13/2/140">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/Y7369G8G0C ">Compensation for Geometric Errors and Improvement in Accuracy through Innovative Design and Advanced Control Strategies</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/140/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1589602"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1589602"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1589602" data-cycle-prev="#prev1589602" data-cycle-progressive="#images1589602" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1589602-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g001-550.jpg?1739438656" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1589602" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g002-550.jpg?1739438658'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g003-550.jpg?1739438659'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g004-550.jpg?1739438660'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g005-550.jpg?1739438661'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g006-550.jpg?1739438662'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g007-550.jpg?1739438665'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g008-550.jpg?1739438666'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g009-550.jpg?1739438667'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g010-550.jpg?1739438669'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g011-550.jpg?1739438670'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g012-550.jpg?1739438671'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g013-550.jpg?1739438672'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g014-550.jpg?1739438674'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g015-550.jpg?1739438676'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g016-550.jpg?1739438678'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g017-550.jpg?1739438679'><p>Figure 17</p></div> --- <div class='openpopupgallery' data-imgindex='17' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g018-550.jpg?1739438682'><p>Figure 18</p></div> --- <div class='openpopupgallery' data-imgindex='18' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g019-550.jpg?1739438683'><p>Figure 19</p></div> --- <div class='openpopupgallery' data-imgindex='19' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g020-550.jpg?1739438686'><p>Figure 20</p></div> --- <div class='openpopupgallery' data-imgindex='20' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g021-550.jpg?1739438687'><p>Figure 21</p></div> --- <div class='openpopupgallery' data-imgindex='21' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g022-550.jpg?1739438688'><p>Figure 22</p></div> --- <div class='openpopupgallery' data-imgindex='22' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g023-550.jpg?1739438688'><p>Figure 23</p></div> --- <div class='openpopupgallery' data-imgindex='23' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g024-550.jpg?1739438689'><p>Figure 24</p></div> --- <div class='openpopupgallery' data-imgindex='24' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g025-550.jpg?1739438690'><p>Figure 25</p></div> --- <div class='openpopupgallery' data-imgindex='25' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g026-550.jpg?1739438692'><p>Figure 26</p></div> --- <div class='openpopupgallery' data-imgindex='26' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g027-550.jpg?1739438694'><p>Figure 27</p></div> --- <div class='openpopupgallery' data-imgindex='27' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g028-550.jpg?1739438698'><p>Figure 28</p></div> --- <div class='openpopupgallery' data-imgindex='28' data-target='article-1589602-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g029-550.jpg?1739438699'><p>Figure 29</p></div></script></div></div><div id="article-1589602-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g001-550.jpg?1739438656" title=" <strong>Figure 1</strong><br/> <p>(<b>a</b>) Network visualization of research themes in CNC geometric error compensation and ultra-precision manufacturing; (<b>b</b>) world production and compensation countries for machines [<a href="#B2-machines-13-00140" class="html-bibr">2</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g002-550.jpg?1739438658" title=" <strong>Figure 2</strong><br/> <p>Machine error sources.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g003-550.jpg?1739438659" title=" <strong>Figure 3</strong><br/> <p>Understanding UPMT errors for improved machining accuracy.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g004-550.jpg?1739438660" title=" <strong>Figure 4</strong><br/> <p>ISO 230-1:2012 geometric error descriptions [<a href="#B65-machines-13-00140" class="html-bibr">65</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g005-550.jpg?1739438661" title=" <strong>Figure 5</strong><br/> <p>Laser interferometer measurement method for (<b>a</b>) position error and (<b>b</b>) rotational error [<a href="#B81-machines-13-00140" class="html-bibr">81</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g006-550.jpg?1739438662" title=" <strong>Figure 6</strong><br/> <p>Measuring based on interferometry * [<a href="#B72-machines-13-00140" class="html-bibr">72</a>]. * FC: Fiber Coupler, PBS: Polarizing Beam Splitter, IM<sub>1</sub>, IM<sub>2</sub>: Interferometer Modules, M<sub>1</sub>, M<sub>2</sub>, M<sub>3</sub>: Mirrors, P<sub>1</sub>, P<sub>2</sub>, P<sub>3</sub>: Polarizers, Q<sub>1</sub>, Q<sub>2</sub>: Quarter-Wave Plates, θ: Angle of Incidence, α: Grating Inclination Angle.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g007-550.jpg?1739438665" title=" <strong>Figure 7</strong><br/> <p>Measuring based on collimation [<a href="#B82-machines-13-00140" class="html-bibr">82</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g008-550.jpg?1739438666" title=" <strong>Figure 8</strong><br/> <p>(<b>a</b>) Diagonal measurement and (<b>b</b>) step-diagonal measurement representation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g009-550.jpg?1739438667" title=" <strong>Figure 9</strong><br/> <p>Laser tracker.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g010-550.jpg?1739438669" title=" <strong>Figure 10</strong><br/> <p>Sequential multilateration representation.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g011-550.jpg?1739438670" title=" <strong>Figure 11</strong><br/> <p>Kinematic errors of milling machine, related to (<b>a</b>) X-axis and (<b>b</b>) related to Y- and Z-axes.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g012-550.jpg?1739438671" title=" <strong>Figure 12</strong><br/> <p>Double ball bar [<a href="#B109-machines-13-00140" class="html-bibr">109</a>]. Reproduced with permission from Archenti et al. [<a href="#B109-machines-13-00140" class="html-bibr">109</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g013-550.jpg?1739438672" title=" <strong>Figure 13</strong><br/> <p>Spherical deviation [<a href="#B101-machines-13-00140" class="html-bibr">101</a>]. Reproduced with permission from Zhong et al. [<a href="#B112-machines-13-00140" class="html-bibr">112</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g014-550.jpg?1739438674" title=" <strong>Figure 14</strong><br/> <p>(<b>a</b>) PDGEs and (<b>b</b>) PIGEs.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g015-550.jpg?1739438676" title=" <strong>Figure 15</strong><br/> <p>A diagram illustrating a laser tracer system for identifying rotary axis errors [<a href="#B150-machines-13-00140" class="html-bibr">150</a>]. Reproduced with permission from Schwenke et al. [<a href="#B107-machines-13-00140" class="html-bibr">107</a>]. (I–III) are positions and (1–4) are reflector locations.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g016-550.jpg?1739438678" title=" <strong>Figure 16</strong><br/> <p>DBB measurement patterns used to identify kinematic error [<a href="#B90-machines-13-00140" class="html-bibr">90</a>]. Reproduced with permission from Uddin et al. [<a href="#B90-machines-13-00140" class="html-bibr">90</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g017-550.jpg?1739438679" title=" <strong>Figure 17</strong><br/> <p>Correction of installation errors in the tool cup.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g018-550.jpg?1739438682" title=" <strong>Figure 18</strong><br/> <p>OMM system setup at each index angle, (<b>a</b>) B-axis and (<b>b</b>) C-axis.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g019-550.jpg?1739438683" title=" <strong>Figure 19</strong><br/> <p>Finished part geometry.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g020-550.jpg?1739438686" title=" <strong>Figure 20</strong><br/> <p>Machining steps on a cubic part.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g021-550.jpg?1739438687" title=" <strong>Figure 21</strong><br/> <p>Machining steps on a cylinder–cubic part.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g022-550.jpg?1739438688" title=" <strong>Figure 22</strong><br/> <p>CAFXYZ-style five-axis system [<a href="#B165-machines-13-00140" class="html-bibr">165</a>]. Reproduced with permission from Wu et al. [<a href="#B165-machines-13-00140" class="html-bibr">165</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g023-550.jpg?1739438688" title=" <strong>Figure 23</strong><br/> <p>Multi-station system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g024-550.jpg?1739438689" title=" <strong>Figure 24</strong><br/> <p>Gematrical errors for (<b>a</b>) PDGEs and PIGEs and (<b>b</b>) ERA.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g025-550.jpg?1739438690" title=" <strong>Figure 25</strong><br/> <p>Example diagram of a straightness error model for the roller patch system using contact elements.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g026-550.jpg?1739438692" title=" <strong>Figure 26</strong><br/> <p>Compensation system flow chart.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g027-550.jpg?1739438694" title=" <strong>Figure 27</strong><br/> <p>Laser interferometer used for position error [<a href="#B132-machines-13-00140" class="html-bibr">132</a>]. Reproduced with permission from Wu et al. [<a href="#B165-machines-13-00140" class="html-bibr">165</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g028-550.jpg?1739438698" title=" <strong>Figure 28</strong><br/> <p>ML model for machine error prediction [<a href="#B229-machines-13-00140" class="html-bibr">229</a>]. Reproduced with permission from Soori et al. [<a href="#B229-machines-13-00140" class="html-bibr">229</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00140/article_deploy/html/images/machines-13-00140-g029-550.jpg?1739438699" title=" <strong>Figure 29</strong><br/> <p>Online DT for machine error prediction [<a href="#B230-machines-13-00140" class="html-bibr">230</a>]. Reproduced with permission from Ward et al. [<a href="#B230-machines-13-00140" class="html-bibr">230</a>].</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/140'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 21 pages, 10018 KiB   </span> <a href="/2075-1702/13/2/139/pdf?version=1739346868" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Vibration-Based Anomaly Detection in Industrial Machines: A Comparison of Autoencoders and Latent Spaces" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/139">Vibration-Based Anomaly Detection in Industrial Machines: A Comparison of Autoencoders and Latent Spaces</a> <div class="authors"> by <span class="inlineblock "><strong>Luca Radicioni</strong>, </span><span class="inlineblock "><strong>Francesco Morgan Bono</strong> and </span><span class="inlineblock "><strong>Simone Cinquemani</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 139; <a href="https://doi.org/10.3390/machines13020139">https://doi.org/10.3390/machines13020139</a> - 12 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> In industrial settings, machinery components inevitably wear and degrade due to friction between moving parts. To address this, various maintenance strategies, including corrective, preventive, and predictive maintenance, are commonly employed. This paper focuses on predictive maintenance through vibration analysis, utilizing data-driven models. This <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/139/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> In industrial settings, machinery components inevitably wear and degrade due to friction between moving parts. To address this, various maintenance strategies, including corrective, preventive, and predictive maintenance, are commonly employed. This paper focuses on predictive maintenance through vibration analysis, utilizing data-driven models. This study explores the application of unsupervised learning methods, particularly Convolutional Autoencoders (CAEs) and variational Autoencoders (VAEs), for anomaly detection (AD) in vibration signals. By transforming vibration signals into images using the Synchrosqueezing Transform (SST), this research leverages the strengths of convolutional neural networks (CNNs) in image processing, which have proven effective in AD, especially at the pixel level. The methodology involves training CAEs and VAEs on data from machinery in healthy condition and testing them on new data samples representing different levels of system degradation. The results indicate that models with spatial latent spaces outperform those with dense latent spaces in terms of reconstruction accuracy and AD capabilities. However, VAEs did not yield satisfactory results, likely because reconstruction-based metrics are not entirely useful for AD purposes in such models. This study also highlights the potential of ReLU residuals in enhancing the visibility of anomalies. The data used in this study are openly available. <a href="/2075-1702/13/2/139">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/K59SK91FU4 ">Vibration-Based Machines Wear Monitoring and Prediction</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/139/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1589183"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1589183"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1589183" data-cycle-prev="#prev1589183" data-cycle-progressive="#images1589183" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery 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data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g004-550.jpg?1739346985'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g005-550.jpg?1739346986'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g006-550.jpg?1739346987'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g007-550.jpg?1739346988'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g008-550.jpg?1739346990'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g009-550.jpg?1739346990'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g010-550.jpg?1739346992'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g011-550.jpg?1739346993'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g012-550.jpg?1739346995'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g013-550.jpg?1739346997'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g014-550.jpg?1739346998'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g015-550.jpg?1739346999'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g016-550.jpg?1739347001'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g017-550.jpg?1739347002'><p>Figure 17</p></div> --- <div class='openpopupgallery' data-imgindex='17' data-target='article-1589183-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g018-550.jpg?1739347002'><p>Figure 18</p></div></script></div></div><div id="article-1589183-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g001-550.jpg?1739346983" title=" <strong>Figure 1</strong><br/> <p>Scheme that represents the training and monitoring phases for a generic industrial process, based on an unsupervised AD approach. The dashed boxes represent the only tasks that require human supervision.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g002-550.jpg?1739346984" title=" <strong>Figure 2</strong><br/> <p>Comparison of the STFT (<b>a</b>) and the FSST (<b>b</b>), applied to the same piece of acceleration signal. The SST approach promotes sparsity in the time–frequency domain.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g003-550.jpg?1739346985" title=" <strong>Figure 3</strong><br/> <p>Graphical representation of a simple AE (<b>a</b>); the input element <span class="html-italic">x</span> is mapped into an <span class="html-italic">n</span>-dimensional latent space—z—and then mapped back into the original data space. Graphical representation of a CAE with a spatial latent space (<b>b</b>); the input image is elaborated through a fully convolutional architecture.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g004-550.jpg?1739346985" title=" <strong>Figure 4</strong><br/> <p>Example of a VAE with a dense latent space (<b>a</b>) and a spatial (sVAE) latent space (<b>b</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g005-550.jpg?1739346986" title=" <strong>Figure 5</strong><br/> <p>Example of a VAE’s training process with different annealing strategies: monotonic annealing (<b>a</b>) and cycling annealing (<b>b</b>). The red curve refers to the product <math display="inline"><semantics> <mrow> <mi>β</mi> <mo>·</mo> <msub> <mi mathvariant="script">L</mi> <mi>KL</mi> </msub> </mrow> </semantics></math>.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g006-550.jpg?1739346987" title=" <strong>Figure 6</strong><br/> <p>Photo of the piezoelectric accelerometer mounted on the platform of the conveyor (measuring axis oriented orthogonally to the platform surface).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g007-550.jpg?1739346988" title=" <strong>Figure 7</strong><br/> <p>Visual representation of the dataset employed. The accelerations have been collected throughout 4 “rounds” for the machinery. Three more rounds have been generated synthetically.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g008-550.jpg?1739346990" title=" <strong>Figure 8</strong><br/> <p>Motor velocity normalization. Starting from the SST spectrogram (<b>a</b>), the frequency axis is normalized with respect to the motor velocity. Then, a linear interpolation of the frequency axis to a predefine normalized frequency vector is performed (<b>b</b>).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g009-550.jpg?1739346990" title=" <strong>Figure 9</strong><br/> <p>Common structure shared by all the four models evaluated in this work. For 2-D convolutional layers, the first number refers to the number of filters, the value between parenthesis to the kernel size.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g010-550.jpg?1739346992" title=" <strong>Figure 10</strong><br/> <p>Results of CAE with dense latente space: (<b>a</b>) train and validation loss histories; (<b>b</b>) boxplots representing the distributions of the reconstruction losses (MAE and ReLU MAE) for each round.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g011-550.jpg?1739346993" title=" <strong>Figure 11</strong><br/> <p>Visualization of the results for the CAE with a dense latent space for a random spectrogram extracted from round 1 (<b>a</b>) and from round 2 modified (<b>b</b>). From top to bottom: original spectrogram, spectrogram reconstructed by the CAE, residual spectrogram, and ReLU residual.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g012-550.jpg?1739346995" title=" <strong>Figure 12</strong><br/> <p>Results of the CAE with a spatial latent space: (<b>a</b>) train and validation loss histories; (<b>b</b>) boxplots representing the distributions of the reconstruction losses (MAE and ReLU MAE) for each round.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g013-550.jpg?1739346997" title=" <strong>Figure 13</strong><br/> <p>Visualization of the results for the CAE with a spatial latent space, for a random spectrogram extracted from round 3 (<b>a</b>) and from round 2 modified (<b>b</b>). From top to bottom: original spectrogram, spectrogram reconstructed by the CAE, residual spectrogram, and ReLU residual.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g014-550.jpg?1739346998" title=" <strong>Figure 14</strong><br/> <p>Results of the VAE with a dense latente space: (<b>a</b>) reconstruction and KL loss histories in training; (<b>b</b>) boxplots representing the distributions of the reconstruction losses (KL divergence, MAE, and ReLU MAE) for each round.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g015-550.jpg?1739346999" title=" <strong>Figure 15</strong><br/> <p>Visualization of the results for the VAE with a dense latent space for a random spectrogram extracted from round 3 (<b>a</b>) and from round 2 modified (<b>b</b>). From top to bottom: original spectrogram, spectrogram reconstructed by the VAE, residual spectrogram, and ReLU residual.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g016-550.jpg?1739347001" title=" <strong>Figure 16</strong><br/> <p>Results of the VAE with a spatial latente space: (<b>a</b>) reconstruction and KL loss histories in training; (<b>b</b>) boxplots representing the distributions of the reconstruction losses (KL divergence, MAE, and ReLU MAE) for each round.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g017-550.jpg?1739347002" title=" <strong>Figure 17</strong><br/> <p>Original spectrogram from round 4, spectrogram reconstructed by the VAE with a spatial latent space, residual spectrogram, and ReLU residual.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00139/article_deploy/html/images/machines-13-00139-g018-550.jpg?1739347002" title=" <strong>Figure 18</strong><br/> <p>Original spectrogram from round 2 modified, spectrogram reconstructed by the VAE with a spatial latent space, residual spectrogram, and ReLU residual.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/139'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 19 pages, 6130 KiB   </span> <a href="/2075-1702/13/2/138/pdf?version=1739269622" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Development of Electrohydraulic Proportional Valve Model for Precise Steering Control in Autonomous Tractors" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/138">Development of Electrohydraulic Proportional Valve Model for Precise Steering Control in Autonomous Tractors</a> <div class="authors"> by <span class="inlineblock "><strong>Yi-Seo Min</strong>, </span><span class="inlineblock "><strong>Yong-Joo Kim</strong>, </span><span class="inlineblock "><strong>Seung-Yun Baek</strong>, </span><span class="inlineblock "><strong>Seung-Min Baek</strong> and </span><span class="inlineblock "><strong>Wan-Soo Kim</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 138; <a href="https://doi.org/10.3390/machines13020138">https://doi.org/10.3390/machines13020138</a> - 11 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Autonomous tractors are emerging as a pivotal technology in agricultural automation. Precise steering control in these tractors requires high-performance electrohydraulic proportional valves (EHPVs). To optimize EHPV performance and reduce development costs and time, simulation analysis serves as a valuable pre-testing tool. This study <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/138/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Autonomous tractors are emerging as a pivotal technology in agricultural automation. Precise steering control in these tractors requires high-performance electrohydraulic proportional valves (EHPVs). To optimize EHPV performance and reduce development costs and time, simulation analysis serves as a valuable pre-testing tool. This study aimed to develop a simulation model capable of predicting the hydraulic characteristics of EHPVs under real-world operating conditions. The model was created using AMESim, incorporating actual tractor operating conditions and valve control signals. The proposed model was validated through experiments conducted on a tractor equipped with an EHPV, evaluating hydraulic characteristics across various engine speeds and steering angular velocities. The simulation model was utilized to analyze the priority valve control flow characteristics of the automatic steering system and the hydraulic response of the EHPV under step inputs at specific engine speed points. The results indicate that the simulation model demonstrated a mean absolute percentage error (MAPE) ranging from 7.45% to 9.79% for hydraulic power. A <i>t</i>-test analysis of hydraulic power indicated no statistically significant difference between the simulation and experimental values under all test conditions. The proposed EHPV simulation model can be utilized for the optimal future design of EHPV systems. <a href="/2075-1702/13/2/138">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Section <a href="/journal/machines/sections/Automation_Systems">Automation and Control Systems</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/138/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1588562"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1588562"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1588562" data-cycle-prev="#prev1588562" data-cycle-progressive="#images1588562" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1588562-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g001-550.jpg?1739269686" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1588562" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g002-550.jpg?1739269687'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g003-550.jpg?1739269690'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g004-550.jpg?1739269690'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g005-550.jpg?1739269692'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g006-550.jpg?1739269693'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g007-550.jpg?1739269694'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g008-550.jpg?1739269697'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g009-550.jpg?1739269699'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g010-550.jpg?1739269701'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1588562-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g011-550.jpg?1739269705'><p>Figure 11</p></div></script></div></div><div id="article-1588562-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g001-550.jpg?1739269686" title=" <strong>Figure 1</strong><br/> <p>Schematic diagram of the hydraulic steering system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g002-550.jpg?1739269687" title=" <strong>Figure 2</strong><br/> <p>Control flow of the automatic steering system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g003-550.jpg?1739269690" title=" <strong>Figure 3</strong><br/> <p>Measurement system for EHPV used in this study.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g004-550.jpg?1739269690" title=" <strong>Figure 4</strong><br/> <p>Simulation model development and validation procedure for the automatic steering system.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g005-550.jpg?1739269692" title=" <strong>Figure 5</strong><br/> <p>Simulation model of the EHPV.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g006-550.jpg?1739269693" title=" <strong>Figure 6</strong><br/> <p>Simulation results of priority valve control flow at various EHPV spool openings.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g007-550.jpg?1739269694" title=" <strong>Figure 7</strong><br/> <p>Simulation analysis results of the priority valve according to hydraulic oil temperature.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g008-550.jpg?1739269697" title=" <strong>Figure 8</strong><br/> <p>Hydraulic characteristics of the EHPV for a step signal.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g009-550.jpg?1739269699" title=" <strong>Figure 9</strong><br/> <p>Regression analysis results of EHPV response characteristics to step signal.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g010-550.jpg?1739269701" title=" <strong>Figure 10</strong><br/> <p>Hydraulic power characteristics of the EHPV under various conditions: case (<b>a</b>) = left turn, engine speed 900 rpm; case (<b>b</b>) = right turn, engine speed 900 rpm; case (<b>c</b>) = left turn, engine speed 1400 rpm; case (<b>d</b>) = right turn, engine speed 1400 rpm; case (<b>e</b>) = left turn, engine speed 2200 rpm; and case (<b>f</b>) = right turn, engine speed 2200 rpm.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00138/article_deploy/html/images/machines-13-00138-g011-550.jpg?1739269705" title=" <strong>Figure 11</strong><br/> <p>Evaluation of hydraulic power prediction accuracy in the EHPV simulation model across various operating conditions: case (<b>A</b>) = left turn, engine speed 900 rpm; case (<b>B</b>) = left turn, engine speed 1400 rpm; case (<b>C</b>) = left turn, engine speed 2200 rpm; case (<b>D</b>) = right turn, engine speed 900 rpm; case (<b>E</b>) = right turn, engine speed 1400 rpm; and case (<b>F</b>) = right turn, engine speed 2200 rpm. Subscripts 16, 21, and 26 denote target steering angular speeds of 0.16, 0.21, and 0.26 rad/s, respectively.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/138'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 14 pages, 5466 KiB   </span> <a href="/2075-1702/13/2/137/pdf?version=1739264205" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="Prediction of Residual Life of Rolling Bearings Based on Multi-Scale Improved Temporal Convolutional Network (MITCN) Model" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/137">Prediction of Residual Life of Rolling Bearings Based on Multi-Scale Improved Temporal Convolutional Network (MITCN) Model</a> <div class="authors"> by <span class="inlineblock "><strong>Keru Xia</strong>, </span><span class="inlineblock "><strong>Qi Li</strong>, </span><span class="inlineblock "><strong>Luyuan Han</strong>, </span><span class="inlineblock "><strong>Zhaohui Ren</strong> and </span><span class="inlineblock "><strong>Hengfa Luo</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 137; <a href="https://doi.org/10.3390/machines13020137">https://doi.org/10.3390/machines13020137</a> - 11 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> The method based on convolution neural networks (CNNs) has been widely developed and applied to residual life prediction, and many excellent results have been achieved. However, CNN models can only learn feature information relative to size, and it is difficult to extract complex <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/137/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> The method based on convolution neural networks (CNNs) has been widely developed and applied to residual life prediction, and many excellent results have been achieved. However, CNN models can only learn feature information relative to size, and it is difficult to extract complex time series features from data of long time series. In addition, the existing models still have some problems, such as capturing the correlation of each time series and generating a large amount of redundant information. In order to alleviate the above problems, this study proposes a residual life prediction method of rolling bearings based on a multi-scale improved temporal convolutional network (MITCN) model. It is used to solve problems such as the low accuracy of bearing life prediction and the difficulty of the temporal convolutional network (TCN) model to capture the correlation of each time series. The model adopts the framework of a time convolution network and has good ability to extract time series information. By introducing a multi-scale expanded causal convolution residual structure, improved temporal convolutional network (ITCN) modules with different expansion factors capture information on different time scales and combine soft threshold functions and channel attention mechanisms to adaptively generate thresholds and eliminate redundant information. Finally, the carbon border adjustment mechanism (CBAM) is an attention mechanism used to enhance useful features and suppress useless features, so as to realize the effective fusion of multi-scale features. The IEEE PHM 2012 challenge data set is hereby used to verify the proposed method, which can effectively solve the problem of the low prediction accuracy of the remaining life of bearings. <a href="/2075-1702/13/2/137">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Topic <a href="/topics/T4O9HU7809">Advanced Manufacturing and Surface Technology</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/137/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1588366"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1588366"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1588366" data-cycle-prev="#prev1588366" data-cycle-progressive="#images1588366" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1588366-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g001-550.jpg?1739264448" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1588366" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g002-550.jpg?1739264449'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g003-550.jpg?1739264450'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g004-550.jpg?1739264451'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g005-550.jpg?1739264453'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g006-550.jpg?1739264455'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g007-550.jpg?1739264456'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1588366-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g008-550.jpg?1739264458'><p>Figure 8</p></div></script></div></div><div id="article-1588366-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g001-550.jpg?1739264448" title=" <strong>Figure 1</strong><br/> <p>Frame of residual life prediction based on the MITCN model.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g002-550.jpg?1739264449" title=" <strong>Figure 2</strong><br/> <p>Details of ITCN.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g003-550.jpg?1739264450" title=" <strong>Figure 3</strong><br/> <p>CBAM type of attention modules.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g004-550.jpg?1739264451" title=" <strong>Figure 4</strong><br/> <p>Details of MITCN.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g005-550.jpg?1739264453" title=" <strong>Figure 5</strong><br/> <p>PRONOSTIA bearing life test platform.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g006-550.jpg?1739264455" title=" <strong>Figure 6</strong><br/> <p>PRONOSTIA bearing life test platform: (<b>a</b>) Bearing 1_1 and (<b>b</b>) Bearing 1_1 horizontal life cycle vibration signals.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g007-550.jpg?1739264456" title=" <strong>Figure 7</strong><br/> <p>Bearing 1_1 character visualization chart in the horizontal direction: (<b>a</b>) time domain features; (<b>b</b>) time–frequency domain characteristics; and (<b>c</b>) trigonometric function characteristics.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00137/article_deploy/html/images/machines-13-00137-g008-550.jpg?1739264458" title=" <strong>Figure 8</strong><br/> <p>MITCN model’s RUL prediction results.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/137'>Full article</a></strong> "></a></div> </div> </div> </div> <div class="expanding-div collapsed"> <div class="generic-item article-item"> <div class="article-content"> <div class="label right label__btn"> <span style="font-size: 12px; color: #1a1a1a;"> 23 pages, 7417 KiB   </span> <a href="/2075-1702/13/2/136/pdf?version=1739321296" class="UD_Listings_ArticlePDF" title="Article PDF" data-name="A Fitness Landscape-Based Method for Extreme Point Analysis of Part Surface Morphology" data-journal="machines"> <i class="material-icons custom-download"></i> </a> </div> <div class="article-icons"><span class="label openaccess" data-dropdown="drop-article-label-openaccess" aria-expanded="false">Open Access</span><span class="label articletype">Article</span></div> <a class="title-link" href="/2075-1702/13/2/136">A Fitness Landscape-Based Method for Extreme Point Analysis of Part Surface Morphology</a> <div class="authors"> by <span class="inlineblock "><strong>Jinshan Sun</strong> and </span><span class="inlineblock "><strong>Wenbin Tang</strong></span> </div> <div class="color-grey-dark"> <em>Machines</em> <b>2025</b>, <em>13</em>(2), 136; <a href="https://doi.org/10.3390/machines13020136">https://doi.org/10.3390/machines13020136</a> - 11 Feb 2025 </div> <div class="abstract-div"> <a href="#" onclick="$(this).next('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> <strong>Abstract </strong> </a> <div class="abstract-cropped inline"> Advancements in Industry 4.0 and smart manufacturing have increased the demand for precise and intricate part surface geometries, making the analysis of surface morphology essential for ensuring assembly precision and product quality. This study presents an innovative fitness landscape-based methodology for extreme point <a href="#" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/136/more" onclick="$(this).parents('.abstract-cropped').toggleClass('inline').next('.abstract-full').toggleClass('inline'); return false;"> [...] Read more.</a> </div> <div class="abstract-full "> Advancements in Industry 4.0 and smart manufacturing have increased the demand for precise and intricate part surface geometries, making the analysis of surface morphology essential for ensuring assembly precision and product quality. This study presents an innovative fitness landscape-based methodology for extreme point analysis of part surface morphology, effectively addressing the limitations of existing techniques in accurately identifying and analyzing extremum points. The proposed approach integrates adaptive Fitness-Distance Correlation (FDC) with a roughness index to dynamically determine the number and spatial distribution of initial points within the pattern search algorithm, based on variations in surface roughness. By partitioning the feasible domain into subregions according to FDC values, the algorithm significantly reduces optimization complexity. Regions with high ruggedness are further subdivided, facilitating the parallel implementation of the pattern search algorithm within each subregion. This adaptive strategy ensures that areas with intricate surface features are allocated a greater number of initial points, thereby enhancing the probability of locating both regional and global extremum points. To validate the effectiveness and robustness of the proposed method, extensive testing was conducted using five diverse test functions treated as black-box functions. The results demonstrate the method’s capability to accurately locate extremum points across varying surface profiles. Additionally, the proposed method was applied to flatness error evaluation. The results indicate that, compared to using only the raw measurement data, the flatness error increases by approximately 3% when extremum points are taken into account. <a href="/2075-1702/13/2/136">Full article</a> </div> </div> <div class="belongsTo" style="margin-bottom: 10px;"> (This article belongs to the Special Issue <a href=" /journal/machines/special_issues/60O4T7V0CM ">Advanced Manufacturing and Assembly Technologies for Aerospace Production Systems</a>)<br/> </div> <a href="#" class="abstract-figures-show" data-counterslink = "https://www.mdpi.com/2075-1702/13/2/136/show" ><span >►</span><span style=" display: none;">▼</span> Show Figures </a><div class="abstract-image-preview "><div class="arrow left-arrow" id="prev1588133"><i class="fa fa-caret-left"></i></div><div class="arrow right-arrow" id="next1588133"><i class="fa fa-caret-right"></i></div><div class="absgraph cycle-slideshow manual" data-cycle-fx="scrollHorz" data-cycle-timeout="0" data-cycle-next="#next1588133" data-cycle-prev="#prev1588133" data-cycle-progressive="#images1588133" data-cycle-slides=">div" data-cycle-log="false"><div class='openpopupgallery cycle-slide' data-imgindex='0' data-target='article-1588133-popup'><span class="helper"></span><img src="data:image/gif;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs=" data-src="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g001-550.jpg?1739321433" alt="" style="border: 0;"><p>Figure 1</p></div><script id="images1588133" type="text/cycle" data-cycle-split="---"><div class='openpopupgallery' data-imgindex='1' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g002-550.jpg?1739321434'><p>Figure 2</p></div> --- <div class='openpopupgallery' data-imgindex='2' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g003-550.jpg?1739321435'><p>Figure 3</p></div> --- <div class='openpopupgallery' data-imgindex='3' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g004-550.jpg?1739321436'><p>Figure 4</p></div> --- <div class='openpopupgallery' data-imgindex='4' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g005-550.jpg?1739321437'><p>Figure 5</p></div> --- <div class='openpopupgallery' data-imgindex='5' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g006-550.jpg?1739321439'><p>Figure 6</p></div> --- <div class='openpopupgallery' data-imgindex='6' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g007-550.jpg?1739321440'><p>Figure 7</p></div> --- <div class='openpopupgallery' data-imgindex='7' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g008-550.jpg?1739321441'><p>Figure 8</p></div> --- <div class='openpopupgallery' data-imgindex='8' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g009-550.jpg?1739321443'><p>Figure 9</p></div> --- <div class='openpopupgallery' data-imgindex='9' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g010-550.jpg?1739321444'><p>Figure 10</p></div> --- <div class='openpopupgallery' data-imgindex='10' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g011-550.jpg?1739321446'><p>Figure 11</p></div> --- <div class='openpopupgallery' data-imgindex='11' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g012-550.jpg?1739321447'><p>Figure 12</p></div> --- <div class='openpopupgallery' data-imgindex='12' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g013-550.jpg?1739321449'><p>Figure 13</p></div> --- <div class='openpopupgallery' data-imgindex='13' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g014-550.jpg?1739321450'><p>Figure 14</p></div> --- <div class='openpopupgallery' data-imgindex='14' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g015-550.jpg?1739321451'><p>Figure 15</p></div> --- <div class='openpopupgallery' data-imgindex='15' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g016-550.jpg?1739321452'><p>Figure 16</p></div> --- <div class='openpopupgallery' data-imgindex='16' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g017-550.jpg?1739321453'><p>Figure 17</p></div> --- <div class='openpopupgallery' data-imgindex='17' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g018-550.jpg?1739321454'><p>Figure 18</p></div> --- <div class='openpopupgallery' data-imgindex='18' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g019-550.jpg?1739321457'><p>Figure 19</p></div> --- <div class='openpopupgallery' data-imgindex='19' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g020-550.jpg?1739321458'><p>Figure 20</p></div> --- <div class='openpopupgallery' data-imgindex='20' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g021-550.jpg?1739321459'><p>Figure 21</p></div> --- <div class='openpopupgallery' data-imgindex='21' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g022-550.jpg?1739321460'><p>Figure 22</p></div> --- <div class='openpopupgallery' data-imgindex='22' data-target='article-1588133-popup'><span class="helper"></span><img src='https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g023-550.jpg?1739321461'><p>Figure 23</p></div></script></div></div><div id="article-1588133-popup" class="popupgallery" style="display: inline; line-height: 200%"><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g001-550.jpg?1739321433" title=" <strong>Figure 1</strong><br/> <p>Schematic of extreme point search on the cross-sectional curve of part surface morphology.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g002-550.jpg?1739321434" title=" <strong>Figure 2</strong><br/> <p>Graph of the function y = cos(x).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g003-550.jpg?1739321435" title=" <strong>Figure 3</strong><br/> <p>Relationship between fitness value and distance to the optimal point.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g004-550.jpg?1739321436" title=" <strong>Figure 4</strong><br/> <p>Curve of the function y = cos(x).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g005-550.jpg?1739321437" title=" <strong>Figure 5</strong><br/> <p>Relationship between fitness value and distance to the optimal point.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g006-550.jpg?1739321439" title=" <strong>Figure 6</strong><br/> <p>Region of valid initial points.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g007-550.jpg?1739321440" title=" <strong>Figure 7</strong><br/> <p>Piecewise function curve graph.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g008-550.jpg?1739321441" title=" <strong>Figure 8</strong><br/> <p>Relationship between fitness value and distance to the optimal point.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g009-550.jpg?1739321443" title=" <strong>Figure 9</strong><br/> <p>Algorithm flowchart.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g010-550.jpg?1739321444" title=" <strong>Figure 10</strong><br/> <p>The surface morphology of Peaks function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g011-550.jpg?1739321446" title=" <strong>Figure 11</strong><br/> <p>The extreme points of Peaks function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g012-550.jpg?1739321447" title=" <strong>Figure 12</strong><br/> <p>The surface morphology of Branin-Hoo function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g013-550.jpg?1739321449" title=" <strong>Figure 13</strong><br/> <p>The extreme points of Branin-Hoo function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g014-550.jpg?1739321450" title=" <strong>Figure 14</strong><br/> <p>The surface morphology of Six Hump Camel Back function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g015-550.jpg?1739321451" title=" <strong>Figure 15</strong><br/> <p>The extreme points of Six Hump Camel Back function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g016-550.jpg?1739321452" title=" <strong>Figure 16</strong><br/> <p>The surface morphology of Ackely function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g017-550.jpg?1739321453" title=" <strong>Figure 17</strong><br/> <p>The extreme points of Ackely Function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g018-550.jpg?1739321454" title=" <strong>Figure 18</strong><br/> <p>The surface morphology of Rastrigin function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g019-550.jpg?1739321457" title=" <strong>Figure 19</strong><br/> <p>The extreme points of Rastrigin function.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g020-550.jpg?1739321458" title=" <strong>Figure 20</strong><br/> <p>Physical model of the test sample.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g021-550.jpg?1739321459" title=" <strong>Figure 21</strong><br/> <p>Experimental procedure.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g022-550.jpg?1739321460" title=" <strong>Figure 22</strong><br/> <p>NCA8107 coordinate measuring machine (CMM).</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a><a href="https://pub.mdpi-res.com/machines/machines-13-00136/article_deploy/html/images/machines-13-00136-g023-550.jpg?1739321461" title=" <strong>Figure 23</strong><br/> <p>Surface morphology model of the test sample.</p> <strong style='display: block; margin-top: 10px; font-size: 18px;'><a style='color: #fff' href='/2075-1702/13/2/136'>Full article</a></strong> "></a></div> </div> </div> </div> </div> <div class="generic-item last-item"> <a class="bold" href="/search?q=&journal=machines&sort=pubdate&page_count=50">More Articles...</a> </div> 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Machines | An Open Access Journal from MDPI