{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:50:46Z","timestamp":1753879846125,"version":"3.41.2"},"reference-count":41,"publisher":"ASME International","issue":"4","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"funder":[{"DOI":"10.13039\/501100013290","name":"National Key R&D Program of China","doi-asserted-by":"publisher","award":["2018YFB2001700"],"award-info":[{"award-number":["2018YFB2001700"]}],"id":[{"id":"10.13039\/501100013290","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011352","name":"Project of State Key Laboratory of High Performance Complex Manufacturing, Central South University","doi-asserted-by":"publisher","award":["ZZYJKT2020-06"],"award-info":[{"award-number":["ZZYJKT2020-06"]}],"id":[{"id":"10.13039\/501100011352","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2021,8,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The modeling of a spiral bevel gear (SBG) is a fundamental work to its design, analysis, and manufacturing. The essential work of modeling SBGs is the generation of tooth surface points that meet the strict accuracy requirement of the SBG industry. Specially, if those points are evenly distributed, the 3D models can be efficiently generated by developing automatic programs, or else the tedious manual modeling process is usually applied with 3D commercial software. Hence, it is very beneficial to accurately generating those evenly distributed points with an approach that can stably and efficiently solve the highly nonlinear equations related to the complicated tooth surface geometry. This work proposed such an approach to the SBG produced by face-milled generated (FMG) method. First, two representations of the geometric meshing theory (GMT) are introduced to calculate tooth surfaces of different cases as closed-form (explicit) results rather than implicit results. Subsequently, a new strategy is employed to accurately and efficiently obtain the tooth surface points that are approximately even-distributed. Furthermore, an advanced geometric iterative optimization algorithm (GIOA) is developed to solve the nonlinear equations in a stable way. With the calculated tooth surface points, a special automatic program is developed to accomplish the 3D modeling of SBGs. Examples are discussed to show the validity of this work.<\/jats:p>","DOI":"10.1115\/1.4049152","type":"journal-article","created":{"date-parts":[[2020,11,19]],"date-time":"2020-11-19T02:51:03Z","timestamp":1605754263000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":3,"title":["An Advanced Comprehensive Approach to Accurately Modeling the Face-Milled Generated Spiral Bevel Gears"],"prefix":"10.1115","volume":"21","author":[{"given":"Shenghui","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha, 410083 Hunan, China"}]},{"given":"Yuansheng","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing;"},{"name":"College of Mechanical and Electrical Engineering, Central South University, Changsha, 410083 Hunan, China"}]},{"given":"Xinru","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China"}]},{"given":"Shengjun","family":"Liu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing;"},{"name":"School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China"}]},{"given":"Jinyuan","family":"Tang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of High Performance Complex Manufacturing;"},{"name":"College of Mechanical and Electrical Engineering, Central South University, Changsha, 410083 Hunan, China"}]}],"member":"33","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"issue":"4","key":"2021022312144426200_CIT0001","doi-asserted-by":"crossref","first-page":"642","DOI":"10.1115\/1.2917055","article-title":"Design and Geometry of Face-Gear Drives","volume":"114","author":"Litvin","year":"1992","journal-title":"ASME J. Mech. Des."},{"issue":"2","key":"2021022312144426200_CIT0002","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1115\/1.2912766","article-title":"A Mathematical Model for the Tooth Geometry of Circular-Cut Spiral Bevel Gears","volume":"113","author":"Fong","year":"1991","journal-title":"ASME J. Mech. Des."},{"issue":"2","key":"2021022312144426200_CIT0003","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0895-7177(93)90004-I","article-title":"A Mathematical Model for the Tooth Geometry of Hypoid Gears","volume":"18","author":"Tsay","year":"1993","journal-title":"Math. Comput. Modelling"},{"issue":"1","key":"2021022312144426200_CIT0004","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1115\/1.2359471","article-title":"Mathematical Model for a Universal Face Hobbing Hypoid Gear Generator","volume":"129","author":"Shih","year":"2006","journal-title":"ASME J. Mech. Des."},{"issue":"1","key":"2021022312144426200_CIT0005","first-page":"1","article-title":"Impacts of Misalignments on Mesh Behaviors of Face-Hobbed Hypoid Gear Considering System Deformation","volume":"7","author":"Yang","year":"2019","journal-title":"IEEE Access"},{"issue":"4","key":"2021022312144426200_CIT0006","doi-asserted-by":"crossref","first-page":"761","DOI":"10.1115\/1.1518502","article-title":"Numerical Determination of Cutting Parameters for the Control of Klingelnberg Spiral Bevel Gear Geometry","volume":"124","author":"Lelkes","year":"2002","journal-title":"ASME J. Mech. Des."},{"issue":"6","key":"2021022312144426200_CIT0007","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1016\/j.mechmachtheory.2006.06.007","article-title":"Mathematical Model for Tooth Surfaces Representation of Face-Hobbed Hypoid Gears and Its Application to Contact Analysis and Stress Calculation","volume":"42","author":"Vimercati","year":"2007","journal-title":"Mech. Mac. Theory"},{"key":"2021022312144426200_CIT0008","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.mechmachtheory.2019.03.042","article-title":"Investigation on the Influence of Work Holding Equipment Errors on Contact Characteristics of Face-Hobbed Hypoid Gear","volume":"138","author":"Liu","year":"2019","journal-title":"Mech. Mach. Theory"},{"issue":"4","key":"2021022312144426200_CIT0009","doi-asserted-by":"crossref","first-page":"044501","DOI":"10.1115\/1.4044745","article-title":"Investigation of Tool Errors and Their Influences on Tooth Surface Topography for Face-Hobbed Hypoid Gears","volume":"142","author":"Liang","year":"2020","journal-title":"ASME J. Mech. Des."},{"issue":"4","key":"2021022312144426200_CIT0010","doi-asserted-by":"crossref","first-page":"041007","DOI":"10.1115\/1.3087540","article-title":"Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors","volume":"131","author":"Dr Simon","year":"2015","journal-title":"ASME J. Mech. Des."},{"issue":"7","key":"2021022312144426200_CIT0011","doi-asserted-by":"crossref","first-page":"071007","DOI":"10.1115\/1.4026264","article-title":"Optimal Tooth Modifications in Face-Hobbed Spiral Bevel Gears to Reduce the Influence of Misalignments on Elastohydrodynamic Lubrication","volume":"136","author":"Simon","year":"2014","journal-title":"ASME J. Mech. Des."},{"issue":"8","key":"2021022312144426200_CIT0012","doi-asserted-by":"crossref","first-page":"064501","DOI":"10.1115\/1.4033045","article-title":"Generation of Non-circular Spiral Bevel Gears by Face-Milling Method","volume":"138","author":"Zheng","year":"2016","journal-title":"ASME J. Manuf. Sci. Eng."},{"issue":"6","key":"2021022312144426200_CIT0013","doi-asserted-by":"crossref","first-page":"064501","DOI":"10.1115\/1.4033396","article-title":"Generation of Non-Circular Bevel Gears With Free-Form Tooth Profile and Tooth Lengthwise Based on Screw Theory","volume":"138","author":"Zheng","year":"2016","journal-title":"ASME J. Mech. Des."},{"issue":"1","key":"2021022312144426200_CIT0014","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1115\/1.2359475","article-title":"Enhanced Algorithms of Contact Simulation for Hypoid Gear Drives Produced by Face-Milling and Face-Hobbing Processes","volume":"129","author":"Fan","year":"2006","journal-title":"ASME J. Mech. Des."},{"issue":"7","key":"2021022312144426200_CIT0015","doi-asserted-by":"crossref","first-page":"1029","DOI":"10.1115\/1.2898878","article-title":"Higher-Order Tooth Flank Form Error Correction for Face-Milled Spiral Bevel and Hypoid Gears","volume":"130","author":"Fan","year":"2008","journal-title":"ASME J. Mech. Des."},{"issue":"5","key":"2021022312144426200_CIT0016","doi-asserted-by":"crossref","first-page":"353","DOI":"10.3390\/met8050353","article-title":"Five-Axis Milling of Large Spiral Bevel Gears: Toolpath Definition, Finishing, and Shape Errors","volume":"8","author":"\u00c1lvarez","year":"2018","journal-title":"Metals"},{"key":"2021022312144426200_CIT0017","doi-asserted-by":"crossref","DOI":"10.1142\/1504","volume-title":"A Geometric Theory of Conjugate Tooth Surfaces","author":"Wu","year":"1992"},{"issue":"4","key":"2021022312144426200_CIT0018","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1115\/1.1518501","article-title":"On the Three Laws of Gearing","volume":"124","author":"Dooner","year":"2002","journal-title":"ASME J. Mech. 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Mater."},{"key":"2021022312144426200_CIT0040","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511547126","volume-title":"Gear Geometry and Applied Theory","author":"Litvin","year":"2004"},{"issue":"3","key":"2021022312144426200_CIT0041","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1007\/s10010-019-00323-y","article-title":"An Adaptive Geometric Meshing Theory for the Face-Milled Generated Spiral Bevel Gears","volume":"83","author":"Wang","year":"2019","journal-title":"Forschung im Ingenieurwesen"}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4049152\/6642968\/jcise_21_4_041008.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/doi\/10.1115\/1.4049152\/6642968\/jcise_21_4_041008.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T12:16:20Z","timestamp":1614082580000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/doi\/10.1115\/1.4049152\/1091593\/An-Advanced-Comprehensive-Approach-to-Accurately"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,23]]},"references-count":41,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,8,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4049152","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"type":"print","value":"1530-9827"},{"type":"electronic","value":"1944-7078"}],"subject":[],"published":{"date-parts":[[2021,2,23]]},"article-number":"041008"}}