Multi-objective optimization model of transmission error of nonlinear dynamic load of double helical gears

IF 2.4 Q2 ENGINEERING, MECHANICAL Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0323
Xingling Yao
{"title":"Multi-objective optimization model of transmission error of nonlinear dynamic load of double helical gears","authors":"Xingling Yao","doi":"10.1515/nleng-2022-0323","DOIUrl":null,"url":null,"abstract":"Abstract In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 10 7 mm 3 , and the coincidence degree is 5.9908. After rounding, the design result is <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msub> <m:mrow> <m:mi>m</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">n</m:mi> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>3</m:mn> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>Z</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>31</m:mn> <m:mo>,</m:mo> <m:mi>β</m:mi> <m:mo>=</m:mo> <m:msup> <m:mrow> <m:mn>20</m:mn> </m:mrow> <m:mrow> <m:mrow> <m:mo>∘</m:mo> </m:mrow> </m:mrow> </m:msup> <m:mo>,</m:mo> <m:msub> <m:mrow> <m:mi>Ψ</m:mi> </m:mrow> <m:mrow> <m:mi mathvariant=\"normal\">d</m:mi> </m:mrow> </m:msub> <m:mo>=</m:mo> <m:mn>1.2</m:mn> </m:math> {m}_{{\\rm{n}}}=3,{Z}_{1}=31,\\beta ={20}^{\\circ },{\\Psi }_{{\\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0323","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract In order to address the impact of reduced transmission stability and reliability caused by volume reduction on the quality of gear transmission, this article proposes a multi-objective optimization model for nonlinear dynamic load transmission errors of double helical gears. This study aims to introduce a multi-objective design method for gear transmission, using the volume and smooth reliability of helical gears as objective functions, and establish a multi-objective optimization design mathematical model for helical cylindrical gear transmission. In order to solve this multi-objective optimization problem, we utilized the optimization toolbox in the scientific calculation software MATLAB with examples. The results show that after the joint optimization design of volume and coincidence degree, it is calculated that the volume after the joint optimization design is still 2.2624 × 10 7 mm 3 , and the coincidence degree is 5.9908. After rounding, the design result is m n = 3 , Z 1 = 31 , β = 20 , Ψ d = 1.2 {m}_{{\rm{n}}}=3,{Z}_{1}=31,\beta ={20}^{\circ },{\Psi }_{{\rm{d}}}=1.2 . The optimization design results show that the joint optimization design with the minimum volume and the maximum coincidence as the objective function can reduce the volume and improve the output stability of the helical gear.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
双斜齿轮非线性动载荷传动误差多目标优化模型
摘要为解决体积减小导致传动稳定性和可靠性降低对齿轮传动质量的影响,提出了双斜齿轮非线性动载传动误差的多目标优化模型。本研究旨在引入一种齿轮传动的多目标设计方法,以螺旋齿轮的体积和光滑可靠性为目标函数,建立螺旋圆柱齿轮传动的多目标优化设计数学模型。为了解决这一多目标优化问题,我们利用科学计算软件MATLAB中的优化工具箱并举例说明。结果表明,在对体积和契合度进行联合优化设计后,计算得出,结合优化设计后的体积仍为2.2624 × 10 7 mm 3,契合度为5.9908。舍入后的设计结果为m n =3,Z 1=31, β =20°,Ψ d =1.2 {m_}=3{{\rm{n}}},{Z_1}=31{, }\beta ={20}^ {\circ, }{\Psi _}=1.2。优化设计结果表明,以最小体积和最大重合为目标函数的联合优化设计可以减小齿轮体积,提高齿轮输出稳定性。{{\rm{d}}}
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
期刊最新文献
Study of time-fractional delayed differential equations via new integral transform-based variation iteration technique Convolutional neural network for UAV image processing and navigation in tree plantations based on deep learning Nonlinear adaptive sliding mode control with application to quadcopters Equilibrium stability of dynamic duopoly Cournot game under heterogeneous strategies, asymmetric information, and one-way R&D spillovers A versatile dynamic noise control framework based on computer simulation and modeling
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1