{"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":"144 1","pages":"0"},"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 mn=3,Z1=31,β=20∘,Ψd=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.
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.