基于拓扑优化的非圆齿轮轻量化设计

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (1): 49-55.

基于拓扑优化的非圆齿轮轻量化设计

刘永平^*, 裴王鹏, 董长斌, 李大伟, 黄传鸿

兰州理工大学机电工程学院, 甘肃兰州 730050

收稿日期:2023-04-14 出版日期:2026-02-28 发布日期:2026-03-05
通讯作者: 刘永平(1973-),男,甘肃靖远人,博士,教授.Email:cameliu@163.com
基金资助:
国家自然科学基金(52265008),甘肃省青年科学基金(23JRRA751),甘肃省教育厅高校教师创新基金(2023A-021)

Lightweight design of non-circular gears based on topology optimization

LIU Yong-ping, PEI Wang-peng, DONG Chang-bin, LI Da-wei, HUANG Chuan-hong

School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received:2023-04-14 Online:2026-02-28 Published:2026-03-05

摘要/Abstract

摘要： 针对非圆齿轮偏心特性导致传动过程存在动不平衡的问题,提出了轻量化设计方法.基于阐明齿轮啮合原理,对非圆齿轮齿面进行数据获取和模型建立.采取多目标拓扑优化方法,结合折衷规划法与灰度关联法,综合考虑不同轮齿位置静应力和动态响应的影响,对非圆齿轮副进行多目标拓扑优化.同时,对轮副在齿宽方向进行尺寸优化,实现非圆齿轮的轻量化设计.通过模型数据测量和动力学仿真结果对比分析了优化前后的传动特性.结果表明,非圆齿轮的整体质量减轻了38.87%,圆周振模态由二阶升至三阶,动平衡特性得到提升,传动更加平稳,传动比更加精确,齿面磨损减轻,齿轮疲劳寿命延长,为非圆齿轮轻量化设计和传动特性优化提供了理论依据.

关键词: 非圆齿轮, 动平衡, 多目标拓扑优化, 轻量化, 动力学仿真

Abstract: A lightweight design method is proposed for non-circular gears with eccentric characteristics leading to dynamic imbalance problems in the transmission process. Based on the elucidation of gear meshing principle, the data acquisition and modeling of non-circular gear tooth surface is realized. A multi-objective topology optimization method is adopted to optimize the spokes of non-circular gears by considering the effects of static stresses and dynamic responses of different gear tooth positions by combining the compromise planning method and the gray correlation method. The spokes are then optimized in the tooth width direction to realize the lightweight design of non-circular gears. The transmission characteristics before and after the optimized design are compared by solid data measurement and dynamics simulation analysis. The results show that the overall weight of the non-circular gear is reduced by 38.87%, and the modal order of its circumferential vibration is increased from 2nd to 3rd order. indicating improved dynamic balance. The optimized gear exhibits smoother transmission, more accurate transmission ratios, reduced tooth surface, and enhanced fatigue life. These results provide a theoretical basis for the lightweight design and transmission characteristics optimization of the non-circular gear.

Key words: non-circular gear, dynamic balance, multi-objective topology optimization, lightweighting, dynamics simulation

中图分类号:

TB114

刘永平, 裴王鹏, 董长斌, 李大伟, 黄传鸿. 基于拓扑优化的非圆齿轮轻量化设计[J]. 兰州理工大学学报, 2026, 52(1): 49-55.

LIU Yong-ping, PEI Wang-peng, DONG Chang-bin, LI Da-wei, HUANG Chuan-hong. Lightweight design of non-circular gears based on topology optimization[J]. Journal of Lanzhou University of Technology, 2026, 52(1): 49-55.

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