考虑载荷变化域的斜齿轮副齿面组合修形稳健设计  

Robust Optimization Design for Combined Tooth Surface Modification of Helical Gear Pair Considering Load Variation Domain

作　　者：徐文博 袁冰 马国亮 禹文涛 Xu Wenbo;Yuan Bing;Ma Guoliang;Yu Wentao(ZRIME Gearing Technology Co.,Ltd.,Zhengzhou 450001,China;School of Mechatronic Engineering,Xi'an Technological University,Xi'an 710021,China;Zhengzhou Research Institute of Mechanical Engineering Co.,Ltd.,Zhengzhou 450001,China)

机构地区：[1]郑机所(郑州)传动科技有限公司,河南郑州450001 [2]西安工业大学机电工程学院,陕西西安710021 [3]郑州机械研究所有限公司,河南郑州450001

出　　处：《机械传动》2024年第8期89-96,共8页Journal of Mechanical Transmission

摘　　要：工程实际中,齿轮副的载荷条件通常不是恒定不变的,而是位于某一变化域中。为了解决考虑载荷变化域的斜齿轮副齿面修形设计问题,首先,构造了基于柔度矩阵法的齿面承载接触方程,并提出了基于能量切片法的齿面法向柔度计算方法,从而建立了修形斜齿轮副传递误差的快速计算方法;其次,基于稳健优化设计理论,以齿轮副传递误差波动量的均值和方差最小为目标,综合采用齿廓修形、螺旋线修形和对角修形,建立了考虑载荷变化域的组合修形参数稳健优化数学模型;然后,将带精英策略的非支配排序的遗传算法与传递误差计算方法相结合,求解得到组合修形参数的Pareto前沿解集;最后,从Pareto前沿解集中选取使传递误差波动量的均值和方差均较小的稳健修形参数,并分析了稳健修形斜齿轮副的传递误差波动量随载荷的变化规律。结果表明,采用所提方法得到的修形齿面对载荷变化表现出较强的稳健性。In engineering practice,the load condition of gear pairs is usually not constant,but located in a variable domain.In order to provide an effective method to solve tooth surface modification design of helical gear pairs considering the load variation domain,firstly,the loaded tooth contact equations are constructed using the flexibility matrix method,the efficient model for calculating the flexibility of potential contact points on tooth sur⁃face based on the energy and slicing method is established,and the fast calculation model of transmission error of modified helical gear pairs is developed.Secondly,combining tooth profile modification,lead modification and bias modification,based on the robust optimization design theory,a multi-objective mathematical model of combined modification parameters considering the load variation region is proposed aiming to minimize the ex⁃pectation and variance of the transmission error fluctuations.And then,the non-dominated sorting genetic algo⁃rithm with elitist strategy is combined with the calculation model of transmission error,the Pareto frontier solu⁃tions of the combined modification parameters are solved,and the robust solution which makes the expectation and variance of transmission error fluctuations smaller is selected.Finally,the transmission error fluctuation of the robust modified helical gear pair considering the load variation domain is investigated.The results show that the modified tooth surface obtained by the proposed method is robust to the load variation.

关 键 词：斜齿轮 齿面修形 稳健优化 接触应力 传递误差 

分 类 号：TH132.41[机械工程—机械制造及自动化]