计入冲击与受载齿轮副时变啮合刚度解析算法  

Analytical Algorithm for Time Varying Mesh Stiffness of Gear Pairs Considering Impact and Loading

作　　者：何泽银[1] 易锋 杨震 伍宏健 裴世丰 HE Zeyin;YI Feng;YANG Zhen;WU Hongjian;PEI Shifeng(School of Mechanotronics and Vehicle Engineering,Chongqing Jiaotong University,Chongqing 400074,China;Technology Center,Chongqing Gearbox Co.,Ltd.,Chongqing 402263,China)

机构地区：[1]重庆交通大学机电与车辆工程学院,重庆400074 [2]重庆齿轮箱有限责任公司技术中心,重庆402263

出　　处：《湖南大学学报（自然科学版）》2024年第12期38-46,共9页Journal of Hunan University:Natural Sciences

基　　金：国家重点研发计划资助项目(2023YFB3406301);重庆市自然科学基金资助项目(cstc2021jcyj-msxmX0562)。

摘　　要：针对目前理论不能准确计算齿轮受载与冲击时刻刚度发生的变化,基于赫兹非线性接触理论,构建有限长线接触弹性理论解析模型,由三维接触斑大小与啮合过程中主曲率半径的变化,得到不同载荷作用下齿轮法向接触刚度;而后结合Weber能量法,提出考虑负载条件下时变啮合刚度修正算法,阐明受载变形与刚度硬化的映射关系;同时建立线外啮合冲击数学模型,根据冲击时刻齿轮副动态接触关系,探究啮入冲击引起的啮合刚度变化规律.研究结果表明,接触刚度曲线与主曲率半径变化规律一致,考虑啮入冲击时,齿轮副啮合刚度产生突变并呈现由大到小的变化规律,随着负载递增,法向接触与综合刚度非线性增大,冲击效应增强,且单齿啮合区域逐渐减小,冲击对刚度的影响越来越明显.Due to the inability of the current theory to accurately calculate the changes in the stiffness of the gear during loading and impact,the Hertz nonlinear contact theory is employed to construct an analytical model of length-limited line contact elasticity theory.The normal contact stiffness of the gear under different loads is obtained from the changes in the three-dimensional contact spot size and the principal curvature radius in the meshing process.Later,using the Weber energy method,a time-varying meshing stiffness correction algorithm considering the load condition is proposed to clarify the mapping relationship between load deformation and stiffness hardening.At the same time,the mathematical model of off-line meshing impact is established,and the change law of the meshing stiffness caused by the meshing impact is investigated according to the dynamic contact relationship of the gear pair at the impact time.The research findings demonstrate that the contact stiffness curve is consistent with the change law of the principal curvature radius.When the meshing impact is considered,the meshing stiffness of the gear pair changes abruptly from the large to the small.As the load increases,the contact and comprehensive meshing stiffness increase non-linearly,the single tooth meshing region gradually decreases,and the impact on the stiffness is more markedly.

关 键 词：刚度变化 赫兹接触 Weber能量法 接触变形 冲击刚度 

分 类 号：TH132.41[机械工程—机械制造及自动化]