摘要
针对齿向修鼓和轴向错位直齿轮副刚度激励的问题,提出了一种通用的时变啮合直齿轮副刚度的解析方法。首先,建立了直齿轮齿向修鼓与轴向错位模型,导出了轮齿副总误差计算式;然后,结合了弹性力学理论、齿接触分析(TCA)以及加载齿接触分析(LTCA),对齿向修鼓和轴向错位的直齿轮副加载状态下的啮合特征进行了计算;基于势能法以及切片理论,建立了改进的几何刚度、耦合刚度、赫兹接触刚度以及齿基刚度模型,并进一步推导了齿向修鼓和轴向错位的直齿轮副时变啮合刚度改进解析式;最后,将该方法的计算结果与有限元结果进行了对比分析,对该解析模型进行了验证,并分析了不同鼓形量与错位量对直齿轮副刚度激励的影响。研究结果表明:提出的齿向修鼓和轴向错位直齿轮副刚度计算方法的计算误差为3%,能够准确且有效地分析齿向修鼓和轴向错位直齿轮副的啮合刚度,为齿轮副传动系统的修形设计提供了理论基础。
In order to study the stiffness excitation of spur gear pairs with tooth length modification and misalignment,a general analytical method of time varying meshing stiffness for spur gear pairs with tooth length modification and misalignment was proposed.Firstly,the models of tooth length modification and misalignment were established,and the formula for calculating the total error of spur gear tooth surface was derived.Then,based on the theory of elasticity,tooth contact analysis(TCA),and loaded tooth contact analysis(LTCA),the meshing characteristics such as contact point,instantaneous contact line and contact trace of spur gear pair with tooth length modification and misalignment under loading were calculated.Based on the potential energy method and slice theory,the geometric stiffness,coupling stiffness,Hertzian contact stiffness,and gear foundation stiffness models were constructed,and then the improved analytical formula of time varying meshing stiffness of spur gear pair with tooth length modification and misalignment was derived.Finally,the proposed analytical model was verified by comparing with the results of finite element method.The stiffness excitation of spur gear pair with tooth length modification and misalignment and the influences of different tooth length modification and misalignment on stiffness excitation of spur gear pair were analyzed.The results show that the calculation error of the proposed method of time varying meshing stiffness for spur gear pairs with tooth length modification and misalignment is 3%,which can accurately and effectively analyze the meshing stiffness of spur gear pair with tooth length modification and misalignment,and provides a theoretical basis for the modification design of gear transmission system.
作者
朱文轩
张书维
王琳
周海川
ZHU Wenxuan;ZHANG Shuwei;WANG Lin;ZHOU Haichuan(School of Mechanical Engineering,Jiangsu College of Safety Technology,Xuzhou 221011,China;School of Automation,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China)
出处
《机电工程》
北大核心
2024年第1期52-61,165,共11页
Journal of Mechanical & Electrical Engineering
基金
国家自然科学基金资助项目(51775272)。
关键词
直齿轮误差
轴向错位
时变啮合刚度
切片理论
势能法
齿接触分析
加载齿接触分析
spur gear error
misalignment
time-varying mesh stiffness
slice theory
potential energy method
tooth contact analysis(TCA)
loaded tooth contact analysis(LTCA)