基于几何学和势能法的直齿轮副时变啮合刚度精确建模及应用  

Accurate Modeling and Application of Time-varying Mesh Stiffness of Spur Gear Pair based on Geometry and Potential Energy Method

作　　者：王晓鹏 刘世军 李纪强 Wang Xiaopeng;Liu Shijun;Li Jiqiang(Zheng Zhou Research Institute of Mechanical Engineering Co.,Ltd.,Zhengzhou 450052,China)

机构地区：[1]郑州机械研究所有限公司

出　　处：《机械传动》2020年第3期91-96,共6页Journal of Mechanical Transmission

摘　　要：时变啮合刚度(TVMS)是齿轮系统动力学研究中的重要参数变量之一,准确地模拟计算TVMS,对分析齿轮传动系统的振动、噪声等相关动力学性能响应指标至关重要。根据渐开线齿轮的啮合运动方程和几何位置关系,提出一种基于几何学和势能法作用的直齿轮副TVMS精确建模方法;实时、有效地分析标准渐开线齿廓的啮合极限边界条件,并结合势能法构建TVMS由物理模型向数学模型转变的计算分析模型;通过数值计算法精确地计算直齿轮副的TVMS,并进行了有限元验证及举例应用。研究表明,在满足齿轮设计承载容许范围内,应合理选取齿宽和轴径尺寸,且可通过两者进行TVMS的小幅度调整而实现刚度优化作用和提高转子系统抗挠度性能等,为后期进行齿轮系统动力学计算作基础性应用研究。Time-varying Mesh Stiffness(TVMS)is one of the important parameter variables in the study of gear system dynamics.It is crucial to accurately simulate TVMS for the analysis of dynamic performance re⁃sponse indexes of gear transmission system such as vibration and noise.On the basis of meshing kinematic equa⁃tion and geometric position relation of involute gear,one accurate modeling method of spur gear pairs based on geometry and potential energy method is proposed.The meshing limit boundary conditions of standard involute profile is analyzed in real-time and effectively,and a computational analysis model of TVMS from physical mod⁃el to mathematical model is constructed which combined with the potential energy method.The TVMS of spur gear pair is calculated accurately by numerical calculation method,and an example is given to illustrate its ap⁃plication.On the allowable range of bearing capacity for gear design,it is necessary to select tooth width and shaft diameter reasonably which makes minor adjustments for TVMS.It is also necessary to make further efforts to optimize stiffness and improve anti-deflection performance of rotor system which provide the later stage of gear system dynamics calculation as a basic application research.

关 键 词：几何学 势能法 直齿轮副 齿轮啮合运动模型 时变啮合刚度 

分 类 号：TH132.41[机械工程—机械制造及自动化]