考虑摩擦的摆线锥齿轮参数激励振动特性研究  

Parametric excitation vibration characteristics of cycloid bevel gear considering friction effect

作　　者：刘志峰[1] 郭春华[1] 杨文通[1] 张志民[1] 蔡力钢[1] Jorge Angeles 

机构地区：[1]北京工业大学机械工程与应用电子技术学院,北京100124 [2]Mc Gill University,Canada

出　　处：《振动与冲击》2014年第16期90-96,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51075006);863项目(SS2012AA040702)

摘　　要：考虑摩擦与参数激励影响建立摆线锥齿轮副啮合模型。以齿轮副啮合点间沿啮合线相对位移为广义坐标,用Lagrange原理建立主、从动齿轮扭转振动平衡方程,通过降阶、解耦及归一化获得系统动力学方程。采用四五阶Runge-Kutta法对动力学方程求解,给出摩擦因子对轮齿啮合点位移响应关系曲线;基于系统参数激励,对比分析有无摩擦时阻尼水平、外载荷、传递误差、刚度及激励频率对振动特性影响规律,给出相应参数激励下位移响应关系曲线。仿真结果表明,摩擦能有效抑制轮齿啮合点参数激励位移响应幅值,使峰值频率发生漂移;摩擦、激励频率均能改变系统运动状态、增加系统运动的复杂性。A meshing model of cycloid bevel gear was established,considering the effect of friction and parameter excitation. The relative displacements along the line of action of gear meshing point was taken as generalized coordinates,the torsional vibration equation of pinion and gear was obtained by using Lagrange principle,and then the system dynamics equation was derived through order reduction,decoupling and normalization. Adopting fourth-fifth order Runge-Kutta method to solve the dynamic equation,the curve of the displacement response at tooth meshing point versus friction factor was given. Under system parameter excitation,the influences of damping level,external load,transmission error,stiffness and excitation frequency on vibration characteristics of meshing point were analysed with and without consideration of friction effect respectively. The displacement response curves corresponding to parameter excitation were also presented.The simulation results show that： the displacement response amplitude at meshing point under parametric excitation is effectively restrained by friction,the peak frequency drifts and the excitation frequency and the friction can both change the motion behavior and increase the complexity of system movement.

关 键 词：摆线锥齿轮 摩擦 参数激励 响应关系曲线 峰值频率漂移 

分 类 号：TH132.4[机械工程—机械制造及自动化]