基于谐波平衡法的非圆面齿轮多参变振动特性研究

考虑齿轮的时变瞬心、刚度和误差等激励问题，基于弹性转角分离原理，构建了非圆面齿轮的量纲一动力学模型.针对时变刚度和瞬心组成的复合参数激励，采用多阶谐波平衡法得到齿轮动力学方程的近似解析解，着重分析了系统的关键参数对振动响应的影响规律以及各参数对振动的灵敏度的影响.研究结果表明:齿轮在复合参数激励下存在复杂的多频响应，响应幅值随转速、偏心率、误差幅值、啮合刚度幅值比以及负载扭矩的增大而呈现不同特点的增大趋势，齿轮系统的各参数取值对自身及其它参数的灵敏度值都将产生较大的影响. 

Multi-Parametric Vibration Characteristics of Noncircular Face Gear Based on Harmonic Balance Method

Considering the time-varying instantaneous center, meshing stiffness and static transmission error, a dimensionless dynamic model of the gear was established based on elastic rotational angle separation method. A multi-term harmonic balance method (HBM) was applied to obtain the approximate analytic solution of the gear under compound excitations composed of the instantaneous center and meshing stiffness. The effects of the system parameters on the dynamic response and the sensitivity of the parameters were analyzed emphatically. Results show that there exist multi-frequency harmonic components in the gear dynamic responses; the vibrational amplitudes grow with different tendencies as the rotational speed, the eccentricity, the error, the amplitude ratio of the meshing stiffness and the load torque increase; and every parameter of the gear has a greater influence on the sensitivity of itself and others.