螺旋锥齿轮非线性振动特性及参数影响

Nonlinear vibration characteristics of helical bevel gear system and parameters influences

引入沿啮合点法向的相对位移,建立了含间隙、时变啮合刚度和传动误差的螺旋锥齿轮传动7自由度动力学模型.运用五阶自适应Runge-Kutta方法对系统非线性振动特性和参数变化对混沌、冲击等行为的影响进行计算分析,得到冲击、非冲击的参数区间.结果表明,随着啮合频率增大、啮合刚度系数增大或啮合阻尼系数减小,系统分别经倍周期分岔、Hopf分岔两种途径进入混沌;随着载荷系数、啮合阻尼系数的增大和啮合刚度系数的减小,混沌和次谐波消减,冲击状况改善,间隙非线性的影响减弱,啮合阻尼系数变化的影响在轻载时更显著,而啮合刚度系数变化的影响在重载时更显著.

By defining the relative displacement along the line of action, a 7 degree-of-freedom dynamic model of helical bevel gear system was developed, where backlash, time-varying mesh stiffness and transmission error were considered. System nonlinear dynamic behavior and effects of parameters variations on chaos and shock behavior were numerically studied by the 5-order self-adaptive Runge-Kutta method, and the parameter ranges of shock and no shock were obtained. The results indicated that the system went to chaos through period-doubling bifurcation with mesh frequency increasing, and through Hopf bifurcation with mesh stiffness coefficient increasing or damping coefficient decreasing. With load coefficient and mesh damping coefficient increasing, and mesh stiffness coefficient decreasing, chaos and sub-harmonic responses subtracted, shocking lightened and gear backlash nonlinearity effect decreased. In addition, damping coefficient variations affected more remarkably in the light load case, while stiffness coefficient variations affected more remarkably in the heavy load case.