复合行星齿轮传动系统非线性动力学建模与振动特性

Nonlinear dynamic modeling of compound planetary gear train sets and vibration characteristics

为了深入研究复合行星轮系的非线性特性,采用集中质量法建立了一种考虑时变啮合刚度、齿侧间隙和齿轮副综合啮合误差的复合行星齿轮系统的非线性动力学模型.通过引入相对啮合位移、无量纲时间尺寸和激励频率对非线性动力学模型进行了无量纲处理,消除了系统的刚体位移.基于变步长Gill积分法编写了计算程序,求解了非线性微分方程组的动态响应.最后,综合运用时间历程图、相图、Poincaré映射和功率谱对各类响应进行了比较和分析,研究了系统在不同无量纲激励频率激励时所表现单周期、拟周期、多周期和混沌的非线性特性,结果发现系统蕴含了丰富的非线性特性,存在着拟周期通过锁相进入混沌的途径.

For an in-depth study of the compound planetary gear train nonlinear characteristics,a nonlinear dynamic model is proposed by employing lumped mass modeling method.The model considers time-varying mesh stiffness,gear mesh errors and gear backlashes.The non-dimensional treatment has been performed by introducing relative meshing displacement,dimensionless time and excitation frequency;and the rigid body displacements have also been removed to facilitate the numerical investigation.The multi-degrees of freedom nonlinear differential equations of system are solved by variable step-size Gill integration method.Finally,various types of response are compared and analyzed by comprehensively using time history,phase trajectory,Poincarésection and power spectrum and the nonlinear characteristics of system,involving single-periodic response,quasi-periodic response,multi-periodic response and chaotic response under different non-dimensional excitation frequency has been presented and investigated.Abundant nonlinear phenomena and the classic quasi-periodic routes to chaos have been revealed in this nonlinear dynamic system.