满足稳定性要求的行星轮系统工作转速区间确定方法

Determination method of working speed range for a planetary gear train based on stability requirement and a nonlinear vibration model

研究满足稳定性要求的行星齿轮系转速区间的确定方法。选取每个激振力周期内相轨迹的位移最大值点为Poincare截面,计算获得的转速分岔图能够同时判别系统的运动状态失稳及振动强度失稳两种失稳形式,结合行星轮系工作转速区间选择的4条原则,可方便地判断满足稳定性要求的系统工作转速区间;以四自由度行星轮系纯扭转非线性振动模型为例,详细阐述满足稳定性要求的行星轮系工作转速区间确定的全过程,通过剔除5类12处不稳定转速区段,获得无量纲转速在0.412 3～1.236 9之间可选的稳定速度区段。

A general determination method of working speed range for a planetary gear train was studied based on stability requirement and a nonlinear vibration model. With the method, a bifurcation diagram with working rotating： speed was calculated by using the method of maximum displacement in order to identify the instability of motion state and the instability of vibration amplitude in a diagram. The system＇s stable working speed range can be determined easily by using the bifurcation diagram and 4 speed range selection principles elaborated here. As an example, the working speed range of a planetary gear train with errors of transmission, time-varying meshing stiffness and gear backlashes was determined and the results revealed that there are 5 kinds of instable speed Ω =0.4123 - 1. 2396. forms and 12 instable speed ranges in the range of dimensionless