行星齿轮非线性振动系统参数稳定域的计算方法

研究了行星齿轮非线性传动系统参数稳定域计算的一般方法.该方法通过选取合理的失稳阀值,根据考查参数域内系统的运动状态选取合适的数值积分时间段,以循环套嵌的手段计算考查参数在各自范围内不同组合下的系统位移响应最大值,比较失稳阀值以判稳,参数稳定域的图形输出等5个步骤完成对行星轮系参数稳定域的计算.最后,以四自由度行星轮系纯扭转非线性振动模型为例,以行星轮输入转速、系统的齿侧间隙以及齿轮副的啮合阻尼系数为考查参数,分别计算得到了系统的单参数稳定域、双参数稳定域以及三参数稳定域,为行星轮系的设计取值提供了重要参考. 

Method of stability region determination for planetary gear train's parameters based on nonlinear vibration model

A general method of stability region determination for a planetary gear train's parameters was studied based on a nonlinear vibration model.There are five steps in the method,and the first step was threshold determination,the second step was deciding numerical integration time according to the motion state of the system when the parameters discussed changed in their test range,the third step was calculating the maximum displacement of the system when the parameters discussed changed in their test range by using nested loop algorithm,the fourth step was stability judgment by comparing maximum displacement with threshold and the last step was making the stability region map of the system.As an example,the stability region determination of a planetary gear train with errors of transmission,time varying meshing stiffness and gear backlashes was studied,and the stable regions of sun gear's rotational speed,backlashes of the system and relative damping ratio were calculated respectively.