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.