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.