Investigation of nonlinear characteristics of the motor-gear transmission system by trajectory-based stability preserving dimension reduction methodology

Gear-motor system is a typically nonlinear system because of many nonlinear factors, such as time-varying meshing stiffness, backlash, and the nonlinear relationship between the electric motor torque and speed. At present, the nonlinear analytical methods can only be used for simplified gear dynamic model. Though the numerical methods can be used for the complicated dynamic model, the quantitative analysis of stability is difficult and rarely conducted. Therefore, a kind of trajectory-based stability preserving dimension reduction (TSPDR) methodology is proposed to investigate nonlinear dynamic characteristics of the gear-motor system. In the TSPDR methodology herein, the complementary cluster center of inertia-relative motion (CCCOI-RM) transformation is chosen and the stability margins are specially defined for distinguishing the stable motion modes of the motor-gear system, to make the TSPDR methodology used in the nonlinear analysis of the gear-motor system. Furthermore, the critical values are obtained for alteration of different motion modes and the nonlinear characteristics of each motion modes are analyzed. At last, combined with modal analysis, the relationship between the stability and resonance of the gear-motor system is revealed.