A new dynamic analytical method for gear transmission system

To obtain the dynamic response of the gear, a new analytical method for solving the system dynamics equation is proposed based on the Euler-Cauchy equation. In this paper, the time-varying meshing stiffness of the system is obtained by using the potential energy method, and the equivalent time-varying damping is obtained based on the Coulomb damping model. Then, the two-degree-of-freedom torsional vibration model of the system is established, and the analytical solution of the differential equation of the torsional vibration of the system is derived by using the Euler-Cauchy equation. Compared with the traditional numerical solution, the correctness of the method is verified. The effects of roughness, lubricating oil viscosity, and rotational speed on the dynamic characteristics of the system were studied. The results show that with the increase of the speed of the gear wheel, the roughness, and the viscosity of the lubricating oil, the amplitude of the dynamic response of the system decreases, and the stability time of the vibration increases. When the rotational speed increases to a certain speed, the dynamic response of the system cannot reach a stable state in a meshing period. Compared with the traditional numerical method, this method can predict the dynamic response of the gear transmission system more conveniently and intuitively, which provides a theoretical basis for further optimization and control of the dynamic response of the gear transmission system.