Investigation of nonlinear vibration of spur gears applying the analytical model

For a long time, the vibration modeling of gear systems was based on the linear vibration theory. However, in the last decades, the nonlinear factors such as backlash, time varying mesh stiffness, friction, transmission error and other imperfections have been taken into account. The aim of this paper is to investigate the nonlinear vibration of spur gear in presence of clearance and the static transmission error. To this end, first the time varying mesh stiffness of tooth is calculated analytically. Then the Governing equations of motion are extracted and are solved through Runge-Kutta method and the effect of the system parameters on its nonlinear vibrational behavior is demonstrated.