An improved time-varying mesh stiffness algorithm and dynamic modeling of gear-rotor system with tooth root crack

When a tooth crack failure occurs, the vibration response characteristics caused by the change of time-varying mesh stiffness play an important role in crack fault diagnosis. In this paper, an improved time-varying mesh stiffness algorithm is presented. A coupled lateral and torsional vibration dynamic model is used to simulate the vibration response of gear-rotor system with tooth crack. The effects of geometric transmission error (GTE), bearing stiffness, and gear mesh stiffness on the dynamic model are analyzed. The simulation results show that the gear dynamic response is periodic impulses due to the periodic sudden change of time varying mesh stiffness. When the cracked tooth comes in contact, the impulse amplitude will increase as a result of reductions of mesh stiffness. Amplitude modulation phenomenon caused by GTE can be found in the simulation signal. The lateral–torsional coupling frequency increases greatly within certain limits and thereafter reaches a constant while the lateral natural frequency nearly remains constant as the gear mesh stiffness increases. Finally, an experiment was conducted on a test bench with 2 mm root crack fault. The results of experiment agree well with those obtained by simulation. The proposed method improves the accuracy of using potential energy method to calculate the time-varying mesh stiffness and expounds the vibration mechanism of gear-rotor system with tooth crack failure.