Mesh stiffness modeling and dynamic simulation of spur gears with body crack under speed fluctuation condition

The traditional method for calculating the time-varying mesh stiffness (TVMS) of cracked gears usually assumes that the root crack is solely located within the gear tooth. Accurate calculation becomes a challenge when the crack propagates into the gear body. In this paper, an improved model for calculating the TVMS of spur gears with crack propagation into the gear body is proposed based on a combined analytical finite element-potential energy method, and the accuracy of the proposed model is verified by the finite element method. A 5-degree-of-freedom (5-DOF) dynamic model with speed fluctuation is developed, taking into account the coupling shaft-bearing stiffness as the support stiffness. Subsequently, a dynamic simulation of a gear system with a gear body crack is conducted. The results indicate that the proposed analytical model can provide relatively accurate mesh stiffness for crack propagation into the gear body. The TVMS decreases as the crack length increases, the decrease in mesh stiffness becomes more significant when considering the influence of the crack on the gear body stiffness. The dynamic response obtained from the proposed dynamic model shows more pronounced pulse characteristics compared to the model that does not consider the influence of shaft stiffness. The low speed and heavy load conditions restrain the speed fluctuation of the gear system. The residual signal is more effective for identifying fault signals than the original signal. The proposed model can provide theoretical and methodological references for diagnosing faults in gear systems with crack propagation into the gear body.