Mesh stiffness modelling and dynamic simulation of helical gears with tooth crack propagation

In order to identify gear crack failure, modelling the mesh stiffness of a cracked tooth is crucial. In this study, an analytical model of the mesh stiffness for cracked helical gears considering the axial mesh stiffness components and the deflection of the gear body has been proposed. Based on the analytical model, the comparison of the mesh stiffness with and without the axial mesh stiffness components or the deflection of the gear body was carried out. Mesh stiffness of three crack propagation scenarios with different crack sizes has been investigated. Simultaneously, a method to detect the crack length has been deduced based on the time period of the mesh stiffness. Simulation has been conducted using a six-degrees-of-freedom helical gear dynamic model in order to study the effect of tooth crack propagation on the dynamic response. Statistical indicators extracted in the time domain and frequency domain were adopted to evaluate the crack propagation level. The results indicated that the analytical model that has been proposed is able to provide a relatively accurate mesh stiffness, taking into consideration the axial mesh stiffness components and the deflection of the gear body. Mesh stiffness reduced with the propagation of the crack size in either the direction of the crack depth or the crack length. Through analysis of the time period of the residual signal from the dynamic transmission error, the crack length was able to be accurately identified. The shape factor in the selected statistical indicators is most sensitive to the tooth crack propagation in the frequency domain.