Study on the calculation method of time-varying meshing stiffness of herringbone gear under the influence of crack-pitting coupling

The vibration characteristics and fault diagnosis of herringbone gears are significantly affected by the time-varying meshing stiffness (TVMS), a crucial internal excitation factor. An analytical model was developed using the potential energy method to thoroughly investigate the impact of crack-pitting coupling on the TVMS of herringbone gears. This model accounted for various factors, such as different crack depths and degrees of pitting. It included 16 different crack depths and degrees of pitting, and analysed the bending stiffness, shear stiffness and axial compression stiffness of the herringbone gear pair under the influence of coupling. The problem was solved using the integral method to examine the effect of crack-pitting coupling on the TVMS of herringbone gears. The calculated TVMS results were then analysed and compared for healthy gears and those with different degrees of crack-pitting coupling faults. A finite element computational model was also established using the finite element method to assess the TVMS of herringbone gears subjected to varying degrees of crack-pitting coupling. Simulation and analysis were conducted to compare the results obtained from the model with those obtained using the analytical method. The results indicate that when the crack reaches 10%, the dominant factor influencing the coupling fault TVMS is pitting. When the crack reaches 30%–50%, the TVMS is jointly influenced by pitting and crack. At 70% crack, the dominant factor is the crack itself. The calculated results were compared to finite element calculations, with a maximum error of 2.5%, confirming the accuracy of the results. The findings of this study can furnish a theoretical foundation for analysing dynamic vibration stability and fault diagnosis in herringbone gear.