Research on the meshing stiffness and vibration response of fault gears under an angle-changing crack based on the universal equation of gear profile

Tooth crack is a non-negligible issue that causes the vibration response of a gearbox. Therefore, the operating status of the gearbox is always detected to remove the presence of dangerous situations. Therefore, the effect of a gear tooth crack on the vibration response of the gearbox is important for the gear condition monitoring. The accuracy of meshing stiffness analytical model is the basis for effective dynamic simulation; for this account, a universal equation of a gear profile that is in reference to the actual process of manufacturing is presented to improve the meshing stiffness model for a cracked tooth. Based on the actual gear profile, in theory, two affecting lines, the parabolic-affecting line (PA) and the straight-affecting line (SA), are introduced to study the effect of an angle-changing crack on the gear mesh stiffness. Afterward, the influence of the angle-changing crack on the vibration response is investigated both in the time domain and in the frequency domain.