Analytical models of mesh stiffness for cracked spur gears considering gear body deflection and dynamic simulation

Accurate mesh stiffness models for cracked spur gears are critical to obtain gearbox failure characteristics. However, the influence of crack on gear body deflection is often ignored by most researchers. In this study, analytical models of mesh stiffness for cracked spur gears considering gear body deflection are proposed. Both the cracked tooth and the adjacent tooth are included to simulate the mesh stiffness with tooth crack. Effects of crack length and inclination angle on mesh stiffness are investigated by these analytical models. Dynamic simulation is conducted by a six-degrees-of-freedom dynamic model incorporating the developed analytical mesh stiffness models. Frequency spectrum analysis and statistical indicators are adopted in order to evaluate the effects of tooth crack. The simulated results reveal that tooth crack produces mesh stiffness reduction in a complete rotation period for both the cracked tooth and the adjacent tooth. The total mesh stiffness is not only affected by the cracked tooth but also by the adjacent tooth due to tooth crack. The proposed analytical models can provide relatively accurate mesh stiffness for cracked spur gears by considering gear body deflection. The dynamic response obtained in this simulation by the proposed model has more obvious impulsive feature than the one without considering the effect of crack on the adjacent tooth and gear body, which are more convenient for tooth crack fault diagnosis.