An analytical method for time-varying mesh stiffness calculation for straight bevel gears under spalling conditions

Abstract Tooth spall is a prevalent gear fault that reduces mesh stiffness and adversely affects transmission ability of gear systems. While plenty of research focuses on tooth spall faults in spur and helical gears, few analytical approaches were established to calculate the time-varying mesh stiffness in straight bevel gears, especially those affected by tooth spall. This deficiency can be attributed to the lack of an accurate tooth spall model. This paper proposes an approach for straight bevel gears mesh stiffness calculation with a curved-bottom spall. The spur gear spall model is modified to adapt to the tooth profile in straight bevel gears. The time-varying mesh stiffness calculation formulas are then revised in spall region. Using potential energy, Hertzian contact stiffness is calculated considering load distribution between gear teeth. The foundation stiffness calculation is updated considering practical gear shape. Tooth stiffness caused by axial forces is also considered. Finite element analysis is utilized for the theoretical method verification, which suggests a high consistency of results between two methods. The low error between the proposed approach and finite element approach implies that the proposed method is acceptable for practical use.