Time-varying mesh stiffness calculation of spur gears with spalling defect

• An analytical method for TVMS calculation of spur gears with spalling is developed.
• A Finite element method is used to verify the proposed model.
• Some differences between analytical method and finite element method are explained.
• Effects of spalling widths, lengths and location on TVMS are analyzed.

Considering the effects of extended tooth contact (ETC), revised fillet-foundation stiffness under double-tooth engagement region, nonlinear contact stiffness and tooth spalling defect, an analytical model for time-varying mesh stiffness (TVMS) calculation of spur gears is established. In addition, the analytical model is also verified by comparing the TVMS under different spalling widths, lengths and locations with that obtained from finite element method. The results show that gear mesh stiffness decreases sharply with the increase of spalling width, especially during the single-tooth engagement; the spalling length only has an effect on the beginning and ending of gear mesh stiffness reduction; the spalling location can affect the range of gear mesh stiffness reduction, and the range will reduce when the spalling location is close to the addendum. This study can provide a theoretical basis for spalling defect diagnosis.