Dynamic modeling of a spline-shaft system including time-varying fretting friction

• A novelty spline meshing stiffness model with fretting friction is proposed. • A new spline-shaft system dynamic model with fretting friction is established. • The significance of fretting friction on spline-shaft dynamics is demonstrated. • The non-uniform clearance impact mechanism on spline-shaft dynamics is elucidated. Splines serve as an important excitation source for the spline-shaft system and have a notable effect on its dynamics. Fretting friction between spline pairs will affect the tooth meshing stiffness (TMS) and spline excitation characteristic. Most previous works ignored the effect of fretting friction on the TMS and adapted the classical Coulomb friction model to calculate the spline friction force. These are unreasonable and will lead to the inability to describe the spline-shaft vibrations accurately. Thus, a novelty spline TMS calculation method considering fretting friction is derived. Moreover, spline non-uniform clearance (NUC) is emphasized in this work, which is more consistent with reality compared to the uniform clearance model. Finally, a spline-shaft system dynamic model is established considering spline tooth pair time-varying and spatial-varying fretting friction. An experiment is carried out to demonstrate the effectiveness of dynamic model. The spline TMS, meshing forces, and shaft dynamics with and without fretting friction are compared. Ultimately, the effects of NUC on meshing force and spline-shaft vibrations are analyzed. This work can offer essential theoretical insights for diagnosing faults and controlling vibrations in the spline-shaft systems.