Time-varying mesh characteristics of a spur gear pair considering the tip-fillet and friction

Considering the effects of the tip-fillet and friction between teeth surfaces, an improved analytical model for time-varying mesh stiffness (TVMS) calculation is further developed based on our previous works (Ma et al. in Mech Mach Theory, 98:64–80, 2016) in which the effects of extended tooth contact, revised fillet-foundation stiffness and nonlinear contact stiffness are taken into account. The proposed model is also verified by comparing the TVMS with that obtained from finite element method. Combined effects of the tip-fillet and friction on the TVMS, loaded transmission error and loaded sharing factor are discussed. The results show that TVMS between double- and single-tooth engagements becomes smooth under the small radii of the tip-fillet, however, an abrupt change of the TVMS from double-tooth contact to single-tooth contact can be observed under the large radii of the tip-fillet. The range of the double-tooth engagement decreases and the single-tooth engagement increases with the increase of the radius of the tip-fillet. In addition, the tooth-surface friction mainly affects the mesh stiffness in single-tooth engagement region due to the change of friction force direction near pitch point, and the extent of variation increases with the increase of friction coefficient. The friction has a larger effect on the TVMS than the tip-fillet for the selected parameters of tip-fillet and friction. This study can provide a basis for the structural design of the spur gears.