On the extended tooth contact and nonlinear dynamics for spur gears—An analytical model

In gear mesh, the extended tooth contact is a natural reaction stemming from the elasticity of solid bodies, which inevitably forces the theoretically separated teeth to engage and increases the actual contact ratio. Consequently, the changed mesh stiffness waveforms will further influence the dynamic response. A lot of works are devoted to mesh stiffness representation and dynamic modeling. However, the correlation between extended tooth contact and nonlinear dynamics still needs in-depth study. Motivated by a deeper understanding of the mesh mechanisms and dynamics, this paper proposed an analytical model attempting to combine the extended tooth contact and gear nonlinear dynamics. Starting from the gear elasticity, an analytical mesh stiffness model is proposed, which extended the application ranges of the popular fillet foundation polynomial formulas and covered both thin-walled and thick-walled gears. Moreover, A load-sharing model is developed, which explicitly represented the correlation between torques and intervals of extended tooth contact. Subsequently, the gear torsional dynamic model is extended to embody the extended tooth contact. A series of comparisons with FEM, existing theoretical models, and experiments demonstrated the acceptable accuracy of the present model. • A wide application scope of fillet foundation stiffness. • Analytically formulated the extended contact region. • A extended dynamic model accounting for extended tooth contact. • Verified both statics and dynamics by existing models or experiments.