A fast, non-implicit SDOF model for spur gear dynamics

Modeling and simulation of the nonlinear dynamic response typical in gear transmissions usually require extensive input from tooth contact analysis combined with data derived from numerical techniques that in turn comprise a time and resource-consuming procedure. In this work, an efficient SDOF model that captures meshing nonlinearities in a non-implicit manner is presented. An extensive geometric analysis designates the underlying physical mechanisms prevailing in tooth meshing enabling incorporation of the effects of backlash, varying mesh stiffness and corner contact. By this analysis, an accurate repositioning method is proposed for involute teeth contact reversal, while a general approximation function for gear pair mesh stiffness including load dependence is formulated and successfully fitted to analytical data. Consequently, distinction between single and double tooth contact is captured through a modified parametric s-curve, including the effect of corner contact. A SDOF dynamical model is formulated for a given pinion rotational velocity and solved numerically. Both static and dynamic results are compared to data available in the literature, showing high agreement with more complex methods, while maintaining the advantages of minimum required pre-calculations and low computational cost.