A dynamic model combining the average and the local meshing stiffnesses and based on the static transmission error for spur gears with profile modification

A dynamic model that evaluates the working condition of general spur gears based on a two-phase approach is presented. A finite element model is preliminary developed to obtain the static transmission error for several angular configurations at different nominal torques. Subsequently, a lumped parameter model is used to evaluate the dynamic behavior of the transmission. An analytical mesh-force formulation is proposed based on polynomial interpolations of the finite element results to accurately model the contact forces and meshing stiffness during the engagement. Two damping models are implemented to obtain a reasonable estimation of the response peaks in resonance conditions. The stability of the main resonance peaks is examined using Poincaré maps. The results are compared with those obtainable using the commonly employed models based either on the average or the local meshing stiffness, highlighting the limitations of these approaches. The proposed formulation combines classical mesh stiffness definitions, thereby achieving a more accurate and efficient mesh-force model.