A proposal for semi-analytical model of teeth contact with application to gear dynamics

In this paper a semi-analytical (SA) algorithm developed for the solution of the contact problem between two mating spur gears is presented and its application to the study of engagement dynamics is shown. Firstly, a quasi-static two-dimensional (2-D) approach is implemented to solve the contact taking into account several flexibility contributions related to the mating gears. In detail, a modified Hertzian model for the investigation of the real contact area considering the variable curvature of the profiles is developed. A comparison between this model and the classical Hertzian model is shown: the limitations of the classical method, for instance the possibility of analyzing bodies with varying curvatures and the peaks of pressure due to corner contact are therefore overcome. Furthermore, all the different tooth and gear deformations due to the meshing interaction are shown. This allows the computation of the Static Transmission Error (STE), main source of vibration and noise. The influence of tooth profile modifications is also highlighted. A comparison of the calculation of the STE with a Finite Element Method (FEM) model and a National Aeronautics and Space Administration (NASA) software is presented. The obtained results are excellent in terms of accuracy, also the computational time gain is highly significant when compared with FEM. Furthermore, after an introduction of two different approaches for the dynamic analysis, a dynamic model that includes the nonlinear meshing stiffness with the possibility of contact loss between teeth and flexible shafts is proposed. The quasi-static results are then used as inputs for the dynamic model and results for different configuration are shown. Finally, conclusions are drawn, and future developments are discussed.