A study of the non-linear dynamic response of spur gear using a multibody contact based model with flexible teeth

This paper proposes a refined methodology to simulate the non-linear dynamic response of spur gears. The multibody model is based on a penalty contact formulation and considers teeth as separated bodies elastically attached to the main body with revolute joints. One of the advantages of this model is that there is no need to use, as a source of excitation, external variables as, for example, time-varying mesh stiffness, and static transmission error input. Moreover, the computational time is reduced if compared to a finite element method (FEM) model. The modelling strategies are preliminary described in detail and a novel analytical procedure for the identification of the elastic parameters is included. A FEM model is used for testing the gears response in quasi static conditions. This preliminary comparison allows to evaluate the accuracy of the estimated stiffness values. After that, dynamic conditions varying the mesh frequency have been introduced to simulate the non-linear behaviour caused by the contact loss at certain rotating speeds. The dynamic transmission error, computed on the basis of the proposed methodology, has been successfully compared with experimental data available in literature.