Research on nonlinear dynamic model and characteristics of a spur gear pair considering the meshing state of multiple pairs of teeth

A meshing cycle of normal contact ratio gear can be divided into three stages, i.e., double pairs of teeth meshing, single pair of teeth meshing and double pairs of teeth meshing. In many previous literatures, for the convenience of research, the dynamic model based on a pair of teeth was usually used to express the dynamic behavior of all pairs of teeth in the entire meshing cycle, which will cause the problem that the established dynamic model cannot fully reflect the influence of the meshing state of each pair of teeth on the dynamic characteristics of the system. Therefore, based on the relevant literature, a nonlinear dynamic model of spur gear pair considering the meshing state of multiple pairs of teeth is proposed in this paper. The new model can fully reflect meshing error, meshing stiffness, backlash of multiple pairs of teeth participating in the meshing at the same time. To compare the differences between the new model and the traditional model, the main factor causing the difference between them is analyzed. Based on the calculation of single pair of teeth and comprehensive meshing error by TCA (tooth contact analysis) method, the effects of different meshing error, contact ratio and meshing damping on the system dynamic characteristics respectively based on the two models are compared and discussed. The results show that the new model can reflect the dynamic behavior of each pair of teeth participating in the meshing at the same time more accurately than the traditional model, especially when contact ratio and meshing damping are large. The new model proposed in this paper lays a foundation for building a more accurate dynamic model of a gear pair (especially the HCR gear pair with the contact ratio greater than 2) and accurately analyzing the dynamic behavior of each pair of teeth in meshing.