Contact dynamic modeling and corner contact analysis of the spur gear pair with pitch deviations

Pitch deviations have a significant effect on the contact state, transmission accuracy and running stability of a gear pair. In this work, a contact dynamic model of a spur gear pair is established on the basis of the pitch deviations. This model consists of three parts: a geometric mathematical model, a time-varying mesh stiffness (TVMS) model, and a dynamic differential equation and contact model. In the first part, mathematical equations are used to represent the tooth profiles of the gear pair with pitch deviations, which lays a foundation for the subsequent assessment of contact. In the second part, considering pitch deviations and the accurate root transition curve, the tooth is simplified as a cantilever beam on the root circle, and the TVMS of the gear pair is deduced using the potential energy method. In the third part, the contact modes of the gear pair with pitch deviations are analyzed, which shows that corner contact may occur during meshing. A mathematical contact judgment method is then proposed to determine eight meshing points (normal meshing points and corner contact meshing points) that may arise in the meshing state. Finally, dynamic differential equations of the gear pair are established. On the basis of the proposed model, effects of different pitch deviations and the random pitch deviations upon the vibration acceleration and the dynamic transmission error (DTE) of the gear pair are studied. The accuracy of the proposed contact dynamic model of the gear pair with pitch deviations is verified by way of an experiment reported in the literature and self-test data. The proposed model and research results lay a foundation for research into performance analysis, design optimization and precision manufacturing.