An improved model for time-varying mesh stiffness of straight bevel gears with a real cross-section using the potential energy method

The vibration of a gear system caused by mesh stiffness is generally recognized as one of the main sources of self-excited vibration of the system. Therefore, accurate calculation of the stiffness is extremely important for the study of the dynamics of the gear system. However, the parameters that calculate time-varying mesh stiffness (TVMS) calculation of straight bevel gears using potential energy method (PEM), such as inertial product and area, still use an approximate tooth cross-section rather than a real. This will cause some errors in TVMS. In order to solve this problem, this paper develops an approximation method based on PEM for determining TVMS of straight bevel gears with a real cross-section, so that the mesh stiffness can be modeled more accurately. Furthermore, to diminish the error in the direct calculation of the overall TVMS of a straight bevel gear, a tooth will be sliced. The mesh stiffness of a tooth segment is calculated under the equivalent gear to obtain the overall mesh stiffness of the tooth. The results indicate that the stiffness changes caused by addendum and base angle decreases as the number of tooth segment increases. What's more, comparing the mesh stiffness between approximate and real cross-sections, it is discovered that the latter has larger values, and their stiffness variations follow the same trend. These findings provide a theoretical basis for the design of straight bevel gears.