The time-varying meshing stiffness of gears is an important excitation source of gear vibration. Accurate calculation of the time-varying meshing stiffness of gears is helpful to retain the characteristic information of actual tooth profile and facilitate experimental verification.
In practical analysis, gear teeth are usually regarded as cantilever beams with variable cross-section by combining potential energy principle with material mechanics theory. There are two basic assumptions when calculating the time-varying meshing stiffness of gears by energy method: (I) it is assumed that there is no tooth surface friction, manufacturing error and transmission error in the gear system when calculating the stiffness; (II) the gear body is regarded as a rigid body. In order to simplify the calculation model of gear meshing stiffness, only the stiffness of the gear teeth in the process of meshing is considered in the calculation process, and the part of the gear with the teeth removed is regarded as a rigid disk. Due to the simplification of the model, the error of meshing stiffness of gears is ignored because our purpose is to study the difference of meshing stiffness between healthy gears and faulty gears.
According to the nature of the involute profile of the gear, the meshing line of the gear is tangent to the base circle of the gear and perpendicular to the involute profile of the gear. Therefore, the meshing force along the meshing line can be divided into two forces FA and FB which are perpendicular to each other:
