When calculating meshing stiffness by quasi-static method, fixed constraints are generally imposed on the center position of each gear and the meshing stiffness of nominal meshing position in a single meshing cycle is calculated. In some studies, the influence of minor changes in the meshing position on the meshing stiffness is neglected, and the meshing stiffness is simplified into the periodic rectangular waveform form. Finally, the meshing stiffness is

In fact, the changes of speed, center distance and meshing state of tooth surface and back of gear drive will cause the meshing position to deviate from the nominal meshing position.The variation of center distance will not only change the amplitude of meshing stiffness, but also change the overlap.

For fixed-shaft gear drive, the influence of tooth profile modification, speed change, center distance change and meshing state change of tooth surface and back on meshing stiffness is deeply analyzed.The engagement position is determined by pressure angle of engagement point, and the analytical expression of engagement position of engagement teeth at any time is derived.

The analytical expressions of dynamic boundary conditions in single and double teeth engagement and modification area are derived.Combining the engagement position and dynamic boundary condition, the engagement stiffness is calculated by analytical method to obtain the dynamic engagement stiffness.