Considering the macro interface friction coefficient, the load component equation along the tooth profile direction is derived, and the mathematical model of time-varying meshing stiffness of spur gear pair with friction effect is established, and the simulation analysis of the example is carried out. The results show that reducing the friction coefficient of the tooth surface can reduce the offset difference of the load, and the friction effect causes the sudden change of the meshing stiffness before and after the alternating change of the friction direction. The larger the friction coefficient is, the more obvious the difference of the meshing stiffness is. The results show that under the condition of sufficient lubrication between gear pairs, the fluctuation of time-varying meshing stiffness curve can be reduced, especially in the single pair meshing interval, and the dynamic and other mechanical properties of the gear device can be improved.
In the micro scale space, the fractal mathematical model for predicting the normal load and normal contact stiffness of rough surface is established by using fractal theory, and the effects of different micro characteristic parameters on the normal load and contact stiffness of macro characteristic are studied. The results show that the parameters such as fractal dimension, roughness amplitude and contact coefficient of cylinder surface do not affect the load and normal stiffness alone, but jointly affect and determine the surface micro morphology characteristics. At the same time, combined with the grade accuracy of gear tooth surface, the engineering application simulation research on the normal contact stiffness of gear pair tooth surface is carried out, and compared with Yang sun model and NASA The results show that the established fractal contact mathematical model can better interpret or cover the normal contact stiffness of multi tooth rough surface features, and different analysis and calculation models can be selected for research and application according to the gear calculation application scenarios.