By introducing the effect of interface characteristics (such as friction, rough surface, etc.) between gears, the comprehensive time-varying stiffness of gears is further studied and applied to an example

(1) Considering the linear friction effect of tooth surface, the calculation formula of load component along the coordinate axis is derived in detail, 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 simulation results show that reducing the friction coefficient of the tooth surface can reduce the offset difference of the load, and the sudden change effect of the meshing stiffness before and after the alternating change of the friction direction is caused by the friction effect. The larger the friction coefficient is, the more obvious the difference of the meshing stiffness is. It is further shown that under the condition of sufficient lubrication between gear pairs, the fluctuation of the time-varying meshing stiffness curve of the gear can be reduced, especially in the single pair meshing interval, and the dynamic and other mechanical properties of the gear device can be improved.

(2) Based on the theory of micro scale space, the fractal contact mathematical model of rough surface is established by using fractal theory. The influence of fractal parameters of different rough surface geometry on normal contact load and normal contact stiffness is studied. The results show that fractal dimension, roughness amplitude, contact coefficient of cylindrical surface and other parameters do not affect the load and normal contact stiffness alone, but affect the normal contact stiffness The results show that the surface micro morphology characteristics are determined by the interaction between them, and there is a certain coordination relationship according to the geometric characteristics of the analyzed object. At the same time, the engineering application of normal contact stiffness of gear pair tooth surface is studied combined with gear tooth surface grade accuracy, and the data is compared with Yang sun model and NASA empirical formula. The results show that the established fractal contact mathematical model can better interpret or cover the normal contact stiffness of multi tooth surface roughness features. For high quality, high parameter and high performance gear service engineering, in addition to the macro and geometric dimensions of the gear, it is also necessary to consider the micro morphology characteristics of the surface under different processing technologies to qualitatively and quantitatively analyze its contact characteristics. Yang sun model and semi empirical formula can be used as the initial Stiffness Prediction of the gear with low quality requirements or the initial stiffness prediction of the new product design Sentence.