In order to compare and display the data intuitively, the single logarithm coordinate drawing method is used to draw the data of simulation results. It can be seen from Figure 1 that the normal load increases with the increase of the real contact area, and decreases first and then increases with the increase of the fractal dimension. According to the change trend, the minimum value of the normal load can be approximately obtained, and the fractal dimension D = 1.50-1.65 is further selected to refine the simulation The results of true analysis are shown in Fig. 1 (b). It can be seen that the three-dimensional topological map is concave, and the change is more obvious with the increase of the real contact area. Combined with the contour map (Fig. 1 (c)), it can be seen that the minimum extreme value of load appears near the fractal dimension D = 1.57. Figure 2 shows that under the effect of different fractal dimensions, the normal contact stiffness increases with the increase of fractal dimension and the real contact area.
Taking the same fractal dimension and contact coefficient of cylinder surface (d = 1.6, λ C = 0.7), the influence of roughness amplitude on normal load and normal contact stiffness is analyzed. As can be seen in Figure 3, the normal load increases with the increase of roughness amplitude, and the normal contact stiffness decreases with the increase of roughness amplitude. From the analysis of the formula, it can be concluded that under the same condition of hardness coefficient, material characteristic coefficient and nominal contact area, the elastic-plastic change occurs with the decrease of roughness amplitude, and the critical area decreases, so as to improve the surface finish of the contact body and effectively improve the normal contact stiffness. The above analysis results show that the fractal parameters D and g of rough surface have different effects on the normal load, but have the same effect on the normal stiffness, which indicates that the anti deformation ability of the tooth surface can be improved by increasing the fractal dimension and finish of the surface.
Figure 4 (d = 1.6, g * = – 100000000000) shows that the normal load increases with the increase of the contact coefficient of the cylinder surface, and presents a nonlinear growth, and the difference growth decreases with the effect of the contact area. The variation curve of the interaction between the normal contact stiffness and the contact area and the contact coefficient of the cylinder surface is the same as that of the normal load curve.
Figures 5 and 6 show the curves of normal load and normal contact stiffness with surface hardness and material characteristic parameters, and both increase with the increase of variables h and φ. Further analysis of the influence of the two on the critical contact area shows that the critical contact area decreases nonlinearly with the increase of surface hardness and material characteristic parameters, but increases with the increase of roughness amplitude, which indicates that under the same cold working process, the application of different materials and heat treatment processes can improve the elastic-plastic critical contact area of the contact body, so as to improve its bearing capacity and strength Resistance to deformation.
Through the above discussion on the influence of parameters, the fractal dimension, roughness amplitude, contact coefficient of cylinder surface and other parameters do not affect the load and normal stiffness alone, but jointly determine the surface micro morphology characteristics, and have a certain coordination relationship according to the geometric characteristics of the analysis object. Therefore, for the engineering application of fractal theory, the influence of surface micro factors on the mechanical properties such as normal load and normal contact stiffness should be comprehensively considered.