In order to accurately calculate the contact stiffness of the fractal surface of cycloid needle wheel, a fractal model considering friction coefficient was proposed. Based on the modified Weierstrass-Mandelbrot function and differential geometry, a two-dimensional rough surface model of cycloidal gear tooth modified by second order parabola method and needle tooth was established. The model showed the morphological characteristics of the complete conjugate tooth profile and the needle tooth in particularly form in the macro and micro field of view, the cycloidal pin wheel was in the elastic deformation stage under meshing load, and the friction force correction factor was introduced. The contact stiffness of two rough contact surfaces at the micro level was calculated. The results showed that the contact stiffnessKnof fractal surface of cycloid needle wheel keeps steady at first and then increases rapidly with the increase of the meshing forceFon the contour, finally the contact stiffness is inclined down. The increase of surface roughnessRaand friction factorμled to the decrease of contact stiffnessKn, and the increase of modification coefficienta1will slow down the increase of contact stiffnessKn. Compared with the Hertz contact stiffness established by the LTCA model, the correctness of the cycloid pin wheel fractal model was verified, and the advantage of transforming the contact stiffnessKnfrom static to dynamic process and from oneness to continuity was demonstrated.
