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During the operation of the ball joint, its service life and transmission efficiency are affected by the internal friction. Taking the ball joint as the research object, based on fractal theory, the friction between the steel ball and the raceway inside the ball joint of an automotive drive shaft system is studied in this paper. During the analysis, the friction between the steel ball and the arc raceway is regarded as the friction between a sphere and an arc raceway surface. In order to describe the friction state more accurately, this paper proposes a correction coefficient to modify the distribution function of contact asperities in the plane, and obtains the distribution function of contact asperities between the sphere and the arc raceway surface. The correction coefficient is related to the load, the size parameters and the material parameters of the steel ball and the raceway.