Abstract: Running-in and wear tests of a piston ring against a cylinder were conducted on a pin-on-disc tester, lubricated by both of CD40 lubricant and CD40 lubricant with additive. The sequence signals of the friction force were collected. The fractal behavior of the frictional forces was studied by means of fractal dimension and muhifractal spectrum. The sequence signals of the friction force are characterized by fractal, and the fractal dimension and muhifractal spectrum of the signals assume a regular variation in the running-in process. The variation of fractal dimension is coincident with the evolution of surface roughness, and the muhifractal spectrum can be used to describe dynamic process of friction surface. Therefore the quantitative analysis of running-in process can be carried out by fractal dimension and muhifractal spectrum of the sequence signals of the friction force.