Abstract: According to variance changing laws of a precise rotor radial rotating error motion, it can be proved that the rotor's motion track is characterized by fractional Brownian motion.Then non-dimension fractal box counting dimension has been adopted to describe the rotor's radial rotating error motion, and it also be taken as a parameter to estimate the complexity of axes motion track.At last, Hurst exponent was adopted to describe the stability of axes rotating motion.

Key words: fractional Brownian motion, variance, fractal box counting dimension, Hurst exponent