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The time series of turbo-unit rotor are tested under 3 different working conditions in this paper, which respectively calculates the largest Lyapunov exponent and correlation dimension, and analyzes and studies these two characteristic quantities. The study results show that: the Lyapunov exponent and correlation dimension of the time series for the generator rotor under different working conditions are obviously different. Therefore, "Lyapunov exponent - correlation dimension" is proposed to act as the quantitative characterization of the fault diagnosis for the generator rotor, which can diagnose and monitor the mechanical faults of the generator rotor. The study also opens up an effective way for diagnosis and prediction over other complex mechanical faults.