A dynamic model of the rotor system supported by active magnetic bearings at both sides is established, the fourth-order Runge-Kutta method is used to simulate. The periodic motion transition of the system and its evolution to chaotic motion are discussed from bifurcation diagrams and phase diagrams. It emphatically analyse the change of crack influencing factor and eccentricity on the system response and stability. The results show that the system presents period motion with appropriate parameter conditions. Large crack fatigue damage and value of eccentricity increases the amplitude and chaotic motion window in the low speed region, decrease the system stability. When the rotor crosses the critical speed range and reaches the high rotational speed region, the stable period-1 motion is dominant.