Research On Nonlinear Dynamic Characteristics Of Single And Double Span Rotor System With Magnetic Bearings

Based on the classic Jeffcott rotor system model, considered of the influence of strongly nonlinear factors such as electromagnetic force, rubbing force and crack force,this paper established single span and double span magnetic bearing rotor system model, In the study of the single span rotor system, the paper also considered the auxiliary bearing support force to the rotor system, Combined with the rotor dynamics and the Newton’s laws of motion to set up the system equations of motion and dimensionless to the equation, used the fourth order Runge Kutta numerical integral method to calculate the equation, used the double parameters figure, bifurcation diagram, phase diagram and poincare map to analyse the nonlinear dynamic characteristics and system stabilities that under the different system parameters, and analysed the influence law of the system parameters to the steady-state responses of the system when the rotating shaft appeared crack before and after, determined the critical parameters that the system movement characteristics have changed under specific parameter quantitatively, through this study can get the speed range of periodic motion, almost periodic motion and chaotic motion of the system, thus,it can provide the reference to the parameters matching, fault prognosis and diagnosis of such rotor systems.The study results show that, for the single span magnetic bearing rotor system, in order to obtain wide and stable working speed range, when the stiffness ratio k values between 1.5to 3.5 and the clearance ratio d0 values between 0.68 to 0.9, the system running stability has improved obviously. When the eccentricity of system have increased, the system movement stability in the area of w? ??20? change worse, under the conditions permit we should reduce the eccentricity as much as possible. Through analysis and comparison, when the rotor system produced a crack the change of the steady-state responses of system are mainly concentrated in the speed ratio w values between 0 to 2.5 speed range, the generation of crack lead to chaos,almost periodic areas increased in system response, the periodic motion mainly appeared in almost periodic motion and the speed range is relatively narrow, the system movement stability declined, at the same time, crack lead to the starting characteristics of rotor system deteriorated. In the double span rotor system, system movement mainly experienced the period 1, periodic motion, almost periodic motion, chaotic motion and period 1 motion,finally the system into the period 1 motion in the area of the speed ratio between 0 to 2. the influence of friction coefficient f, stiffness ratio k31 on the steady-state response of the system is weak, while the system presents rich dynamic behavior when other system parameters have changed.