Effects of Nonlinearity of Magnetic Force on Passing Through a Critical Speed of a Rotor With a Superconducting Bearing

High-T_c superconducting magnetic levitation systems have a feature of noncontact stable levitation. Recently, flywheel energy storage systems using superconducting magnetic bearings have reached its validation phase. Also, varied combinations of magnetic bearings have been used in this system. However, increase in amplitude has become a problem because of its low damping. Also, nonlinear phenomena can occur in such low-damping systems using electromagnetic force. This study investigates vibration reduction of a rotor system with an electromagnet. The nonlinearity of the magnetic force is taken into consideration in the case. First of all, we developed an essential model of a rotor supported by a superconductor, a permanent magnet and an electromagnet. Equations were derived by taking into account the nonlinearity of the electromagnetic force. These equations were then calculated by using the Runge-Kutta method. Numerical results show vibration reduction of the rotor by changing the electromagnetic force at appropriate rotating speed. Good agreements were obtained between experimental results and numerical results. In summary, changing of not only linear stiffness but also nonlinear stiffness affects vibration reduction of a rotor supported by a superconducting bulk, a permanent magnet, and an electromagnet.