Nonlinear theoretical analysis of contacting forward whirling vibration of a rotating shaft supported by a repulsive magnetic bearing

A repulsive magnetic bearing is a passive magnetic bearing which consists of two polarized permanent ring magnets. When a pair of axially polarized ring magnets is set their direction of magnetism in the same direction, it supports the radial displacement passively and the system only needs the active control of the axial direction. A rotating shaft supported by a radial repulsive magnetic bearing may come into contact with a backup bearing during its passage of critical speed, as the damping of the repulsive magnetic bearing is small. This paper investigates the contact vibration during its passage of critical speed. Particularly, the influence of the axial displacement of the shaft to the repulsive magnetic bearing on the rotational speed of escapement from the contact vibration is focused. As a result, it is clarified that the rotational speed of the escapement from the contact vibration decreases as the axial displacement increases. This is explained by the influences of the changes of both the linear stiffness and the nonlinear coefficient of the restoring force in the radial direction along with the change of the axial displacement. This result is validated experimentally. Furthermore, influences of various parameters on the rotational speed of escapement are clarified.