Stiffness of Magnetic Bearings Subjected to Combined Static and Dynamic Loads

Abstract

This paper investigates the stiffness of a magnetic bearing that is subjected to the combined action of static and dynamic loads. Since their sum cannot exceed the saturation load, a large static load will imply that the bearing can carry only a small dynamic load. This smaller dynamic load together with the practical vibration amplitude define a practical upper bound to the dynamic stiffness. This paper also presents approximate design formulas and curves for this stiffness capacity as a function of the ratio of dynamic and static loads. In addition, it indicates that vibrations larger than a certain gap fraction can destabilize the magnetic bearing. This gap fraction, called the critical gap fraction, depends on the dynamic and static load ratio. For example, if the dynamic load is half of the static load, the use of more than 25 percent of gap can destabilize the bearing.

Fault tolerance of magnetic bearings with material path reluctances and fringing factors

“…Apply Ampere's loop law, Gauss's law, and the conservation law of fluxes of the magnetic circuit to obtain a matrix relation (4) The reluctances in the magnetic bearing can be partitioned into the gap reluctance matrix and the material path reluctance matrix 5The gap reluctance matrix is (6) The material path reluctance matrix is defined as (7) where, as shown in the equation at the bottom of the next page. The coil turn matrix is (8) The magnetic flux vector is then described as (9) The flux density in the air gap may be substantially reduced due to the leakage and fringing effects. Allaire [11] showed that the flux leakage and fringing effects in a thrust magnetic bearing can be approximated by a simple scaling factor.…”

“…Bornstein [7] derived equations to express the dynamic load capacity. Rao et al [8] shows that the stiffness capacity of a magnetic bearing can be described as a function of the ratio of dynamic and static loads.…”