Fault tolerance of homopolar magnetic bearings

This paper develops the theory for a fault-tolerant, permanent magnet biased, homopolar magnetic bearing. If some of the coils or power amplifiers suddenly fail, the remaining coil currents change via a novel distribution matrix such that the same magnetic forces are maintained before and after failure. Lagrange multiplier optimization with equality constraints is utilized to calculate the optimal distribution matrix that maximizes the load capacity of the failed bearing. Some numerical examples of distribution matrices are provided to illustrate the new theory. Simulations show that very much the same dynamic responses (orbits or displacements) are maintained throughout failure events (up to any combination of 5 coils failed for the 8 pole magnetic bearing) while currents and fluxes change significantly. The overall load capacity of the bearing actuator is reduced as coils fail. The same magnetic forces are then preserved up to the load capacity of the failed bearing.