This paper presents an analytical method to facilitate design of a spherical magnetic bearing (SMB) for a multi-DOF rotational stage. Both passive and active regulations of the SMB are considered. We formulate the SMB dynamic model along with the method of computing the magnetic force and torque required to null any deviation of the rotor, which requires solving the magnetic field. For this, we introduce and validate a general method, referred to here as distributed-multi-pole (DMP) modeling method which requires only a limited set of known (numerical or experimental) field solutions, to derive closed-form solutions for precise calculation of the magnetic field around a permanent magnet (PM). The DMP method has been validated by comparing its modeled potential field and flux density against analytical solutions, as well as the computed force (using DMP modeled field) against published experimental data; both show excellent agreement. Finally, we demonstrate the concept feasibility of the spherical magnetic bearing, and analyze its dynamics and control performance using the DMP modeled field and computed force/torque.

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