Exact Analytical Model for Magnetic Field Computation of Eccentric Harmonic Magnetic Gear with Halbach Array

Abstract

Halbach array has unilateral magnetic effect, so the eccentric harmonic magnetic gear (EHMG) with Halbach array has higher torque density than the traditional EHMG with radial magnetization. An exact analytical model for the air-gap magnetic field of EHMG with Halbach array based on hyperbolic cotangent transformation is proposed. The relative permeability function is solved and used to correct the air-gap magnetic field caused by the stator and rotor permanent magnets acting separately when concentric. The analytical solution of the air-gap magnetic field of EHMG with Halbach array is obtained by superposition of the corrected eccentric air-gap magnetic field. The static torque of low-speed inner rotor is calculated by Maxwell tensor method. The analytical solutions of the air-gap magnetic field and the static torque are consistent with the finite element solutions, which verifies the effectiveness and correctness of the analytical model.