Optimization design of magnetic field generator using double pairs of round-corner saddle coils for a spherical motor

Based on the rotational coaxial effect that the lateral coupling magnetic moment drives the axis of the permanent magnet rotor toward the axis of the spatial universal rotating magnetic field (SURMF), a two-degree-of-freedom permanent magnet spherical motor (PMSM), which is composed of a universal following mechanism and a novel magnetic field generator (MFG), is proposed, the MFG consists of two groups of round-corner saddle (RCS) coils and one group of Helmholtz coils by three-axis orthogonal nesting to generate the SURMF to actuate the PMSM. The contribution of the paper lies in a double optimization design method for the RCS coils. First, based on the Biot-Savart law, an independent variable transformation method is proposed to realize the magnetic field modeling of the RCS coils, which lays a foundation for the optimization design of the MFG. Second, regarding power consumption and magnetic field homogeneity as objective functions, the general structure parameters of the right angle saddle coils are optimized by a particle swarm optimization algorithm, thereafter, the detailed round corner parameters of the RCS coils with good manufacturability are optimized similarly. The simulations and experiments show that the coils have accurate structural coefficients and good magnetic field homogeneity, along with the accurate control path of the PMSM driven by the MFG.