Analytical Research Of Induction Spherical Motor Based On Second-order Vector Magnetic Potential

The traditional multi-degree-of-freedom(multi-DOF)actuators or multi-DOF motion platforms are realized by connecting or paralleling the single-DOF motor,which has some problems in structure and control.As a kind of mechanical device that can achieve the multi-DOF motion,the spherical motors can play a unique advantage in robot joint drive and satellite attitude control and have gradually become a research focus of domestic and international because of compact structure,high precision,no motion singularity and so on.At the same time,with the emergence of some new magnetic materials,it is possible to meet the performance requirements of special structure motor with complex magnetic circuit.This dissertation takes a soft magnetic composite(SMC)material induction spherical motor as the research object,and the magnetic field and electromagnetic torque are analyzed based on the equivalent surface current.Firstly,the structure and working principle of the induction spherical motor are introduced.The stator iron-core is made of SMC material and the spherical rotor is designed with a double-layer structure,which the outer layer is made of copper material with excellent conductivity and the inner layer is made of SMC material with good magnetic properties.After the magnetic pole of the target magnetic field is determined,the distribution law of stator coils is obtained and the split-phase electrification strategy of stator coils is given according to the winding excitation mode of the ordinary rotating machine.Secondly,taking the rotating magnetic field around the Z axis as an example,a three-dimensional analytical model for calculating the air-gap dynamic magnetic field of the spherical induction motor is proposed.And this model combines the spherical harmonic expansion method with the second-order vector magnetic potential method.Using the geometrical equivalence principle of the cylinder and the dihedral cone,the spherical quadrilateral equivalent current sheet model of stator iron-core coil is obtained,and then the current density distribution on the external spherical surface of the stator teeth can be obtained by the spherical harmonic expansion.With the current density distribution and other boundary conditions,the spherical harmonics description of the air-gap flux density is obtained by solving Laplace’s equations and Helmholtz equation based on the second-order vector magnetic potential.Then,based on the distribution of the dynamic magnetic field in the air gap,the Maxwell tensor method is used to derive the analytical model of the electromagnetic torque.Finally,the correctness of analytical expressions can be verified by comparing the FEM results with the theoretical analysis of the magnetic field and electromagnetic torque.Meanwhile,an experimental control platform of spherical induction motor is built,in which the experimental prototype is designed and manufactured using modularity technique and the effectiveness of the electromagnetic model in proved according to the obtained electromagnetic torque and magnetic field experimental dates.