Torque Analysis And Stator Optimization Of A Permanent Magnet Spherical Motor

Traditional robot joints are combined by more than one motor. If the permanentmagnet (PM) spherical motor that can achieve the three-DOF (3-D) motion is used,the mechanical structure is greatly simplified, the position accuracy and the responsespeed of transmission systems are improved. The kind of motor present its uniqueadvantages and potential prospect in engineering application. At present, the study onthe spherical motor is in the early stage of exploration.The paper presents a novel permanent magnet spherical motor. The3-Dsimulation model of the PM spherical motor is established, the magnetic fielddistributions of motor and stator are analyzed by magnetic equivalent circuit (MEC)method, the Maxwell stress tensor (MST) method is applied to analyze theelectromagnetic force and torque, the stator winding inductance is calculated withenergy method, the stator winding’s power consumption is calculated by Ohm’s law.The stator size is optimized with multi-objective immune algorithm.The magnetic field distributions of stator are analyzed by MEC method. For thestator, first, based on the body current model of the PM, the relationship between thecurrent density and PM magnetization was derived, and then the equivalent PM modelof the stator coil was obtained. Furthermore, the PM model and the air region weremeshed in cylindrical coordinates. Taking the symmetry and analogy with electriccircuit into account, the magnetic field boundary conditions were represented by thecorresponding states of nodes and branches of the reluctance elements. Finally, asimplified2-D MEC network was obtained. The expressions of the reluctances andmagnetomotive force sources of the element were deduced, and the spatialdistribution of flux density was analyzed by means of the average magnetic energy.Based on this, the MST method is applied to analyze the electromagnetic forceand torque, the corresponding torque matrix is given, and the relationship between themotor torque and winding location is obtained. The stator winding inductance iscalculated with energy method, the stator winding’s power consumption is calculatedby Ohm’s law Compared with the FEM, this method is proved to have a high accuracyand helpful to the optimization design of the PM spherical motor. The stator size is optimized with multi-objective immune algorithm. Firstly, asummary of previous work is done, Secondly, a novel multi-objective optimizationtheory-artificial immune algorithm-is introduced. Finally, the spherical stator shapeis optimized with the artificial immune algorithm in order to obtain the maximumtorque and maximum inductance and minimum power consumption. The results provethat the artificial immune algorithm is an effective way to optimize the stator shape.