3-D Magnetic Field Analysis Of A Halbach Array PM Spherical Motor

Widespread application of the robot and manipulator has necessitated the development of the motors which are capable of making multi-DOF motion. The PM spherical motor becomes a new research direction of the PM motor. It is not suitable to copy indiscriminately the research method and experience of the traditional PM motor for the PM spherical motor. The research on the PM spherical motor, a pioneering study and advanced subject, is in theory exploration stage at present. The main research contents are limited on magnetic model, kinematics and dynamics analysis. The current research results indicate that lower energy index and poor torque-angle characteristic are disadvantages of the PM spherical motor.Halbach array can be applied into the PM spherical motor in order to improve the motor performance. A design concept of a Halbach array PM spherical motor is proposed. The fundamental principle of the Halbach array PM spherical motor is demonstrated. By using the Laplace equation and correct boundary conditions, the magnetic field is formulated. Harmonic components of magnetic field alongφandθdirection are studied. A study is made on the variations of air gap magnetic field with parallel magnetization directions along different spatial positions in each magnet segment. Magnetization angles and arrangement mode of magnetic poles are also studied, which lay a foundation for optimum design of the Halbach array PM spherical motor. A comparison is made between the Halbach array PM spherical motor and the conventional parallel magnet array spherical motor in terms of spherical harmonic components and amplitude of air gap flux density, which shows that, compared with the latter, the Halbach array PM spherical motor is more effective in improving air gap magnetic field distribution.In order to validate the analytical method, magnetic field analysis with FEM is offered. The effects of magnet thickness, the permeability of rotor core and stator core on air gap magnetic field are also studied. A comparison is made among different magnet structures in terms of spherical harmonic components. The results produced by analytical method and finite element method are basically in agreement.Three-dimensional (3-D) torque model and back-EMF model of the Halbach array PM spherical motor are given in order to study the motor characteristics furthermore. The torque models produced by different magnet structures are compared and the results are validated by FEM. In the end, two manufacturing methods of Halbach array magnets are also discussed.According to the structural characteristics of the spherical magnetic poles, some kinds of Halbach array spherical magnets with multi-layer poles which can be applied to the PM spherical motor are proposed. The magnetization mechanisms of the Halbach array spherical magnets with multi-layer poles are studied. The magnetic fields produced by different Halbach array spherical magnets with multi-layer poles are analyzed using FEM. The effects of magnetization directions of some magnets and the magnet thickness on the magnetic field are also discussed, which can lay a theoretical foundation for the optimization design of magnets.Based on the magnetic field model and 3-D magnetic field measurement, a position identification method is presented. The analysis results of the positioning process show that the rotor position can be determined by the rotation angles of the motor, which revolve around three reference axis of the stator. Furthermore, the coordinates of the point, where the magnetic field are measured, are obtained from the rotation angles. According to the magnetic field model and the rotation transformation theory, the nonlinear relationship between the measured value of magnetic flux density and the rotation angles is obtained. So by solving the nonlinear equation, the rotation angles are obtained and the rotor position is identified. The validity is verified through the simulation.