Hongfeng Li

3-D Magnetic Field and Torque Analysis of a Novel Halbach Array Permanent-Magnet Spherical Motor

We present a three-dimensional (3-D) torque model based on spherical harmonic functions of a Halbach array permanent-magnet (PM) spherical motor. Using the torque model, we show how to realize three-degree-of-freedom motion. We compare the Halbach array PM spherical motor and the conventional parallel magnet array spherical motor in terms of spherical harmonic component and amplitude of the torque. We discuss our study of variations of air-gap magnetic field with parallel magnetization directions along different spatial positions in each magnet segment. We also discuss the parasitic effect of the proposed spherical Halbach array magnet. We have verified our results by finite-element method.

Research on Torque Calculation Method of Permanent-Magnet Spherical Motor Based on the Finite-Element Method

In this paper, the finite-element method (FEM) is used to calculate the spinning torque of the permanent-magnet (PM) spherical motor. Three-dimensional (3-D) FE model of the PM spherical motor is established. Spinning torque distribution on the spherical surface and its variation curve on the equator are obtained respectively. In order to avoid the complicated torque calculation process under 3-D magnetic field and thus reduce the computational burden, the torque calculation method based on the 2-D conversion model is proposed. This method equivalently simplifies the magnetic field of the spherical PMs and the shape of cylindrical stator windings to be simulation parameters of the 2-D conversion model. With these parameters, 2-D conversion model of the PM spherical motor is established. Spinning torque variation curves obtained by the 3-D model and the 2-D conversion model respectively are compared and the results agree extremely well. By comparing the maximum static torque (MST) obtained under different configuration parameters of the PM spherical motor, it is found that the errors are within the allowable range. Therefore, the reliability of the proposed torque calculation method in the paper is verified. Finally, based on the 2-D conversion model, variation curves of the MST with the length of the air gap, the ampere turns, the length of stator windings and the outer radius of stator windings are obtained, and they are validated by those based on the 3-D model. These results can provide the basis for the optimization of the PM spherical motor.

Magnetic Field Analysis of 3-DOF Permanent Magnetic Spherical Motor Using Magnetic Equivalent Circuit Method

The paper studies the magnetic field distribution of three degree-of-freedom (3-DOF) permanent magnet (PM) spherical motor adopting the 3-D magnetic equivalent circuits (MEC) method. Compared with the analytical method and finite element analysis (FEA) method, the MEC has such desirable attributes as moderate computational effort and reasonable accuracy. The model of PM spherical motor is evenly meshed into elements in spherical coordinates, and the expressions of reluctances and magnetomotive force (MMF) sources in the element have been deduced. Given that magnetic field of the PM spherical motor distributes in the whole space, to reduce the number of elements and increase the solving speed, an approximate equipotential surface is adopted based on the simplified magnetic circuit, and the different magnetic boundary conditions are represented by the corresponding states of nodes and branches of the elements. Finally, the MEC network, which represents half of the magnetic pole and the corresponding air region of the motor, is built. Flux density distribution is calculated by means of the proposed model and verified by the FEA method.

Modeling, Analyzing, and Parameter Design of the Magnetic Field of a Segmented Halbach Cylinder

The Halbach magnet array has become more and more attractive in many electromagnetic engineering domains such as electrical motors for its potential features such as self-shielding and providing sinusoidal field distribution. This paper develops analytical models formulated in polar coordinates for predicting the field distribution of a segmented Halbach magnet cylinder with or without back iron. Based on the analytical models, the relationships between the air-gap flux density and four design parameters including pole-pair number, segment number per pole, permanent-magnet radial dimension, and air-gap length are analyzed. Further, the Taguchi method is employed to identify the settings of design parameters and determine the parameters which have a significant effect on the field distribution. The analytical models are verified by taking advantage of the finite-element method (FEM), which shows that all the results can be of considerable use in the design of permanent-magnet machines.

Design and Analysis of a Variable Arc Permanent Magnet Array for Spherical Motor

This paper presents the design and analysis of a variable arc magnet array comprising two segments per pole for permanent magnet (PM) spherical motor. The harmonic model for radial air-gap flux density distribution is solved by magnetic scalar potential equation using spherical harmonic series and validated by finite-element method. After the influence of magnet array parameters on the fundamental harmonics amplitude and higher harmonic content of the air-gap flux density is analyzed, the optimization of four-pole magnet array is performed in which the higher harmonics of the radial air-gap flux density are minimized. The final design is compared with iron-cored classical array and air-cored equal arc Halbach array, and the result shows that for a given relative volume of magnetic material the proposed variable arc magnet array produces lower higher harmonic content than the other two arrays.

Spherical harmonic analysis of a novel Halbach array PM spherical motor

A design concept of a Halbach array permanent magnet (PM) spherical motor is proposed in this paper. Based on spherical harmonic functions, the three dimensional (3-D) magnetic fields produced by ball-shaped Halbach array rotor and parallel-magnetization rotor are analyzed. The pole-arc coefficient concept for conventional magnet array spherical motor is developed. The optimum pole-arc coefficient of the conventional parallel PM spherical motor is discussed in order to reduce magnetic flux density waveform distortion and increase magnetic flux density. A comparison is made between the Halbach array PM spherical motor and the conventional parallel magnet array spherical motor in terms of spherical harmonic component and amplitude of air gap flux density, which shows that, compared with the latter, the Halbach motor is more effective in improving air gap field distribution. Magnetization angle and arrangement mode of magnetic poles are studied, which lay a foundation for optimum design of Halbach array PM spherical motor.

Torque Analysis of Spherical Permanent Magnetic Motor with Magnetic Equivalent Circuit and Maxwell Stress Tensor

The paper discusses the torque characteristics of spherical permanent magnetic (PM)motor adopting three-dimensional (3D)magnetic equivalent circuit(MEC). Taking into account the unsaturation of the magnetic field, the rotor and the stator are meshed in spherical coordinates and cylindrical coordinates respectively, and then the expressions of the reluctances and magnetomotive force(MMF) have been deduced. According to the relative position between the coordinate systems, the magnetic field in the air gap has been obtained by transforming the coordinate systems. Based on this, the Maxwell stress tensor(MST)method is applied to analyze the electromagnetic force and torque, the corresponding torque matrix is given, and the relationship between the motor torque and winding location is obtained. Compared with the finiteelement method(FEM), this method is proved to have a high accuracy and helpful to the optimization design of the PM spherical motor.

Study on the position identification of a Halbach array permanent magnet spherical motor

Halbach array permanent magnet (PM) spherical motor offers a number of attractive features. This paper described the structure, working principle and analytical equations of magnetic field of the Halbach array PM. Based on the magnetic field distribution and three-dimensional (3-D) magnetic field measurement, a position identification method was present. The analysis results of the positioning process show that the motor position can be determined by the rotation angles of the motor, which revolves around three reference axis of the stator. Furthermore, the coordinate of point, where magnetic field was measured, is 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 was obtained. So by solving the nonlinear equation, the rotation angles were obtained and the motor position was identified. The validity was verified through the simulation.

Levitation Force Analysis for Spherical Permanent Magnet Bearingless Motor

This paper presents a synthesis method of magnetic levitation force in spherical permanent magnet (PM) motor, which overcomes the adverse impact of friction torque because there is no direct contact between the stator and rotor. Using the theorem of force translation, Lorentz force of a single coil is equivalent to a force and a moment of couple exerted on the rotor center, so the independent control on levitation force can be achieved. This paper analyzed the position change of stator coils in spherical coordinates when the eccentric rotor moves in three degrees-of-freedom (3-DOF), and then the control equation of levitation force is established. The required magnetic levitation force can be synthesized by controlling the stator currents. Simulation model in MATLAB is created, furthermore the relationships between coil currents and magnetic levitation force, eccentric deviation are studied. The results show that the synthesis method of levitation force is feasible and can provide a basis for control system design.

Field-Circuit Hybrid Method for Magnetic Actuator Using a Laminate Composite

The magnetic actuator using a laminate composite of piezoelectric (PZT) and magnetostrictive materials (MM) achieves active control of magnetic force without Joule heat loss. To study its characteristics, the field-circuit hybrid method is proposed based on the equivalent magnetic circuit and the finite element analysis (FEA) of piezoelectric and magnetic fields. The strain of laminate composite under different voltage is obtained through the piezoelectric FEA. On the basis of magnetostrictive equation, the MM branch in the magnetic circuit of the actuator is transformed equivalently, the work point of the actuator is determined, and the corresponding FEA model of magnetic analysis is then set up. The relationships between magnetic force, gap, and voltage are discussed by the hybrid method, which can be expanded into the design and analysis of the magnetostrictive actuator and sensor to improve simulation efficiency and precision.