永磁球形电动机磁场优化与转子方位检测
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摘要
基于电磁原理的永磁球形电动机能够实现三自由度运动，其结构和运行机理新颖，表现出独特的优势，具有广泛的应用前景。但是，与常规电动机相比，永磁球形电动机的磁场分布、转矩和控制方法也存在较大的差异。目前，永磁球形电动机的研究处于探索阶段，虽然在电磁设计、分析和运动控制等方面取得一定的进展，但尚未达到实际应用的要求，需要作更深入的研究。
本文提出一种新型的球面Halbach阵列永磁球形电动机，给出其结构和工作原理。针对球形转子的Halbach阵列磁体结构，利用球谐波理论建立了永磁球形电动机磁场的解析模型，分析了气隙磁场基波和谐波的分布形式。研究了Halbach阵列磁体厚度、磁体张角和材料性能参数对气隙磁场分布的影响。
为了获得理想的磁场分布和充分利用磁性材料，利用永磁球形电动机气隙磁场的解析模型，以气隙磁场正弦性和磁材体积为目标函数，建立了永磁球形电动机磁极优化的数学模型。利用粒子群算法进行了Halbach阵列磁极极型的多目标优化设计，给出了优化设计方案，分析了优化设计结果。
根据洛仑兹力公式建立了单个空心线圈在永磁球形电动机气隙磁场中的转矩模型，分析了线圈结构参数和气隙对电磁转矩的影响。在此基础上，建立了针对多个空心线圈的转矩方程，提出了基于能量最优原理的转矩合成算法以及绕等效旋转轴正交方向分组的转矩合成算法。
为了实现永磁球形电动机的闭环控制，提出了一种基于光学原理的球形转子方位传感器。此方位传感器利用两个光学检测圆环检测球形转子表面绘制的经线和纬线，通过获得的交点计算球形转子的ZYZ欧拉角。推导了此方位传感器的静态特性方程，分析了方位传感器的性能参数，进行了实验验证。
根据永磁球形电动机的运动特点，建立了电动机的正逆运动学模型，推导了雅可比公式。在此基础上，采用拉格朗日方程建立了永磁球形电动机的动力学模型。提出了高次多项式轨迹规划算法和线性插值轨迹规划算法，进行了仿真验证。
A PM spherical motor is electromagnetism-based multi-degree-of-freedomactuator with novel structure and operation principle. The kind of motor present itsunique advantages and potential prospect in engineering application. However, thereis also distinct diversity with the spherical motor in magnetic field distribution, toqueand control methods, if compared with conventional electric motor. At present, thestudy on the spherical motor is in the early stage of exploration. The advancement inthe electromagnetism design, analysis and motion control of the motor can not meetthe requirement of practical application and intensive study is required.
The thesis presents a novel design concept of PM spherical motor with Halbacharray on rotor surface and the structure and operational principle are given. Theanalytical model of the magnetic field for the spherical rotor with Halbach arraymagnet is established with the spherical harmonic theory and the fundamental andharmonic of the magnetic field is analyzed. The effect of the magnet structureparameters and material property on the magnetic field distribution is analyzed.
To obtain ideal magnetic field distribution and make the best of magnetic material,the analytical model of magnetic field of PM spherical motor in air gap is used toestablish the mathematics model for pole shape optimization of PM spherical rotorwith Halbach array which take the fundamental percentage and magnetic materialvolume as objective functions. Particle swarm algorithm is used to perform the multiobject optimization and the optimization schemes are obtained. The optimizationresult is presented.
The analytical toque model of PM spherical motor for individual hollow windingin the air gap magnetic field is established according to Lorentz law. The effect of thewinding structure parameters and air gap width on the toque is analyzed. The resultanttoque model for multi windings is established on the basis of above analysis. Thetoque resultant algorithm for multi windings based on the principle of minimumenergy and grouping of dividing the windings into three groups orthogonal to eachother along equivalent spinning axis.
An optics-based orientation sensor for spherical rotor is presented for the closeloop control of spherical motor. The sensor uses two ring detectors to detect thelongitude and latitudes on rotor surface. The intersection points obtained are used to compute ZYZ angle of rotor. The static characteristics of the sensor are deduced andthe performance parameters are analyzed. The sensor is verified experimentally.
According to the motion of PM spherical motor, the forward and inversekinematics model and the Jacobi formula are deduced. On this basis, Lagrangeequation is used to establish the dynamics model for PM spherical motor.Higher-degree polynomial algorithm and linear interpolation algorithm of trajectoryplanning are presented and verified with simulation methods.
本文提出一种新型的球面Halbach阵列永磁球形电动机，给出其结构和工作原理。针对球形转子的Halbach阵列磁体结构，利用球谐波理论建立了永磁球形电动机磁场的解析模型，分析了气隙磁场基波和谐波的分布形式。研究了Halbach阵列磁体厚度、磁体张角和材料性能参数对气隙磁场分布的影响。
为了获得理想的磁场分布和充分利用磁性材料，利用永磁球形电动机气隙磁场的解析模型，以气隙磁场正弦性和磁材体积为目标函数，建立了永磁球形电动机磁极优化的数学模型。利用粒子群算法进行了Halbach阵列磁极极型的多目标优化设计，给出了优化设计方案，分析了优化设计结果。
根据洛仑兹力公式建立了单个空心线圈在永磁球形电动机气隙磁场中的转矩模型，分析了线圈结构参数和气隙对电磁转矩的影响。在此基础上，建立了针对多个空心线圈的转矩方程，提出了基于能量最优原理的转矩合成算法以及绕等效旋转轴正交方向分组的转矩合成算法。
为了实现永磁球形电动机的闭环控制，提出了一种基于光学原理的球形转子方位传感器。此方位传感器利用两个光学检测圆环检测球形转子表面绘制的经线和纬线，通过获得的交点计算球形转子的ZYZ欧拉角。推导了此方位传感器的静态特性方程，分析了方位传感器的性能参数，进行了实验验证。
根据永磁球形电动机的运动特点，建立了电动机的正逆运动学模型，推导了雅可比公式。在此基础上，采用拉格朗日方程建立了永磁球形电动机的动力学模型。提出了高次多项式轨迹规划算法和线性插值轨迹规划算法，进行了仿真验证。
A PM spherical motor is electromagnetism-based multi-degree-of-freedomactuator with novel structure and operation principle. The kind of motor present itsunique advantages and potential prospect in engineering application. However, thereis also distinct diversity with the spherical motor in magnetic field distribution, toqueand control methods, if compared with conventional electric motor. At present, thestudy on the spherical motor is in the early stage of exploration. The advancement inthe electromagnetism design, analysis and motion control of the motor can not meetthe requirement of practical application and intensive study is required.
The thesis presents a novel design concept of PM spherical motor with Halbacharray on rotor surface and the structure and operational principle are given. Theanalytical model of the magnetic field for the spherical rotor with Halbach arraymagnet is established with the spherical harmonic theory and the fundamental andharmonic of the magnetic field is analyzed. The effect of the magnet structureparameters and material property on the magnetic field distribution is analyzed.
To obtain ideal magnetic field distribution and make the best of magnetic material,the analytical model of magnetic field of PM spherical motor in air gap is used toestablish the mathematics model for pole shape optimization of PM spherical rotorwith Halbach array which take the fundamental percentage and magnetic materialvolume as objective functions. Particle swarm algorithm is used to perform the multiobject optimization and the optimization schemes are obtained. The optimizationresult is presented.
The analytical toque model of PM spherical motor for individual hollow windingin the air gap magnetic field is established according to Lorentz law. The effect of thewinding structure parameters and air gap width on the toque is analyzed. The resultanttoque model for multi windings is established on the basis of above analysis. Thetoque resultant algorithm for multi windings based on the principle of minimumenergy and grouping of dividing the windings into three groups orthogonal to eachother along equivalent spinning axis.
An optics-based orientation sensor for spherical rotor is presented for the closeloop control of spherical motor. The sensor uses two ring detectors to detect thelongitude and latitudes on rotor surface. The intersection points obtained are used to compute ZYZ angle of rotor. The static characteristics of the sensor are deduced andthe performance parameters are analyzed. The sensor is verified experimentally.
According to the motion of PM spherical motor, the forward and inversekinematics model and the Jacobi formula are deduced. On this basis, Lagrangeequation is used to establish the dynamics model for PM spherical motor.Higher-degree polynomial algorithm and linear interpolation algorithm of trajectoryplanning are presented and verified with simulation methods.
引文
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