Halbach 阵列同心式磁力齿轮全局解析法分析与优化设计
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摘要
Halbach阵列同心式磁力齿轮依靠磁场作用传递转矩，其输入和输出之间非接触性传递使它具有转矩密度高、运行效率高和过载保护等优点。此种磁力齿轮内外转子采用同心式结构，有效地提高了永磁体的利用率，其转矩密度和运行效率较传统结构有较大的提高，因此具有较好的应用前景。
本课题是国家自然科学基金项目“磁通解耦型磁力变速永磁无刷电机研究”(51177097)的研究内容之一，对新型结构的磁力传动装置进行研究。
本文采用矢量磁位全局解析法对Halbach阵列同心式磁力齿轮展开研究，具体做了以下几方面的研究：
第一，采用二维全局解析法计算同心式磁力齿轮气隙磁场。求解场域划分为内外转子永磁体、内外两层气隙和调磁定子的槽形区域，3类子区域的拉普拉斯方程和泊松方程通过边界连续条件建立联系。得到内外两层气隙区域的矢量磁位磁通密度解析表达式，计算了内、外两层气隙磁场；利用Maxwell应力张量法计算了内外转子电磁转矩；将气隙磁场波形和内外转子电磁转矩波形分别与二维有限元FEMM软件计算波形作比较，两者结果一致性好；在此基础上，分析了两层气隙的谐波磁场和电磁转矩的静态特性。
第二，根据Halbach阵列充磁原理，推导出Halbach阵列充磁下的数学模型，也是采用全局解析法计算Halbach阵列同心式磁力齿轮内、外气隙磁场及其转矩，分析对比了两种充磁方式下磁力线的分布，将全局解析法计算结果与有限元软件FEMM计算结果进行了比较；同时也对两种充磁方式下气隙谐波大小和转矩做了比较。两种充磁方式下计算的波形与有限元计算结果的吻合也为磁力齿轮的参数优化设计奠定了基础。
第三，从提高磁力齿轮的转矩密度出发，首次将MATLAB优化工具箱中的遗传算法运用到磁力齿轮优化设计中，在优化的过程中，不再进行人工干预，较有限元法优化设计方便、快捷。根据所选模型的优化目标，选取对优化目标影响较大的参数作为优化变量，选择合适的算子及概率，同时根据各参数和静态转矩之间的关系确定各参数的取值范围；用全局解析法计算优化后磁力齿轮电磁转矩，并且与磁力齿轮优化前电磁转矩作比较，结果明显优于优化前，计算结果表明，该优化算法是正确的和有效的。
第四，根据优化设计参数，画出图纸，制造了一台传动比为-4.25:1的Halbach阵列同心式磁力齿轮，磁力齿轮的铁损耗是其主要损耗，空载试验对其铁损耗进行了分析；而负载试验进行的是磁力齿轮传动装置在某一固定转速时，整个负载区间磁力齿轮传动装置的传递效率问题。从实验结果看，样机的电磁转矩密度和传递效率均较高，具有推广应用的价值。
同心式磁力齿轮在采用Halbach阵列充磁方式下，气隙磁场相互迭加使得一侧的磁场强度大幅度提升，可以提高转矩密度；并且气隙磁场正弦分布程度较高，谐波含量小。为研究低转速大转矩磁力齿轮复合电机提供了可能。
A concentric magnetic gear with Halbach permanent-magnet arrays, whose input sides isphysically isolated with the output sides, transfers torque by magnetic field, it has many merits,for example: high torque density, efficiency and high overload protection and so on. Such innerand outer rotor’s magnetic gear adopts concentric structure, which effectively improves theutilization of the permanent magnet. Its torque density and efficiency are higher than traditionalstructures’; therefore, it has better prospects.
This project is one part of the National Natural Science Foundation of flux decoupling-typemagnetic variable speed permanent magnet brushless motor (51177097), and its purpose is toresearch on the new structure of the magnetic transmission.
In this thesis, the works focus on an exact analytical method for a concentric magnetic gearwith Halbach permanent-magnet arrays, and the main works include the following ones:
Firstly, an exact2-dimensional analytical method is used to calculate the magnetic fielddistribution in a concentric magnetic gear. The analytical method is based on the resolution ofLaplace’s and Poisson’s equations for each sub-domain, i.e., inner and outer permanent magnetrotors, inner and outer air-gaps, and slots. The globe solution is obtained using boundary andcontinuity conditions. It’s easy to obtain the analytical expressions of air-gap flux density, andcalculate the internal and external rotor electromagnetic torque by Maxwell stress tensor method.Compared air-gap magnetic field distributions and electromagnetic torque computed by theanalytical method with those obtained from the2-dimensional finite element method (FEM). Inaddition, it analyzes the harmonics of the air-gap magnetic field and the static characteristics ofelectromagnetic torque
Secondly, according to the magnetizing principle of Halbach arrays, it deduces themathematical model of Halbach array magnetization. An exact2-dimensional analytical methodhas also been adopted to calculate the magnetic field distribution and its torque, Analyzed andcompared the distribution of magnetic lines in the two magnetic modes, the exact analyticmethod calculation results are compared with finite element software FEMM calculated results, at the same time, it also do a comparison of air gap harmonics size and torque. The agreement ofthe results between the analytical method and FEM can lay the foundation for parameteroptimization design of magnetic gear.
Thirdly, in order to enhance the magnetic gear’s torque density, it is the first time to applythe genetic algorithm optimization toolbox of Matlab(GAOT) to optimal design of magnetic gear,in the optimization process, it is no longer human intervention and it’s quicker and easier thanthe finite element method. Depending on the optimal targets, it selects some parameters for moreoptimization goals as optimization variables, and selects the appropriate operator and probability.Based upon the relationships between various parameters and static torque, the ranges of valuesfor the parameter are determined. After then, an exact analytical method is calculated theelectromagnetic torque of magnetic gear, the results are compared with the before tuning ofmagnetic gear, the better results show that the optimization algorithm is correct and valid.
Finally, based on the optimum design parameters and drawings, the magnetic gear withHalbach arrays is manufactured, which ratio is-4.25:1. From the no-load test, Iron loss is themain loss of magnetic gear, and the load test is about transmission efficiency of the magneticgear when the magnetic gear drives at a fixed speed. From the experimental results, the torquedensity and transmission efficiency of prototype are very high, it has the value of promotion andapplication.
Under using Halbach arrays of magnetization for a concentric magnetic gear, because ofmagnetic field mutual superposition, which makes one side of the air-gap magnetic fieldsstrength improved significantly, and can improve the torque density. At the same time, theair-gap magnetic field distribution of sinusoidal is very high and the harmonic is small. It ispossible to study on combination electrode for a low speed large torque magnetic gear.
本课题是国家自然科学基金项目“磁通解耦型磁力变速永磁无刷电机研究”(51177097)的研究内容之一，对新型结构的磁力传动装置进行研究。
本文采用矢量磁位全局解析法对Halbach阵列同心式磁力齿轮展开研究，具体做了以下几方面的研究：
第一，采用二维全局解析法计算同心式磁力齿轮气隙磁场。求解场域划分为内外转子永磁体、内外两层气隙和调磁定子的槽形区域，3类子区域的拉普拉斯方程和泊松方程通过边界连续条件建立联系。得到内外两层气隙区域的矢量磁位磁通密度解析表达式，计算了内、外两层气隙磁场；利用Maxwell应力张量法计算了内外转子电磁转矩；将气隙磁场波形和内外转子电磁转矩波形分别与二维有限元FEMM软件计算波形作比较，两者结果一致性好；在此基础上，分析了两层气隙的谐波磁场和电磁转矩的静态特性。
第二，根据Halbach阵列充磁原理，推导出Halbach阵列充磁下的数学模型，也是采用全局解析法计算Halbach阵列同心式磁力齿轮内、外气隙磁场及其转矩，分析对比了两种充磁方式下磁力线的分布，将全局解析法计算结果与有限元软件FEMM计算结果进行了比较；同时也对两种充磁方式下气隙谐波大小和转矩做了比较。两种充磁方式下计算的波形与有限元计算结果的吻合也为磁力齿轮的参数优化设计奠定了基础。
第三，从提高磁力齿轮的转矩密度出发，首次将MATLAB优化工具箱中的遗传算法运用到磁力齿轮优化设计中，在优化的过程中，不再进行人工干预，较有限元法优化设计方便、快捷。根据所选模型的优化目标，选取对优化目标影响较大的参数作为优化变量，选择合适的算子及概率，同时根据各参数和静态转矩之间的关系确定各参数的取值范围；用全局解析法计算优化后磁力齿轮电磁转矩，并且与磁力齿轮优化前电磁转矩作比较，结果明显优于优化前，计算结果表明，该优化算法是正确的和有效的。
第四，根据优化设计参数，画出图纸，制造了一台传动比为-4.25:1的Halbach阵列同心式磁力齿轮，磁力齿轮的铁损耗是其主要损耗，空载试验对其铁损耗进行了分析；而负载试验进行的是磁力齿轮传动装置在某一固定转速时，整个负载区间磁力齿轮传动装置的传递效率问题。从实验结果看，样机的电磁转矩密度和传递效率均较高，具有推广应用的价值。
同心式磁力齿轮在采用Halbach阵列充磁方式下，气隙磁场相互迭加使得一侧的磁场强度大幅度提升，可以提高转矩密度；并且气隙磁场正弦分布程度较高，谐波含量小。为研究低转速大转矩磁力齿轮复合电机提供了可能。
A concentric magnetic gear with Halbach permanent-magnet arrays, whose input sides isphysically isolated with the output sides, transfers torque by magnetic field, it has many merits,for example: high torque density, efficiency and high overload protection and so on. Such innerand outer rotor’s magnetic gear adopts concentric structure, which effectively improves theutilization of the permanent magnet. Its torque density and efficiency are higher than traditionalstructures’; therefore, it has better prospects.
This project is one part of the National Natural Science Foundation of flux decoupling-typemagnetic variable speed permanent magnet brushless motor (51177097), and its purpose is toresearch on the new structure of the magnetic transmission.
In this thesis, the works focus on an exact analytical method for a concentric magnetic gearwith Halbach permanent-magnet arrays, and the main works include the following ones:
Firstly, an exact2-dimensional analytical method is used to calculate the magnetic fielddistribution in a concentric magnetic gear. The analytical method is based on the resolution ofLaplace’s and Poisson’s equations for each sub-domain, i.e., inner and outer permanent magnetrotors, inner and outer air-gaps, and slots. The globe solution is obtained using boundary andcontinuity conditions. It’s easy to obtain the analytical expressions of air-gap flux density, andcalculate the internal and external rotor electromagnetic torque by Maxwell stress tensor method.Compared air-gap magnetic field distributions and electromagnetic torque computed by theanalytical method with those obtained from the2-dimensional finite element method (FEM). Inaddition, it analyzes the harmonics of the air-gap magnetic field and the static characteristics ofelectromagnetic torque
Secondly, according to the magnetizing principle of Halbach arrays, it deduces themathematical model of Halbach array magnetization. An exact2-dimensional analytical methodhas also been adopted to calculate the magnetic field distribution and its torque, Analyzed andcompared the distribution of magnetic lines in the two magnetic modes, the exact analyticmethod calculation results are compared with finite element software FEMM calculated results, at the same time, it also do a comparison of air gap harmonics size and torque. The agreement ofthe results between the analytical method and FEM can lay the foundation for parameteroptimization design of magnetic gear.
Thirdly, in order to enhance the magnetic gear’s torque density, it is the first time to applythe genetic algorithm optimization toolbox of Matlab(GAOT) to optimal design of magnetic gear,in the optimization process, it is no longer human intervention and it’s quicker and easier thanthe finite element method. Depending on the optimal targets, it selects some parameters for moreoptimization goals as optimization variables, and selects the appropriate operator and probability.Based upon the relationships between various parameters and static torque, the ranges of valuesfor the parameter are determined. After then, an exact analytical method is calculated theelectromagnetic torque of magnetic gear, the results are compared with the before tuning ofmagnetic gear, the better results show that the optimization algorithm is correct and valid.
Finally, based on the optimum design parameters and drawings, the magnetic gear withHalbach arrays is manufactured, which ratio is-4.25:1. From the no-load test, Iron loss is themain loss of magnetic gear, and the load test is about transmission efficiency of the magneticgear when the magnetic gear drives at a fixed speed. From the experimental results, the torquedensity and transmission efficiency of prototype are very high, it has the value of promotion andapplication.
Under using Halbach arrays of magnetization for a concentric magnetic gear, because ofmagnetic field mutual superposition, which makes one side of the air-gap magnetic fieldsstrength improved significantly, and can improve the torque density. At the same time, theair-gap magnetic field distribution of sinusoidal is very high and the harmonic is small. It ispossible to study on combination electrode for a low speed large torque magnetic gear.
引文
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