精密运动平台用永磁直线同步电机的磁场分析与电磁力研究
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摘要
永磁直线同步电机（Permanent Magnet Linear Synchronous Motor，PMLSM）具有推力密度高、响应速度快；可靠性好、效率高；可控性好、精度高等显著优点，广泛应用在精密运动平台中，实现高速长行程运动和微米级、亚微米级的定位精度。由于初级铁心纵向开断，直线电机存在特有的纵向端部效应，同时受齿槽效应、横向端部效应和外悬效应等因素的影响，气隙磁场发生了很大的畸变。受现有加工制造、安装精度及人为等因素的限制，永磁直线同步电机三维空间磁场分布存在非对称性，产生了寄生力或力矩，使电机系统产生振动和噪音。本文以精密运动平台用永磁直线同步电机为研究对象，针对以上问题开展计及齿槽效应、端部效应和外悬效应的永磁直线同步电机磁场精确解析、三维电磁力分析以及性能参数分析与优化设计的研究。
本文首先分别建立基于永磁体等效磁化强度法和电枢绕组等效面电流法的永磁直线同步电机层分析模型，根据对称和非对称的边界条件得到无铁心和无槽PMLSM永磁体励磁磁场与电枢反应磁场。考虑到铁心开齿槽和永磁体斜极的拓扑结构，分别建立考虑齿槽效应和斜极效应的分析模型，推导气隙相对磁导分布函数和斜极、类V形斜极磁极结构的参数等效转换表达式，得出斜极有铁心PMLSM的永磁体励磁磁场与电枢反应磁场。结合不同的边界条件，建立的计及齿槽效应和斜极效应永磁直线同步电机磁场分析方法具有广泛的适应性。上述分析为后续完善计及端部效应的永磁直线同步电机磁场精确解析方法奠定理论基础。
由于短初级长次级PMLSM动子铁心在纵向和横向方向均为有效长，电机纵向端部和横向端部的磁场发生很大的畸变，分别针对纵向和横向端部效应及外悬效应展开研究。在纵向端部效应静态模型的基础上，建立能模拟纵向端部效应的铁心端部虚拟边界模型，得出在动子运动过程中短初级有铁心PMLSM纵向端部区域的磁场分布。建立考虑外悬效应的有铁心PMLSM横向端部效应分析模型，研究揭示外悬效应机理和不同外悬长度对横向端部磁场的影响规律，并分析横向端部效应与外悬效应的内在关系。采用等效磁荷法和镜像法精确解析无铁心PMLSM的三维空载气隙磁场，分析横向端部效应对气隙磁场的影响规律。最终建立计及各种效应的永磁直线同步电机磁场精确解析方法。
在计及齿槽效应、斜极效应、端部效应和外悬效应的永磁直线同步电机磁场分析方法的基础上，以精密运动平台中常用的具有代表性的无铁心和有铁心PMLSM作为具体研究对象，开展三维电磁力研究。先阐述永磁直线同步电机寄生力的定义及其主要产生原因，揭示出永磁直线同步电机寄生力及其波动的产生机理。推导无铁心PMLSM的三维电磁力表达式，研究揭示绕组端部产生的电磁推力和初级、次级发生横向偏移时产生的横向寄生力的变化规律。之后，采用改进积分路径的麦克斯韦应力法推导有铁心PMLSM定位力与空载法向力、电磁推力和负载法向力；在建立斜极永磁体等效为载流导体的分析模型基础上，推导斜极有铁心PMLSM横向寄生力表达式，揭示斜极有铁心PMLSM横向力及其波动的产生机理，并研究极槽配比、永磁体倾斜长度、外悬长度、相电流等电磁参数对横向力及其波动的影响规律。研制旋转伺服电机+滚珠丝杠副加载的直线电机气浮测试平台，并开展PMLSM样机电磁力测试研究。
基于精密运动平台的应用背景，分别确定无铁心和有铁心PMLSM关键的性能参数，开展性能分析、多目标优化设计和两种类型电机性能对比评估等方面的研究。对于无铁心PMLSM，分析非重叠和重叠集中绕组电机的最佳极槽配比；研究揭示永磁体和电枢绕组的结构、尺寸对推力体积密度、推力质量密度、电机常数和推力波动的影响规律。对于有铁心PMLSM，提出齿槽效应和纵向端部效应分离法，推导齿槽定位力与齿槽效应空载法向力、端部定位力与端部效应空载法向力解析式，研究得到矩形、斜极和类V形磁极结构对两种效应的定位力和负载法向力影响规律。之后，以非重叠绕组无铁心PMLSM为案例，开展基于多种群遗传算法和权重系数相结合的电机多目标优化设计研究。最后，对无铁心PMLSM和有铁心PMLSM进行性能对比评估，并总结出精密运动平台用永磁直线同步电机的选型准则。
Permanent Magnet Linear Synchronous Motor (PMLSM) has the advantages of high thrust density, fast response, high reliability, high efficiency, good controllability and high precision. It is widely used in the precision motion platform. Realize long stroke movement with high speed and the location accuracy of micron order, submicron order. Due to the primary iron core break lengthways, linear motor has the unique longitudinal end effect, and under the influence of slot effect, transverse edge effect, overhang effect and so on, gap magnetic field occur a lot of distortion. Under the restrictions of the existing processing and manufacturing, installation accuracy and the artificial factors, the magnetic field distribution in three dimensional space of PMLSM exist asymmetry, engender the parasitic force or moment, make the motor system produce vibration and noise. In this paper a PMLSM that based on precision motion platform as the research object, aim at the above problems, consider slot effect, end effect and overhang effect to carry out the research of the magnetic field accurate analysis, three dimensional electromagnetic force analysis, performance parameter analysis and optimal design for PMLSM.
Firstly, establish analysis model for PMLSM based on permanent magnet equivalent magnetization method and armature winding equivalent surface current method respectively, according to the symmetric and asymmetric boundary conditions to get permanent magnet excitation magnetic field and armature reaction magnetic field for air core and slotless PMLSM. Considering the topological structure of core opening alveolus and permanent magnet skewed, establish analysis model considering slot effect and skewed effect respectively, deduce air gap permeance relative distribution function and the parameter equivalent transform formula for skewed and V-shaped skewed magnetic pole structure, reaching permanent magnet excitation magnetic field and armature reaction magnetic field for iron core PMLSM. In combination with different boundary conditions, the magnetic field analytical method of PMLSM that consider slot effect and skewed effect has a wide range of adaptability. The above analysis laid a theoretical foundation for the following magnetic field accurate analysis method of PMLSM considering the end effect.
On account of short primary and long secondary PMLSM mover iron core are effective length in both longitudinal and transverse direction, motor in longitudinal end and transverse edge magnetic field occur a lot of distortion, aiming at longitudinal end effect, transverse edge effect and overhang effect respectively to research. On the basis of longitudinal end effect static model, establish core end fictitious boundary method that can simulate longitudinal end effect, obtain Short primary iron core PMLSM longitudinal end regional magnetic field distribution during mover in motion. Establish iron core PMLSM transverse edge effect analysis model considering overhang effect, research and reveal the influence rule on overhang effect mechanism and different overhang length to transverse edge magnetic field, and analyze the internal relations of transverse edge effect and overhang effect.Use the equivalent magnetic charge method and image method to accurately analyze the three dimensional no load air gap magnetic field of air core PMLSM, analyze the influence rule on overhang effect to air-gap magnetic field. At last, establish accurate analysis method of consider all kinds of effects to realize PMLSM magnetic field.
On the basis of magnetic field analytical method of PMLSM that considering slot effect, skewed effect, end effect and overhang effect, commonly and representative air core and iron core PMLSM in precision motion platform as the specific research object. Carry out the research of three-dimensional electromagnetic force. First, state the definition of the parasitic force for PMLSM and its main generating reason, reveal the mechanism of production of the parasitic force and its wave for PMLSM. Deduce the expression of three dimensional electromagnetic force for air core PMLSM, research and reveal the change rule of the electromagnetic force in winding overhang and the transverse parasitic force occurred when the lateral deviation to primary and secondary happened. Later, use the Maxwell stress method in improved integral path to deduce the iron core PMLSM location force, no load normal force, electromagnetic thrust and load normal force; On the basis of establishing the analysis model for skewed permanent magnet equivalent to current-carrying conductor, deduce the expression for the lateral parasitic force of skewed iron core PMLSM, reveal the lateral force of skewed iron core PMLSM and its generating mechanism of fluctuation, and study the influence rule on electromagnetic parameters such as different pole/slot ratio, Slope length of permanent magnet, overhang length and phase current parameters to lateral force and its fluctuation. Developed the test platform for rotating servo motor+ballscrew deputy load air bearing and tested the prototype for PMLSM.
Finally, bass on the application background of the precision motion platform, confirm crucial performance parameters for air core and iron core PMLSM respectively, carry out the research of the aspects such as performance analysis, multiobjective optimization design and the performance comparisons and assessment for the two kinds of motor.To air core PMLSM, analyze the best pole/slot ratio for non-overlapping and overlapping concentrated winding motor; research and reveal the influence rule of the structure and size for permanent magnet and armature winding to the thrust per volume, thrust per coils quantity, motor constant and thrust ripple. To iron core PMLSM, put forward separation method for slot effect and longitudinal end effect, deduce the analytic expression of slot location force and slot effect no load normal force, end position force and end effect no load normal force, obtain the effect law about rectangle, skewed and V-shaped permanent magnet structure for the two kinds of positioned force and load normal force. Then let the non-overlapping winding air core PMLSM as example, carry out the study of motor multiobjective optimization design on the basis of the combination of multiple population genetic algorithm(MPGA) and weight coefficient. At last, proceed performance comparison and assessment to air core PMLSM and iron core PMLSM, and summarized the model selection norm of PMLSM that based on precision motion platform.
本文首先分别建立基于永磁体等效磁化强度法和电枢绕组等效面电流法的永磁直线同步电机层分析模型，根据对称和非对称的边界条件得到无铁心和无槽PMLSM永磁体励磁磁场与电枢反应磁场。考虑到铁心开齿槽和永磁体斜极的拓扑结构，分别建立考虑齿槽效应和斜极效应的分析模型，推导气隙相对磁导分布函数和斜极、类V形斜极磁极结构的参数等效转换表达式，得出斜极有铁心PMLSM的永磁体励磁磁场与电枢反应磁场。结合不同的边界条件，建立的计及齿槽效应和斜极效应永磁直线同步电机磁场分析方法具有广泛的适应性。上述分析为后续完善计及端部效应的永磁直线同步电机磁场精确解析方法奠定理论基础。
由于短初级长次级PMLSM动子铁心在纵向和横向方向均为有效长，电机纵向端部和横向端部的磁场发生很大的畸变，分别针对纵向和横向端部效应及外悬效应展开研究。在纵向端部效应静态模型的基础上，建立能模拟纵向端部效应的铁心端部虚拟边界模型，得出在动子运动过程中短初级有铁心PMLSM纵向端部区域的磁场分布。建立考虑外悬效应的有铁心PMLSM横向端部效应分析模型，研究揭示外悬效应机理和不同外悬长度对横向端部磁场的影响规律，并分析横向端部效应与外悬效应的内在关系。采用等效磁荷法和镜像法精确解析无铁心PMLSM的三维空载气隙磁场，分析横向端部效应对气隙磁场的影响规律。最终建立计及各种效应的永磁直线同步电机磁场精确解析方法。
在计及齿槽效应、斜极效应、端部效应和外悬效应的永磁直线同步电机磁场分析方法的基础上，以精密运动平台中常用的具有代表性的无铁心和有铁心PMLSM作为具体研究对象，开展三维电磁力研究。先阐述永磁直线同步电机寄生力的定义及其主要产生原因，揭示出永磁直线同步电机寄生力及其波动的产生机理。推导无铁心PMLSM的三维电磁力表达式，研究揭示绕组端部产生的电磁推力和初级、次级发生横向偏移时产生的横向寄生力的变化规律。之后，采用改进积分路径的麦克斯韦应力法推导有铁心PMLSM定位力与空载法向力、电磁推力和负载法向力；在建立斜极永磁体等效为载流导体的分析模型基础上，推导斜极有铁心PMLSM横向寄生力表达式，揭示斜极有铁心PMLSM横向力及其波动的产生机理，并研究极槽配比、永磁体倾斜长度、外悬长度、相电流等电磁参数对横向力及其波动的影响规律。研制旋转伺服电机+滚珠丝杠副加载的直线电机气浮测试平台，并开展PMLSM样机电磁力测试研究。
基于精密运动平台的应用背景，分别确定无铁心和有铁心PMLSM关键的性能参数，开展性能分析、多目标优化设计和两种类型电机性能对比评估等方面的研究。对于无铁心PMLSM，分析非重叠和重叠集中绕组电机的最佳极槽配比；研究揭示永磁体和电枢绕组的结构、尺寸对推力体积密度、推力质量密度、电机常数和推力波动的影响规律。对于有铁心PMLSM，提出齿槽效应和纵向端部效应分离法，推导齿槽定位力与齿槽效应空载法向力、端部定位力与端部效应空载法向力解析式，研究得到矩形、斜极和类V形磁极结构对两种效应的定位力和负载法向力影响规律。之后，以非重叠绕组无铁心PMLSM为案例，开展基于多种群遗传算法和权重系数相结合的电机多目标优化设计研究。最后，对无铁心PMLSM和有铁心PMLSM进行性能对比评估，并总结出精密运动平台用永磁直线同步电机的选型准则。
Permanent Magnet Linear Synchronous Motor (PMLSM) has the advantages of high thrust density, fast response, high reliability, high efficiency, good controllability and high precision. It is widely used in the precision motion platform. Realize long stroke movement with high speed and the location accuracy of micron order, submicron order. Due to the primary iron core break lengthways, linear motor has the unique longitudinal end effect, and under the influence of slot effect, transverse edge effect, overhang effect and so on, gap magnetic field occur a lot of distortion. Under the restrictions of the existing processing and manufacturing, installation accuracy and the artificial factors, the magnetic field distribution in three dimensional space of PMLSM exist asymmetry, engender the parasitic force or moment, make the motor system produce vibration and noise. In this paper a PMLSM that based on precision motion platform as the research object, aim at the above problems, consider slot effect, end effect and overhang effect to carry out the research of the magnetic field accurate analysis, three dimensional electromagnetic force analysis, performance parameter analysis and optimal design for PMLSM.
Firstly, establish analysis model for PMLSM based on permanent magnet equivalent magnetization method and armature winding equivalent surface current method respectively, according to the symmetric and asymmetric boundary conditions to get permanent magnet excitation magnetic field and armature reaction magnetic field for air core and slotless PMLSM. Considering the topological structure of core opening alveolus and permanent magnet skewed, establish analysis model considering slot effect and skewed effect respectively, deduce air gap permeance relative distribution function and the parameter equivalent transform formula for skewed and V-shaped skewed magnetic pole structure, reaching permanent magnet excitation magnetic field and armature reaction magnetic field for iron core PMLSM. In combination with different boundary conditions, the magnetic field analytical method of PMLSM that consider slot effect and skewed effect has a wide range of adaptability. The above analysis laid a theoretical foundation for the following magnetic field accurate analysis method of PMLSM considering the end effect.
On account of short primary and long secondary PMLSM mover iron core are effective length in both longitudinal and transverse direction, motor in longitudinal end and transverse edge magnetic field occur a lot of distortion, aiming at longitudinal end effect, transverse edge effect and overhang effect respectively to research. On the basis of longitudinal end effect static model, establish core end fictitious boundary method that can simulate longitudinal end effect, obtain Short primary iron core PMLSM longitudinal end regional magnetic field distribution during mover in motion. Establish iron core PMLSM transverse edge effect analysis model considering overhang effect, research and reveal the influence rule on overhang effect mechanism and different overhang length to transverse edge magnetic field, and analyze the internal relations of transverse edge effect and overhang effect.Use the equivalent magnetic charge method and image method to accurately analyze the three dimensional no load air gap magnetic field of air core PMLSM, analyze the influence rule on overhang effect to air-gap magnetic field. At last, establish accurate analysis method of consider all kinds of effects to realize PMLSM magnetic field.
On the basis of magnetic field analytical method of PMLSM that considering slot effect, skewed effect, end effect and overhang effect, commonly and representative air core and iron core PMLSM in precision motion platform as the specific research object. Carry out the research of three-dimensional electromagnetic force. First, state the definition of the parasitic force for PMLSM and its main generating reason, reveal the mechanism of production of the parasitic force and its wave for PMLSM. Deduce the expression of three dimensional electromagnetic force for air core PMLSM, research and reveal the change rule of the electromagnetic force in winding overhang and the transverse parasitic force occurred when the lateral deviation to primary and secondary happened. Later, use the Maxwell stress method in improved integral path to deduce the iron core PMLSM location force, no load normal force, electromagnetic thrust and load normal force; On the basis of establishing the analysis model for skewed permanent magnet equivalent to current-carrying conductor, deduce the expression for the lateral parasitic force of skewed iron core PMLSM, reveal the lateral force of skewed iron core PMLSM and its generating mechanism of fluctuation, and study the influence rule on electromagnetic parameters such as different pole/slot ratio, Slope length of permanent magnet, overhang length and phase current parameters to lateral force and its fluctuation. Developed the test platform for rotating servo motor+ballscrew deputy load air bearing and tested the prototype for PMLSM.
Finally, bass on the application background of the precision motion platform, confirm crucial performance parameters for air core and iron core PMLSM respectively, carry out the research of the aspects such as performance analysis, multiobjective optimization design and the performance comparisons and assessment for the two kinds of motor.To air core PMLSM, analyze the best pole/slot ratio for non-overlapping and overlapping concentrated winding motor; research and reveal the influence rule of the structure and size for permanent magnet and armature winding to the thrust per volume, thrust per coils quantity, motor constant and thrust ripple. To iron core PMLSM, put forward separation method for slot effect and longitudinal end effect, deduce the analytic expression of slot location force and slot effect no load normal force, end position force and end effect no load normal force, obtain the effect law about rectangle, skewed and V-shaped permanent magnet structure for the two kinds of positioned force and load normal force. Then let the non-overlapping winding air core PMLSM as example, carry out the study of motor multiobjective optimization design on the basis of the combination of multiple population genetic algorithm(MPGA) and weight coefficient. At last, proceed performance comparison and assessment to air core PMLSM and iron core PMLSM, and summarized the model selection norm of PMLSM that based on precision motion platform.
引文
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