高精度永磁直线伺服电机法向力波动分析与抑制方法研究
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摘要
直线电机直接驱动技术极大地提高了伺服系统的快速反应能力、运动精度和高速进给能力，已成为现代高档数控机床最具代表性的先进技术之一。单边平板型有铁心伺服用永磁直线同步电机（PMLSM）由于具有推力大，功率密度高的特点，是目前应用最为广泛的一种直线电机，但由于齿槽效应、端部效应及磁场谐波的影响，电机在运行过程中初、次级之间存在较大的法向力波动，法向力的波动引起的摩擦力摄动和机床振动极大地影响了机床的加工精度。本文针对平板型有铁心PMLSM法向力波动的产生机理及削弱方法进行了系统的研究，主要内容如下：
研究PMLSM法向力波动与磁场各次谐波之间的关系以及法向力与推力之间相关性。在分析永磁体磁动势谐波、电枢反应磁动势谐波以及气隙磁导谐波的基础上，根据Maxwell Stress Tensor法和积分法推导初级端齿无限长PMLSM法向力波动的解析表达式，揭示法向力波动的规律。接着从气隙磁场储能的角度，通过解析法分析法向力与切向电磁推力的相关性，综合考虑削弱齿槽效应、端部效应以及负载扰动引起的法向力波动的方法对切向电磁推力的影响。
研究电机参数对法向力波动的影响规律。齿顶宽度、极弧系数对法向力波动有直接的关系，首先解析分析齿顶宽度、极弧系数对齿槽效应引起的法向力波动（简称为齿槽法向力波动）幅值和次数的影响规律；然后采用有限元法验证不同齿顶宽度和不同极弧系数下的齿槽法向力波动情况以及对推力性能的影响程度，为高性能直线电机优化设计提供理论指导。
研究永磁磁极三段错位削弱齿槽法向力波动的方法。首先分析电机初级齿顶开辅助槽和不等极弧系数组合削弱推力波动的方法对削弱法向力波动的规律，进而分析这两种方法的局限性；在此基础上，根据相位反相抵消的原理，提出永磁磁极三段错位法削弱甚至抵消主要次谐波齿槽法向力波动，同时避免电机产生横向俯仰运动，并采用有限元分析法验证该方法的有效性。
研究分相电流补偿控制策略削弱端部效应引起法向力波动（简称为端部法向力波动）的方法。端部法向力波动是法向力波动的主要分量，根据分数槽绕组永磁直线伺服电机三相绕组的特殊分布规律，提出了抑制端部法向力波动的分相电流补偿控制策略，在分相电流补偿控制时，遵循推力性能最优、法向力波动最小的原则；接着研究了端部法向力波动的补偿模型建模方法；最后采用Ansoft系列软件Simplorer和Maxwell联合仿真验证该补偿控制策略的有效性。
设计永磁直线伺服电动机样机以及法向力测试系统验证理论和方法的正确性。针对初级端齿无限长12槽8极整体磁极及三段错位磁极PMLSM的法向力进行稳态测量，验证磁极三段错位法削弱齿槽法向力波动的有效性；针对分相电流补偿控制的12槽11极PMLSM进行法向力测试，验证分相电流补偿控制策略削弱端部法向力波动的可行性和有效性。
Linear motor direct drive technology greatly improves the rapid response capability,motion precision and high-speed feed capability of the servo system, which has become one ofthe most representative advanced technology of modern top-grade CNC machine tools. Thesingle-side flat-plate core servo-used permanent magnet linear synchronous motor (PMLSM)with the characteristics of big thrust, high power density, has been the most widely used linearmotor at present. However, due to the impact of slot effect, end effect and magnetic fieldharmonics, there is the large normal force ripple between the mover and stator when the motoris operating, and the friction force perturbation and machine tool vibration caused by thenormal force ripple will influence the accuracy of machine tool greatly. The producingmechanism and weakening methods of the normal force ripple in flat-plate core PMLSM aresystematically studied in this dissertation. Major works are listed as follows:
The relation of the PMLSM normal force ripple and magnetic field harmonics and therelativity of the normal force and thrust force are studied. Based on the analysis of thepermanent magnet MMF harmonics, armature MMF harmonics and air gap permeanceharmonics, the normal force ripple analytical expression of the primary end tooth infinitelylong PMLSM can be derived using Maxwell Stress Tensor method and integration method toreveal the law of the normal force ripple. From the perspective of air gap magnetic fieldenergy, the relativity of the normal force and tangential electromagnetic thrust is analyzedusing analytical method, and the influence of the weakening methods of the normal forceripple caused by slot effect, end effect and load disturbance on the tangential electromagneticthrust is comprehensively considered.
The effect law of motor parameters on the normal force ripple is study. The normal forceripple is directly related with the tooth tip width and pole arc coefficient. Firstly, the effect lawof the tooth tip width and pole arc coefficient on the amplitude and time of normal force ripplecaused by slot effect (cogging normal force ripple for short) is analytically analyzed. Then thefinite element method (FEM) is adopted to verify the cogging normal force ripple conditionand its influence degree on the thrust performance under different tooth tip widths and pole arccoefficients, which provides theoretical direction for the optimal design of high-performance linear motor.
The method of three-section permanent magnets staggered weakening normal force rippleis studied. The law that the method of motor primary tooth tip auxiliary slotting combined withunequal pole arc coefficient to weaken the thrust ripple weakens the normal force ripple isanalyzed, and then the limitation of the two methods is analyzed. On this basis, three-sectionpermanent magnets staggered method is proposed to weaken and even cancel the mainsubharmonic cogging normal force ripple, and to simultaneously avoid the motor producingtransverse pitch motion according to the reversed phase cancellation principle. The FEM isadopted to verify the validity of this method.
The method of the phase separation current compensation control strategy weakening thenormal force ripple caused by end effect (end normal force ripple for short) is studied. The endnormal force ripple is the main component of the normal force ripple. Based on the specialthree-phase winding distribution law of fractional slot winding permanent magnet linear servomotor, the phase separation current compensation control strategy is proposed to restrain theend normal force ripple. The principle of thrust performance optimization and normal forceripple minimum is followed when the phase separation current compensation control isadopted. Then the compensation model established method of the end normal force ripple isstudied. Finally, Ansoft series software Simplorer and Maxwell are both adopted to simulateand to verify the validity of this compensation control strategy.
The permanent magnet linear servo motor prototype and normal force test system aredesigned to verify the correctness of theory and method. The normal force static measurementof the primary end tooth infinitely long12-slot8-pole whole magnets or three-sectionstaggered magnets PMLSM is carried out to verify the validity of three-section magnetsstaggered method weakening the cogging normal force ripple. The normal force measurementof12-slot11-pole PMLSM adopting the phase separation current compensation control iscarried out to verify the feasibility and validity of the phase separation current compensationcontrol strategy weakening the end normal force ripple.
研究PMLSM法向力波动与磁场各次谐波之间的关系以及法向力与推力之间相关性。在分析永磁体磁动势谐波、电枢反应磁动势谐波以及气隙磁导谐波的基础上，根据Maxwell Stress Tensor法和积分法推导初级端齿无限长PMLSM法向力波动的解析表达式，揭示法向力波动的规律。接着从气隙磁场储能的角度，通过解析法分析法向力与切向电磁推力的相关性，综合考虑削弱齿槽效应、端部效应以及负载扰动引起的法向力波动的方法对切向电磁推力的影响。
研究电机参数对法向力波动的影响规律。齿顶宽度、极弧系数对法向力波动有直接的关系，首先解析分析齿顶宽度、极弧系数对齿槽效应引起的法向力波动（简称为齿槽法向力波动）幅值和次数的影响规律；然后采用有限元法验证不同齿顶宽度和不同极弧系数下的齿槽法向力波动情况以及对推力性能的影响程度，为高性能直线电机优化设计提供理论指导。
研究永磁磁极三段错位削弱齿槽法向力波动的方法。首先分析电机初级齿顶开辅助槽和不等极弧系数组合削弱推力波动的方法对削弱法向力波动的规律，进而分析这两种方法的局限性；在此基础上，根据相位反相抵消的原理，提出永磁磁极三段错位法削弱甚至抵消主要次谐波齿槽法向力波动，同时避免电机产生横向俯仰运动，并采用有限元分析法验证该方法的有效性。
研究分相电流补偿控制策略削弱端部效应引起法向力波动（简称为端部法向力波动）的方法。端部法向力波动是法向力波动的主要分量，根据分数槽绕组永磁直线伺服电机三相绕组的特殊分布规律，提出了抑制端部法向力波动的分相电流补偿控制策略，在分相电流补偿控制时，遵循推力性能最优、法向力波动最小的原则；接着研究了端部法向力波动的补偿模型建模方法；最后采用Ansoft系列软件Simplorer和Maxwell联合仿真验证该补偿控制策略的有效性。
设计永磁直线伺服电动机样机以及法向力测试系统验证理论和方法的正确性。针对初级端齿无限长12槽8极整体磁极及三段错位磁极PMLSM的法向力进行稳态测量，验证磁极三段错位法削弱齿槽法向力波动的有效性；针对分相电流补偿控制的12槽11极PMLSM进行法向力测试，验证分相电流补偿控制策略削弱端部法向力波动的可行性和有效性。
Linear motor direct drive technology greatly improves the rapid response capability,motion precision and high-speed feed capability of the servo system, which has become one ofthe most representative advanced technology of modern top-grade CNC machine tools. Thesingle-side flat-plate core servo-used permanent magnet linear synchronous motor (PMLSM)with the characteristics of big thrust, high power density, has been the most widely used linearmotor at present. However, due to the impact of slot effect, end effect and magnetic fieldharmonics, there is the large normal force ripple between the mover and stator when the motoris operating, and the friction force perturbation and machine tool vibration caused by thenormal force ripple will influence the accuracy of machine tool greatly. The producingmechanism and weakening methods of the normal force ripple in flat-plate core PMLSM aresystematically studied in this dissertation. Major works are listed as follows:
The relation of the PMLSM normal force ripple and magnetic field harmonics and therelativity of the normal force and thrust force are studied. Based on the analysis of thepermanent magnet MMF harmonics, armature MMF harmonics and air gap permeanceharmonics, the normal force ripple analytical expression of the primary end tooth infinitelylong PMLSM can be derived using Maxwell Stress Tensor method and integration method toreveal the law of the normal force ripple. From the perspective of air gap magnetic fieldenergy, the relativity of the normal force and tangential electromagnetic thrust is analyzedusing analytical method, and the influence of the weakening methods of the normal forceripple caused by slot effect, end effect and load disturbance on the tangential electromagneticthrust is comprehensively considered.
The effect law of motor parameters on the normal force ripple is study. The normal forceripple is directly related with the tooth tip width and pole arc coefficient. Firstly, the effect lawof the tooth tip width and pole arc coefficient on the amplitude and time of normal force ripplecaused by slot effect (cogging normal force ripple for short) is analytically analyzed. Then thefinite element method (FEM) is adopted to verify the cogging normal force ripple conditionand its influence degree on the thrust performance under different tooth tip widths and pole arccoefficients, which provides theoretical direction for the optimal design of high-performance linear motor.
The method of three-section permanent magnets staggered weakening normal force rippleis studied. The law that the method of motor primary tooth tip auxiliary slotting combined withunequal pole arc coefficient to weaken the thrust ripple weakens the normal force ripple isanalyzed, and then the limitation of the two methods is analyzed. On this basis, three-sectionpermanent magnets staggered method is proposed to weaken and even cancel the mainsubharmonic cogging normal force ripple, and to simultaneously avoid the motor producingtransverse pitch motion according to the reversed phase cancellation principle. The FEM isadopted to verify the validity of this method.
The method of the phase separation current compensation control strategy weakening thenormal force ripple caused by end effect (end normal force ripple for short) is studied. The endnormal force ripple is the main component of the normal force ripple. Based on the specialthree-phase winding distribution law of fractional slot winding permanent magnet linear servomotor, the phase separation current compensation control strategy is proposed to restrain theend normal force ripple. The principle of thrust performance optimization and normal forceripple minimum is followed when the phase separation current compensation control isadopted. Then the compensation model established method of the end normal force ripple isstudied. Finally, Ansoft series software Simplorer and Maxwell are both adopted to simulateand to verify the validity of this compensation control strategy.
The permanent magnet linear servo motor prototype and normal force test system aredesigned to verify the correctness of theory and method. The normal force static measurementof the primary end tooth infinitely long12-slot8-pole whole magnets or three-sectionstaggered magnets PMLSM is carried out to verify the validity of three-section magnetsstaggered method weakening the cogging normal force ripple. The normal force measurementof12-slot11-pole PMLSM adopting the phase separation current compensation control iscarried out to verify the feasibility and validity of the phase separation current compensationcontrol strategy weakening the end normal force ripple.
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