磁悬浮永磁直线电动机研究
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摘要
摩擦阻力是制约数控机床直线驱动系统性能的重要因素，将磁悬浮永磁直线电动机应用于数控机床系统中，既省去了中间机械传动机构，又能够有效解决削弱高精高速数控机床摩擦阻力的问题，同时具有低功耗、装置简单、体积小重量轻等优势。本文在国家自然科学基金项目(50975181)的资助下，以磁悬浮永磁直线电动机为研究对象，针对其关键技术问题开展以下工作：
针对削弱直线电机数控机床摩擦阻力的要求，提出了一种具有两套绕组的磁悬浮永磁直线电动机结构。在分析该电机运行机理的基础上，讨论了电枢绕组及定子的结构形式和特点。根据磁力线不能交叉及最小磁阻路径原理，依据电机尺寸确定各漏磁通的存在条件和积分区域，建立了该电机极间漏磁解析计算模型，通过解析计算与有限元计算的比较验证了理论推导的有效性。
磁悬浮永磁直线电动机具有直线进给和垂直悬浮的复合运动形式，由于两套绕组产生的磁场共用一个磁路，推力与悬浮力之间存在耦合，基于以上特点并为了更加直观地对电磁力进行描述，在对几种数学建模方法比较的基础上，从气隙磁场能量的观点建立了电机的数学模型。针对推力与悬浮力的解耦问题，提出推力绕组采用id0，悬浮绕组采用iq0的控制方式，详细分析了该电机的解耦特征。
基于磁悬浮永磁直线电动机内不同磁场互相耦合、动子需要同时实现进给和悬浮运行的特点，提出了该种电机的电磁设计思路和原则。采用有限元法对电机进行性能分析，考察了悬浮绕组及推力绕组电流对气隙磁场的影响，重点分析了参数对该电机性能的影响，确定了优选参数。并深入分析了电机的电感参数。一方面验证了电机设计方法的正确性，另一方面为样机的设计与研制提供必要的参考数据和技术依据。
为了使推力、悬浮力获得更好的平稳性，计算了推力与悬浮力的波动力并进行了分量分离，获取了产生波动力的主要因素。采用优化动子铁心长度的方法削弱边缘效应引起的波动。基于毕奥-萨伐尔定理和虚位移法推导出电机悬浮力波动的表达式，证明改变永磁体结构形式可以减小悬浮力的波动，进而采用斜极的方法削弱由齿槽效应引起的波动。
针对该电机悬浮子系统的控制问题进行研究，首先建立了悬浮子系统的数学模型，为了提高系统对输入信号跟踪特性以及对于负载扰动的鲁棒性，提出一种非线性H∞鲁棒控制策略。通过构造存储函数的方法直接推导描述悬浮系统非线性H∞鲁棒控制的控制律。仿真结果表明，控制系统跟踪给定信号的能力以及抑制扰动的能力均良好，系统具有较强的鲁棒性。
最后，在上述理论研究的基础上制作了一台样机，搭建了系统的实验平台并对样机进行了实验。实验结果证明了电机具有较为良好的性能，验证了本文所提出的理论分析和设计方法的正确性，为进一步深入研究该种电机及其控制方法奠定了理论和技术基础。
Friction is one of the most important factor that restrict linear drive systemperformance of numerical control (NC). Magnetic suspension permanent magnet linearmotor is applied to NC，it not only eliminate transmission mechanism but also caneffectively impair the friction of NC, at the same time has many advantages, such as lowpower consumption，simple devices，small size and light weight. The systemic researchworks are done from taking the magnetic suspension permanent magnet linear motor asstudy object under the support by National Natural Science Foundation of China, the keytechnologies of study object are dicussed in this dissertation as follows:
To satisfy the requirements of impairing the friction of NC, the magnetic suspensionpermanent magnet linear motor which has two windings in the mover is researched anddesigned. On the basis of analysis the operating principle of motor, analyze the structureand characteristics of armature windings and secondary stator. According to the magneticfield lines can not cross and the minimum reluctance path principle, determine theexistence condition and integral region of leakage fluxes, the calculation model ofinterpolar leakage fluxes of the motor is established, further its validity is verified throughthe comparison of analytical solution and finite element method.
The two movement patterns of magnetic suspension permanent magnet linear motormover are straight feed and vertical suspension. As the magnetic field generated by twosets of windings has the same magnetic path in common, the thrust is coupled with thesuspension force. Based on the above features，in order to establish mathematical model ofelectromagnetic forces accurate and intuitive, on the basis of comparison of severalmathematical modeling methods, further modeling of the motor is presented in view of the air gap energy. In order to achieve thrust and suspension force decoupling, a controlmethod is presented that thrust winding id0and suspending windingiq0, furtherelectromagnetic decoupling characteristics of the motor is researched.
Based on the coupling of magnetic suspension permanent magnet linear motor, themover is required to realize straight feed and vertical suspension. The idea and principle ofelectromagnetic design are provided in order to meet particularity of the motor. Study ofimpact of suspension windings current and thrust windings current on the air-gap fluxdensity magnetic field is done, the effect of key parameters on performance of actuator isalso investigated, and inductance characteristics are analyzed. On the one hand it confirmsthe correctness of motor design method, on the other hand it provides necessary referencedata and technical base for the experimental prototype design and manufacture.
Aiming at the stability of electromagnetic force, the force ripple is made variableseparation for obtaining the major factors that impact the performance of theelectromagnetic force. The method of optimization iron-cored length is adopted to designthe motor for reducing force ripple caused by end effect. In order to reduce force ripplecaused by cogging effect, obtained analytical suspension force ripple model based on BiotSavart law and virtual displacement method, and prove that effect of suspension forceripple after altering permanent magnet configuration, further thrust and suspension forceripple is reduced by applying skewing pole.
In the aspect of control strategy of the suspension subsystem, firstly mathematicalmodel of suspension subsystem is established. For improving the tracking performance andthe robustness, a nonlinear H∞robust control strategy is presented. Two controllaw used indescribing nonlinear H∞robust controllers are obtained by defining proper storage function.The results of simulation indicate that controllers can guarantee a good disturbancerestraint as well as the tracks of input signals, the robustness of the suspension subsystemis improved.
Finally, the experiment platform of magnetic suspension permanent magnet linearmotor system is built，and some experiments of prototype motor are done. Correctness andfeasibility of theoretical analysis and design method are partly verified through theexperiment results, and foundation of theory and technology is laid on further research onthis kind of machine.
针对削弱直线电机数控机床摩擦阻力的要求，提出了一种具有两套绕组的磁悬浮永磁直线电动机结构。在分析该电机运行机理的基础上，讨论了电枢绕组及定子的结构形式和特点。根据磁力线不能交叉及最小磁阻路径原理，依据电机尺寸确定各漏磁通的存在条件和积分区域，建立了该电机极间漏磁解析计算模型，通过解析计算与有限元计算的比较验证了理论推导的有效性。
磁悬浮永磁直线电动机具有直线进给和垂直悬浮的复合运动形式，由于两套绕组产生的磁场共用一个磁路，推力与悬浮力之间存在耦合，基于以上特点并为了更加直观地对电磁力进行描述，在对几种数学建模方法比较的基础上，从气隙磁场能量的观点建立了电机的数学模型。针对推力与悬浮力的解耦问题，提出推力绕组采用id0，悬浮绕组采用iq0的控制方式，详细分析了该电机的解耦特征。
基于磁悬浮永磁直线电动机内不同磁场互相耦合、动子需要同时实现进给和悬浮运行的特点，提出了该种电机的电磁设计思路和原则。采用有限元法对电机进行性能分析，考察了悬浮绕组及推力绕组电流对气隙磁场的影响，重点分析了参数对该电机性能的影响，确定了优选参数。并深入分析了电机的电感参数。一方面验证了电机设计方法的正确性，另一方面为样机的设计与研制提供必要的参考数据和技术依据。
为了使推力、悬浮力获得更好的平稳性，计算了推力与悬浮力的波动力并进行了分量分离，获取了产生波动力的主要因素。采用优化动子铁心长度的方法削弱边缘效应引起的波动。基于毕奥-萨伐尔定理和虚位移法推导出电机悬浮力波动的表达式，证明改变永磁体结构形式可以减小悬浮力的波动，进而采用斜极的方法削弱由齿槽效应引起的波动。
针对该电机悬浮子系统的控制问题进行研究，首先建立了悬浮子系统的数学模型，为了提高系统对输入信号跟踪特性以及对于负载扰动的鲁棒性，提出一种非线性H∞鲁棒控制策略。通过构造存储函数的方法直接推导描述悬浮系统非线性H∞鲁棒控制的控制律。仿真结果表明，控制系统跟踪给定信号的能力以及抑制扰动的能力均良好，系统具有较强的鲁棒性。
最后，在上述理论研究的基础上制作了一台样机，搭建了系统的实验平台并对样机进行了实验。实验结果证明了电机具有较为良好的性能，验证了本文所提出的理论分析和设计方法的正确性，为进一步深入研究该种电机及其控制方法奠定了理论和技术基础。
Friction is one of the most important factor that restrict linear drive systemperformance of numerical control (NC). Magnetic suspension permanent magnet linearmotor is applied to NC，it not only eliminate transmission mechanism but also caneffectively impair the friction of NC, at the same time has many advantages, such as lowpower consumption，simple devices，small size and light weight. The systemic researchworks are done from taking the magnetic suspension permanent magnet linear motor asstudy object under the support by National Natural Science Foundation of China, the keytechnologies of study object are dicussed in this dissertation as follows:
To satisfy the requirements of impairing the friction of NC, the magnetic suspensionpermanent magnet linear motor which has two windings in the mover is researched anddesigned. On the basis of analysis the operating principle of motor, analyze the structureand characteristics of armature windings and secondary stator. According to the magneticfield lines can not cross and the minimum reluctance path principle, determine theexistence condition and integral region of leakage fluxes, the calculation model ofinterpolar leakage fluxes of the motor is established, further its validity is verified throughthe comparison of analytical solution and finite element method.
The two movement patterns of magnetic suspension permanent magnet linear motormover are straight feed and vertical suspension. As the magnetic field generated by twosets of windings has the same magnetic path in common, the thrust is coupled with thesuspension force. Based on the above features，in order to establish mathematical model ofelectromagnetic forces accurate and intuitive, on the basis of comparison of severalmathematical modeling methods, further modeling of the motor is presented in view of the air gap energy. In order to achieve thrust and suspension force decoupling, a controlmethod is presented that thrust winding id0and suspending windingiq0, furtherelectromagnetic decoupling characteristics of the motor is researched.
Based on the coupling of magnetic suspension permanent magnet linear motor, themover is required to realize straight feed and vertical suspension. The idea and principle ofelectromagnetic design are provided in order to meet particularity of the motor. Study ofimpact of suspension windings current and thrust windings current on the air-gap fluxdensity magnetic field is done, the effect of key parameters on performance of actuator isalso investigated, and inductance characteristics are analyzed. On the one hand it confirmsthe correctness of motor design method, on the other hand it provides necessary referencedata and technical base for the experimental prototype design and manufacture.
Aiming at the stability of electromagnetic force, the force ripple is made variableseparation for obtaining the major factors that impact the performance of theelectromagnetic force. The method of optimization iron-cored length is adopted to designthe motor for reducing force ripple caused by end effect. In order to reduce force ripplecaused by cogging effect, obtained analytical suspension force ripple model based on BiotSavart law and virtual displacement method, and prove that effect of suspension forceripple after altering permanent magnet configuration, further thrust and suspension forceripple is reduced by applying skewing pole.
In the aspect of control strategy of the suspension subsystem, firstly mathematicalmodel of suspension subsystem is established. For improving the tracking performance andthe robustness, a nonlinear H∞robust control strategy is presented. Two controllaw used indescribing nonlinear H∞robust controllers are obtained by defining proper storage function.The results of simulation indicate that controllers can guarantee a good disturbancerestraint as well as the tracks of input signals, the robustness of the suspension subsystemis improved.
Finally, the experiment platform of magnetic suspension permanent magnet linearmotor system is built，and some experiments of prototype motor are done. Correctness andfeasibility of theoretical analysis and design method are partly verified through theexperiment results, and foundation of theory and technology is laid on further research onthis kind of machine.
引文
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