动圈式磁浮平面电机电磁结构设计与优化研究
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摘要
磁浮平面电机是一种平面运动机构,动子通过磁场悬浮在定子表面并实现大行程平面运动。由于磁浮方式没有机械接触,相比于依靠直线电机正交组合驱动的传统平面运动机构,具有运动结构简单、无摩擦磨损和运动质量轻等特点,易于实现高速和高加速,并利于双工件台交换,是新型高性能光刻机的核心驱动部件以及下一代极紫外光刻机的运动必需部件。
电磁结构是磁浮平面电机的硬件基础,获得驱动效率高、谐波干扰小、工艺性好的平面电机电磁结构,是磁浮平面电机设计的核心。
论文提出了一种新的永磁阵列结构,研究了基于该结构的动圈式磁浮平面电机。具体进行了电机磁场的建模分析,并推导了更加精确的电机电磁力和力矩计算模型：建立了用于控制的计算模型；进行了动圈式磁浮平面电机的综合设计,以及对电机特性的仿真评估。主要研究内容和成果有：
对Halbach永磁阵列结构进行改进,提出了一种新的阵列拓扑结构,将截面为等腰梯形的直四棱柱引入到电机永磁阵列的结构设计中。与现有的Halbach永磁阵列相比,该结构使电机获得了更高的磁场强度,同时使磁场分布具有更好的谐波特性。
采用谐波法,建立了带有梯形永磁体的二维Halbach永磁阵列磁场分布的数学模型。通过采用投影法、傅里叶级数法、磁标量法、分离变量法和待定系数法等方法,推导出了该永磁磁浮平面电机磁场的磁场强度分布公式,并根据电磁场边界条件,计算出了磁场磁通密度分布的谐波模型。
在电磁力与力矩计算中,提出一种三维磁场中线圈圆弧拐角的力和力矩的精确积分方法,将目前电机线圈使用的矩形简化模型提高到全尺寸精确计算模型,并可用于实时计算。与现有的计算模型相比,该模型有效提高了电机电磁力和力矩的计算精度。
进行了电机电磁结构的优化分析。从提高磁场强度和降低高次谐波的角度出发,采用遗传优化方法进行了电机磁场的优化,使得永磁阵列在相同材料、极距和厚度的情况下,具有更高的磁场强度和更好的磁场分布特性,由此提高电机的驱动能力；从提高单位质量的线圈产生的驱动力出发,采用二次规划等优化方法,获得线圈的最佳尺寸。
在动圈式磁浮平面电机电磁结构的设计中,从电机的可控性、端部效应和线圈的排列方式等角度出发,综合分析了电机设计需要考虑的问题,并通过多种设计方案的对比,建立了实现高效率、低功耗的设计过程与方法。
对新型电机的特性进行了分析和评估。通过对电机的永磁体工作点进行分析,确定了永磁体磁通密度最低点所处的位置,以及永磁体的退磁曲线,选定了合适的永磁材料；通过对涡流损耗进行分析,确定了涡流损耗的来源,建立了降低涡流损耗的方法：通过对线圈阵列的发热进行分析,得到了各种工况下的温度分布情况,为冷却系统的设计提供基础；通过对自感、互感和反向电动势等特性进行分析,确定了线圈端口电压的计算方法；通过对磁场强度、电机驱动力和谐波特性进行评估,得到了样机的具体特性。
论文通过有限元仿真验证了磁场谐波模型、简化解析模型的正确性,通过全谐波模型验证了线圈全尺寸实时控制模型的精确性。基于以上电磁结构、模型和方法,本文建立的磁浮平面电机的电磁结构设计和优化方法,可为该新型驱动部件的设计、应用和控制提供技术基础。
Magnetically levitated planar actuators, which are planar motion structures, are composed of a stator and a translator. The translator of these planar actuators is suspended above the stator with no support other than magnetic fields, and can realize large range planar motion. Because of the active magnetic bearing the translator can move in six degrees-of-freedom. Compared with the traditional xy-drives with stacked linear motors, this type of planar motors with simple structure, high speed and high precision can be used in ultra violet and extreme ultra violet semiconductor lithography systems as one lynchpin of them.
Electromagnetic structure is the basis of magnetically levitated planar actuators. Therefore, designing an electromagnetic structure with higher efficiency, lower harmonic interference, and better manufacturability is one lynchpin of improving the performance of a magnetically levitated planar motor.
This thesis researches on a novel magnetically levitated planar actuator with moving coils. A new2-D Halbach permanent magnet array with higher flux density and lower harmonic components is presented. The flux density distribution of the new array is modeled and analyzed, and the simple analytical model of which for real-time control is built. A more accurate real-time control model for planar motors is solved. The synthesis design method for this motor is established, and the characters of the electromagnetic structure of the motor are analyzed and estimated by simulation. The main research contents and achievements are as follows,
Firstly, by improving the current Halbach permanent magnet arrays, a new2-D Halbach magnet array with trapezoidal magnets is invented and adopted in the design of the planar motor. The trapezoidal magnets, which have a45°magnetization direction, can reduce the high-order harmonics and increase the intensity of the magnetic field in the air-gap.
Secondly, the harmonic model of the flux density distribution of the new array is solved by using the Fourier Series Method and the scalar magnetic potential equation.
Thirdly, a more accurate real-time control model of the magnetically levitated ironless planar motor is solved by deriving the numerical model of the corner segments of the coil with the theory of the composite numerical integral rule and the Newton-Leibniz formula.
Fourthly, a special optimization method for the electromagnetic structure of this new planar motor is built. The new array has higher magnetic field intensity with low high-order harmonics in the air-gap by minimizing the high-order harmonics in z-component of the flux density distribution between those two models. The coil requires the highest force produced by per unit mass with the sequential quadratic programming optimization method.
Then, the design method of the new planar motor is built by synthesis considering the controllability of the motor, end effects of the magnet array, and coil arrangement. Subsequently, four planar actuator configurations are designed and compared. The design proposal with the lowest power dissipation is selected.
Finally, the characters of the electromagnetic structure of the motor such as the work point of the magnet array, the eddy-current damping, the copper loss, and the electromotive force are analyzed and estimated by simulation. By analyzing the work point of the magnet array, the material of the array is selected. By analyzing the eddy-current damping, the method of reducing the damping force is built. By analyzing the thermal distribution of the coil array under different conditions, the design foundation of the cooling system for the motor is established. By analyzing the self-inductance, the mutual inductance, and reverse electromotive force, the calculation method of the port voltage of the coil is derived. And by estimating the flux intensity of the magnet array, the thrust force and the force ripples of the motor, the characters of the electromagnetic structure of the motor is obtained.
In this thesis, the correctness of the harmonic model and the analytical model of the magnetic flux density of the motor is verified by using the finite-element method, and the accuracy the new real-time control model is checked by the full harmonic model of the planar motor used by Jansen. Based on the electromagnetic structure, the model, the design and the optimization method of the new motor, this thesis presents a fundamental theory of designing and optimizing the electromagnetic structure of the novel magnetically levitated planar actuator.
电磁结构是磁浮平面电机的硬件基础,获得驱动效率高、谐波干扰小、工艺性好的平面电机电磁结构,是磁浮平面电机设计的核心。
论文提出了一种新的永磁阵列结构,研究了基于该结构的动圈式磁浮平面电机。具体进行了电机磁场的建模分析,并推导了更加精确的电机电磁力和力矩计算模型：建立了用于控制的计算模型；进行了动圈式磁浮平面电机的综合设计,以及对电机特性的仿真评估。主要研究内容和成果有：
对Halbach永磁阵列结构进行改进,提出了一种新的阵列拓扑结构,将截面为等腰梯形的直四棱柱引入到电机永磁阵列的结构设计中。与现有的Halbach永磁阵列相比,该结构使电机获得了更高的磁场强度,同时使磁场分布具有更好的谐波特性。
采用谐波法,建立了带有梯形永磁体的二维Halbach永磁阵列磁场分布的数学模型。通过采用投影法、傅里叶级数法、磁标量法、分离变量法和待定系数法等方法,推导出了该永磁磁浮平面电机磁场的磁场强度分布公式,并根据电磁场边界条件,计算出了磁场磁通密度分布的谐波模型。
在电磁力与力矩计算中,提出一种三维磁场中线圈圆弧拐角的力和力矩的精确积分方法,将目前电机线圈使用的矩形简化模型提高到全尺寸精确计算模型,并可用于实时计算。与现有的计算模型相比,该模型有效提高了电机电磁力和力矩的计算精度。
进行了电机电磁结构的优化分析。从提高磁场强度和降低高次谐波的角度出发,采用遗传优化方法进行了电机磁场的优化,使得永磁阵列在相同材料、极距和厚度的情况下,具有更高的磁场强度和更好的磁场分布特性,由此提高电机的驱动能力；从提高单位质量的线圈产生的驱动力出发,采用二次规划等优化方法,获得线圈的最佳尺寸。
在动圈式磁浮平面电机电磁结构的设计中,从电机的可控性、端部效应和线圈的排列方式等角度出发,综合分析了电机设计需要考虑的问题,并通过多种设计方案的对比,建立了实现高效率、低功耗的设计过程与方法。
对新型电机的特性进行了分析和评估。通过对电机的永磁体工作点进行分析,确定了永磁体磁通密度最低点所处的位置,以及永磁体的退磁曲线,选定了合适的永磁材料；通过对涡流损耗进行分析,确定了涡流损耗的来源,建立了降低涡流损耗的方法：通过对线圈阵列的发热进行分析,得到了各种工况下的温度分布情况,为冷却系统的设计提供基础；通过对自感、互感和反向电动势等特性进行分析,确定了线圈端口电压的计算方法；通过对磁场强度、电机驱动力和谐波特性进行评估,得到了样机的具体特性。
论文通过有限元仿真验证了磁场谐波模型、简化解析模型的正确性,通过全谐波模型验证了线圈全尺寸实时控制模型的精确性。基于以上电磁结构、模型和方法,本文建立的磁浮平面电机的电磁结构设计和优化方法,可为该新型驱动部件的设计、应用和控制提供技术基础。
Magnetically levitated planar actuators, which are planar motion structures, are composed of a stator and a translator. The translator of these planar actuators is suspended above the stator with no support other than magnetic fields, and can realize large range planar motion. Because of the active magnetic bearing the translator can move in six degrees-of-freedom. Compared with the traditional xy-drives with stacked linear motors, this type of planar motors with simple structure, high speed and high precision can be used in ultra violet and extreme ultra violet semiconductor lithography systems as one lynchpin of them.
Electromagnetic structure is the basis of magnetically levitated planar actuators. Therefore, designing an electromagnetic structure with higher efficiency, lower harmonic interference, and better manufacturability is one lynchpin of improving the performance of a magnetically levitated planar motor.
This thesis researches on a novel magnetically levitated planar actuator with moving coils. A new2-D Halbach permanent magnet array with higher flux density and lower harmonic components is presented. The flux density distribution of the new array is modeled and analyzed, and the simple analytical model of which for real-time control is built. A more accurate real-time control model for planar motors is solved. The synthesis design method for this motor is established, and the characters of the electromagnetic structure of the motor are analyzed and estimated by simulation. The main research contents and achievements are as follows,
Firstly, by improving the current Halbach permanent magnet arrays, a new2-D Halbach magnet array with trapezoidal magnets is invented and adopted in the design of the planar motor. The trapezoidal magnets, which have a45°magnetization direction, can reduce the high-order harmonics and increase the intensity of the magnetic field in the air-gap.
Secondly, the harmonic model of the flux density distribution of the new array is solved by using the Fourier Series Method and the scalar magnetic potential equation.
Thirdly, a more accurate real-time control model of the magnetically levitated ironless planar motor is solved by deriving the numerical model of the corner segments of the coil with the theory of the composite numerical integral rule and the Newton-Leibniz formula.
Fourthly, a special optimization method for the electromagnetic structure of this new planar motor is built. The new array has higher magnetic field intensity with low high-order harmonics in the air-gap by minimizing the high-order harmonics in z-component of the flux density distribution between those two models. The coil requires the highest force produced by per unit mass with the sequential quadratic programming optimization method.
Then, the design method of the new planar motor is built by synthesis considering the controllability of the motor, end effects of the magnet array, and coil arrangement. Subsequently, four planar actuator configurations are designed and compared. The design proposal with the lowest power dissipation is selected.
Finally, the characters of the electromagnetic structure of the motor such as the work point of the magnet array, the eddy-current damping, the copper loss, and the electromotive force are analyzed and estimated by simulation. By analyzing the work point of the magnet array, the material of the array is selected. By analyzing the eddy-current damping, the method of reducing the damping force is built. By analyzing the thermal distribution of the coil array under different conditions, the design foundation of the cooling system for the motor is established. By analyzing the self-inductance, the mutual inductance, and reverse electromotive force, the calculation method of the port voltage of the coil is derived. And by estimating the flux intensity of the magnet array, the thrust force and the force ripples of the motor, the characters of the electromagnetic structure of the motor is obtained.
In this thesis, the correctness of the harmonic model and the analytical model of the magnetic flux density of the motor is verified by using the finite-element method, and the accuracy the new real-time control model is checked by the full harmonic model of the planar motor used by Jansen. Based on the electromagnetic structure, the model, the design and the optimization method of the new motor, this thesis presents a fundamental theory of designing and optimizing the electromagnetic structure of the novel magnetically levitated planar actuator.
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