洛仑兹平面电机的结构动态特性研究
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摘要
洛仑兹平面电机是由三个洛仑兹直线电机(Y1、X和Y2)组合而成的新型永磁平面电机,可实现三自由度平面定位运动。任何来自于外部激励或自身内部的微小振动,都会对系统定位精度带来极大影响,所以应对洛仑兹平面电机结构动态特性及振动进行深入地研究。本文以洛仑兹平面电机为研究对象,以理论分析、数值计算和物理实验为研究方法,结合了结构动力学、弹性力学及电磁场等相关理论,辨识了洛仑兹平面电机法向电磁动力学参数,建立了系统结构振动的有限元模型,计算了洛仑兹平面电机的实特性值、频率响应和瞬态响应等结构动态特性,分析了定、动子间法向振动传递机理及影响因素。其主要内容和成果包括：
采用等效面电流法推导了三维永磁体磁场及通电线圈产生的磁场,建立了空间位置、磁钢与线圈尺寸、面磁化电流密度与气隙磁场的函数关系式,并建立了洛仑兹平面电机的磁通链及驱动电路等数学模型；在水平运动方向上,对三个洛仑兹直线电机进行坐标转换及驱动力解耦,建立了电磁动力学模型,为系统运动控制建模打下基础；在法向振动方向上,建立了洛仑兹平面电机的定、动子振动方程,得到了定子挠度与法向电磁力、电流等的关系,分析了定、动子之间法向电磁力的传递过程,阐明了电流激励下定、动子间耦合振动传递机理。
运用三维电磁场有限元数值计算和模态实验来辨识法向电磁刚度,运用模态分析法、能量守恒原理及模态实验来辨识法向电磁阻尼。根据洛仑兹平面电机实际的连接和约束关系,采用手动六面体网格剖分,加载等效的法向电磁弹簧,建立洛仑兹平面电机的系统结构动力学有限元模型。基于该结构有限元模型,编写结构系统动态计算程序,计算得到了洛仑兹平面电机的实特性值、频率响应和瞬态响应等结构动态特性。
基于洛仑兹平面电机结构动态特性分析,进一步分析了激励电流、法向位移和运动速度等参数对系统动态特性及定、动子耦合振动传递的影响。其中,建立了载流线圈的拉格朗日方程和定子的耦合振动方程,理论分析了激励电流和法向位移对动力学特性的影响。运用有限元数值计算,得到了电流和法向位移与动子固有频率的关系。计算了在不同运动速度下,瞬态涡电流和瞬态电磁阻尼的大小。分析运动速度越大,形成的涡电流就越大,产生的电磁阻尼也就越大。这些研究结果为洛仑兹平面电机的结构优化及运动控制策略打下良好基础。
搭建了洛仑兹平面电机原理样机和实验测试系统,进行了气隙磁场和推力常数测试,得到实际气隙磁场大小及分布,并与电磁有限元模型仿真结果进行对比,验证了三维磁场有限元模型的合理性和计算的正确性；运用LMS系统进行了动力学振动测试,得到了系统的固有频率、振型、频域响应、时域响应等结果,与结构动力学有限元模型计算结果进行对比,验证了法向电磁动力学参数辨识的正确性和系统结构有限元模型的合理性。
本文研究揭示了洛仑兹平面电机定、动子耦合振动传递产生的机理,提出了法向电磁动力学参数辨识方法,阐明了电流和法向位移等参数对系统动态特性及耦合振动传递的影响程度,为超精密平面定位系统的设计、制造和优化提供了理论依据。
Lorentz planar motor is a novel permanent magnet planar driving system propelled by linear Lorentz force, which consists of three Lorentz linear motors (Y1、X and Y2). It can achieve 3 degree of freedom positioning, i.e. translation along the X and Y directions and rotation about Z axis, Rz. The positioning stage is drived directly by Lorentz planar motor. Some microvibrations from external or internal excitations will impact the positioning accuracy of the stage. Therefore, dynamic characteristic and normal vibration of Lorentz planar motor should be deeply researched. In the thesis, the Lorentz planar motor is our research object. Our research method is theoretical analysis, numerical simulation and physical experiment. Some theories of structure dynamics, flexible mechanism and electromagnetic field are adopted. The normal electromagnetic parameters are identified using 3D finite element method and modal testing. The 3D electromagnetic finite element model, structural dynamic model and normal vibration model of Lorentz planar motor are achieved by numerical computing and physical experiment. Researches are focusing on the dynamic characteristic analysis and normal vibration transmission of the Lorentz planar motor. Contents and results as follows,
Firstly, the 3D magnetic field in the airgap generated by permanent magnets and coils is derived by using the equivalent surface current method. The relations of sizes and positions of magnets and coils, surface magnetization current density and magnetic field of airgap are obtained. Magnetic flux linkage equations and mathematical model of Lorentz planar motor are established. Based on calculation and analysis of Lorentz forces, an electromagnetic dynamic model, which is ready for motion control in X, Y and Rz directions, is established. The normal vibration transmission between the stator and mover is illustrated. Normal vibration models of the stator and mover are built separately, which is used for obtaining the relations among structure deflections, electromagnetic forces and currents.
Secondly, the normal electromagnetic stiffness is identified using 3D finite element method and modal testing. The electromagnetic damping ratio is effectively identified by modal testings. According to the actual connections and constraints of Lorentz planar motor, structural dynamic finite element model of the planar motor system is established by adopting manually hexahedral mesh and loading equivalent normal electromagnetic springs. Based on structural finite element model, dynamic computation procedures are compiled and the structure dynamic characteristics are in-depth computed, including the normal frequencies, frequency response and transient response.
Then, in order to reveal some important parameters influencing on dynamic characteristics of Lorentz planar motor, we focus on analyzing the excitation current, Z-displacement and velocity in motion directions, which is a solid foundation for the motion control strategy and stuctural optimization of the Lorentz planar motor.
Finally, a testing system of Lorentz planar motor has been set up, and the magnetic field in airgap and motor's thrust constant by experiments are achieved. The distribution of airgap's magnetic field by experiments verifies that 3D magnetic field simulation results are in good agreement with experimental results. The normal frequencies, model shape, frequency domain response and time domain response are obtained by modal testings using LMS system. Modal testing results verify that dynamic parameter identifications are accurate and structural finite element model is reasonable.
In this dissertation, the dynamic characteristics of Lorentz planar motor are revealed, and the phenomenon of vibration transmission between stator and mover is clarified, and the methods of parameter identification of electromagnetic dynamics are proposed. These simulation models and methods will provide theoretical guidelines for mechanical structure design, optimization and control strategies, as well as the conclusions have been effective used in the research on the ultra-precision positioning stage.
采用等效面电流法推导了三维永磁体磁场及通电线圈产生的磁场,建立了空间位置、磁钢与线圈尺寸、面磁化电流密度与气隙磁场的函数关系式,并建立了洛仑兹平面电机的磁通链及驱动电路等数学模型；在水平运动方向上,对三个洛仑兹直线电机进行坐标转换及驱动力解耦,建立了电磁动力学模型,为系统运动控制建模打下基础；在法向振动方向上,建立了洛仑兹平面电机的定、动子振动方程,得到了定子挠度与法向电磁力、电流等的关系,分析了定、动子之间法向电磁力的传递过程,阐明了电流激励下定、动子间耦合振动传递机理。
运用三维电磁场有限元数值计算和模态实验来辨识法向电磁刚度,运用模态分析法、能量守恒原理及模态实验来辨识法向电磁阻尼。根据洛仑兹平面电机实际的连接和约束关系,采用手动六面体网格剖分,加载等效的法向电磁弹簧,建立洛仑兹平面电机的系统结构动力学有限元模型。基于该结构有限元模型,编写结构系统动态计算程序,计算得到了洛仑兹平面电机的实特性值、频率响应和瞬态响应等结构动态特性。
基于洛仑兹平面电机结构动态特性分析,进一步分析了激励电流、法向位移和运动速度等参数对系统动态特性及定、动子耦合振动传递的影响。其中,建立了载流线圈的拉格朗日方程和定子的耦合振动方程,理论分析了激励电流和法向位移对动力学特性的影响。运用有限元数值计算,得到了电流和法向位移与动子固有频率的关系。计算了在不同运动速度下,瞬态涡电流和瞬态电磁阻尼的大小。分析运动速度越大,形成的涡电流就越大,产生的电磁阻尼也就越大。这些研究结果为洛仑兹平面电机的结构优化及运动控制策略打下良好基础。
搭建了洛仑兹平面电机原理样机和实验测试系统,进行了气隙磁场和推力常数测试,得到实际气隙磁场大小及分布,并与电磁有限元模型仿真结果进行对比,验证了三维磁场有限元模型的合理性和计算的正确性；运用LMS系统进行了动力学振动测试,得到了系统的固有频率、振型、频域响应、时域响应等结果,与结构动力学有限元模型计算结果进行对比,验证了法向电磁动力学参数辨识的正确性和系统结构有限元模型的合理性。
本文研究揭示了洛仑兹平面电机定、动子耦合振动传递产生的机理,提出了法向电磁动力学参数辨识方法,阐明了电流和法向位移等参数对系统动态特性及耦合振动传递的影响程度,为超精密平面定位系统的设计、制造和优化提供了理论依据。
Lorentz planar motor is a novel permanent magnet planar driving system propelled by linear Lorentz force, which consists of three Lorentz linear motors (Y1、X and Y2). It can achieve 3 degree of freedom positioning, i.e. translation along the X and Y directions and rotation about Z axis, Rz. The positioning stage is drived directly by Lorentz planar motor. Some microvibrations from external or internal excitations will impact the positioning accuracy of the stage. Therefore, dynamic characteristic and normal vibration of Lorentz planar motor should be deeply researched. In the thesis, the Lorentz planar motor is our research object. Our research method is theoretical analysis, numerical simulation and physical experiment. Some theories of structure dynamics, flexible mechanism and electromagnetic field are adopted. The normal electromagnetic parameters are identified using 3D finite element method and modal testing. The 3D electromagnetic finite element model, structural dynamic model and normal vibration model of Lorentz planar motor are achieved by numerical computing and physical experiment. Researches are focusing on the dynamic characteristic analysis and normal vibration transmission of the Lorentz planar motor. Contents and results as follows,
Firstly, the 3D magnetic field in the airgap generated by permanent magnets and coils is derived by using the equivalent surface current method. The relations of sizes and positions of magnets and coils, surface magnetization current density and magnetic field of airgap are obtained. Magnetic flux linkage equations and mathematical model of Lorentz planar motor are established. Based on calculation and analysis of Lorentz forces, an electromagnetic dynamic model, which is ready for motion control in X, Y and Rz directions, is established. The normal vibration transmission between the stator and mover is illustrated. Normal vibration models of the stator and mover are built separately, which is used for obtaining the relations among structure deflections, electromagnetic forces and currents.
Secondly, the normal electromagnetic stiffness is identified using 3D finite element method and modal testing. The electromagnetic damping ratio is effectively identified by modal testings. According to the actual connections and constraints of Lorentz planar motor, structural dynamic finite element model of the planar motor system is established by adopting manually hexahedral mesh and loading equivalent normal electromagnetic springs. Based on structural finite element model, dynamic computation procedures are compiled and the structure dynamic characteristics are in-depth computed, including the normal frequencies, frequency response and transient response.
Then, in order to reveal some important parameters influencing on dynamic characteristics of Lorentz planar motor, we focus on analyzing the excitation current, Z-displacement and velocity in motion directions, which is a solid foundation for the motion control strategy and stuctural optimization of the Lorentz planar motor.
Finally, a testing system of Lorentz planar motor has been set up, and the magnetic field in airgap and motor's thrust constant by experiments are achieved. The distribution of airgap's magnetic field by experiments verifies that 3D magnetic field simulation results are in good agreement with experimental results. The normal frequencies, model shape, frequency domain response and time domain response are obtained by modal testings using LMS system. Modal testing results verify that dynamic parameter identifications are accurate and structural finite element model is reasonable.
In this dissertation, the dynamic characteristics of Lorentz planar motor are revealed, and the phenomenon of vibration transmission between stator and mover is clarified, and the methods of parameter identification of electromagnetic dynamics are proposed. These simulation models and methods will provide theoretical guidelines for mechanical structure design, optimization and control strategies, as well as the conclusions have been effective used in the research on the ultra-precision positioning stage.
引文
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