基于边界法向磁通密度逐点测量的无旋磁场重构方法及其应用
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摘要
磁场是实现电能与机械能转换的重要媒质,准确获取其空间分布是工程科学中一个共性基础课题。本论文提出并研究一种基于边界法向磁通密度逐点测量的无旋磁场重构方法。该方法以标量磁势拉普拉斯方程描述无旋空间内磁场,通过传感器逐点测量空间边界面上的法向磁通密度分布,进而以测量结果为边界条件求解拉普拉斯方程,计算(重构)出整个空间内的磁场分布。作为一种测量与计算相结合的方法,该方法较传统的测量方法具有测量量少、测量简单易实现及可获得完整空间内磁场分布等优点,较传统的计算方法具有无需获知励磁系统信息、精度高、模型简单且计算量小、易得到解析解等优点,是对现有磁场获取方法的一种有益补充,可被广泛应用于各种磁性系统的研究中。
论文在系统研究空间磁场无旋特性及其基本微分方程、以边界法向磁通密度为边界条件的微分方程求解理论、基于等弦高准则的自适应测量方法以及基于边界磁通迭代优化的二次重构方法等相关理论与方法的基础上,进而通过电磁流量计(管段式、插入式)测量空间内磁场与电磁马达(三自由度球形马达、三相励磁旋转马达)工作空间内磁场的重构实例,对磁场重构方法及其基础理论进行不同励磁源(电磁铁、永磁体)、不同磁场类型(稳态、似稳态)、不同边界条件(黎曼边界条件、混合边界条件)、不同重构空间(规则、非规则几何空间)及不同求解方法(数值、解析、分域解析)下的全面、深入阐述与验证。在此基础上,开展电磁流量计(机械能转电能)与电磁马达(电能转机械能)的电-机械能量转换特性研究,提出并研究基于测量空间内磁场重构的电磁流量计干标定方法及基于转子外围空间磁场重构的三自由度球形电磁马达力矩计算方法：前者以测量空间内磁场重构模型为核心,采用多场耦合(磁场、电场与流场)数值计算判定流量计一次传感器灵敏度系数,实现无需任何实际液体情况下的流量计标定,在不经任何实流标定修正的情况下标定误差小于0.5%,为有效解决大口径电磁流量计标定这一国际性难题提供了新的方案；后者基于转子外围空间磁场的解析重构模型,采用洛伦兹力法建立马达力矩解析计算模型,为马达控制模型参数估计等后续研究奠定基础。
论文主要研究内容如下：
1.无旋磁场重构理论的研究。
从磁场重构基本思想出发,基于空间磁场的无旋特性,以标量磁势拉普拉斯方程作为描述此类磁场的基本微分方程,进而系统研究如何为求解这一微分方程提供适当的边界条件,针对三个关键问题：边界条件确定、测量点优化以及真实边界构造,分别研究以边界法向磁通密度为边界条件的微分方程求解理论、基于等弦高准则的自适应测量方法以及基于边界磁通迭代优化的二次重构方法等相关理论与方法。通过对以上基础理论与方法的系统研究,形成基于边界法向磁通密度逐点测量的无旋磁场重构方法。
2.电磁流量计测量空间内磁场重构及干标定方法研究。
管段式电磁流量计：研究通过霍尔探头逐点扫描方式确定电磁流量计测量管内壁法向磁通密度分布的方法与装置,以此为基础重构电磁流量计测量空间内的三维磁场分布,其中包括测量点优化、盲区磁场二次重构等理论的实际应用与验证；研究电磁流量计数学模型,以磁场重构模型结合权重函数数学模型与测量介质的流体动力学模型,提出并研究基于多场耦合数值计算的电磁流量一次传感器灵敏度系数计算方法,实现电磁流量计干标定,并通过与理想流场和非理想流场下的实流标定(湿标定)数据对比对该方法进行实验验证。
插入式电磁流量计：针对插入式探头外围非规则测量空间内磁场,首先研究其数值重构方法,进而提出并研究一种针对非规则场域内磁场的分域解析重构方法。
3.电磁马达工作空间内磁场重构及力矩计算方法研究。
三自由度球形电磁马达：基于已获取的关于该三自由度球形电磁马达的相关数据,研究并验证其转子外围工作空间磁场的数值和解析重构方法；利用现有测量数据噪声较大的特点,就测量噪声对测量点优化算法的影响等问题展开讨论与分析；在此基础上,通过洛伦兹力法建立基于磁场重构解析模型的马达力矩计算模型,并进行与现有实验数据的对比验证。
三相励磁旋转马达：研究并利用三相励磁旋转磁场随空间分布的周期复现特性,以霍尔传感器阵列实时测量一个特征区域上的边界法向磁通密度分布,并以此对整个边界进行法向磁通密度的数据重构；研究马达工作空间内似稳态无旋磁场的动态重构方法,并进行实验验证。
Magnetic fields play an important role in converting electrical energy to mechanical energy or vise verse. Accurately determining the distribution of the magnetic field in space is fundamental in many engineering applications. A method based on measured boundary conditions for reconstructing the curl-free magnetic field distribution in 3D space is formulated and evaluated in this dissertation. In this method, a magnetic scalar potential obeying Laplace's equation is defined to describe the curl-free magnetic field. Then, the normal magnetic flux density on the boundary surface is measured by sensor to provide the necessary boundary conditions. Thirdly, the field distribution is computated (reconstructed) by solving the Laplace's equation of the magnetic scalar potential with the measured boundary conditions. This approach is essentially a coupled measurement-calculation method requiring less costly measurements compared with conventional measurement methods. Compared with conventional computation methods, it relaxes the assumption of known magnetic structures, has higher precision, requires less and easier computation, and its mathematical model is easy to be analytically solved. This reconstruction method which overcomes several short-comings of the existing methods used to determine magnetic field distribution can be widely used in studies of various magnetic systems.
The dissertation begins with a detailed presentation of the reconstruction theory, including the followings; the governing partial differential equation of the curl-free magnetic field, solution of the governing equation with the distribution of the normal magnetic flux density on the boundary surface, an adaptive method based on chord-height criteria to determine the locations for taking measurements, and an estimation method based on iterative optimization to determine the boundary magnetic field in measurement-dead-domain etc. The reconstruction method is then evaluated in the context of two practical applications; electromagnetic flowmeters (pipe and inserted styles) and electromagnetic motors (three-freedom spherical motor and three-phase rotating motor). These practical applications also illustrate and validate the reconstruction method with different magnetic exciting units (electromagnet or permanent magnet), different state magnetic fields (static or quasi-static), different type boundary conditions (Neumann or mixed), different reconstruction spaces (regular or irregular geometries) and different solution methods (numerical, analytical or divisionally analytical). Through this reconstruction method, the energy conversion performances of the flowmeters (mechanical to electrical) and motors (electrical to mechanical) are further investigated. A dry calibration method of the electromagnetic flowmeter based on the reconstruction of the magnetic field in the measuring volume, and an analytical calculation method of the three-freedom spherical motor's torque based on the reconstruction of the magnetic field around the rotor, are proposed and studied respectively. The dry calibration method determines the sensitivity of the flowmeter transducer through a numerical multi-physics computation. The relative error of the result is smaller than 0.5% (without any correction) compared with the data obtained by the flow-rig method. As requiring no actual flow, the dry calibration is particularly useful for calibrating large-diameter EMFs where conventional flow-rig methods are often costly and difficult to implement. For the electromagnetic motor, the analytically reconstructed magnetic field around the rotor provides a means to calculate the motor torque in closed-form through Lorentz force method, which presents an advantage for motor controls etc.
The remainder of the dissertation offers the following:
1. The theory for reconstructing curl-free magnetic fields
The basic idea of the magnetic field reconstruction method is introduced firstly. A magnetic scalar potential obeying Laplace's equation is then defined as the governing partial differential equation to describe the curl-free magnetic field. The method to obtain the required boundary conditions for solving the Laplace's equation is investigated, during which three key problems are especially studied including boundary condition determination, selection of the locations for taking measurements and estimation of the boundary magnetic field in the measurement-dead-domain. For these problems, a solution method with the normal magnetic flux density on the boundary surface, an adaptive measurement method based on chord-height criteria, and an estimation method based on iterative optimization are respectively proposed and studied. Upon above theory studies, a method based on measured boundary conditions for reconstructing the curl-free magnetic field distribution in 3D space is provided.
2. Field reconstruction in the measuring volume of electromagnetic flowmeter and its application in dry calibration.
Pipe type electromagnetic flowmeter: An automated equipment based on the proposed Hall probe scanning method is developed to measure the normal component of the magnetic flux density on the boundary surface of the measuring pipe. With the measured boundary condition, the magnetic field distribution in the measuring pipe is reconstructed. During this progress, the efficient methods to determine the locations for taking measurements and the estimation method of the measurement-dead-domain field are applied and validated. The mathematical model of the electromagnetic flow measurement is studied. Next, a method numerically solving a coupled set of multi-physic equations with measured boundary conditions for the magnetic, electric and flow fields in the flowmeter is proposed and studied to determine the sensitivity of the flowmeter transducer. The method was experimentally verified by comparing the dry calibrated sensitivity of an actual flowmeter against a standard flow-rig test, and by examining the effects of distorted inflow on the sensitivity.
Inserted type electromagnetic flowmeter: To realize the magnetic field reconstruction in the irregular geometry space around the flow velocity probe, numerical and divisionally analytical methods are studied respectively.
3. Field reconstruction in the working space of an electromagnetic motor and its application in torque calculation
Three-DOF spherical motor: With the experimental data obtained by previous researches, numerical and analytical reconstruction methods of the magnetic field around the rotor are studied and validated. In addition, the effect of measurement noise on the accuracy of the adaptive method has been investigated. With the analytical reconstruction model of the magnetic field around the rotor, an analytical calculation model of the motor torque based on Lorentz force law is obtained and experimentally validated against published data.
Three-phase rotating motor: The Hall sensor array method is applied to measure the component of the normal magnetic flux density distribution on the boundary region corresponding to one characteristic set of the stator in real time. The field distribution on the whole boundary is estimated from the measured data, based on its periodic feature along the boundary. Then, dynamical reconstruction method of the quasi-static no-curl magnetic field in the working space is studied and validated.
论文在系统研究空间磁场无旋特性及其基本微分方程、以边界法向磁通密度为边界条件的微分方程求解理论、基于等弦高准则的自适应测量方法以及基于边界磁通迭代优化的二次重构方法等相关理论与方法的基础上,进而通过电磁流量计(管段式、插入式)测量空间内磁场与电磁马达(三自由度球形马达、三相励磁旋转马达)工作空间内磁场的重构实例,对磁场重构方法及其基础理论进行不同励磁源(电磁铁、永磁体)、不同磁场类型(稳态、似稳态)、不同边界条件(黎曼边界条件、混合边界条件)、不同重构空间(规则、非规则几何空间)及不同求解方法(数值、解析、分域解析)下的全面、深入阐述与验证。在此基础上,开展电磁流量计(机械能转电能)与电磁马达(电能转机械能)的电-机械能量转换特性研究,提出并研究基于测量空间内磁场重构的电磁流量计干标定方法及基于转子外围空间磁场重构的三自由度球形电磁马达力矩计算方法：前者以测量空间内磁场重构模型为核心,采用多场耦合(磁场、电场与流场)数值计算判定流量计一次传感器灵敏度系数,实现无需任何实际液体情况下的流量计标定,在不经任何实流标定修正的情况下标定误差小于0.5%,为有效解决大口径电磁流量计标定这一国际性难题提供了新的方案；后者基于转子外围空间磁场的解析重构模型,采用洛伦兹力法建立马达力矩解析计算模型,为马达控制模型参数估计等后续研究奠定基础。
论文主要研究内容如下：
1.无旋磁场重构理论的研究。
从磁场重构基本思想出发,基于空间磁场的无旋特性,以标量磁势拉普拉斯方程作为描述此类磁场的基本微分方程,进而系统研究如何为求解这一微分方程提供适当的边界条件,针对三个关键问题：边界条件确定、测量点优化以及真实边界构造,分别研究以边界法向磁通密度为边界条件的微分方程求解理论、基于等弦高准则的自适应测量方法以及基于边界磁通迭代优化的二次重构方法等相关理论与方法。通过对以上基础理论与方法的系统研究,形成基于边界法向磁通密度逐点测量的无旋磁场重构方法。
2.电磁流量计测量空间内磁场重构及干标定方法研究。
管段式电磁流量计：研究通过霍尔探头逐点扫描方式确定电磁流量计测量管内壁法向磁通密度分布的方法与装置,以此为基础重构电磁流量计测量空间内的三维磁场分布,其中包括测量点优化、盲区磁场二次重构等理论的实际应用与验证；研究电磁流量计数学模型,以磁场重构模型结合权重函数数学模型与测量介质的流体动力学模型,提出并研究基于多场耦合数值计算的电磁流量一次传感器灵敏度系数计算方法,实现电磁流量计干标定,并通过与理想流场和非理想流场下的实流标定(湿标定)数据对比对该方法进行实验验证。
插入式电磁流量计：针对插入式探头外围非规则测量空间内磁场,首先研究其数值重构方法,进而提出并研究一种针对非规则场域内磁场的分域解析重构方法。
3.电磁马达工作空间内磁场重构及力矩计算方法研究。
三自由度球形电磁马达：基于已获取的关于该三自由度球形电磁马达的相关数据,研究并验证其转子外围工作空间磁场的数值和解析重构方法；利用现有测量数据噪声较大的特点,就测量噪声对测量点优化算法的影响等问题展开讨论与分析；在此基础上,通过洛伦兹力法建立基于磁场重构解析模型的马达力矩计算模型,并进行与现有实验数据的对比验证。
三相励磁旋转马达：研究并利用三相励磁旋转磁场随空间分布的周期复现特性,以霍尔传感器阵列实时测量一个特征区域上的边界法向磁通密度分布,并以此对整个边界进行法向磁通密度的数据重构；研究马达工作空间内似稳态无旋磁场的动态重构方法,并进行实验验证。
Magnetic fields play an important role in converting electrical energy to mechanical energy or vise verse. Accurately determining the distribution of the magnetic field in space is fundamental in many engineering applications. A method based on measured boundary conditions for reconstructing the curl-free magnetic field distribution in 3D space is formulated and evaluated in this dissertation. In this method, a magnetic scalar potential obeying Laplace's equation is defined to describe the curl-free magnetic field. Then, the normal magnetic flux density on the boundary surface is measured by sensor to provide the necessary boundary conditions. Thirdly, the field distribution is computated (reconstructed) by solving the Laplace's equation of the magnetic scalar potential with the measured boundary conditions. This approach is essentially a coupled measurement-calculation method requiring less costly measurements compared with conventional measurement methods. Compared with conventional computation methods, it relaxes the assumption of known magnetic structures, has higher precision, requires less and easier computation, and its mathematical model is easy to be analytically solved. This reconstruction method which overcomes several short-comings of the existing methods used to determine magnetic field distribution can be widely used in studies of various magnetic systems.
The dissertation begins with a detailed presentation of the reconstruction theory, including the followings; the governing partial differential equation of the curl-free magnetic field, solution of the governing equation with the distribution of the normal magnetic flux density on the boundary surface, an adaptive method based on chord-height criteria to determine the locations for taking measurements, and an estimation method based on iterative optimization to determine the boundary magnetic field in measurement-dead-domain etc. The reconstruction method is then evaluated in the context of two practical applications; electromagnetic flowmeters (pipe and inserted styles) and electromagnetic motors (three-freedom spherical motor and three-phase rotating motor). These practical applications also illustrate and validate the reconstruction method with different magnetic exciting units (electromagnet or permanent magnet), different state magnetic fields (static or quasi-static), different type boundary conditions (Neumann or mixed), different reconstruction spaces (regular or irregular geometries) and different solution methods (numerical, analytical or divisionally analytical). Through this reconstruction method, the energy conversion performances of the flowmeters (mechanical to electrical) and motors (electrical to mechanical) are further investigated. A dry calibration method of the electromagnetic flowmeter based on the reconstruction of the magnetic field in the measuring volume, and an analytical calculation method of the three-freedom spherical motor's torque based on the reconstruction of the magnetic field around the rotor, are proposed and studied respectively. The dry calibration method determines the sensitivity of the flowmeter transducer through a numerical multi-physics computation. The relative error of the result is smaller than 0.5% (without any correction) compared with the data obtained by the flow-rig method. As requiring no actual flow, the dry calibration is particularly useful for calibrating large-diameter EMFs where conventional flow-rig methods are often costly and difficult to implement. For the electromagnetic motor, the analytically reconstructed magnetic field around the rotor provides a means to calculate the motor torque in closed-form through Lorentz force method, which presents an advantage for motor controls etc.
The remainder of the dissertation offers the following:
1. The theory for reconstructing curl-free magnetic fields
The basic idea of the magnetic field reconstruction method is introduced firstly. A magnetic scalar potential obeying Laplace's equation is then defined as the governing partial differential equation to describe the curl-free magnetic field. The method to obtain the required boundary conditions for solving the Laplace's equation is investigated, during which three key problems are especially studied including boundary condition determination, selection of the locations for taking measurements and estimation of the boundary magnetic field in the measurement-dead-domain. For these problems, a solution method with the normal magnetic flux density on the boundary surface, an adaptive measurement method based on chord-height criteria, and an estimation method based on iterative optimization are respectively proposed and studied. Upon above theory studies, a method based on measured boundary conditions for reconstructing the curl-free magnetic field distribution in 3D space is provided.
2. Field reconstruction in the measuring volume of electromagnetic flowmeter and its application in dry calibration.
Pipe type electromagnetic flowmeter: An automated equipment based on the proposed Hall probe scanning method is developed to measure the normal component of the magnetic flux density on the boundary surface of the measuring pipe. With the measured boundary condition, the magnetic field distribution in the measuring pipe is reconstructed. During this progress, the efficient methods to determine the locations for taking measurements and the estimation method of the measurement-dead-domain field are applied and validated. The mathematical model of the electromagnetic flow measurement is studied. Next, a method numerically solving a coupled set of multi-physic equations with measured boundary conditions for the magnetic, electric and flow fields in the flowmeter is proposed and studied to determine the sensitivity of the flowmeter transducer. The method was experimentally verified by comparing the dry calibrated sensitivity of an actual flowmeter against a standard flow-rig test, and by examining the effects of distorted inflow on the sensitivity.
Inserted type electromagnetic flowmeter: To realize the magnetic field reconstruction in the irregular geometry space around the flow velocity probe, numerical and divisionally analytical methods are studied respectively.
3. Field reconstruction in the working space of an electromagnetic motor and its application in torque calculation
Three-DOF spherical motor: With the experimental data obtained by previous researches, numerical and analytical reconstruction methods of the magnetic field around the rotor are studied and validated. In addition, the effect of measurement noise on the accuracy of the adaptive method has been investigated. With the analytical reconstruction model of the magnetic field around the rotor, an analytical calculation model of the motor torque based on Lorentz force law is obtained and experimentally validated against published data.
Three-phase rotating motor: The Hall sensor array method is applied to measure the component of the normal magnetic flux density distribution on the boundary region corresponding to one characteristic set of the stator in real time. The field distribution on the whole boundary is estimated from the measured data, based on its periodic feature along the boundary. Then, dynamical reconstruction method of the quasi-static no-curl magnetic field in the working space is studied and validated.
引文
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