A Method Based On Measured Boundary Conditions For Reconstructing Curl-Free Magnetic Field And Its Applications

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 fieldsThe 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 calculationThree-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.