A Method Based on Measured Boundary Conditions for Reconstructing the Magnetic Field Distribution of an Electromagnetic Mechatronic System

This paper presents a cost-effective method for reconstructing the magnetic field distribution (MFD) from measured data of an electromagnetic mechatronic system (EMS). MFD predictions and measurements for model-based force/torque calculation and magnetic sensors are common problems in EMS where permanent magnets (PMs) and/or electromagnets are employed. In this method, the MFD is reconstructed in the current-free space by solving the Laplace's equation of a magnetic scalar potential with measured boundary conditions (BCs). The reconstruction method, which relaxes the assumption of known magnetic structures commonly made in the magnetic models for design analysis, requires only the normal component of the magnetic flux density on its boundary surface. Two practical applications are given to illustrate the reconstruction method. The first example illustrates the reconstruction of the MFD from published data of a spherical rotor with embedded PMs for a ball-joint-like motor, where the MFD is essential for the Lorentz force computation. The second example reconstructs the MFD in a circular pipe of an electromagnetic flowmeter, where the MFD is essential for the sensitivity computation. Both reconstructions have been experimentally validated by comparing the MFD against measured data. Both comparisons show excellent agreements. In addition, a gradient-based data distribution on MFD is also discussed to illustrate how the BCs are employed for the reconstruction process.