Magnetic field sensing of 3D printed Halbach arrays

This paper investigates magnetic field amplification in Halbach arrays. A Halbach array, composed of permanent magnets, is arranged to produce a strong magnetic field on one side and a weak field on the other. This configuration has numerous scientific and engineering applications. The literature review surveys representative implementations. In this work, we propose and validate a cost-effective approach for designing and fabricating Halbach magnet arrays. Specifically, in our experiments, we employ a low-cost Hall-effect sensor to measure the Halbach array's magnetic flux density. Hall-effect sensors are well suited for measuring magnetic fields owing to their accuracy, ease of integration, low cost, and simplicity. Thus, analytical expressions for the magnetic flux density are derived from the magnetic scalar potential using the magnetostatic approximation to Maxwell's equations and a Fourier-series expansion. We then determine and compare the magnetic flux density through experimental measurements, numerical simulations, and analytical calculations. Numerical simulations are performed using the open-source Python package Magpylib, followed by an exponential regression analysis of both experimental and simulated data. These procedures can be implemented without resorting to costly full three-dimensional magnetostatic simulations or specialized laboratory equipment and may be suited for imperfect physical models by inclusion of experimentally-fitted adjustment proportionality factor ξ. Notably, the maximum relative error between the simulation and experimental results is approximately 11% for the Halbach array with large size permanent magnets.