# Magnetic field sensing of 3D printed Halbach arrays

## TL;DR

This paper presents a cost-effective method for designing and testing Halbach magnet arrays using low-cost sensors and simulations.

## Contribution

A low-cost approach for measuring and modeling Halbach arrays using Hall-effect sensors and open-source simulations is proposed and validated.

## Key findings

- A Hall-effect sensor was successfully used to measure magnetic flux density in Halbach arrays.
- Numerical simulations using Magpylib showed a maximum relative error of about 11% compared to experiments.
- The method avoids expensive 3D magnetostatic simulations and specialized equipment.

## Abstract

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 \documentclass[12pt]{minimal}
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