Foundational Study on Magnetic-Chain-Based Magnetic Flux Leakage Detection for High-Throughput Screening of Under-Magnetized Small Permanent Magnets

Abstract

Small permanent magnets are indispensable functional components in smart electronic products, where the stability of magnetization directly influences actuation, positioning, sensing, acoustic output, and overall system reliability. In industrial production, however, the final magnetic performance of a small magnet is sensitive to raw-material fluctuations, local field nonuniformity, fixture tolerance, and process disturbance during magnetization. The dominant failure mode is insufficient magnetization intensity, which creates under-magnetized or “NG” parts. Existing commercial inspection equipment usually adopts a discrete strategy in which each magnet is measured independently. Although this approach offers high accuracy, its serial nature limits throughput and is increasingly incompatible with large-scale manufacturing. To support high-speed screening, this work develops a foundational study of magnetic-chain-based magnetic flux leakage (MFL) detection using Hall sensing and finite-element analysis. Rather than treating each magnet as an isolated inspection target, the method organizes multiple magnets into a chain and evaluates whether the leakage-field distribution along the chain can preserve sufficient contrast for reliable NG identification. A three-dimensional Ansys Maxwell model is established using NdFe36 permanent magnets, with a single under-magnetized magnet embedded at the center of the chain. The study first constructs the batch-detection framework, then investigates the signal morphology obtained along vertical and horizontal sensing directions, and finally introduces direction-dependent threshold metrics for quantitative discrimination. For magnet lengths of 10, 8, and 6 mm, the vertical-direction thresholds are 40.35, 37.95, and 31.71, respectively, whereas the horizontal-direction thresholds are 27.99, 29.35, and 28.35. The results show that each magnet produces a quasi-N-shaped leakage signature in the vertical direction and a quasi-parabolic signature in the horizontal direction. More importantly, the vertical arrangement consistently provides stronger NG contrast and clearer waveform separation. This work therefore solves a key early-stage problem for magnetic-chain inspection: how to preserve both throughput and signal distinguishability in a batch-screening configuration. The study provides a physically interpretable detection metric, identifies the more favorable sensing direction, and offers direct guidance for subsequent equipment design, algorithm development, and extension toward more complex magnetic-chain inspection scenarios.