Design of magnetic tunnel magnetoresistance displacement sensor with optimized magnet array

To address the demand for miniaturized displacement measurement, this paper proposes a tunnel magnetoresistance (TMR) displacement sensor based on a four-magnet array and presents an integrated investigation involving theoretical modeling, structural parameter analysis, and experimental validation. A magnetic field model is established to describe the relationship among displacement, magnetic field response, and sensor output. Finite element simulations are further performed to investigate the effects of air gap and lateral offset on the magnetic field distribution and output characteristics. Based on these analyses, eight prototypes with different structural parameters are fabricated and evaluated through static calibration, dynamic response testing, and eccentric shaft experiments. The results show that the in-line four-magnet configuration without lateral offset exhibits better monotonicity and static linearity than the offset configurations. Although nonlinear deviation appears near the ends of the full stroke, restricting the effective working range to 2-18 mm significantly improves the linear output behavior, and the optimized prototype achieves a BFSL error of 2.45%FS. Dynamic and eccentric shaft experiments further demonstrate that the proposed sensor can stably track periodic displacement variations and shows good agreement with the overall trends obtained using commercial reference sensors. These results demonstrate the feasibility of using four-magnet-array field modulation for displacement sensing and provide a useful reference for the parameter-oriented design and performance evaluation of TMR displacement sensors.