A Statistical Investigation into Assembly Tolerances of Gradient Field Magnetic Angle Sensors with Hall Plates

Magnetic field-based sensors are used for reliable applications in automotive and aerospace industry because of their robustness. The electrification of powertrains and propulsion requires gradiometric sensing principles, because they suppress ubiquitous electromagnetic disturbances very efficiently. A prominent solution for the mass market uses a small permanent magnet attached to the end of a rotatable shaft and a small sensor chip with four Hall plates placed on the rotation axis and ahead of the magnet. Small misplacements of chip and magnet lead to errors in the detected angle of the shaft. The lateral position errors and tilts of the magnet and the chip give eight degrees of freedom (DoF). This large number of DoF and the nonlinearity of the system obscure the view on how to optimize such angle sensor systems. Therefore, this work presents a statistical description of angle errors caused by assembly tolerances. Probability distributions of angle errors are given and marked differences to Gaussian distributions are shown. The influence of spacing between sensor and magnet and the dominant influence of the shape of the magnet are clarified. The results obtained by numerical computations are in excellent agreement to recently published analytical theories. This work gives evident conclusions for statistical optimizations of such angle sensor systems.