A 3-D Field Solution for Axially Polarized Multi-Pole Ring Permanent Magnets and its Application in Position Measurement

Axially polarized multi-pole ring permanent magnets are industrially valuable in the construction of sensors and actuators. Available analytic field solutions for these magnets typically provide spatially incomplete or imaginary-valued results that do not reflect real-world measurement. This article presents simplified and real-valued 3-D field solutions for axially polarized ring magnets. The individual components are expressed in terms of elementary functions and incomplete elliptic integrals for easy evaluation with standard scientific computing libraries. These models are employed to analyze the effects of nonidealities in magnetic position systems. Demonstrations are offered through simulation and experimental measurement of two real-world ring permanent magnets, along with comparisons to prior models.