Numerically Stable Magnetic Field Expressions for End-of-Shaft Angle Sensing Systems

The design of end-of-shaft angle sensing magnetic positioning systems (MPS) requires accurate field computations in the sensing area for the magnetostatic inversion procedure. Highly resolved field computations on a 3-D domain make FEM simulations unfeasible and favour analytical solutions. Analytical textbook field solutions of a number of standard magnet shapes are however numerically unstable along symmetry axes, body edges as well as in the far field. For the particular application of an end-of-shaft system, only a particular instability close to the symmetry axis, ρ → 0 plays a detrimental role. We stabilize the field equation by mathematical reformulation of naturally occurring numerically unstable combinations of elliptic integrals in the derivation. The resulting formulas or even their ready-to-use implementation in the freely available Python package Magpylib can be used without limitations for end-of-shaft MPS designs.