Parametric characterization of approximation functions for the axial and lateral force between electromagnets and spherical permanent magnets

The interaction between magnetic objects has been widely explored due to their range of applications, which usually involves complex calculations regarding magnetic forces. This paper presents approximation functions to describe the force generated between cylindrical electromagnets and spherical permanent magnets. These functions consider the electrical current that passes through the electromagnets, and the geometry of the devices to associate their relationship through parametric adjustments. A nonlinear least mean square parameter estimation method yields electromagnetic functions in axial and lateral directions in the relative configuration of the magnetic devices. An own developed measurement device is used to get the experimental data that leads to the functions characterization. The functions are developed considering a piecewise approximation depending on the relative distance between the electrical and permanent magnets. The modeling strategy leads to an accurate and precise representation of the force between the magnetic devices, as the correlation index and relative errors indicate.