Approximation of electromagnetic force axial distribution in “single excitation coil – permanent magnet runner” module based on modified Kloss function

An elementary part of various electromagnetic devices or linear electric machines is a module consisting of an excitation coil and a permanent magnet (PM runner). The electromagnetic force axial distribution in this “single excitation coil – PM runner” module is usually determined by numerical field calculations at discrete runner positions. When solving the mathematical model, a table containing discrete values of the electromagnetic force axial distribution is usually used (the so-called lookup table). The authors of this article decided to find a simple analytic function that approximates the calculated discrete electromagnetic force function with technically sufficient accuracy and the smallest possible number of coefficients. After many attempts, they proposed the modified Kloss function with 2 coefficients denoted as S′ and M′, the values of which for the best approximation have to be determined using the optimization algorithm e.g. the Hooke–Jeeves algorithm. This analytical function reflects perfectly the nature of the discrete electromagnetic force axial distribution determined by the numerical field calculations and approximates the discrete function with fully satisfactory accuracy.