Semi-Analytical 3D Force Calculation of an Ironless Cylindrical Permanent Magnet Actuator for Magnetic Levitation Systems

The semi-analytical calculation of magnetic forces is currently an interesting alternative to the timeconsuming three-dimensional finite-element modeling (3D-FEM) due to its high accuracy and low computational cost. This paper presents novel equations for determining the magnetic forces of a cylindrical permanent magnet actuator used in high precision magnetic levitation positioning systems. Compared to the already available equations in literature, these equations consider the magnetic forces as a function of the current magnet position. Moreover, these equations are also suitable for designing and analyzing the cylindrical permanent magnet actuator. The results of our force equations and the verification by 3D-FEM and measurements are presented in this paper.