Theory of Proportional Solenoids and Magnetic Force Calculation

Proportional solenoids are wellknown and used in a wide range of applications today. However, the theory behind the functional principle of proportional magnetic actuators is not very well represented in literature. This paper discusses methods of influencing the characteristic force-strokecurves of magnetic actuators by means of different pole geometries. The conical design of the stator pole, which is primarily used to accomplish proportional solenoids, is analyzed by both a simple analytic reluctance model and a FEM model created with the AC/DC module of COMSOL Multiphysics. Furthermore, three different approaches of magnetic force calculation in COMSOL Multiphysics are introduced showing their advantages and disadvantages. The three methods are Maxwell Stress Tensor (COMSOL default method), Maxwell Tensile Force and the method of virtual displacement.