Application of the Thermal Fin Approximation to Modeling Voice Coil Magnetic Fields and Performance

This paper develops an approximate analytical model to describe the magnetic fluxes, forces, and armature reaction in cylindrical voice coil actuators and related electric machines. Magnetic flux is assumed to either lie in an inner region of the actuator and parallel to its axis, or in an outer region of the actuator and oriented radially. A differential reluctance model is derived for this set of assumptions, with a structure and solution set similar to those involved in extended-surface heat transfer (“fins”) and lossy transmission lines. Particular solutions for the force constant, motor constant, coil inductance, and variable-reluctance force are found for a symmetric motor with opposed axial permanent magnets on either side of an iron flux concentrator. The model results for this topology are validated using finite-element analysis and experimental measurements from a prototype.