Computation of electromagnetic forces from finite element field solutions

Designers of electromechanical devices often need to predict magnetic forces from finite element solutions with good accuracy. This paper considers two common methods of force computation, namely the Maxwell stress tensor (MST) and the Coulomb virtual work (CVW) methods. These methods require the definition of either an integration path (in the MST method) or a sheared layer (in the CVW method), and results have been found to depend on the path or layer selected. This difficulty is associated with local errors in the computed field, which can translate into significant force errors. To overcome the problem, this paper investigates a particular implementation based on the CVW method. In this implementation, the predicted force is computed from several layers of distorted elements of the free space region surrounding a body under force thereby increasing the number of elements contributing to the force computation. Two practical examples are considered. One is a linear case, consisting of two infinitely long parallel conductors of rectangular cross section for which an analytical result is possible and the other is a severely nonlinear case for which the axial force in an axially symmetric actuator has been measured experimentally. The improved accuracy of the new implementation compared with the MST method and the CVW method with a single sheared layer is demonstrated.