Forces on Conductor Segments and Magnetized Ferrous Cores using a Three Dimensional Finite Element Vector Potential Method

This paper presents two finite element based methods for the calculation of forces on conductor segments and magnetized ferrous cores in three dimensional magnetic fields. The formulation is based on the three dimensional magnetic vector potential and the curl curl equation. Results of use of the two methods in the calculation of forces in two examples are reported. The first example is that of two currentcarrying conductors (bus bars), while the second example is that of an iron cored armature (coil) and keeper. These two relatively simple examples were chosen for purposes of comparing the three dimensional finite element results with existing two dimensional methods and closed form approximations. The results of comparison of these forces are presented here. This comparison confirms the validity and desirability of the present 3D formulation of forces by highlighting some of the limitations of the known analytical and two dimensional methods in certain applications. The two methods presented here are applicable to a variety of problems of force calculations in various electrical devices and machinery.