An improved nodal method for circuit and multi-slice magnetic field coupled finite element analysis

A general and simple method to couple arbitrarily connected circuits and multi-slice magnetic fields in the time stepping finite element analysis of electromechanical devices and electrical machines is presented in detail. The merits of the proposed method are that the sparsity of the finite element equations is improved, the formulations to be described will allow unequal division of the axial length of the motor in the multi-slice model, the stranded windings (with negligible eddy current) and solid conductors (with eddy current) in the field domain can be connected arbitrarily with the external circuits, and the coefficient matrix of the system is symmetrical and the nonlinear power electronic elements can be easily maneuvered in the formulations. As illustrating examples, the proposed approach is used to simulate the operations of a brushless d.c. motor and a hard disk drive spindle motor.