Date of Award

Winter 1992

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Charles K Taft


The work involves the magnetic modeling of a variable reluctance and a hybrid stepping motor. The model combines two traditional methods for creating a magnetic model. Nonlinear two dimensional finite element analysis is combined with nonlinear lumped element modeling to create a three dimension lumped model. The two dimensional finite element analysis is used to numerically calculate the effective reluctance function of the motor tooth region. After the finite element analysis is completed, a two terminal tooth region reluctance element that is a function of both rotor angle and tooth region flux density results. The two terminal lumped element is then used to represent the tooth region of the motor in a lumped parameter model. The process by which the tooth region finite element field solution is transformed into the two terminal lumped reluctance is a new modeling approach; and, it is the foundation of the modeling method in this dissertation.

Torque, back EMF, and inductance are some of the more important motor parameters predicted by the modeling method. The model predictions are compared to experimental data in the dissertation. The final motor parameter predictions from the model correlated quite well with experimental data.

Also included in the dissertation is a unique derivation which defines the constraints that a region must satisfy such that a general three dimensional region of non-homogenous material can be modeled as a two terminal lumped reluctance element. The final restrictions imposed on the general three dimensional region are quite liberal.

A method for solving any arbitrarily connected network of nonlinear lumped reluctances and sources is shown in detail. The method was developed specifically for use in this dissertation research, however, it is general enough to be applied to a wide variety of lumped element magnetic problems. The method explains how a Newton-Raphson iteration loop can be used to solve the nonlinear matrix equation created by the nonlinear network of reluctances.