Date of Award

Spring 2002

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Colin P. Britcher

Committee Member

Thomas E. Alberts

Committee Member

Donald L. Kunz

Committee Member

W. Steven Gray

Committee Member

Nelson J. Groom


This dissertation is a study of new modeling techniques developed for magnetic suspension systems. The techniques discussed are modifications of magnetic circuit theory and fundamental eddy current models. The techniques are compared against experimental test results and finite element data. The information gained from the experimental testing is used to provide insight into magnetic bearing design.

A small-gap modeling technique called extended circuit theory is developed that incorporates information about the system gained from finite element data, or experimental data, to be included in the analytic model. The variations between the classical magnetic circuit model and the finite element model are used to develop performance coefficients, which are in turn incorporated into the extended circuit model. The coefficients modify the classical theory to account for magnetomotive force losses, flux leakage and flux fringing. The theory is developed from fundamental principles. The techniques used to determine, and predict, the coefficients are discussed. The use of this method in optimal bearing design is also discussed.

The extended circuit model is verified against experimental test results of a family of magnetic actuators. The actuators consist of a “C-shaped” stator and a flat armature. The pole separation distance was varied along with the location of the biasing permanent magnets and the windings. The permanent magnets were placed either on the pole faces, in the center of the armature, or at both locations, and the windings were wound on poles of the stator or on the back of the stator, resulting in a total of 22 design permutations. The experimental performance of each design is analyzed and efficiency trends are discussed.

The diffusive model for eddy currents is analyzed along with the lumped parameter model to explore the “half-order” behavior of eddy currents commonly observed in experimental testing. A fractional order eddy current model is developed and compared against finite element data and experimental test results. The models developed are based on a frequency dependent resistance. The implications of using fractional order modeling techniques, along with control considerations, are discussed.