Magnetostatic Field Calculation Research Articles

A Fourier series approach to magnetostatic field calculations involving magnetic material

The effect of iron on the uniformity of the field produced by an axisymmetric thick solenoid is considered. Using a Fourier series approach, an exact solution for the vector potential A is found and from this the magnetic induction B is derived. The results are compared with those obtained from previous approximate methods.

Magnetostatic field calculations in the presence of iron using a Green’s function approach

An alternative method to that of Caldwell [J. Phys. D 12, 1653 (1979)] is used to calculate the effects of iron on the magnetic field produced by a current-carrying axisymmetric conductor. In this way a neater solution is obtained by constructing the Green’s function from an eigenfunction expansion. Good agreement with the previous results is achieved and an indication is given of the advantages of this Green’s function approach.

Computation of magnetostatic fields in three-dimensions based on Fredholm integral equations

An integral equation method is described for solving three-dimensional magnetostatic problems involving linear permeability interfaces and current sources. The interface is replaced by magnetic charges in free space to provide an equivalent interface condition. Application has been made to leakage field calculations in transformers. Numerical methods are combinations of analytical formulas and numerical integration; basis functions approximate the charge distribution.

Magnetostatic field calculations associated with superconducting coils in the presence of magnetic material

A brief account is given of relevant magnetostatic field calculations in iron-free systems concerning the uniformity of the field produced by current-carrying axi-symmetric conductors. The effects of iron on the uniformity of the field produced by such a conductor are then considered. Using a perturbation analysis a simple analytic expression is obtained which describes the field close to the axis of symmetry. Some of the advantages of this method over traditional finite-difference methods are noted.

Magnetostatic field computation by finite element formulation

Recent years have witnessed considerable research activity in the application of digital-computer methods for the determination of the electro-magnetic fields in electrical machinery through the solution of Maxwell's equations, while taking full account of the magnetic saturation. Two distinct numerical approaches are evident in the literature: Finite-Difference Method and Finite-Element Method. The author has presented in the recent years a finite difference formulation for 3-dimensional numerical solutions of the nonlinear electromagnetic field problems in terms of potential functions, and has applied for the analysis of the end-zone fields of aerospace homopolar alternators and solid-rotor induction motors. The present work is directed towards the finite-element formulation for the numerical solution of three-dimensional nonlinear magnetostatic field problems. A variational principle is developed here utilizing the vector potential concept. The approach is based on variational methods in which a corresponding energy functional for the nonlinear case is minimized over the entire region. The minimization is performed by means of the finite-element method and the resultant set of nonlinear algebraic equations is solved through iterative schemes.