Magnetic circuits

The analysis of Maxwell and Kirchhoff models was undertaken in the [D 1 050v2] dossier. The aim of this dossier is to present applications of these approaches, based mainly on the analysis of equivalent circuits. The examples chosen are typical of problems that can be encountered.

The first example is typical of circuits such as transformers and electromagnets. It illustrates the decomposition into partial permeances.

In contrast to an analytical approach, the second example shows how to design an electromagnetic structure of a given shape to generate a force of fixed intensity.

The losses occurring in ferromagnetic structures are described using a simplified electromagnetic circuit model for eddy currents. It is thus possible to describe these losses and highlight the parameters on which they depend.

Voice coil actuators have the great advantage of generating a force proportional to the current. They have numerous applications in loudspeakers, robots, positioning machines and so on. Under certain conditions, however, they may exhibit a variable reluctance parasitic force, which will be highlighted, along with ways of eliminating it.

Many actuators or motors are made up of facing toothed structures. If they can be modeled efficiently by finite element methods, it may be worthwhile to use equivalent circuit modeling. Variable permeances can be determined by approximating field lines by straight lines and arcs.

The complex magnetic structure of the hybrid stepper motor is difficult to control, even using finite elements. A magnetic equivalent circuit model is proposed, using in particular the permeance model already studied.

The basic principles of electromagnetism in the stationary (low-frequency) domain, and the resulting methodology for magnetic circuits, are described in [D 1 050v2] . It will be referred to systematically for the equations used in this document.