Magnetic cores in Flux

Introduction

Electromagnetic devices such as motors, generators, actuators, transformers, and electromagnets are most frequently built from pieces of magnetic materials with a high magnetic permeability. Their purpose is to confine, guide and reinforce the magnetic field created by the coils or magnets integrating the device, by reducing flux leakage into the air. They lead to an increased magnetic coupling between parts and to a high energy density stored in the field. These features are highly desirable for electromechanical transducers, since they tend to improve their performances.

Such pieces are collectively called magnetic cores in the practice of Electrical Engineering. They include the rotors and stators of rotating machinery, the static and moving parts of electromechanical actuators and are usually ferromagnetic. Moreover, they are also conductive to a lesser or greater extent, making them susceptible to the development of eddy currents, notably in the case of alternating current devices. Both phenomena may lead to frequency-dependant losses that impact their performances and that must be accounted for during design.

This user guide chapter discusses the representation of magnetic cores in Flux. These may be modeled using different region types and materials, leading to different approaches for the evaluation of iron losses. The choice depends on a tradeoff between the complexity of the resulting model and on the extent of the physical phenomena that the user is willing to represent. The following topics are covered:

Region types representing magnetic cores

Magnetic cores may be constructed from solid pieces of ferromagnetic metals (e.g. iron) conformed to the desired shape, specially in the context of direct-current applications (i.e., no eddy currents). In the general case of time-varying currents and fields, the induced currents and the corresponding losses must be limited by the designer. This is usually accomplished by one of the following strategies:

  1. alloying with a different material such as silicon, to increase resistivity;
  2. using highly-permeable materials with a very high resistivity (e.g., ferrites);
  3. using materials composed by insulated grains (e.g., sintered or pressed iron powders) to mold the desired shape for the core;
  4. stacking insulated laminations of highly-permeable electrical steel.
Given these four categories, Flux provides three dedicated region types (surface regions in 2D or volume regions in 3D) adapted to the representation of magnetic cores:
  • Magnetic non conducting regions: a region with a magnetic material assigned (hysteretical or not) and in which eddy currents are not allowed to flow. This region is well-suited to represent bulk cores in categories 1, 2 and 3 above.
  • Laminated magnetic non conducting regions: also a region with a magnetic material assigned and in which eddy currents cannot flow, but with specializations that simplify the representation of cores formed from a stack of electrical steel sheets (category 4 above). For instance, this region type accounts for the insulation of the laminations, which reduces the effective volume filled with steel. It may also account for magneto-mechanical effects related to the manufacturing of the stack (e.g., punching of the electrical steel sheets) that further modify the magnetic property B(H) of the region.
  • Solid conductor regions: a region where the assigned material has magnetic B(H) and electrical J(E) properties to account for eddy currents during the solving process; the accuracy is enhanced but the required computational resources are increased. This region allows representing bulk cores in categories 1, 2 and 3 above, as well as stacks of steel sheets (category 4 above) in 3D projects.

Evaluating losses in magnetic cores

Evaluating the iron losses in magnetic cores is of paramount importance for the design of efficient electromagnetic devices. However, this computation depends on the non-linear, hysteretic B(H) constitutive relations of the material integrating the core.

A full representation of hysteresis in a finite element simulation requires a time-domain simulation (i.e., a Transient Magnetic application in Flux) and significant computational resources, leading to long processing times. To circumvent this drawback, alternative techniques for evaluating losses in magnetic cores without explicitly accounting for the hysteretical nature of their materials during resolution are also available in Flux.

These two main approaches for computing iron losses in magnetic cores available in Flux are outlined below:
  1. À posteriori approach: a non-hysteretical material is assigned to the region describing the core. After resolution, a field distribution that is assumed sufficiently close to the real distribution in the core (i.e., the distribution that would be computed with the representation of hysteresis) is obtained. Then, while in post-processing, empirical or phenomenological models are applied to the obtained field distributions to estimate the losses. Flux implements two of these loss models:
    • a modified version of the Bertotti model, which belongs to the family of Steinmetz-like models for iron losses;
    • the Loss Surface model, which relies on magnetic measurements.
    Both these models apply in Flux to Laminated magnetic non conducting regions.
  2. À priori approach: a material implementing a model of hysteresis is assigned to the region describing the core in a Transient Magnetic simulation. Flux implements two such models:
    • the Preisach model;
    • the Jiles-Atherton model.
    Both these models can apply in Flux to Magnetic non conducting regions or to Solid conductor regions, thus enabling the user to take static hysteresis into account or the dynamic one also, respectively. Once the scenario is solved, the obtained solution accurately represents the space distribution and time evolution of the fields, without any further post-processing required. The iron losses during a given time interval become promptly available through predefined quantities or sensors.
The following pages further discuss each approach in Flux: