Assigning a Thin Layer (Air Gap) Boundary for a Magnetostatic or Transient Solver

When two parts of the domain are separated by a thin volume representing an air gap, it can be modeled using a Thin Layer boundary condition. This boundary creates a scalar potential discontinuity across the two sides of the surface based on its thickness. The magnetic permeability of the air gap is assumed to be equal to that of free space.

This boundary condition can be used to model narrow air gaps, such as those in power transformers, inductors, or any other electric device forming a magnetic circuit with an air gap without needing to explicitly model (and mesh) this gap.

Note: The thin layer cannot be a closed shell encompassing a conductor and does not support a mechanical movement, i.e., the boundary condition cannot be applied to the interface of moving and stationary bodies.

For the 3D Magnetostatic and Transient solvers, the thin layer for an air gap is defined purely in terms of its thickness. It is assumed to be made of air (non-conducting material with relative magnetic permeability equal to one).

To define a thin layer boundary:

  1. Select the section of the geometry on which you want to apply the boundary condition (typically a sheet object or face of a 3D body).

  2. Click Maxwell 3D > Boundaries > Assign > Thin Layer to open the Thin Layer dialog box.

  3. Enter a name for the boundary in the Name box, or accept the default.

  4. Enter the thickness of the thin layer and the unit of measure. It must be a value greater than zero. The use of variables is supported.

  5. Optionally, click Use Defaults to revert to the default values in the window.

  6. The Defaults tab allows you to control default values. The Save Defaults button saves the values currently defined on the Thin Layer tab as the defaults to be assigned to new impedance boundaries. Revert to Standard Defaults clears existing user-defined values and replaces them with the standard default values.

  7. Click OK to assign the boundary to the selected object.

The Project Manager tree lists the newly assigned thin layer boundary in the tree. You can select the boundary in the tree to view and edit its thickness in the Properties window. You can also double-click the boundary entry in the tree to open it for editing in the Thin Layer dialog box.

Getting Better Convergence with the Thin Layer Model

For a magnetostatic or transient simulation, the thin layer model for air gaps requires the duplication of the scalar potential to create a field discontinuity beyond the dimension of the sheet object and correctly represent the fringing flux effects. The Maxwell solver automatically duplicates the potential in one layer of elements from the gap edges. However, during the mesh adaptive process, the lateral elements may become too small and thus too close to the gap sides. This results in a low convergence of the mesh adaptive steps as the magnetic energy on such elements becomes more important. To improve convergence, the user can extend the sheet object manually (see figure below). Better convergence is observed by raising its lateral sides from one to three times the air gap thickness (δ≅3e) depending on the model geometry.