Lamination Module¶

The Lamination module addresses the modelling of laminated ferromagnetic cores — stacks of thin ferromagnetic sheets separated by insulating interlayers. This is the standard core construction in power and distribution transformers, induction motors, generators, reactors, and inductors.

Why laminations?¶

A solid ferromagnetic core exposed to a time-varying magnetic flux develops eddy currents that close in the bulk and dissipate a significant fraction of the throughput power as ohmic loss. Cutting the core into thin sheets oriented along the dominant flux direction and electrically isolating the sheets from each other interrupts these loops: the eddy-current path is restricted to the cross-section of a single sheet, and the per-unit-volume loss drops roughly as \(d^2\), where \(d\) is the sheet thickness. Typical sheet thicknesses for power applications are \(0.2\)–\(0.5\,\mathrm{mm}\) (grain-oriented or non-oriented silicon steel for mains-frequency transformers and motors) down to a few tens of micrometres for high-frequency cores.

Resolving every sheet on the simulation mesh is prohibitive for industrial cores, which typically carry \(10^3\)–\(10^4\) sheets. The module therefore treats the stack as an anisotropic continuum and adds a sheet-scale correction that recovers the in-sheet eddy-current losses lost in the homogenisation.

Physical picture¶

A laminate is characterised in its local frame \(\{\vec{e}_\alpha, \vec{e}_\beta, \vec{e}_\gamma\}\), with \(\vec{e}_\gamma\) along the stack and \((\vec{e}_\alpha, \vec{e}_\beta)\) spanning the lamination plane, by

• the stacking direction \(\vec{e}_\gamma\) — unit vector normal to the sheets,
• the sheet thickness \(d\) of a single ferromagnetic layer,
• the stacking factor \(F \in (0, 1]\) — volume fraction of the magnetic phase (the remaining \(1-F\) is the insulator),
• the sheet's magnetic permeability \(\mu\) and electric conductivity \(\sigma\).

Two eddy-current channels arise in the stack:

The first channel survives the homogenisation and is captured by an anisotropic continuum; the second is sub-grid by construction and must be added back via a sheet-scale correction.

Contents¶

The module currently provides one material per magnetic model — both implementing the homogenised continuum plus the first-order in-sheet eddy-current correction.