Stranded Coil

A stranded coil is a coil that is wound with a wire that is made up of multiple strands. The strands are not modelled individually but homogenized to a single body.

This approximation is valid when the individual wires have a small diameter compared to the skin depth of the material so that the current remains uniformly distributed over the cross-section of the wire.

Current Density Calculation

The current density of a straight, constant cross-section coil is given by

\[\mathbf{J} = I \cdot \boldsymbol{\tau} = I \frac{1}{n_t S_c} \mathbf{z}\]

where \(I\) is the applied electric current, \(S_c\) is the cross-sectional area of the coil, \(n_t\) are the number of turns and \(\mathbf{z}\) is the unit vector in the direction of the coil.

In general, \(\boldsymbol{\tau}\) the turn vector density is calculated to ensure that non-constant cross-sections non-straight coils are correctly modelled, the current density is correctly homogeneously distributed across a cross-section, and the current density is divergence free.

Note that the specification of a fill-factor is required when modeling the Ohmic losses in the coil to correctly account for the reduced cross-sectional area due to the insulation between the strands.

Also note that the thermal conductivity of the coil is orthotropic as heat can be conducted along the strands but not across them.

API

A stranded coil can be created using the following Python code:

from mufem.electromagnetics.coil import CoilTypeStranded

coil_type = CoilTypeStranded(number_of_turns=280)