Orientation of the unit cell in coil conductor regions with losses and detailed geometrical description

Introduction

The orientation of the unit cell of a coil conductor region with losses and detailed geometrical description may be adjusted by the user in Flux 2D and in Flux 3D.

The description of the unit cell is used by Flux for homogenization purposes during the resolution of the FEM problem. When possible, adjusting its spatial orientation to match the real configuration of the winding leads to improved results, notably in the case of coils with a relatively small number of turns.

The procedure to orient the unit cell is detailed in the following sections.

In Flux 2D

In the dialog box dedicated to the creation of a coil conductor region (which is a face region in Flux 2D), ticking the option Compute coil losses in the Coil Losses Models tab will allow the user to select the Detailed description (consider proximity and skin effects) subtype from the Winding geometry drop-down menu. Choosing this subtype will display two additional tabs in the bottom part of dialog box, namely the Strand Definition and the Orientation and Units tabs.

The user may fine-tune the spatial orientation of the unit cell associated to the region in the Orientation and Units tab in Flux 2D by providing two parameters:

The coordinate system defining the orientation of the unit cell.
A real number representing the rotation angle of the unit cell with respect to this coordinate system, measured in the angular unit of that coordinate system.

The figures in Table 2 below illustrate the effect of inclining the winding pattern. This modified orientation of the unit cell may be obtained by choosing a rotation angle of -45 degrees in the standard coordinate system XY1 of a Flux 2D project.

Table 1. Providing a rotation angle in the Orientation and Units tab tilts the unit cell, allowing the representation of slanted winding arrangements.

Note: The coordinate system selected in the Orientation and Units tab also determines the horizontal and vertical directions mentioned in the Strand definition tab for "rectangular section wire" template or unit cell. The direction of the first coordinate of the system corresponds to the horizontal dimension, while the vertical dimension is along an orthogonal direction.

In Flux 3D

In Flux 3D, the coil conductor region with losses and detailed geometrical description is a volume region. Consequently, the data required to orient the unit cell in the Orientation and Units tab is slightly different when compared to Flux 2D.

More specifically, a coordinate system and a rotation angle are also required, but the user must also provide the three components of a vector lying upon a cross section of the coil conductor region to orient it in three-dimensional space.

The specific cross section of the volume region to be considered in the orientation procedure is implicitly determined by Flux 3D when the user orients the current sense of the coil conductor region in accordance with the following rules:

For an "open" coil with External terminals: the cross section to be considered is the input terminal of the coil conductor region.
For a "closed" coil with Internal terminals: the cross section to be considered is the single input/output terminal of the coil conductor region.
For some coil geometries, the cross-section that would be predicted by the two previous rules may not be orthogonal to the current flow direction. Under such circumstances, the cross section to be considered is the face orthogonal to the current flow that is nearest to the input terminal, considering the sense of the current flow.

Table 2 summarizes the data required to manage the orientation of the unit cell in the Orientation and Units tab.

Table 2. Data required to manage the orientation of the unit cell of a coil conductor region with losses and detailed geometrical description in Flux 3D.
Element	Function
Coordinate system for definition	Coordinate system for the definition of the orientation vector.
Orientation vector $\vec{v}$ (three components)	Vector lying upon the cross section considered for orientation and defining the horizontal direction (for rectangular section wires) *
Rotation angle θ	Supplementary rotation angle of the orientation vector

Note: * If the orientation vector is not in the section plane, Flux 3D will consider its projection on the coil conductor region cross section.

Examples of unit cell orientation in Flux 3D are available in Table 2 for two simple configurations of closed and open coils, with the rotation angle set to zero. The orientation vectors are defined in the coordinate system drawn in the figures.

Table 3. Examples of unit cell orientation for a closed coil with Internal terminals and for an open coil with External terminals in Flux 3D.
Closed coil conductor region in Flux 3D. Open coil conductor region in Flux 3D.	$\vec{v}$ (1, 0, 0)	Horizontal dimension parallel to OX Vertical dimension parallel to OY
	$\vec{v}$ (0, 1, 0)	Horizontal dimension parallel to OY Vertical dimension parallel to OX
	$\vec{v}$ (0, 0, 1)	Not allowed, since direction OZ corresponds to the current direction.