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Transformer model 2D vs. 3D

Example courtesy of Sergey Chishko

When modeling an electromechanical device, a designer needs to keep in mind that a 2D problem set introduces an error in a field distribution in comparison with a 3D problem solution. However, a solving process of 2D problems is multiple times faster than of 3D. In this example the main (front) and side views of the transformer are modeled to demonstrate that a contribution of front and end sides of a coil to the total magnetic flux in the core is negligible.

Problem type:
Plane-parallel problem of DC magnetics.

Geometry:
Transformer model 2D vs. 3D

Given:
All dimensions are in millimeters;
Core has a linear relative permeability of μ = 1000;
Coil conducts constant current I = 5 A.

Problem:
Obtain and compare the values of magnetic flux over the cross section of a transformer leg holding the coil for transformer's front and side view problems sets.

Solution:
To study the impact of end effects on the total magnetic flux in the transformer two models are simulated: front view and side view.
Front-view model (2D) considers only a part of a coil with a current direction "in" and "out" of the plane and neglecting end effects of "front" and "end" coil parts with currents flowing along the plane. Side-view (2D) model considers only "front" and "end" coil parts.
Both models features the same number of turns of the coil and the current.

Results
Front-view model magnetic flux is -77.7 uWb (98.3%).
Side-view model magnetic flux is -1.3 uWb (1.7 %).
Coil end parts produce only 1.7% of the total magnetic flux and could be neglected in most cases.

Magnetic flux in cross sections of the transformer in front and side models:

Transformer magnetic flux 2D vs. 3D

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