Of Circuits and Conductors
Antti Lehikoinen ????
Consulting Electric Motor Designer | FEA Developer | D.Sc.
I love the concept of 'circuits' and 'conductors' in 2D finite element analysis. There are just so many varieties and options to choose from.
Different circuits
Let's consider a 3-phase winding. You could either choose to fix the current density in the coils, the total phase current, or the input voltage. The conductors themselves you could model as infinitely stranded, or as solid conductors, or even model each individual strand as a point (at least I could). Or, you could mix and match several options in one circuit.
And of course, there are different circuits as well, like rotor and damper cages, or DC excitation windings.
Different conductors
For solid conducting blocks, you have even more options. A typical assumption is that the net current in each block is zero. However, the exact formulation still depends on if you are considering a single PM, or a solid shaft extending beyond your symmetry region. After all, you want the net current of the entire shaft to be zero, not just the segment you are modelling. And you are utilizing symmetry sectors, right, to speed up your computations?
Or, you could even have small block, like an inter-pole filler made from stainless steel in a high-speed SPM, that 'wraps around' the boundary of your sector. Well, this situation could be avoided by rotating the pole a bit, so that the symmetry boundary falls on the interface between the magnet and the pole gap. But, it is supremely handy to always have the d-axis in the middle of your symmetry sector.
And finally, there are more esoteric conductors. For instance, you could approximate the damping effect of in-lamination eddies, to account for the widening of BH loop at high frequencies. Or, you could include a 3D model for the electric potential, to account for say axial segmenting of PMs. Or, you could even include such model outside the 2D domain, for modelling the end-ring of a copper-coated high-speed induction motor.
Example
Finally, let's take a look at an example. Below, you see a (crappy) outrunner BLDC motor. The stator winding is fed with a fixed current density, while the zero-net-current approach is used for the permanent magnets. The rotation speed is 8000 rpm, the airgap is shortish at 1 mm, and the magnets are not segmented so the resulting current densities (color scale at Apeak/mm^2) are quite high.
Anyways, there is a clear concentration of losses whenever a magnet passes a tooth tip.
The example was calculated with EMDtool, as can all the other examples listed here.