E08 — 24-slot / 18-bar 4-pole induction machine with skewed rotor bars

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What you need to run it: the Python API, the Machines module and Core Pro. Opening the model and reading results that are already there never requires a licence. Core Pro covers the rotor-bar skew, Crank-Nicolson time integration and the time-harmonic extraction - which is most of what this example is for.

At a glance

Quantity	Value	Unit
Speed	1425	rpm
Electrical frequency	50.0	Hz
Slip	0.050	—
Average torque	10.677	N·m
Torque ripple	17.8	%
Mechanical power	1.593	kW
Efficiency	70.24	%
Power factor	0.589	—
Total losses	675.1	W
Max B, stator tooth	1.754	T
Mesh	9698 nodes, 17715 elements, P1	—
Wall time, end to end	618	s

The induction machine with everything switched on that E07 deliberately left off:

• skewed rotor bars, solved as three axial slices coupled to each other;
• the deep-bar effect — eddy currents inside the bars themselves, not just the resistance the circuit sees;
• Crank-Nicolson time integration instead of backward Euler;
• trapezoidal teeth on both stator and rotor.

Same frame as E07 — 120 mm outside, 90 mm stack, four poles, 50 Hz — so the two are directly comparable machine for machine.

This is the slowest model in the set: roughly twenty minutes end to end. Skew multiplies the work by the slice count, and the run needs six electrical periods for the rotor to settle.

Why this one solves half the machine

E07 gets away with a quarter. This machine cannot do better than a half, whatever you do to it, and the bar count is why.

The symmetry sector is the greatest common divisor of coils per phase, poles and rotor bars. Eighteen bars is 2 × 9, so it carries a single factor of two. Any even pole count already shares that factor, and so does any layer count, so the divisor is 2 for every combination — a half machine, always. E07's 28 bars carries two factors of two, and a double-layer winding brings a third, which is what lets it reach a quarter.

Twelve slots and nine bars over 180°, and because the sector holds two poles the cut is closed periodically — the opposite of E07's anti-periodic cut.

The design

Layer	Radii (mm)	Set by
shaft bore	1.700	derived from rotor shaftThickness 10
rotor shaft	1.7 → 11.7	shaftThickness 10
rotor yoke	11.7 → 21.7	coreThickness 10
rotor bars	21.7 → 34.7	slotDepth 13, slotWidth 3.5, 18 bars
air gap	34.7 → 35.0	airGap 0.3
stator bore	35.000	ID 70
slot bottom	48.000	slotDepth 13, slotWidth 3.0, 24 slots
stator OD	60.000	OD 120, back iron 12

The rotor yoke is thinner than E07's to give radius to a deeper bar. Depth over width is 3.7 here against E07's 2.5, and the bar is elongated on purpose — a deep bar is what makes the skin effect worth modelling.

Skew is one stator slot pitch, 15° mechanical, which is the classical choice, over three slices. Three is the smallest count that represents a linear skew rather than a single straight cut.

Winding and materials

Stator core and rotor yoke	M-19 Steel, nonlinear BH
Rotor shaft	1020_steel
Rotor bars	conductivity 2.4 × 10⁷ S/m on the region, same as E07
Winding	three-phase distributed double layer, q = 2, full pitch
Turns per coil	26
Slot fill	0.42
Parallel branches	2
End winding	20 mm extension

Two parallel branches against E07's four is the main reason this run's current density and copper losses are higher at the same 20 A excitation — fewer parallel paths means more current per conductor. It keeps the winding simple against a 180° sector rather than a 90° one. If you want the cleanest possible comparison of skew and deep-bar physics against E07, set the branch count to 4 and re-run.

Iron loss uses the same fitted coefficients as E07, so the two machines' iron losses are directly comparable.

Operating point

Excitation	20 A peak, slip 0.05, shaft speed 1425 rpm
Supply	50 Hz, 1500 rpm synchronous
Eddy currents	on in the rotor bars, off everywhere else
Skew	15° mechanical over 3 slices, solved together
Time integration	Crank-Nicolson, with two backward-Euler startup steps
Extraction	time-harmonic method, locked-rotor stage at 12.5 Hz
Window solved	six electrical periods, 48 steps each
Elements	first order, deliberately

The locked-rotor stage is where the deep bar shows up. Run at a real, non-zero rotor frequency — a quarter of line frequency here — a bar this deep has already started to leave its DC regime, so the extracted rotor resistance is an AC resistance rather than the geometric one. That is the reason for choosing the time-harmonic extraction method on this machine.

First-order elements on purpose. Skew at second order costs roughly eleven times the wall time per step, and this run is already the most expensive one here at first order.

Running it

Open im_24s18r_trap_skew.nbl and press Solve, and leave it running. The solved field is not shipped: three coupled slices over 288 steps write a 644 MB file.

From Python:

python build_im_24s18r_trap_skew.py                 # build, solve, analyse, report
python build_im_24s18r_trap_skew.py --no-solve      # geometry and mesh only
python build_im_24s18r_trap_skew.py --no-skew       # the unskewed control run

Skew and Crank-Nicolson both need a Core Pro licence; the machine itself does not.

What to look at

What the skew costs and what it buys. The classical skew factor for one slot pitch is 0.9886, so less than half a per cent off the fundamental flux linkage. Almost anything else that moves between the skewed and unskewed runs is the slot-harmonic suppression that skew is actually for. Run --no-skew and compare the torque ripple directly — that comparison is the most useful thing in this model.

How the slices are solved. They are not three independent runs averaged afterwards. One conductor threads all three slices, so they share a current, and the solver assembles them into one system with a single circuit block. That is what makes a skewed cage more expensive than three times a single slice, and it is also what makes it right.

Crank-Nicolson against backward Euler. Second-order accuracy in time for the same step count. On a smooth transient it lets you take fewer, larger steps for the same error; near a switching discontinuity it can ring, which is why the run starts with two backward-Euler steps before switching over.

The bar current profile is in rotor_bar_current.csv. Compare it with E07's: a skewed rotor's bars carry a noticeably less even distribution, and the bar sitting against the periodic cut is the low outlier.

Open questions in this run

Three things in this model are reported as they came out rather than tidied, and they are worth knowing before you lean on the numbers.

The bar current spread is wide — about three to one between the lowest and highest bar, against roughly two and a half to one on E07. The low bar is the one against the periodic sector cut. That is plausibly a genuine consequence of a periodically cut, skewed rotor, since that bar's three slices see a different angular relationship to the travelling field than a bar deep inside the sector. It has not been confirmed against an independent calculation.

The implied slip runs above the commanded one. Bar loss divided by airgap power should track the slip you asked for; here it comes out higher. The direction is what the deep-bar effect should do — a higher effective AC bar resistance — but the size of it has not been cross-checked against an independent skin-effect calculation.

The power balance closes to about 5 % rather than the fraction of a per cent the PM examples manage. It is likely the same root cause as the item above: something in how per-slice bar loss and mechanical power are summed against each other.

None of these is run-to-run noise — the model is deterministic and rebuilds identically. If your work depends on absolute rotor loss on a skewed cage, run the --no-skew and eddy-currents-off comparisons below and treat the differences as the result rather than any single absolute figure.

Try this next

• --no-skew — the same machine with the twist removed. This is the comparison the example exists for.
• Turn the bar eddy currents off with everything else unchanged. That isolates the deep-bar contribution to the extracted rotor resistance, and it is the most direct way to chase the implied-slip question above.
• Set parallel branches to 4 to match E07, which removes the winding difference and leaves only the skew and deep-bar physics between the two machines.
• Make the bar shallower, closer to E07's proportions, and watch the deep-bar effect fade out of the extracted resistance.

About these numbers

The dimensions are invented but plausible: a four-pole 50 Hz machine of roughly 1 kW on the same frame as E07, not a copy of a published design. The validated induction machine lives in the validation dossier, and that is where an accuracy question belongs.

More from this run