Four Loss Mechanisms, Each Dominant Somewhere Different
A traction motor at its best point converts 97 per cent of what it is given. The design problem is not that number — it is that the missing three per cent moves around.
Magnets and Motors · Part 3 — The Machine · Chapter 8 · 21 min read
A traction motor at its best point converts 97 per cent of what it is given. The design problem is not that number — it is that the three per cent moves around, and the mechanism that dominates at 2,000 rpm is not the one that dominates at 15,000.
0.393 %/°C
Copper resistivity rise
2.3 mm
Skin depth at 800 Hz
t²
How eddy loss scales with lamination
~150 µΩ·cm
Sintered NdFeB resistivity — it is a metal
8.1 — The three per cent moves around
Why this matters
Copper loss dominates at low speed, where torque and therefore current are highest. Iron and AC-copper loss dominate at high speed, where frequency is highest. The efficiency island sits in between — which is precisely why gear ratio selection is an efficiency decision, not just a top-speed one.
8.2 — Copper loss, and the runaway hiding in it
P = I²R, straightforwardly. But copper’s resistivity rises 0.393 per cent per °C, so a winding at 150 °C has about 51 per cent more resistance than at 20 °C. More loss makes it hotter, and hotter makes more loss.
The loop is stable in a well-cooled motor and is exactly what fails in a poorly cooled one.
8.3 — AC copper loss — skin and proximity effect
δ = √( ρ / (π · f · μ) )
δ = skin depth · ρ = resistivity · f = frequency · μ = permeability. For copper this reduces to δ ≈ 66/√f millimetres.
- •50 Hz → 9.3 mm
- •400 Hz → 3.3 mm
- •800 Hz → 2.3 mm — an EV motor with 4 pole pairs at 12,000 rpm
- •1.6 kHz → 1.6 mm
Skin depth at 800 Hz is the same order as a hairpin conductor’s dimension. Current crowds to the surface, and the proximity effect from neighbouring conductors’ fields makes it worse, concentrating current in the slot-opening end of the bar.
In plain English
The mitigations are all geometric: shallower bars near the slot opening, more parallel conductors in series, transposition, and accepting a lower fill factor in the top layer. It is a real design tension — the hairpin’s fill-factor win and its AC-loss penalty come from the same property.
8.4 — Iron loss — two different frequency laws
- •Hysteresis loss is the energy consumed walking the B–H loop once per cycle: the loop’s area, times frequency. P_h ∝ f · Bⁿ with n around 1.6 to 2. Reduced by using a magnetically soft steel with a narrow loop.
- •Eddy current loss comes from currents induced in the steel itself by the changing flux. P_e ∝ f²B²t²/ρ, where t is the lamination thickness. Note the two exponents: frequency squared and thickness squared.
Adding about 3 per cent silicon raises resistivity from roughly 12 to 48 µΩ·cm — a four-fold cut in eddy loss for free — while also reducing magnetocrystalline anisotropy so the material magnetises more easily. Laminating into 0.35 mm sheets, or 0.20 to 0.25 mm for high-speed machines, attacks the t² term directly.
Important
Rotating machines use non-oriented steel, not grain-oriented. Transformer steel is grain-oriented, with superb properties along one direction and poor properties across it — which suits a transformer where flux only ever runs one way. In a motor the flux direction rotates continuously through every angle, so an isotropic material wins despite worse best-case numbers.
8.5 — Magnet eddy loss — the loss inside the loss
Sintered NdFeB is a metal, with a resistivity around 150 µΩ·cm. Harmonics in the airgap field — from slotting, from PWM switching, from winding MMF — induce eddy currents in the magnets themselves.
Technical framing
This matters far beyond its size in a loss budget, because the heat is generated inside the magnet — in the part of the machine with the lowest temperature limit and the worst thermal path to coolant.
The standard fix is segmentation: cutting each magnet into several axially or circumferentially insulated pieces to break up the current loops, at the cost of more parts and more assembly. Ferrite, being an insulating oxide, has no such loss at all — one of its few genuine technical advantages.
8.5.1 — Windage and bearings
Both scale steeply with speed — windage roughly as ω³ — and are negligible below a few thousand rpm. At 18,000 rpm in an oil-cooled machine they stop being negligible, and oil churning in the airgap becomes a real design constraint on how much cooling you can actually apply.
8.6 — The efficiency island
Important
The peak efficiency number in a brochure is one point on this surface, and it is rarely where the vehicle spends its time. Urban driving clusters at low speed and low torque — the bottom-left, where efficiency is worst — which is why cycle-weighted efficiency, not peak efficiency, is the number that predicts range.
Quick check: test yourself
1.Why is gear ratio an efficiency decision rather than only a top-speed one?
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2.A supplier proposes 0.20 mm laminations instead of 0.35 mm. What do you get and what do you pay?
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3.Magnet eddy loss is small in a loss budget. Why does it get engineered against so hard?
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Chapter summary
- ✓Efficiency is not one number. Copper loss dominates at low speed, iron and AC-copper loss at high speed, and the island between them is what gear ratio selection targets.
- ✓Copper resistivity rises 0.393 %/°C, so a hot winding has about 51 per cent more resistance at 150 °C — a feedback loop that is stable only if cooling is adequate.
- ✓Skin depth in copper is roughly 66/√f mm, giving 2.3 mm at the 800 Hz an EV motor runs at — the same order as a hairpin bar, so AC resistance climbs during highway cruising.
- ✓Eddy loss scales as f²B²t², which is why silicon content and lamination thickness are the two levers, and why motors use non-oriented rather than grain-oriented steel.
- ✓Magnet eddy loss matters out of proportion to its size because the heat appears inside the component with the lowest temperature limit.
Frequently asked questions
Why does lamination thickness matter so much?+
Because eddy current loss goes as P ∝ f²B²t²/ρ — frequency squared and thickness squared. Halving lamination thickness quarters eddy loss. The costs are stamping, a lower stacking factor since each sheet carries its own insulation coating, and a stack that is harder to handle. 0.35 mm is the industrial default; 0.20 mm is what high-speed traction pays for. Adding about 3 per cent silicon attacks the same term from the other side, raising resistivity from roughly 12 to 48 μΩ·cm.
What is skin depth and why does it matter at 800 Hz?+
Skin depth δ = √(ρ/(π·f·μ)), which for copper is about 66/√f millimetres — 9.3 mm at 50 Hz, 3.3 mm at 400 Hz, 2.3 mm at 800 Hz. An EV motor with 4 pole pairs at 12,000 rpm runs at 800 Hz electrical, so skin depth is the same order as a hairpin conductor’s dimension. Current crowds to the surface and the proximity effect from neighbouring conductors makes it worse, concentrating current at the slot-opening end of the bar.
Why do rotating machines use non-oriented steel rather than transformer steel?+
Because grain-oriented steel has superb properties along one direction and poor properties across it, which suits a transformer where flux only ever runs one way. In a motor the flux direction rotates continuously through every angle, so an isotropic material wins despite worse best-case numbers.
Why does magnet eddy loss matter more than its size suggests?+
Because the heat is generated inside the magnet — in the part of the machine with the lowest temperature limit and the worst thermal path to coolant. Sintered NdFeB is a metal with resistivity around 150 μΩ·cm, so harmonics in the airgap field from slotting, PWM switching and winding MMF induce currents in the magnets themselves. The standard fix is segmentation: cutting each magnet into several insulated pieces to break up the current loops, at the cost of more parts and more assembly. Ferrite, being an insulating oxide, has no such loss at all.
Why is peak efficiency a misleading number?+
Because it is one point on a surface, and rarely where the vehicle spends its time. Urban driving clusters at low speed and low torque — the bottom-left of the efficiency map, where efficiency is worst. Cycle-weighted efficiency, not peak efficiency, is the number that predicts range.
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Magnets and Motors is an original educational series on permanent magnets and electric machines. Datasheet ranges, temperature coefficients and efficiency figures are representative standard-condition literature values, not measurements of a specific product, and sources differ on several. Always verify against the specific magnet and lamination datasheets in use before making design, procurement or certification decisions.