What does motor thermal management calculate?

Motor losses (winding copper loss, core iron loss, magnet eddy loss etc.) are computed by electromagnetic analysis and used as heat sources for thermal analysis of windings, core and magnets. Insulation and magnet demagnetisation impose temperature limits, setting continuous output and how long short-term overloads can last. It also guides coolant-channel design.

Why couple electromagnetics and heat?

Copper's resistance rises about 0.4% per kelvin. Higher temperature raises resistance and copper loss, raising temperature further. At 200 A, a fixed 20 °C resistance gives 125 °C, but including the rise gives 157 °C — 32 K higher — with loss increasing to 3.7 kW. Skipping coupling badly underestimates temperature.

How much current can flow briefly?

Winding heat capacity slows the temperature rise, allowing more than the continuous current for a while. Here, with 1,925 J/K heat capacity and a 48 s time constant, stepping from 150 A continuous to 400 A reaches the 180 °C insulation limit in 12 s. Peak output for acceleration or hill climbing is limited by such times.

Motor Thermal Management

Category: Coupled Analysis – Electromagnetic-Thermal | Revised 2026-10-01

Theory: losses and temperature feed each other

Overview

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What sets a motor's continuous output?

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Usually winding temperature. Winding insulation has a temperature limit (180 °C for class H, for example), beyond which life shortens sharply. Most winding heat is copper loss, proportional to current squared and resistance. But copper's resistance rises with temperature, so the hotter it gets the more it heats, heating further. Without this effect, temperature is badly underestimated at high currents. Briefly, winding heat capacity slows the rise, allowing currents above the continuous rating; how long is also found by coupling current and temperature.

Steady winding temperature

$$ T = T_c + R_{th}\,3I^2 R_{20}\left[1 + \alpha(T - 20)\right]\ \Rightarrow\ T = \frac{T_c + k(1 - 20\alpha)}{1 - k\alpha},\quad k = 3 R_{th} I^2 R_{20} $$

R₂₀ is phase resistance at 20 °C (20 mΩ), α copper's temperature coefficient (0.00393 /K), R_th winding-to-coolant thermal resistance (0.025 K/W), T_c coolant temperature (65 °C) and I rms phase current. Where the denominator reaches zero, no equilibrium temperature exists.

Short-term overload

$$ C\frac{dT}{dt} = 3I^2R_{20}\left[1 + \alpha(T - 20)\right] - \frac{T - T_c}{R_{th}},\qquad \tau = R_{th} C $$

C is winding heat capacity (5 kg copper × 385 J/kgK = 1,925 J/K); the time constant is 48 s.

Coffee Break Trivia

Insulation classes and life

Winding insulation for motors and transformers is classed by withstand temperature (class A 105 °C, B 130 °C, F 155 °C, H 180 °C and so on). Insulation life shortens sharply with temperature; a long-used rule of thumb halves it for every 10 °C rise. EV motors must deliver high power from small packages, so they often run close to insulation limits, and the accuracy of cooling and temperature prediction drives performance.

Worked examples

Example 1: current and steady winding temperature

Phase current (rms)	Coupled temperature	Constant-R estimate	Copper loss
100 A	83.8 ℃	80.0 ℃	750 W
150 A	110.8 ℃	98.8 ℃	1,832 W
200 A	157.4 ℃	125.0 ℃	3,696 W
250 A	239.7 ℃	158.8 ℃	6,988 W

Continuous current within the class H 180 °C limit is 217 A; above 412 A no equilibrium temperature exists (thermal runaway).

Example 2: short-term overload

Condition	Value
Steady at 150 A	110.8 ℃
Time to 180 °C after stepping to 400 A	12.0 s
Winding time constant	48 s

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At 250 A it's 80 K above the constant-resistance estimate.

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The larger the current, the stronger the effect of temperature raising resistance, which raises losses further. At 250 A resistance is about 1.86 times its 20 °C value, and loss grows by the same factor. A constant-resistance estimate of 159 °C looks within limits, but the real 240 °C would destroy the insulation. Motor analysis therefore feeds winding resistance as a function of temperature into the electromagnetic calculation and iterates with the thermal one to equilibrium. Within the winding, the deepest slot regions and end turns, where heat escapes poorly, are hottest, so evaluate maximum rather than average temperature. Rising magnet temperature risks demagnetisation, so rotor temperature is checked too.

Analysis workflow

Compute copper, iron and magnet losses per operating point with electromagnetic analysis.
Build a thermal network or 3D thermal model of windings, core, magnets and cooling.
Make resistance and magnet properties temperature-dependent and iterate electromagnetics and heat.
Compute temperature histories over drive cycles (acceleration, cruise, climbing).
Calibrate thermal resistances against winding thermocouples and rotor temperature measurements.

Coffee Break Trivia

“There was margin in the test”

In one motor design, a constant-resistance thermal analysis gave 140 °C windings at continuous rating, 40 K below the limit. Yet prototype tests reached 175 °C at the winding's hottest point under the same conditions. Coupling temperature-dependent resistance raised the average about 20 K, and slot bottoms and end turns ran about 15 K above average. Revising coolant channels and improving end-turn cooling cut the peak at continuous rating to 155 °C.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Constant resistance	Temperature underestimated	Couple with temperature
Evaluating average temperature	Local hot spots missed	Use maximum temperature
Steady-state only	Peak output underrated	Compute transients
Ignoring magnet temperature	Demagnetisation	Analyse the rotor
Omitting harmonic losses	Losses underestimated	Use inverter waveforms

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