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Motor

Motor Heat Dissipation

Calculate motor heat dissipation, temperature rise, and operating temperature from input power and efficiency.

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Formula

P_loss = P_in × (1−η), ΔT = P_loss × Rθ

Rθ— Winding-to-ambient thermal resistance (°C/W)
ΔT— Temperature rise above ambient (°C)

How It Works

Motor heat dissipation is the thermal power that must be removed to prevent winding insulation breakdown. Total losses equal input power minus mechanical output power: P_loss = P_in − P_out = P_in × (1 − η). The dominant loss component is copper loss (P_Cu = I² × R_winding), which rises with the square of current and therefore the square of load torque. The motor's thermal resistance (R_θ, in °C/W) determines steady-state temperature rise: ΔT = P_loss × R_θ. Insulation class limits the maximum winding temperature (Class B: 130 °C, Class F: 155 °C, Class H: 180 °C).

Worked Example

A 24 V, 100 W brushed DC motor operates at 80% efficiency under continuous load. Thermal resistance (winding to ambient) is 1.8 °C/W. Ambient temperature is 35 °C. Class F insulation. Step 1 — Input power: P_in = P_out / η = 100 / 0.80 = 125 W Step 2 — Heat dissipated: P_loss = P_in − P_out = 125 − 100 = 25 W Step 3 — Steady-state winding temperature rise: ΔT = P_loss × R_θ = 25 × 1.8 = 45 °C Step 4 — Absolute winding temperature: T_winding = T_ambient + ΔT = 35 + 45 = 80 °C Step 5 — Margin to Class F limit: Margin = 155 − 80 = 75 °C — adequate for continuous operation Result: At 80% efficiency and 35 °C ambient, the motor runs 80 °C in the winding — well within Class F limits. If efficiency dropped to 70%, P_loss = 42.9 W and T_winding = 35 + 77 = 112 °C — still within limits but with only 43 °C margin.

Practical Tips

  • ✓Use a thermal camera or embedded thermistor to measure steady-state temperature in the actual mounting configuration — datasheet R_θ values assume free-air convection
  • ✓For servo and positioning applications with frequent starts and stops, model the thermal time constant (τ = R_θ × C_thermal) to ensure the motor cools between bursts
  • ✓Derate maximum continuous current by 3–5% per degree Celsius of ambient temperature above 25 °C when operating in high-temperature environments

Common Mistakes

  • ✗Assuming the motor body temperature equals the winding temperature — winding hot-spot can be 30–60 °C higher than the measured case temperature
  • ✗Running a motor at stall (zero speed) for more than a few seconds — without shaft rotation, cooling airflow stops and thermal resistance rises sharply, causing rapid heat build-up
  • ✗Ignoring duty cycle — a motor may tolerate 150% of rated current for 10 s intermittently even though it would overheat at that level continuously

Frequently Asked Questions

Some motor datasheets list R_θ (winding-to-ambient or winding-to-case). If not available, measure it experimentally: run the motor at a known power dissipation until thermal equilibrium, then measure winding temperature (via resistance change or embedded thermistor) and divide ΔT by P_loss.
Select an insulation class with at least 20–30 °C margin above your worst-case calculated winding temperature. Class F (155 °C) is standard for industrial motors. Class H (180 °C) is used in high-ambient or high-duty-cycle applications. Higher-class insulation typically costs more and may affect motor size.
Yes — high PWM frequency reduces current ripple and I²R copper losses. However, eddy current and hysteresis losses in the stator laminations increase with frequency. For brushed DC motors, frequencies above 20 kHz are generally optimal. For BLDC motors, the optimal switching frequency depends on the specific lamination material and thickness.

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