Motor Thermal Estimator
Estimate BLDC motor temperature rise and safe operating time.
Parameters
Steady State
-- °C
Time to Limit
-- s
Initial Power
-- W
Note: Results shown in SI units internally. Temperature rise calculations performed in Kelvin.
Chart appears after calculation.
Lumped Parameter Model
The motor is treated as a single thermal node with averaged heat capacity.
$$ C_{th} \frac{dT}{dt} = P_{in} - \frac{T - T_{amb}}{R_{th}} $$
- Heat In: Joule heating ($I^2R$). Resistance rises with temperature.
- Heat Out: Convection to air. Depends on surface area and airflow.
- Thermal Mass: Sum of (mass × specific heat) for copper, iron, aluminum.
Steady State
At equilibrium, heat in equals heat out. Including resistance temperature coefficient:
$$ \Delta T_{ss} = \frac{I^2 R_0}{\frac{1}{R_{th}} - I^2 R_0 \alpha} $$
If the denominator goes negative, thermal runaway occurs.