Temperature Rise⚠ unverified
Electrical / Motors · Compute the steady-state temperature rise of a motor
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| P_loss | Ploss | W | 1.0 | Dissipated power loss |
| Rth | Rth | K/W | 1.0 | Thermal resistance |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | ΔT | K | Steady-state temperature rise above ambient, in kelvin (K) |
The science & history
Understanding the Parameters
- $P_{loss}$ — the copper, iron, and mechanical losses that become heat (see Motor Efficiency).
-
$R_{th}$ — how many kelvin the temperature rises per watt of heat; set by the housing, cooling (natural, fan, liquid), and mounting.
-
$\Delta T$ — the equilibrium rise; the absolute winding temperature is $T_{ambient} + \Delta T$.
Derivation (Approaching a Proof)
In the thermal–electrical analogy, heat flow $P$ plays the role of current and temperature difference $\Delta T$ the role of voltage, with a thermal resistance $R_{th}$ (K/W) linking them. At steady state all the dissipated power flows out through that resistance, so by the thermal Ohm's law
$$\Delta T = P_{loss}\,R_{th}.$$
This is the equilibrium of the first‑order thermal system whose transient is governed by the Motor Thermal Time Constant $\tau = R_{th}C_{th}$: the temperature climbs exponentially toward $\Delta T$ and reaches $63\%$ of it after one time constant.
History
Lumped thermal‑resistance modelling of electrical machines matured alongside insulation standards (the NEMA/IEC temperature classes A, B, F, H), which cap allowable rise to protect winding insulation and set a motor's continuous rating.
Related Concepts: Motor Thermal Time Constant, Motor Efficiency, RC Time Constant
Notes: Registry calculator temperature-rise (unverified). Single‑node lumped model; real motors
have several thermal nodes (winding, iron, frame) with different resistances and capacitances.