Motor Thermal Duty-Cycle Design: RMS Current, Copper Loss, Efficiency, and Validation

Start With the Complete Duty Cycle

Acceleration, constant-speed work, braking, dwell, and repeated starts impose different current and speed conditions. Record each interval long enough to capture electrical peaks and over enough cycles to represent the motor thermal time scale.

Hot Winding Resistance and Copper Loss

Copper resistance rises with winding temperature. That change increases I²R loss at a commanded current, but it can reduce current in a voltage-limited motor. The electrical and thermal calculations therefore interact and may require iteration.

Check individual points with the Motor Copper Loss Calculator, and use the DC Motor Stall Current Calculator separately for resistance-limited fault and startup boundaries.

Build a Loss Budget, Not a Single-Loss Model

Efficiency Is an Operating-Point Map

Motor efficiency is low near no load because fixed losses dominate, rises around a useful mid-load region, and falls as copper and thermal losses grow. Controller efficiency and mechanical transmission efficiency are separate unless the measurement boundary explicitly includes them.

The Motor Efficiency Calculator compares consistent power boundaries, while the Motor Torque, Power & Speed Calculator converts measured torque and speed into shaft power.

Thermal Networks and Intermittent Duty

A lumped thermal RC model is useful when its parameters are identified for the actual motor, mounting, airflow, and sensor location. Multiple nodes are often needed because the winding, stator, housing, and ambient do not share one temperature.

Worked Duty-Cycle Check

A repeating 10 s cycle carries 6 A for 2 s, 2 A for 6 s, and 0 A for 2 s. The RMS current is √[(6²×2 + 2²×6)/10] = 3.10 A, not the 2.4 A arithmetic average. With a 0.50 Ω hot winding, average copper loss is about 4.8 W. If shaft output during the loaded intervals averages 20 W over the complete cycle and all motor input averages 27 W, cycle efficiency is 74.1%; do not claim that the unaccounted 2.2 W beyond copper loss is zero or assign it to one mechanism without measurement.

Derating and Design Decisions

• Derate for maximum ambient, restricted airflow, enclosure heating, altitude where relevant, and mounting variation.
• Include repeated acceleration and reversing rather than only steady running.
• Check magnet temperature, insulation class, bearing grease, brushes, connectors, driver, and nearby PCB limits.
• Account for torque margin as winding resistance rises and bus voltage falls.
• Use current limiting and supervisory protection that match both semiconductor and motor thermal time scales.
• Keep measurement uncertainty and production spread in the final margin.

Verification Workflow

1. Define the measurement boundary and complete mechanical duty cycle.
2. Capture synchronized current, voltage, speed, torque, and ambient conditions.
3. Calculate segment RMS current and copper energy from unrounded data.
4. Measure hot winding resistance quickly or use embedded temperature sensing.
5. Map efficiency at representative torque-speed-temperature points.
6. Fit thermal parameters from heating and cooling tests rather than guessing them.
7. Repeat at maximum ambient, minimum supply, blocked ventilation, and production extremes.
8. Verify shutdown, cooldown, retry, and sensor-fault behavior.

Common Mistakes

• Using average current instead of RMS current for copper heating.
• Calculating loss with cold resistance only.
• Calling copper loss total motor loss.
• Applying one efficiency value to every torque-speed point.
• Combining motor and controller efficiency without stating the boundary.
• Ignoring acceleration, braking, and repeated starts.
• Treating case temperature as winding hot-spot temperature.
• Guessing thermal resistance from a different motor or mounting.
• Using rounded displayed values in an iterative loss model.
• Validating only at room temperature and continuous speed.

Scope Boundary

This guide provides duty-cycle, loss-budget, and validation methods. It does not provide universal motor thermal constants, safe winding temperatures, demagnetization limits, certified overload ratings, or a substitute for manufacturer data and instrumented testing. Nonlinear magnetic behavior, detailed CFD, and spatial winding hot spots require higher-fidelity models.