Why stall torque specifications are routinely misused
Why is the stall torque on a data sheet almost never a usable design number, and what should be used in its place?
Stall torque is the torque a motor produces at zero speed with rated voltage applied. At that condition there is no back-EMF, so current is limited only by the terminal resistance, and the shaft is not moving, so the mechanical output power is exactly zero. Every watt drawn from the supply is going into heat.
That makes stall torque a useful number for exactly two purposes: predicting the current a jam will draw, and bounding the torque a mechanism might see if it stops. It is used, instead, for sizing. "Stall torque is 42 mN·m and I need 8, so I have five times margin" is the most common sizing error in compact motion, and it is wrong in three separate ways.
Reason one: the motor cannot hold it
The limit on continuous torque is thermal, not magnetic. Current heats the winding as the square of current, and the winding has an insulation temperature limit. The torque a motor can produce forever is the torque whose current produces a steady-state temperature rise the insulation survives, in the actual ambient temperature, with the actual mounting and airflow.
For the illustrative machine used across these articles, the continuous limit is a small fraction of stall. That is not unusual. Continuous torque in the range of ten to twenty percent of stall is ordinary for small brushed motors, and it depends on mounting: a motor bolted to a metal chassis will hold more than the same motor in a plastic housing with still air around it.
Reason two: stall torque falls as the motor heats
The data sheet value is a cold value. Two effects reduce it as the machine warms, and they compound.
R(T) = R25 · [1 + 0.00393 · (T − 25)]
- R(T)
- winding resistance at temperature T, Ω
- R25
- winding resistance at 25 °C, Ω
- 0.00393
- temperature coefficient of resistance of copper, per K
The magnet contributes the second effect. Remanence falls with temperature at roughly 0.11 to 0.12 percent per kelvin for common neodymium grades and roughly twice that for ferrite, and the torque constant falls with it. A 100 K rise therefore costs a further ten percent or so on a neodymium machine. Taken together the hot stall torque can be near sixty percent of the value printed on the sheet, and the value on the sheet is the one people divide by to get their margin.
Reason three: something else is the fuse
In a gearmotor, motor stall torque multiplied by the reduction ratio usually exceeds the gearhead's torque rating by a wide margin. A motor that stalls at 42 mN·m behind a 100:1 reduction presents several newton meters at the output, and a small gearhead is not built for that. The first thing to fail in a jam is frequently a gear tooth, an output bearing or a press fit, not the motor.
- Check the gearhead momentary torque rating against motor stall torque times ratio, not against the application torque.
- Check the shaft and the coupling. A stalled motor applies its stall torque through the shaft into whatever the mechanism has hit.
- Check the drive. If the controller current limit is below stall current, the drive rather than the motor sets the real jam torque, and the calculation should use the limited current.
- Decide deliberately which element is intended to be the weak point, and state it in the specification.
What to use instead
The peak efficiency point is a genuinely useful design target, and it has a closed form. Maximizing output over input for the linear machine gives a current of the geometric mean of no-load and stall current, and an efficiency that depends only on their ratio.
Imax η = √(I0 · IS), ηmax = (1 − √(I0 / IS))²
- I0
- no-load current, A
- IS
- stall current, A
- ηmax
- peak efficiency of the ideal linear machine
| Figure | What it is | Valid use | Invalid use |
|---|---|---|---|
| Stall torque | Torque at zero speed, cold, at rated voltage | Predicting jam current and bounding mechanism loads | Sizing. Dividing it by a factor to get a working torque |
| Torque at peak power | Half of stall torque, by construction | Understanding where the machine stops gaining output | A continuous operating point. Efficiency there is about 50 percent |
| Torque at peak efficiency | The geometric mean current point, roughly a tenth of stall | Choosing a running point for a continuously operating mechanism | A peak or acceleration rating |
| Continuous torque | The torque whose current produces an acceptable steady temperature | Sizing, once ambient and mounting are stated | Quoting without stating the ambient temperature and mounting it assumes |
What to ask for, and what to measure
-
Ask for continuous torque with its conditions
Ambient temperature, mounting, and the insulation limit it is referenced to. Without those three, a continuous torque figure is not comparable between suppliers.
-
Measure current in the running mechanism
Current converts to torque through the torque constant, so one meter reading places the mechanism on the curve above and settles most sizing arguments.
-
Measure the temperature rise at the real duty cycle
A thermocouple on the housing plus a resistance measurement of the winding before and after a run gives the winding rise directly, since copper resistance is a thermometer.
-
Decide and test the jam case
If the mechanism can stall, either limit the current in the drive, or verify by test what fails first and how long it takes.
Winding resistance as a thermometer is worth using. Measure the cold resistance, run the duty cycle, stop and measure again quickly, and the ratio gives the average winding temperature through the coefficient above. It is the most accessible measurement of the quantity that actually limits the motor.
How the number is produced, and why sources disagree
There are two ways a stall torque figure reaches a data sheet. It can be measured, by locking the shaft against a torque transducer and applying rated voltage. It can also be computed, as the torque constant multiplied by stall current, where stall current itself is computed from voltage over terminal resistance. The two do not agree, and neither is wrong.
A measured value depends on how long the measurement window is. Current begins heating the winding immediately, resistance climbs, and the reading falls while it is being taken. Read at 100 milliseconds and read at 5 seconds are different numbers from the same motor. A computed value avoids that by describing a motor that is always at 25 °C, which no stalled motor is.
The practical consequences are worth stating. Comparing a measured stall torque from one supplier against a computed one from another is not a comparison of motors. And a published stall torque, however it was produced, is a room-temperature figure that the machine holds for a fraction of a second, which is the point of this article.