# Torque

Torque is the force applied to a lever, multiplied by its distance from the lever's fulcrum but it is often thought of as "rotational force." It is the basic measure of a motor, but most motors produce different amounts of torque depending on thier current rotational speed. The maximum force a motor can resist, keeping its shaft still against that force, is called the holding torque. Torque can also be defined as the the power output of an engine divided by its current rotational speed. The varying torque output over a range of speeds can be measured with a dynamometer, and shown as a torque curve. Internal-combustion engines produce useful torque only over a limited range of rotational speeds. Electric motors produce torque over a much broader range of speeds but most produce less torque at very low or very high speeds.

Stepper motors produce maximum torque when the shaft is not moving and the stators are aligned with the coils (holding torque) and torque decreases with increasing speed. The dynamic, "detent" or "pull out" torque required to continue moving from one step to the next, is normally much less than holding torque for stepper motors. See "measuring stepper torque" In a stepper motor, torque is directly proportional to Ampere-turns or current times the turns of wire through which it passes. Voltage influcences how quickly the current builds, and how far it builds, but it is the resulting current, and not the voltage that builds the inductive field in the stepper motor which holds position.

When purchasing motors for which the pull out torque is not known, it can be estimated at less than half, and often less than 1/10th the holding torque.

Sean Brehney says:

Motors convert electric power to mechanical power, similar to the way a gearbox converts mechanical power at one speed to mechanical power at another speed. A single number, the gear ratio, captures the way this transformation happens in a gearbox, except for frictional loss. It is similar with electric motors. You can compute the torque-amp constant (Kt) from the speed-voltage constant (Kv) and vice versa. There are several sets of units which these numbers can be expressed in. The most convenient set for conversion from Kt to Kv and back is to have Kv in volts per radian per second and Kt in Newton-meters per amp. Note that Pin=V*I with Pin in watts, V in volts, and I in amps, and Pout=omega * tau with omega being speed in radians per second, tau being torque in Newton-meters, and Pout still in watts. If we equate Pin=Pout, then some re-arranging gives us V/omega = tau/I or Kv=Kt

The above calculation is for a two-terminal device (where there is only one current and one voltage). A three-wire motor like BLDC can have several different Kv,Kt relationships depending on how you drive it. For the simplest kind of drive where you are only powering two of the three wires at any given time, the Kv,Kt relationships are pretty much the same as above (the brushed, two-terminal case) - there is actually a correction factor of about 0.95, but 5% error is in the noise for most purposes.

{For an example motor with} Kv=170 RPM/Volt. 1 RPM is 2*pi radians per minute or 0.105 radians/second. So this is 17.85 radians per second per volt. Above, I defined Kv in volts per radian per second, which is the reciprocal of this, so the value we want is 1/17.85 = 0.056 V/radians/sec which also implies 0.056 Newton-meters per amp.

{If that motor has a} max rated current of 65 amps, this would be 3.64 Newton-meters or 32 inch pounds. This motor could probably not really handle 65 amps for more than a few seconds without overheating (unless you had forced airflow), but during those few seconds, I don't think you would be able to hold the shaft still (shaft is 0.157 inch radius, so 204 pounds of friction would be needed to hold it stalled)

Torque is expressed as distance times Force. The SI standard unit is Newton - Meters (Nm) but more common units are grams per centemeter (g-cm) or ounce inches (oz-in)

 Convert oz-in in-lb ft-lb N-m N-cm dy-cm Kg-m Kg-cm g-cm to oz-in in-lb ft-lb N-m N-cm dy-cm Kg-m Kg-cm g-cm

dy-cm g-cm N-cm kg-cm N-m oz-in lb-in lb-ft 1 980.7 100,000 980,700 10,000,000 70,620 1,130,000 13,560,000 0.00102 1 102 1,000 10,200 72.01 1,152 13,830 0.000,01 0.9807 1 9.807 100 0.7062 11.3 135.6 0.000,001,02 0.001 0.102 1 10.20 0.072,01 1.152 13.83 0.000,000,1 0.000,098,07 0.01 0.098,07 1 0.007,062 0.113 1.356 0.000,014,16 0.013,89 1.416 13.89 141.6 1 16 192 0.000,000,885 0.000,868,10 0.0885 0.8679 8.85 0.0625 1 12 0.000,000,073,75 0.000,0723,4 0.007,375 0.072,34 0.7375 0.005,208 0.083,33 1

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