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What determines the maximum torque of a DC motor? How is this related to the equations

$$E=k\omega$$ $$T=kI$$

where

  • $E$ is electromagnetic force / voltage (V)
  • $\omega$ is rotational speed (rad/s)
  • $T$ is torque (Nm)
  • $I$ is current (A)
  • $\phi$ is flux (Wb)
  • $k$ is the motor constant (V/(rad/s)=Nm/A) such that $k=K\phi$
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Torque of a motor is directly proportional to current. Therefore, the maximum torque a motor can produce is limited by the maximum current it can handle.

The maximum steady state current a motor can handle is limited by the heat it can safely dissipate, which is proportional to the square of the current. This means you have to be careful with that spec. Just 41% more current causes twice the heating, and twice internal temperature rise above ambient, which is likely to cause damage.

It is possible to exceed the maximum allowed steady current for short periods of time. Some motors may actually come with such specifications. To really push a motor to its limits without damage requires tracking the assumed temperature. You usually model the temperature as slowly decaying to ambient with a time constant you usually have to guess at or measure. This could be multiple minutes. You can get some idea of this by knowing the maximum allowed steady state current and making a assumption about internal temperature above ambient.

This kind of system lets you do some short pulses of somewhat higher current, which you then pay for in a lower allowed maximum current for some time afterwards.

Generally you don't want to exceed the maximum allowed steady current by 2x, especially for a brushed motor where there are other limits on the current. Even for a brushless DC motor with good temperature modeling, I'd consider 3-4x a upper limit on short bursts of current intended for extra torque.

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