Electronic – Calculate Back EMF from Torque Constant

Conceptually, you have to think about this slightly differently. The way I think you are thinking about this is kind of like torque in a vehicle. A car with more torque is going to accelerate more quickly and is associated with an increase in speed. In other words, you press on the gas pedal to increase the speed and you need torque to do that.

However, when you are talking about the relationship between speed and torque of a DC motor, then you have to think about it differently. For a given motor with a constant input voltage, the speed of the motor is going to be determined by the load on the motor shaft. For a given load, the only way to increase the speed is to increase the voltage. And this increase in speed will require some more torque to accelerate but after it reaches its new speed, the torque will back off to its original torque (unless, of course, the load is dependent on speed - like in a fan).

So maybe a better way for you to think about it is instead of saying "Torque and speed in a DC motor are said to be inversely proportional" you say "For a given voltage, torque and speed in a DC motor are said to be inversely proportional." A speed-torque curve that you see on data sheets is only valid for the rated voltage and the motor will operate on that curve. So if torque goes up, the speed will follow that curve and go down.

You consult with the manufacturer. They may have information on short term overload performance, or performance at <100% duty cycles.

If they don't, or if they won't stand by their motor under specified overload conditions, then you can't rely on the motor.

However in non safety critical applications such as hobbyist or experimental conditions, you can estimate a range of conditions under which it'll probably work.

Loosely, you can use it for short enough bursts that it won't exceed its rated temperature - 1.1Nm at a 50% duty cycle gives the same mean torque load as 0.55Nm continuous operation, and therefore, for short enough bursts, should be safe - leaving the question, what does "short enough" mean?

That's where the thermal time constants come in. They have the same meaning as the time constant (= RC) in an RC network, allowing you to calculate the rate at which the voltage (or temperature here) rises to its final value.

One simple way of using this is to calculate the half-life or time taken to reach half the final value, which is 0.693* the time constant, or 32 seconds for the (46s) winding time constant. After 32 seconds at twice the rated power, it will reach half the final temperature, which should be within the temperature rating.

Of course it needs to cool before repeating the operation, or subsequent 32 second bursts may exceed the rated temperature.

Modeling that properly would require simulation, including heat transfer to the case (whose temperature rises more slowly, with a much longer time constant) and cooling terms according to airflow past the windings (if it's not a sealed motor) or over the case if it is. You can use R-C networks and an electrical simulator like the built-in one to approximate the thermal model.

Or experiment on a motor.

But (without having done the simulation), if your application allows running the motor less than 50% of the time, in bursts less than about 15 seconds with cooling periods of 30 seconds, I think it'll probably work.