# What determines the continous ratings of electric motors?

I've seen variations of this torque-speed curve for brushless DC motor performance, and I'm curious what criteria determine the rated torque and speed of permanent magnet DC motors in general.

Does thermal dissipation of joule heating limit the max continuous torque? Do mechanical limitations (max bearing speed due to friction, mechanical stress, etc.) limit the max continuous speed? Are there any "rules of thumb" for predicting the max continuous torque and speed of electric motors?

Does thermal dissipation of joule heating limit the max continuous torque?

Yes. Auxiliary cooling or enhanced self cooling can extend the max continuous torque, but that is generally only economically practical with large motors. Th

Do mechanical limitations (max bearing speed due to friction, mechanical stress, etc.) limit the max continuous speed?

Yes. Bearing friction is usually the limiting factor, but better bearings can extend the maximum speed to the point that mechanical stress can become a factor. Aerodynamic drag (windage) can also become a factor. The size of any sell cooling fan or rotor fins could get to be a major consideration.

There is also a minimum continuous speed / torque limitation imposed by the self cooling limits.

Are there any "rules of thumb" for predicting the max continuous torque and speed of electric motors?

I have seen some "rule of thumb" on this site that I believe was stated for very small DC motors. I believe it was stated as a percentage of the maximum calculated joule heating.

• I imagine you need detailed information (perhaps a numerical methods simulation?) of the motor to try predicting it's thermal limit for max torque, correct? Same goes for mech limits of bearings, yes? – techSultan Jan 29 '18 at 17:26
• Yes. Detailed information is required, but good motor specifications should provide the limits. As a minimum, maximum continuous torque or power at rated speed should be specified by the manufacturer. Manufacturers that sell lots of motors may verify the specifications by testing. Prior to computers, the ratings were predicted by hand calculations, but it was very tedious. – Charles Cowie Jan 29 '18 at 17:57
• What were some of the calculations used? Are there any IEEE or NEMA standards that explain these rating prediction calculations? – techSultan Feb 2 '18 at 16:55
• I have a 1940 book that presents design procedures for brushed, wound-field DC machines, wound-field synchronous machines, and wound-rotor induction motors. It provides a lot of equations, some graphical techniques and some empirical data. The initial presentation for DC machines required 125 pages including presentations of equations and procedures for individual aspects of the design. The results of a sample design presented for a 15 Hp DC motor includes numerical values for about 100 design details. The presentation of the sample design required 122 pages. – Charles Cowie Feb 2 '18 at 22:41

In the continuous torque zone, the torque is limited because the current is limited. And the current is limited because it gives rise to power dissipation in the wingdings. This is due to winding resistance. The power dissipation is I^2 * R. In many types of motors, including induction and BLDC motors, torque and current are proportional.

Before I go on, I need to explain something. For the most part, induction motors try to rotate at a speed proportional to the supplied AC frequency (minus a little bit of slippage). BLDC motors are synchronous to commutation frequency. For both, along the constant torque line, from low speed to rated speed, the built-in assumption in the graph you have shown is that the voltage and frequency are ramped up together. Said another way, on the constant torque line, V/f is held constant.

It is further assumed that from the rated speed to the maximum speed, the voltage is held constant at the rated voltage, while the frequency is ramped upward to increase motor speed. Since the motor is an inductive load, the increasing frequency at fixed voltage results in decreased current, and thus decreased torque.

Hopefully that explains everything.