I propose we model this loss electrically as a resistor, as is commonly done in the texts I’ve seen on AC machines. Physically, it arises from many sources, but the copper wire resistance of the stator, and the resistance of the conductors in the rotor dominate. If we were to increase the current through the wire and rotor conductors (as we’d have to do to get more torque) the current through these conductors also has to increase proportionally. Sure, we get more torque and thus more mechanical power out of the motor, but, if we double the current, the loss increases by the square, (P=I^2 R in a resistive component) so 4 times the resistive loss. Our original 190W of loss becomes 760W. And if we triple the current, the resistive loss again increases by the square, so 9 times 190W = 1710W of loss.
Without a mod to the cooling system, being able to dissipate 9 times the power means roughly 9 times the rise over ambient (assuming here that radiative loss is not significant for a motor's cooling).
This is simply not the way a motor works my friend. :)
The efficiency of the motor includes the resistive loss, and the efficiency is roughly fixed assuming the saturation points aren't reached.
Lets use the 80% efficiency example.
At 1hp, it's 932w in and 746w (1hp) out, and 186w of motor heating.
At 3hp, it's 2796w in, and 2238w (3hp) out, and 558w of motor heating.
Lets say the motor efficiency tapers off to 75% when it's over driven. This would mean:
2984w in, 2238(3hp) out, and 746w of motor heating.
What does it take to handle and increase of 4x the heating on a motor?
Lots of easy options. 4x the airflow over the motor surface, 2x the airflow and 2x the delta-T, a motor mount that sinks to the large metal frame of the machine (as my lathe motor does), or lots of other options.
Now think about this. When they make the 3hp version of the motor in the same NEMA frame/package, if the efficiency is similar, and the winding resistance is setup to enable it to draw the current needed to make the power, is there any difference? ;)
I play with the motor speed all the time for an easy adjustment, I think it's likely the biggest advantage of a VFD. If I need to chug through some harsh rough cuts or whatever, the current of course naturally ramps up as the slip% increases, and keeps ramping till it hits the VFD's programmed phase current limits (giving roughly 3hp). I just do hobby work rather than production work, so my loading is different than factory machine running constantly of course. I make a cut, measure, changing tooling, check run-out, make another cut, measure, work the math to figure out how much to trim off next, etc. Lots of time where the motor is just sitting spinning the lathe unloaded, and with the field weakening, it pulls a little under an amp at 220v (measuring power into the VFD) just free running. It's definitely getting cooling time and a friendly duty cycle. Most lathe jobs I do are finished in maybe ~20mins if I had to take a wild guess, it's not like I time myself when I'm just tinkering in the garage. In a situation with my Lathe where I needed extended high torque, I would gear down and freq up the motor to 90hz or so, which would of course let the phase currents decrease and still maintain the same torque at the lathe.
Lots and lots of ways to skin a cat. :) Lots of motor options, drive options, and setup of motors and drives.
If you guys run your machines making cuts that put maximum motor loading on them long periods continuously, then by all means, get the toughest setup you can find, maybe over-size the motor.
I may have badly perceived the posters intent for the machines use, but it seemed to me like he was more of a hobbiest like myself looking to add some function and ease of use to a machine, and do it on a tight budget.
I offered a suggestion that has been working great for me. Didn't mean to stir up any trouble. :(