I would welcome this discussion in classroom
Let me say this most people miss the details
When you as a 1790 rpm motor you tell me a lot with just that much information
1790 means it was manufactures for use in the US. It’s a 4 pole motor rated to run on 60HZ system and as you say it has a rated slip of 10 rpms. And if it is truly running at 1790 it producing it’s rated output torque. It also tells me that on 50hz system it would be running at approximately 1490 rpm’s
But it would still have the same volts to hertz ratio 8 volts per hertz 60hz / 480V 50hz / 400V
You can take it down to 10hz or up to 120hz or even higher it you want
Having said that you still did not answer the original question
How do you calculate the output torque at zero speed / RPM
In your reply you used 10 rpm’s to calculate the torque while there is no question that a squirrel cage motor will develop 100% torque at as slow as 1 rpm but all of the formulas require an rpm number to calculate the torque and number 0 just does not work.
And to add another question, what is output torque of a 4 pole 60hz squirrel cage motor running at exactly 1800 RPM ( Remember exactly 1800 rpm not 1790) assuming the power input frequency is 60hz
I had hoped to side-step the 0 rpm debate. I guess it didn't work
For a motor, the torque (according to my limited understanding) has to do with the induced current in the rotor, current-carrying conductors crossing magnetic lines of flux, etc.
So I guess I'll re-phrase my answer. The torque at 0 rpm is dependant on the current into the motor, and the slip that the motor is rated for.
No math here - my reasoning is that the math is worked out for a motor at rated rpm, slip, poles, driven at 60 Hz or 50 Hz.
Since the motor torque is known at rated speed, with rated current, and 50 or 60 Hz input ... that is what it generates at 0 hz. The rotor current, flux, et al is not the same, but it should be close enough if you are not using good test instruments
If the VFD drives the motor at rated current, rated slip, you will get about rated torque
As for torque over the rated speed, I need more information. Does the VFD have more voltage to apply?
For a 208V VFD driving a 208V motor - the torque goes down. Back-of-the-napkin numbers would be rated torque * 1790/1800
For a 575V VFD driving a 208V VFD rated motor with the properly rated motor insulation, torque should be constant up to (575/208*1800)-10 rpm. Rated current will give you rated output torque at rated slip.
If the motor is not 'pushing' rated load, it has less slip, will turn slightly faster, and generate less torque. If it is trying to 'push' over rated load, it will have more slip ... if it is supplied proportionally more current then it will drive the load. Up to breakdown torque. If the VFD is limiting motor current below what the motor needs to generate the required torque, the motor will stall.
IMHO