On Mon, 01 Oct 2012 22:59:35 -0500, Jon Elson
wrote:

Ned Simmons wrote:



I'll bet the generator outputs 415 Hz if the motor is running at
synchronous speed, which, assuming it's an induction motor, it never
does. In other words, the generator is nominally 415 Hz to account for
the motor's slip.

415 Hz / 400 Hz = 1800 RPM / 1715 RPM

Nope, doesn't quite work out. The alternator has to have an integral
number of poles. To get 415 Hz at 1800 RPM it would need 13.333
poles. 14 poles and 1778.6 RPM (29.64 RPS) gives 415 Hz.
1779 RPM is reasonable for a larger 3-phase induction motor.
If your line voltage were a bit low, the slip would be greater, and
the motor would spin slower, although not by much. To get down to
400 hz the motor would need to spin at 28.57 RPS or 1714 RPM.
I doubt you could get it to slip that much without burning up the
motor rotor.

Jon

Yes, I probably should have said 415Hz unloaded instead of at
synchronous speed.

You left a factor of 2 out of the formula that relates relates the
number of motor poles to synchronous speed.

rps = 2f / P

But setting that aside, if the number of generator poles is 7x the
number of motor poles, and assuming a 4 pole motor, the frequency will
be 420Hz @ synchronous speed, 415Hz @ 1779 RPM, and 400Hz @ 1715 RPM.

Double the RPMs for a 2 pole motor, in which case the synchronous
speed is 3600 RPM.

A normal 3 phase motor might turn 1779 RPM with a very light load;
1750 - 1760 loaded is more typical, and 1725 RPM motors are common.
The difference between 1715 and 1725 is less than 1%. Motors with much
higher slip are available, but not necessary here, at least on paper.

--
Ned Simmons