In the context of cogging and crawling of induction motor, the (6k +_ 1) components of rotating mmf wave rotates with 1/(6k+_1) of synch speed, how? What intrigues me is, since the speed is proportional to frequency, how could the high frequency components of the rotating mmf wave rotate with lesser speed than that of synchronous speed of the fundamental?
Good question. I'm not an expert on induction motors, but from looking at the topic on-line there are numerous references to "cogging" and "crawling", which are quite separate phenomena.
- "Cogging" results from the alignment of the stator & rotor slots (or poles) which could lead to a complete failure to start (torque due to magnetic alignment > rotating field induced current torque). Simply solved for an N slot stator by using N+1 slots in the rotor, and/or skewing the rotor slots by one pitch along the length of the rotor)
- In "crawling", the motor starts, but at some integer fraction of nominal synchronous speed, the motor (under some load) stops accelerating and remains "stuck" at the lower speed. The harmonic most often quoted is 7, and I suspect the mechanism is limited to 3-phase machines, as the (rather vague) explanations dismiss third harmonics on the basis that they balance out in a 3-phase system.
I think the explanation might run along the following lines:
Let's assume that the fundamental current is absent: what behaviour would we expect? Clearly, given sufficient current, the motor should run up 7x nominal speed, i.e.7S, not S/7, (where S = synchronous speed). So, the mechanism is more subtle than this...... the three phases generate a rotating field, and at the fundamental the physical poles are driven with voltage vectors spaced 120 degrees apart. Consider the phase of the odd harmonics from 3 to 9 (subtract whole integers of 360):
1 3 5 7 9
1Ø 120 0 240 120 0
2Ø 240 0 120 240 0
3Ø 0 0 0 0 0
Third and 9th appear to be "stationary", 5th is travelling "backwards" and 7th "forwards" relative to the fundamental.
That's as close as I can get to an explanation!
here we are basically talking about space harmonics and not time harmonics. hence line frequency or time variation of mmf has same frequency for both 5th and fundamental space harmonics. But for 5th order harmonics we can assume a presence of imaginary poles which are 5 times those present in case of fundamental harmonics. by relation N=120f/P => N*P=constant.Therefore 5 times the number of poles would lead to 5 times decrease in speed.
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