Effect of no of Poles of Rotor
Effect of no of Poles of Rotor
(OP)
Hi,
What is the effect of the no of poles of the rotor on the motor performance, if it's more,equal or less than the no of poles of stator?
Thanks
What is the effect of the no of poles of the rotor on the motor performance, if it's more,equal or less than the no of poles of stator?
Thanks






RE: Effect of no of Poles of Rotor
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(2B)+(2B)' ?
RE: Effect of no of Poles of Rotor
RE: Effect of no of Poles of Rotor
My comments applied to motors such as squirrel cage induction motors, wound rotor induction motors, synchronous motors used in power systems. I would exclude motors with multi-speed windings where the definition of pole gets a little tricky.
Let me offer a simple proof that under certain very-common ASSUMPTIONS and SIMPLIFICATIONS for analysing these types of motors (listed below), we cannot develop any torque if the number of poles on the stator is not equal to the number of poles on the rotor.
ASSUMPTIONS:
1 – The poles are equally spaced around the periphery of the stator.
2 – The torque is developed by the fundamental component of the flux. That fundamental component of the flux for a winding with P pole pairs is something like cos(P * theta + beta) where theta is the mechanical angle coordinate going from 0 to 2*Pi around circumference of the machine, poles is the number of poles of a given winding.
SIMPLIFICATIONS:
1 – The permeability of the iron is so much higher than air that we consider it infinite => flux can be determined from mmf and airgap dimension without regard for iron. Also implies total magnetic energy can be determined from airgap flux density without regard for iron flux density.
2 – Flux density is uniform in the radial direction at a given position in the airgap.
3 – assume 2-d geometry... neglect end fringing
SYMBOLS:
Ps = Number of pole pairs of stator (an integer)
Pr = Number of pole pairs of rotor (an integer)
Bs = [fundamental portion of] airgap flux density attributable to stator current
Bsmax = max value os Bs
Br = [fundamental portion of] airgap flux density attributable to rotor current
Brmax = max value of Br
Btot = Bs + Br = total airgap flux density
Theta = mechanical angle coordinate going from 0 to 2*Pi around circumference of the machine
Beta = angle between rotor field reference point and stator field reference point (reference point is where flux is maximum).
W = magnetic energy density (within the airgap)
Wtot = total energy (integrated over the entire airgap)
dV = differential volume element of airgap
R = airgap radius
L = machine length
Te = electromagnetic torque
With these assumptions, simplifications, definitions, we can express the flux contributions of the stator and rotor at a given instant in time as follows:
Bs = Bsmax * cos(Ps*theta)
Br = Brmax * cos(Pr*theta+beta)
Btot = Bs + Br
W = Btot^2 / mu0 = (1/mu0) * [ Bsmax * cos(Ps*theta) + Brmax * cos(Pr*theta+beta)] ^2
Expand the square
W = (1/mu0) * [ Bsmax^2 * cos^2(Ps*theta) + Brmax^2 * cos^2(Pr*theta+beta) + 2*Bsmax * Brmax * cos(Ps*theta)*cos(Pr*theta+beta)]
Wtot = int(W dV) = R* L * g * int (W dtheta, theta = 0.. 2*pi)
Wtot = R* L * g / mu0 * int [ Bsmax^2 * cos^2(Ps*theta) + Brmax^2 * cos^2(Pr*theta+beta) + 2*Bsmax * Brmax * cos(Ps*theta)*cos(Pr*theta+beta)], theta = 0..2*Pi
Break this up into three terms based on the three terms within square brackets:
Wtot = Wtot1 + Wtot2+Wtot3 where:
Wtot1 = R* L * g / mu0 * int [ Bsmax^2 * cos^2(Ps*theta) ], theta = 0..2*Pi
Wtot2 = R* L * g / mu0 * int [ Brmax^2 * cos^2(Pr*theta+beta)], theta = 0..2*Pi
Wtot3 = R* L * g / mu0 * int [2*Bsmax * Brmax * cos(Ps*theta)*cos(Pr*theta+beta)], theta = 0..2*Pi
Te = d/dbeta (Wtot) where current <=> flux density are treated as constant during the differentiation (only one state variable changes at a time and we choose to vary theta).
Develop three torques Te1, Te2, Te3 based on three components of energy
Te1 = d/dbeta (Wtot1) = 0 ! We know it is zero because beta does not appear in the expression.
Te2 = d/dbeta (Wtot2) = 0 ! This is a little harder to see. But we should note that the quantity being integrated is periodic and the integration interval is an integer number of periods. If we shift the function being integrated by a different amount beta, it will still be integrated over and integer number of periods and the result is therefore still the same (the integral of a periodic function over any continuous integer number of of periods doesn’t change if we start at a different place but continue the same integer-period integration interval). Since the integral doesn’t change with beta, the derivative with respect to beta is zero, Te2 = 0.
Te3 = d/dbeta (Wtot3) = d/dbeta (R* L * g / mu0 * int [2*Bsmax * Brmax * cos(Ps*theta)*cos(Pr*theta+beta)], theta = 0..2*Pi).
It may be intuitive that this integral Te3 is zero whenever Pr <> Ps. The reason is that we have an integral of product of two sinusoids over an interval which is an integer number of both their periods. Therefore we should recognize the integral is related to the average value of the products. It is analogous to the situation of power as product of periodic voltage and current. For simplicity assume we have sinusoidal voltage and distorted current (such as sinusoidal voltage supplying a saturating inductor). From this familiar situation we already know that the fundamental component of the current carries average (real) power, but the harmonics of the current carry zero real power because they are a different frequency than the voltage.
In case the intuition falls short, we can trudge further on the math path. I have developed a math proof Te3 = 0 (using the computer to do the differentiation, integration, and some of the algebra). It supports what our intuition already told us, Te3 is zero in all cases except when Ps = Pr. I'm having a hard time uploading in this new format of eng-tips (internet explorer is my browser). Any suggestions?
I’m not particularly familiar with switched reluctance motors and stepper motors. If what mnada says is true (I can’t really confirm or disprove it), then I would suspect the definition of pole (and associated definition of the fundamental flux density) is different than what I have used.
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(2B)+(2B)' ?
RE: Effect of no of Poles of Rotor
"I have developed a math proof Te3 = 0"
Should have been
"I have developed a math proof Te3 = 0 [b] in all cases except when Pr = Ps"[b/]
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(2B)+(2B)' ?
RE: Effect of no of Poles of Rotor
" (only one state variable changes at a time and we choose to vary theta)."
should've been:
" (only one state variable changes at a time and we choose to vary beta)."
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(2B)+(2B)' ?
RE: Effect of no of Poles of Rotor
Does anyone else have this problem?
Here is a link to the file that I intended to post:
https:
I created the link using dropbox. This is the first time I've tried to use dropbox to share a link and I'm not sure if it works.
Is the link above accessible to you guys?
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(2B)+(2B)' ?
RE: Effect of no of Poles of Rotor
Sorry if all this is irrelevant to the types of motor you're interested in.
I'd still be interested in answers to my questions about attachments.
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(2B)+(2B)' ?