the slip at which maximum torque occured varies as the resistance of the rotor is changed. But in some book i read that there is no relation between torque and resistance of rotor. Please explain the relation if any other than the above said.

 

Hi,

Yes, it depends on type of the asynchronic motor you are using. Common motor is squirrel motor
whose rotor resistance is constant, so slip
for max torque is stable. But for some motor
with changable rotor resistance, you can get
different slip of max torque through connecting
different rotor resistance.

 

I assume your talking about AC Induction motors?

I got this info from:
The Control Techniques Drives and Controls handbook.
IEE Power and Energey Series 35
Published by The Institute of Electrical Engineers, London, UK
2001

A disadvantage of the squril-cage machines is its fixed rotor charactersitc. The starting torque is directly related to the rotor circuit impedance, as is the percentage slip when running at load and speed.

Ideally, a relatively high rotor impedance is required for good starting perfomranc (torque against current) and low rotor impedance for full-load speed slip (and high efficiency)....

...not sure if this is part of what your looking for. Check out the handbook. You might be able to get it from Amazon or Control Techniques website.

Cameron Anderson
Motion Control Specialist
St. Paul, MN

 

For induction machine, developed torque is directly proportional to the square of the rotor current times the rotor resistance divided by the slip.

Torque = t
rotor current = i
rotor resistance = r
slip = s
rotor speed (rad/sec)= w

Then t=(3 x i(squared) x r/s)/w

 

The amount of starting torque which a given motor develops depends, within certain limits, on the resistance of the rotor winding.

Starting torque is usually expressed as a percent of the full-load torque, with a corresponding increase in slip and a decrease in efficiency. In fact, all the desirable characteristics are so interrelated that it is impossible to make one of them surpassingly good without adversely affecting the others.

 

Your understanding that (maximum) torque is not dependent on rotor resistance, is correct.

The torque equation contains several expressions involving rotor resistance divided by slip. Differentiation with respect to slip yields slip (max). This value does not differ greatly from rotor resistance divided by stator and rotor reactances. Thus, when the value for slip (max) is inserted in the torque equation, rotor resistance is cancelled.

If you need the compete torque expression and its differentiation, please contact me.

Regards,
Phil Corso, PE
Boca Raton, FL
( TAL-2 @ webtv.net )

 

Responding to off-list requests for my offer (Tue, Aug 27, 4:08 pm) to provide proof that max torque is independent of rotor resistance:

Based on the pi model of an induction motor:
T = [(V1^2)(R2/S)] / [ (R1+K(R2/S)^2 + (X1+KX2)^2 ]
Where:
T = torque.
V1 = stator input voltage.
R1, X1 = impedance, Z1, stator.
R2, X2 = impedance, Z2, rotor, referred to stator.
K = [ 1-(Z1)(Ym) ].
Ym = Mag circuit admittance = [ (1/Rm)-j(1/Xm) ]
Rm,Xm= loss resistance & magnetic reactance, respectively.
S = slip

Differentiating T with respect to S to find Smax, yields:
Smax = [KR2] / [ sqrt (R1^2+(X1+X2)^2) ],
but because K is approximately equal to unity, Smax = R2 / (X1+X2). Substituting this value into the equation for torque results in: Tmax = [V1^2] / { 2K sqrt [ R1^2 +(X1+KX2)^2 ] + R1 }.

Therefore, Tmax is independent of rotor resistance. Q.E.D.!

If the equation is unreadable, send me your Fax No. and your company affiliation, and I will Fax a copy to you.

Regards,
Phil Corso, PE
Boca Raton, FL
( TAL-2 @webtv.net )

 

John, thanks for being so observant. I was beginning to believe that no-one read my comments.

First, the dropped R1. You are correct. I neglected to mention that since R1^2 is much so smaller than the term (X1+X2)^2, it can be ignored.

Second, the missing parenthesis. Once again, you are correct. The term (R1+K(R2/s) ) is squared and then added to the term (X1+X2) squared. The
open/close parenthesis count is now balanced.

Finally, you missed my error mentioning use of the " pi " model.
Actually the more accurate " T " model is correct, i.e., stator impedance Z1 to the left, Rm and Xm both shunted to ground, and then
rotor impedance Z2 to the right.

Regards,
Phil Corso, PE
(Boca Raton, FL)