induction motor with superconducting rotor - produce any torque? 2

[electricpete]

Maybe not a practical question.

Let's say we built an induction motor with ideal superconducting rotor (zero resistance).
Is there any speed at which it would be capable of producing steady state torque?

I say the answer is no. And therefore any basic explanation of how an induction motor works which does not mention rotor resitance is incomplete.

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[Warpspeed]

It seems to me that the reason they place a copper or aluminium squirrel cage bars in the rotor is to reduce the electrical resistance to eddy currents. This reduces slip speed, rotor temperature rise, and raises motor efficiency.

Silver bars would probably be better, and superconducting bars even better still. I guess a superconducting rotor would run at synchronous speed and have zero slip ?

 

[jbartos]

Suggestion: Visit

http://www.reliance.com/prodserv/motgen/b2776_1.htm

http://www.reliance.com/news/press_releases/press_7_19.html

http://www.manufacturing.net/ctl/article/CA190702

(for HTS wires on the rotating shaft instead of copper)

http://www.eng-tips.com/viewthread.cfm?spid=367&newpid=367&sqid=86585

etc. for more info

 

[aolalde]

That is a challenging question; I think that in practice superconductors never reach zero resistance. In the theoretical assumption that an induction motor cage reaches zero resistance, from the equivalent circuit, the electromagnetic power developed Pd is:

Pd= I2^2*r’2*(1-s)/s

If r’2=0-------> Pd = 0

By the other hand, to increase Pd when r’2 tends to zero, (1-s)/s must tend to infinity.
(1-s)/s--->infinity then s --> 0

If we have no slip, the induced voltage is zero (the rotor has synchronous speed). But this is a contradiction since any load to the shaft needs a mechanical power to keep moving.

I think that with zero resistance in the rotor no accelerating torque is developed and the motor never reaches a speed close to synchronism.

 

[jbartos]

Suggestion: Visit

http://www.supermachines.org/documents/papers/HTS Hyst motor .pdf

for: Torque of Hysteresis Machine

http://www.ohsaki.t.u-tokyo.ac.jp/~tsuboi/papers/asc02_4lf05.pdf

for: Torque slip characteristic
and
Development of prototype superconducting linear induction motor for steel making processes
Tsukamoto, O. Amemiya, N. Yamagishi, K. Sato, S. Sato, K. Takao, T. Shimizu, H.
Yokohama Nat. Univ., Japan;
This paper appears in: Applied Superconductivity, IEEE Transactions on

Publication Date: Jun 1995
On page(s): 976- 979
Volume: 5, Issue: 2
ISSN: 1051-8223

-----------------------------------------------------------
Abstract:
The authors describe how they are developing technologies of a superconducting linear induction motor (SLIM) for steel making process applications. They have developed and tested a prototype SLIM and this paper presents configurations and test results of the SLIM.<>

 

[rbulsara]

Without pretendig to be an expert of machine design, I would tend to agree with electricpete.

Even superconductor have resistnace and severe 'heat' problem as mentioned in above papers. Zero resistance would creat infinte current which will not make anything work.

A good analogy is like having no friction, most mechanical activity will loose control without it. So would would be contorl of electrical current control without impedance.

 

[Warpspeed]

There are several electrical devices that function because they have negative resistance characteristics over part of the operating range. They can amplify and oscillate under perfectly stable conditions. The tunnel diode is a good example.

I do not see zero resistance being a problem. Zero impedance is not a problem either. Impedances very close to zero can be created with negative feedback at amplifier outputs for example. The results are neither unstable or totally out of control.

 

[rbulsara]

warspeed:

What will be current with R=0 and V=2V.?

 

[rbulsara]

Also I negative R is not necessarily less than zero? or is it? -ve R will have a absolute value.

V/-R=-I which only indicates current in opposite direction, much different than infinity.

 

[Warpspeed]

rbulsara:

If resistance is zero, voltage will always be zero, and current somewhere between zero and infinity (undefined). Power dissipation will be zero as well.

Ohms law still applies.

Negative resistance is not zero, you are right it will have a finite value. it is like XC and XL, they behave in opposite and complimentary fashion, and when added together (at resonance) can equal zero.

 

[rbulsara]

Source Voltage is indepedent of the load R.

Voltage drop IR will be zero not the source Voltage.

 

[rbulsara]

or in other words if R is =0 (being only impedance) there will be huge short ciruit=loosing control!!!

 

[electricpete]

Those are all good comments.

I like aolalde's explanation. Based on the equivalent circuit we will expect no torque at any speed other than syncronous. At syncronous speed the behavior is a little ambiguous.

So it seems to me that when we try to physically explain how an induction motor works, the explanation should address the rotor resistance... it is an essential for torque production.

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[Warpspeed]

Source voltage is not really independent of the load, this would only be true if the source impedance is also zero.

I find the whole concept bizarre and difficult to get my head around.

For instance a blob of superconducting "stuff" will hover in a stationary magnetic field continuously and defy gravity in a completely stable fashion. I suppose if it tries to move (fall), vast (infinite?) internal eddy currents flow, creating a repulsive opposing field, so it resists any physical movement. I have read somewhere that this test is a common one applied for testing superconducting materials in the laboratory.

Within a few seconds the superconductor usually warms up above critical temperature destroying the superconductivity. It then suddenly crashes to the ground.

Placing a dead short across a high voltage low impedance source may seem that the current rises instantly to infinity totally out of control, but does it really ?

I would say it is entirely predictable if you know all the circuit ac and dc parameters.

 

[electricpete]

I haven't followed all the comments by warpspeed andrb. One thing I will say is current does not become infinite for any non-syncronous speed since it will be limited by inductance. Warpspeed maybe you are addressing the syncronous case. As aolalde pointed out above there is a 0/0 type solution going on there. Not well defined and I can't find the solution to that case.

There was some some hidden agenda in my question. I wanted to be able to motivate the idea that torque output in an induction motor is inextricably tied with rotor resistance. Specifically the torque associated with generator action to feed rotor I^2*R losses in one reference frame is the same torque that is associated with motor output in another reference frame.

Experiment #1 (Simple generator action)
Take an induction motor. Replace the stator with a stationary permanent magnet creating a stationary field.
Try to rotate the rotor slowly. At speed N we induce a rotor voltage E= N*K*Phi (N=speed,Phi=flux, K=proportionality constant). Neglecting the effects of inductance (valid at slow speeds), the current which flows is E/R2 =N*K*Phi/R2 and the power dissipated in the rotor resistance is P=E^2/R2 = N^2*K^2*Phi^2/R2. Assuming the system is frictionless, we must provide input mechanical power to produce this output heat. Pinput = 2*Pi*Torque*N = Pdissipated = N^2*K^2*Phi^2/R2
Torque = N*K^2*Phi^2/(R2*2*Pi) = N*K'*Phi^2/R2 (where K'=K^2/2Pi).
Bottom line: We supply a mechanical input torque which is proportional to speed an inversely proportional to R2.

Experiment #2 (Simple generator action in another reference frame)
Repeat experiment #1 except this time set the magnet in motion CW at speed Nsync (syncronous speed) and view everything from the reference frame of the rotating magnet. If we try to push the rotor CCW at speed Nslip with respect to our (rotating) reference frame, we will have to apply mechanical CCW torque proportional to the slip speed and inversely proportional to R2. Since the mechanical torque is in same direction as the relative motion of the rotor in our reference frame, it appears as input power. The amount of that mechanical input power is given by 2*Pi*T*Nslip. That mechanical input power is converted into rotor resistive losses.

Experiment #3 – (Generator action within a motor)
Examine what happened above in experiment #2, but express everything in terms of a stationary reference frame. The rotor is traveling CW at speed = Nsync-Nslip. The mechanical torque is exactly the same as in experiment #2…. it is CCW and proportional to Nslip and inversely proportional to R2. Since the mechanical torque is in opposite direction as the motion of the rotor (CW), it appears as output power. The amount of that mechanical output power is given by 2*Pi*T*(Nsync-Nslip).

When we change reference frames, the torques remained the same. But power does not remain the same because P=2*Pi*T*speed and speed is relative to reference frame. But there is no violation of conservation of power. There is extra input power 2*Pi*T*Nsync not discussed above which will be required in experiment #3 to keep the magnet rotating at CW Nsync while torque T is applied. When we subtract away from this the same rotor resisitve losses as experiment 2 (2*Pi*T*Nslip), we are left with the experiment #3 output power 2*Pi*T*(Nsync-Nslip)

To me this is a satisfying intuitive physical explanation of an induction motor (hidden behind the equations and reference frames). Neglecting inductance is equivalent to an assumption that slip speed is small enough to stay in the linear range where T~slip speed. It is not as detailed or as versatile as the equivalent circuit but I like it a lot better than the typical hollow explanation that we usually hear: "The stator field induces current into the rotor and the rotor current interacts with the stator field to produce torque".

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[Warpspeed]

electricpete, a masterly explanation of how an induction motor works.

Funnily enough, I and another regular contributor to Eng-Tips are at this time building an experimental eddy current engine dyno that works as per your Experiment #1. It uses a water cooled hollow mild steel rotor, or it would rapidly melt down.

My argument is that in your Experiment #2 if the rotor used superconducting bars in the cage, slip would actually be zero and I^R losses in the rotor would be zero as well.

 

[jbartos]

Comment: The prototypes of superconducting induction motor is already developed and functions (rotary and linear). See my links above.
The original posting question rotor resistance Rr convergence to zero for superconductive induction motor rotor. Assuming that the slip s is also converging to zero, then
Rr/s~0/0 which is normally considered an indeterminate expression. To evaluate it, it is necessary to know how fast Rr converges to zero and how fast s is converging to zero. In practical terms, Rr will be very small and s will be very small. Obviously, the goal is to have Rr/s approaching to zero, or Rr approaching to zero faster than s to have a highly efficient induction motor. This is the case, torque is produced and the currently developed superconductive induction motors evidence it.

 

[jbartos]

Comment on aolalde (Electrical) Apr 8, 2004 marked ///\\That is a challenging question; I think that in practice superconductors never reach zero resistance.
///True\\ In the theoretical assumption that an induction motor cage reaches zero resistance, from the equivalent circuit, the electromagnetic power developed Pd is:

Pd= I2^2*r’2*(1-s)/s

If r’2=0-------> Pd = 0
///Yes and no. It depends on the correct mathematical relationship for the torque, and for the slip convergence to zero. The goal is to have r'2/s very small so that the motor efficiency is very high.\\ By the other hand, to increase Pd when r’2 tends to zero, (1-s)/s must tend to infinity.
(1-s)/s--->infinity then s --> 0
///Yes. This is where a mathematically indeterminate relationship 0 time infinity materializes. Then, r'2 convergence to zero has to be compared to (1-s)/s convergence to the infinity to make the proper conclusion. Else, the indeterminate relationship stays inconclusive.\\ If we have no slip, the induced voltage is zero (the rotor has synchronous speed). But this is a contradiction since any load to the shaft needs a mechanical power to keep moving.
///Yes. True. However, a proper perception of the machine power conversion, including mathematical equations is needed. In fact, the superconductive induction motors are turning and producing torque-speed characteristics.\\ I think that with zero resistance in the rotor no accelerating torque is developed and the motor never reaches a speed close to synchronism.
///Yes, as referred to the well-known relationship for the induction motor torque from textbooks.\\

 

[charlierod]

Ideally, there should be no torque because electromagnetic field from stator and rotor would be aligned (the current induced in rotor if any would lag 90 degrees from induced voltage in rotor bars). This is a question i asked myself some time ago while studying induction motor fundamentals.

Considering in depth aspects about superconductors, magnetic saturation and so on(real situation) is another thing.

 

[electricpete]

I agree with all of these comments. Good point by Charlierod in an induction motor the rotor power is given by voltage times current times cos of angle. With no resistance there is no real power. That model does not quite extend to exactly sync speed where power factor is not relevant. Now we have zero voltage and zero resistance. What current flows is indeterminant.

jbartos talks about convergences as R->0 and s->0. I think that aolalde has well addressed that it depends upon the constraints imposed. If we constrain the motor to carry a given load, than as R->0 we can always pick a s proportionately smaller s to carry a given load. The problem is that as R->0 the values of s are constrained to a narrower and narrower band about s=0. The result is that when R=0 the torque speed curve has a discontinuity at s=0. It don't think we can talk about convergence and limits in the presence of a discontinuity. In contrast we can talk about limit as x->0 of sin(x)/x because there is no discontinuity at 0. I may be wrong that limit or convergence does not apply to this situation. If I can be proven wrong I would be interested to hear.

I read the first three articles about superconducting motor from Reliance/DOE etc and it was a sync motor.

I took a quick look at the linear induction motor but I couldn't quite understand what was going on there.

I guess there is one thing I am not sure of. Does superconducting mean 0 resistance or resistance almost zero? Zero resistance sounds like electrical equivalent of a perpetual motion machine, but I don't know enough to know the answer.




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