3-Phase Induction Motor 4

[kingtutley]

Ok, here is another newbie question.

I understand the physics behind the induction motor and the electromechanics, but what I don't get is the slip.

I know the math behind it, but I don't understand how it the rotor can be running slower than the rotating field.

Here's what I mean: I have a motor starting under no-load condition. The 3-phase rotating field induces the voltage on the rotor and the rotor begins to turn from bring push/pulled, right? Ok. Now when the rotor reaches full speed, it is said to be running slower than the stator field rotation. How is this possible? If the rotor is running slower than the field it would eventually stall wouldn't it -- like a synchronous motor being dragged beyond the torque limit? I understand that there should be a phase angle difference, but it seems to me that it has to be running at the same speed as the field in order to keep running.

So, what am I missing?

 

[sreid]

The key point that seems to be missed in induction motor operation explanations is that the rotor field moves synchronously with the stator field. The slip induces currents in the rotor but the stator and rotor magnetic vectors rotate at the stator frequency.

Load is picked up by a change in the angle between the stator and rotor magnetic vectors.

 

[waross]

When the stator field is in synch with the rotor field, there is a force between the fields, but the force is axial and no torque is developed. As the rotor field lags behind the stator field, the magnetic fields interact to produce torque.
The field in a synchronous motor is continuous and a few degrees of lag are sufficient to produce torque.
The field in an induction motor is induced by transformer action and at synchronous speed the frequency of the magnetic field is zero Hz. At zero Hz there is no transformer action. As the rotor starts to slip behind synchronous speed, the frequency of the current induced in the rotor increases. A few percent slip will result in enough rotor frequency to produce a field and the resulting torque. AS the rotor speed approaches synchronous speed the rotor frequency approaches zero. At synchronous speed, the rotor frequency is zero and transformer action stops. Hence no torque. As the slip increases the load current will increase. At a few percent slip the load current will balance the load.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[kingtutley]

I understand that, to a degree, but I still don't get why it would keep running.

If you overload a synchronous motor so that it cannot produce enough torque to overcome the load the phase angle between the stator and rotor increases to a point where they are no longer in synch and the motor stops. Why would this not happen to an induction motor if the rotor is always slower that the stator?

To over simplify my question, if I am driving a car at some speed and my partner is driving a different car at a speed only a few percent faster than mine, and the cars are attached to one another with some kind of rope, eventually the rope will break because my speed is constantly slower that the other.

Am I mixing something up here?

I understand that if the rotor is moving at exactly the same speed as the stator field there would be no induction and hence no torque, but as soon as it slows enough to slip behind the stator field a current will be induced and a torque appplied, but why would the frequency of rotation be less than that of the stator field?

Sorry this is so long, but I really don't get that.

 

[7anoter4]

See:

http://www.geocities.com/vijayakumar777/inductionmotor/inductionmotor.html

May be useful.
Regards

 

[waross]

The frequency in the rotor field is quite low. It is the difference between the synchronous speed and the rotor speed.
eg: 1800 rpm - 1760 RPM = 40 RPM. 40 RPM = 6.7 Hz. If you increase the torque requirements the motor current will increase and the motor will eventually stall. Don't think rope, think fluid coupling or canoe paddle.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[electricpete]

I think you are using a sync motor model
P = |E1| * |E2 | * sin(delta) / XL
T = P / w
where delta is angle between rotor field and applied stator field.

If you wish to apply the same model to an induction motor, you have to recognize that the rotor field does NOT rotate at the same speed as the rotor (unlike a sync motor whose field does rotate at the same speed). The angle of the rotor field is a relatively inaccessible quantity. Also I think a careful study would show that |E2| is not a constant as we sometimes treat it for sync machine.

====================
Here is a better way to look at it:
T = k * mmfs*mmfr* sin(delta_sr) [equation 1]
T = k * mmfm*mmfr* sin(delta_mr) [equation 2]

where
mmfs = radial airgap mmf associated with stator current.
mmfr = radial airgap mmf associated with rotor current.
mmfm = magnetizing reactance = mmfs - mmfr
delta_sr = angle between mmfs and mmfr
delta_mr = angle between mmfm and mmfr

Equation 1 hopefully looks familiar (it can be derived directly from conservation of energy). Equation 2 can be derived from equation 1 if we treat the mmf's as vector quantities. Start with the definition of magnetizing mmf:
mmfm = mmfs - mmfr
Right-side Cross product each side of equation by mmfr
mmfm x mmfr = mmfs x mmfr - mmfr x mmfr
recognize that mmfr x mmfr = 0
mmfm x mmfr = mmfs x mmfr
convert cross product to trig:
mmfm x mmfr = mmfs x mmfr
mmfm mmfr sin(delta_mr) = mmfs mmfr sin(delta_sr)
This last equation forms the bridge between equations 1 and 2.

With that under our belt, from equation 2 we see that the torque is not dependent only on the angle (as for sync motor) but also on the mmfr which will vary with load. Specifically, as we increase load, the rotor slows down, we have higher slip frequency, higher voltage induced into rotor, higher rotor current, higher rotor mmf, and from equation 2 higher torque.

If we were looking at a sync motor, rotor mmf is constant and angle is the only thing that can vary and we have maximum corresponding to max angle. Again, not so for induction motor. Rotor mmf is an additional parameter which vareis and provides a stabilizing effect.... motor seeks the speed where motor torque matches load torque.


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[electricpete]

By the way, there is a limit of max torque that will be reached by an induction motor (breakdwon torque). This is related to the fact that as we increase slip beyond a certain point, rotor reactance (proportional to slip freq) starts to get very large and also changes the angle in the wrong direction. This effect is negligible in the operating range below nameplate power. In this region, torque is roughly proportional to slip speed. This behavior in the linear operating range can be derived very simply by noting that induced rotor voltage is proportional to slip speed, rotor current is proportional to slip speed, and therefore rotor mmf and machine torque proportional to slip speed. Changes in sin of the angle in this region are a relatively minor secondary effect.

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[kingtutley]

Ok, so does the stator field pass the rotor field? That is, overtake and pass?

That question does not really make sense.

Let me try again.

2 cyclists on a round track. 1 is stator, 1 is rotor. Let's assume there is a small load so that there is always some torque present.

The stator drives/pushes the rotor, right? but if the stator is always faster than the rotor, won't the stator leave the rotor behind until it overtakes it again some time in the future?

 

[electricpete]

No. The rotor field moves FASTER than the rotor. It moves at the same speed as the stator field.

Look at a two pole motor.

Stator freq is Fstator

Rotor mechanical speed is Frotor

Slip speed is Fstator - Frotor

Rotor Current frequency is slip frequency Fslip = Fstator - Frotor

How fast is rotor field? If the frequency were 0 (dc), than it would be same as rotor speed. But due to the time-varying rotor field, the rotor field rotates forward relative to rotor at frequency of the rotor current which is Fslip = Fstator - Nrotor

So the speed of rotor field is speed of rotor plus slip frequency

Frotorfield = Nrotor + (Fstator - Nrotor) = Fstator


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[kingtutley]

I'm getting closer to 'eureka', but not quite there yet.

OK. I was going wrong thinking about permanent poles on the rotor for one. I was not really thinking about a squirrel cage. My mistake.

The magtetic north rotates around the inside of the stator. When there is a north pole on the stator, there is, I guess, a south pole induced on the rotor, right? So this works because you can "instananeously" change the voltage that is induced in the rotor, but the current has not stopped and the field induced by this current has not collapsed. This would tend to pull the rotor along until, speeding up, slowly decreasing the current and, hence the induced field. This because the rotor coils are not being cut by the stator flux as much as when it was stationary.

Am I getting warmer?

 

[jraef]

Here is a cool little animation that shows what is going on in the cage rotor bars. It's a good visualization of the lag in response.

http://www.ece.umn.edu/users/riaz/animations/squirrelcage.html

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[electricpete]

Since we get into the subject of lag of response and discussion of this torque angle... it brings about a very surprising and nonintuitive aspect which was discussed in this thread: thread237-179713

Specifically, regardless of which torque angle we look at (delta_mr or delta_sr), the steady state torque angle lies between 90 and 180 degrees (NOT between 0 and 90 degrees as we might expect if we expect to simplistically compare this to a synchronous machine). Blasphemy you say... that is an unstable region. It is in fact unstable for a sync machine which can only vary it's phase angle to match load, but it is not unstable for an induction motor which also varies rotor current and rotor mmf to match load (equation 2).

You can confirm that the angle between 90 and 180 is shown in jraef's link if you take a screenshot and carefully measure the angles as in slide 1 of my attachment to this message.

The reason becomes clear from fairly straightforward phasor analysis of the induction motor equivalent circuit shown in slide 2 below to this message.

===========================
By the way, a small correction to my post 22 Sep 08 13:30 above - I should have defined mmfm = mmfs + mmfr instead of mmfm = mmfs-mmfr. Doesn't make any difference in the proof of transition between equation 1 and 2 because 2nd term on rhs became 0... doesn't matter + 0 or -0.

And I will mention that in jraef's link we are looking at delta_mr since "flux density wave" presumably refers to airgap flux density which is a result of vector sum of rotor and stator mmf's, which I called mmfm for magnetizing.

That is probably a lot more math approach than you may be interested. But perhaps an illustration that motors are not so simple as we are somtimes led to believe.

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[electricpete]

And speaking of motors not being as simple as we may be led to belive, another tangent that I think is very interesting: do you think the torque produced in an induction motor arises from simple force on conductor principle F = qV x B = L I x B? If so , you are wrong... the torque-producing force acts primarily on the iron. More details of that here:

http://home.comcast.net/~electricpete1/torque_web/

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[kingtutley]

This is very complicated, in my opinion and I thank you al for your help.

I think I have it now.

Does the magnetic field induced in the rotor always lag the magnetic field in the stator?

This would be my guess because the physical rotor is moving slower than the stator field.

It does not seem right that this would produce a larger torque than say a synchronous machine with a fixed rotor field.

I know that the highest currents and therefore the largest magnetic field will be produced in the rotor when starting. Is that why it can produce more torque? Because as the load increases and the rotor slows, more flux cuts the rotors, increasing the current and the strength of the resulting marnetic field?

I know it is possible to load the rotor to the point of stopping motion, but is there a point, similar to a sychronous machine, where the rotor slips "out of synch" and stops or is it just a gradual slowing due to increased load?

 

[electricpete]

Here's my two cents. Others please jump in and add your own comments

Does the magnetic field induced in the rotor always lag the magnetic field in the stator?

Yes.

This would be my guess because the physical rotor is moving slower than the stator field.

To my way of thinking, it lags for the same reason that a sync motor lags. Power is transferred from the leading field to the lagging field.

It does not seem right that this would produce a larger torque than say a synchronous machine with a fixed rotor field.

I'm not sure which is capable of producing more torque. The basis for the short-time torque limits is different. I believe that the momentry torque limit for sync machine is based on keeping theta a comfortable margin below 90 degrees to avoid pole slip (stability margin). The short-time torque limit for induction motor comes from a different reason discussed above (rotor leakage reactance at high slip frequency).

I know it is possible to load the rotor to the point of stopping motion, but is there a point, similar to a sychronous machine, where the rotor slips "out of synch" and stops or is it just a gradual slowing due to increased load?

There is no point where an induction motor will slip out of sync. Loading beyond breakdown torque is unstable (speed will decrease rapidly and current increase rapidly) because the motor delivers less torque in response to increased load. Typically motor protection would trip.

I know that the highest currents and therefore the largest magnetic field will be produced in the rotor when starting. Is that why it can produce more torque?

More torque than what? Starting torque is tyupically higher than nameplate torque and the high current is a contributor. However there is also poor power factor at starting which reduces starting torque compared to breakdown torque.


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[electricpete]

The short-time torque limit for induction motor comes from a different reason discussed above (rotor leakage reactance at high slip frequency).

This was referring to discussion of breakdown torque.

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[LionelHutz]

The rotor field always lags the stator field but is rotating at the same speed as the stator field.

It doesn't always produce a larger torque than a synchronous machine.

An induction motor does not produce the most torque when starting. The torque generally is around rated torque from 0 to 80% speed or so.

A synchronous motor usually has squirrel cage's in the motor poles and is typically started as an induction motor but it is also usually a very poor induction motor because it wasn't primarily designed to be an induction motor.

An induction motor has a very pronounced torque peak, typically around 92-95% of full speed. This peak is also typically around 2-2.5 times the motor rated torque. If you load the motor more than this torque peak it will stall very quickly.

I suggest you go to a motor manufacturer's web site and look up some speed vs torque curves if you don't understand this.

 

[kingtutley]

So, the behvior of the induction motor mimics the synchronous motor in that beyond a certain point of loading, the motror stalls quickly.

I assume the stalled induction motor rotor will experience very large currents due to the continuing stator field (assuming motor protection failed for whatever reason) and would eventually -- probably quickly -- exceed its thermal limit and begin breaking down the conductor insulation.

 

[kingtutley]

For a wound rotor motor, there is a set of windings per phase, right? If it is a 4-pole motor (2-pole pair) there would be 2 sets of windings (2 per phase) on the Stator, right? Does the number of windings increase on the rotor also when increasing the number of poles?

For a squirrel cage motor, is there a similar change in the number of rods used in the rotor or is it a fixed number? Since they are all shorted at the ends, I would tend to think it is some fixed quantity.