Trouble Comprehending Rotating Magnetic Fields

[HydroGuy]

I understand three-phase motors and how the phase offset could produce a rotating magnetic field and a torque. But what about single-phase induction motors? I don't understand how they would be constructed at all. I know that a single-phase induction motor won't self start, but I don't know how it would be setup to work at all. On a simple two pole motor, if both poles are fed from a 120V 60 Hz sinewave, wouldn't both be the same polarity at the same time? Can anyone explain how it works?

Slightly unrelated, but do all inductors impart a 90 degree phase shift? All they are is a coil of wire, correct? Does a 30 turn not shift more than a 1 turn coil?

 

[TurtleMeister]

There are a couple of methods used to create the rotating magnetic field in a single phase induction motor. One method is to have an auxiliary winding in the motor which is physically shifted 90 degrees between the poles of the main winding. This aux winding is connected through a capacitor which provides the electrical 90 degree phase shift. These motors have moderate starting torque. Some motors have a centrifugal switch that turns the aux current off once the motor reaches a specific RPM. These motors have a higher starting torque because the aux can be designed for intermittent duty. Very small motors use the shaded pole technique where a copper ring is placed on a part of each field pole. Shaded pole motors have a very low starting torque. You've probably seen these types of motors in window fans.

Yes, all inductors have a 90 degree current lag regardless of their size. The inductor with 30 turns will have a greater inductive resistance than a smaller inductor but the phase shift will be the same.

 

[Bob S]

The types of starting circuits for single-phase induction motors all shifted the phase of the starting circuit in a variety of ways. Usually, a centrifugal switch on the rotor (squirrel cage) disconnected the starting circuit as the RPM approached the synchronous RPM. The types of starting circuits were:

1) Capacitor start - uses capacitor to shift phase of starting coil.
2) Split phase - uses more resistive starting coil to shift phase (see below).
3) Shaded pole - uses permanent shorted stator poleface winding to shift phase.
4) Repulsion start - used shorted windings on armature (squirrel cage) to start motor.
5) Permanent capacitor run - two separate identical pole windings, one with permanent series capacitor.

The complex impedance of a series resistor and inductance is Z(w) = R + jwL. The phase shift of this circuit is theta = tan^-1(R/L), so the phase shift can be accomplished by changing the resistance of a winding or by changing the number of turns on pole to change phase shift. The repulsion-start method, which had a starting commutator on the armature, required the least starting surge current of all the methods, and was used on single-phase induction motors up to about 1940 (I think). Capacitor-start motors are now used for this application.

See a picture of a repulsion-start commutator in post #4 in thread https://www.physicsforums.com/showthread.php?t=301555

 

[HydroGuy]

Could you explain why one coil of wire phase-shifts the same as a 100 coil wire? I just can't comprehend that. What about a half coil of wire? 45 degrees? You know what I mean...? I know that there is always some inherit inductance in any current-carrying line, which could be modeled as an inductor. But wouldn't that mean that the current should ALWAYS lag the voltage by 90 degrees in any AC circuit, even without a true inductor? See what I'm getting at here?

And thanks for the help with the motor... I understand how you can use those methods to get it to start turning, but I don't understand how a two pole stator can effectively turn a rotor once it gets going.

 

[Bob S]

The secret in induction motors is the "squirrel cage" of shorted copper conductors imbedded in the laminated iron rotor. Eddy currents are induced in this structure whenever the rotor RPM drops below the synchronous RPM, and the eddy currents interact with the stator magnetic fields (using the Lorentz force F = I x B) to create a torque. The decay time constant of the eddy currents in the squirrel cage are several cycles of the 50Hz/60Hz frequency. If the squirrel cage rotates 180 degrees on a 2-pole motor, or 90 degrees on a 4-pole motor, in half a cycle, the eddy currents are minimized. If the RPM lags more under load, the eddy currents increase more, creating more torque.

The magnetic poles on the stator are fixed in location; 2-pole 180 degrees (3600 RPM), 4-pole 90 degrees (1800 RPM), 6-pole 60 degrees (1200 RPM), etc. The current flowing in the coils on these poles is always alternated at 0 degrees or 180 degrees, determined by its connection to the mains, to give the apparent field rotation. The rotor rotation can be either clockwise or counterclockwise, and be synchronous. All the poles have the same phase lag; tan^-1((L/R)), so the phase shift pole-to-pole is always 180 degrees. But the current does not lag the voltage by the full 90 degrees, because the coil winding has finite resistance as well as inductance. All electric motors (with one exception) are inherently inductive, and have an inductive power factor. The power factor is worst when the motor is running on a light or no load. When under high load, the power factor [cos(theta)] is highest.
[Edit] You asked about inductance of current-carrying lines. In coaxial cables, the equivalent circuit model is a long repetition of a series inductance L (plus a little wire resistance) followed by a shunt capacitance C, plus repeats. It turns out that the shunt capacitance "cancels out" the inductance, leading to a nearly real coax cable impedance Z = sqrt(L/C).
Bob S

 

[subtech]

Speaking very generally, when considering single phase motors one should visualise a pulsing magnetic field eminating from the stator windings and not a rotating one. During the positive portion of the cycle, the uppermost stator pole could be likened to the North pole of a magnet. (of course the lower pole would be the opposite, the South pole of the magnet). As the applied emf alternates the upper pole then becomes like the South pole of a magnet and the lower pole becomes the North.
The magnetic field created by induced current flow in the rotor is "pulled" along with the pulsing/alternating magnetic field of the stator.

 

[Bob S]

For a four-pole induction motor (synchronous speed = 1800 RPM), a quadrupole field is induced in the rotor and sustained by the currents in the squirrel cage. The ac fields (currents) in the four stator poles are

I₁(wt) = I sin(wt)
I₂(wt) = I sin(wt-pi)
I₃(wt) = I sin(wt-2pi)
I₄(wt) = I sin(wt-3 pi)

or

I₁(wt) = I sin(wt)
I₂(wt) = I sin(wt+pi)
I₃(wt) = I sin(wt+2pi)
I₄(wt) = I sin(wt+3 pi)

depending on rotation. But wait, they are actually the same.

 

[HydroGuy]

The secret in induction motors is the "squirrel cage" of shorted copper conductors imbedded in the laminated iron rotor. Eddy currents are induced in this structure whenever the rotor RPM drops below the synchronous RPM, and the eddy currents interact with the stator magnetic fields (using the Lorentz force F = I x B) to create a torque. The decay time constant of the eddy currents in the squirrel cage are several cycles of the 50Hz/60Hz frequency. If the squirrel cage rotates 180 degrees on a 2-pole motor, or 90 degrees on a 4-pole motor, in half a cycle, the eddy currents are minimized. If the RPM lags more under load, the eddy currents increase more, creating more torque.

The magnetic poles on the stator are fixed in location; 2-pole 180 degrees (3600 RPM), 4-pole 90 degrees (1800 RPM), 6-pole 60 degrees (1200 RPM), etc. The current flowing in the coils on these poles is always alternated at 0 degrees or 180 degrees, determined by its connection to the mains, to give the apparent field rotation. The rotor rotation can be either clockwise or counterclockwise, and be synchronous. All the poles have the same phase lag; tan^-1((L/R)), so the phase shift pole-to-pole is always 180 degrees. But the current does not lag the voltage by the full 90 degrees, because the coil winding has finite resistance as well as inductance. All electric motors (with one exception) are inherently inductive, and have an inductive power factor. The power factor is worst when the motor is running on a light or no load. When under high load, the power factor [cos(theta)] is highest.
[Edit] You asked about inductance of current-carrying lines. In coaxial cables, the equivalent circuit model is a long repetition of a series inductance L (plus a little wire resistance) followed by a shunt capacitance C, plus repeats. It turns out that the shunt capacitance "cancels out" the inductance, leading to a nearly real coax cable impedance Z = sqrt(L/C).
Bob S

Thanks. Where does the shunt capacitance of a current-carrying wire come from? How does it exactly cancel out the inductance? Can anyone address my questions regarding inductors and coils, and why a loop causes an exact 90 degree phase lag in current (discarding resistance)?

It just seems that what you are taught in class is that "inductors" cause phase lag of 90 degrees in a simple RL circuit. But realistically, inductance is everywhere and can be modeled as an "inductor". So shouldn't current lag voltage close to 90 degrees in many cases even without the presence of a true inductor?

Also, I don't really understand how an inductor, essentially a coil of wire, causes this exact phase shift. Why don't more coils cause more phase shift?

 

[Bob S]

Thanks. Where does the shunt capacitance of a current-carrying wire come from? How does it exactly cancel out the inductance? Can anyone address my questions regarding inductors and coils, and why a loop causes an exact 90 degree phase lag in current (discarding resistance)??

Hello Hydroguy-
These are good questions. In a coaxial cable, or other wire in close proximity to the wire carrying the return current, there is a mutual capacitance. Often in coaxial cables, extra capacitance is added using polyethylene or similar dielectric. The result is that the "characteristic impedance" of the cable (not to be confused with resistance) is Z = sqrt(L/C). The ratio of the series inductance L per unit length, and the shunt capacitance C per unit length, is real (not reactive like either an inductance or capacitance). If you write the full impedance representation of L and C in the frequency domain, they are jwL and 1/jwC, where j = 90 degrees and w = 2 pi times frequency. So that in the impedance ratio, the jw cancels out. Electrical engineers model these transmission lines as a ladder of series L and capacitance C sections.

It just seems that what you are taught in class is that "inductors" cause phase lag of 90 degrees in a simple RL circuit. But realistically, inductance is everywhere and can be modeled as an "inductor". So shouldn't current lag voltage close to 90 degrees in many cases even without the presence of a true inductor??

The phase lag for a simple RL circuit is arctangent(L/R), so it is 90 degrees only when the resistance is zero.

Also, I don't really understand how an inductor, essentially a coil of wire, causes this exact phase shift. Why don't more coils cause more phase shift?

The inductance L of a coil of wire is proportional to the square of the number of turns of wire, so more turns means higher inductance. But the phase shift is still arctangent(L/R), so the phase shift increases, but cannot reach 90 degrees until the series resistance is zero.
Bob S

 

[HydroGuy]

Thanks Bob S - good stuff.

Lets say we had a superconducting wire with R=0 hooked up to an ideal voltage source at 60 Hz. If we twisted the superconducting wire into a loop, would it create an inductor? Would the current then lag the voltage by 90 degrees?

It would it depend on the load, right? What if the load itself was simply the superconducting wire, bent into a loop at one point. This would obviously pose some major issues with R=0 but let's ignore that if possible. I'm just imagining playing around with the wire and bending it into different shapes. Would I be affecting the inductance at all by changing the shape? But since there is no resistance or capacitance, the current would lag the voltage no matter what I guess.

Eh, I've gone off topic, but kind of cool to think about.

 

[Bob S]

Thanks Bob S - good stuff.
Lets say we had a superconducting wire with R=0 hooked up to an ideal voltage source at 60 Hz. If we twisted the superconducting wire into a loop, would it create an inductor? Would the current then lag the voltage by 90 degrees? Eh, I've gone off topic, but kind of cool to think about.

Hello Hydroguy-
MRI (magnetic resonance imaging) magnets used for medical diagnostic applications are superconducting magnets with an inductance in the 10's of Henrys. Once they reach full current (and fields exceeding 1.5 Tesla), the superconducting magnet leads can be shorted together, and the current will persist for a long time (persistent mode), because the overall cable resistance is of the order of 10 nano-ohms. So the L/R time constant is like 10^9 seconds (10's of years) and the phase lag is arctangent(L/R) = 89.999 999 994 degrees, so getting close to 90 degrees.

[Correction] L/R is a time constant, not a phase shift. The phase shift is arctan(wL/R), where w = 2 pi frequency. So if period = 1/f = 1 year, then the phase shift = 89.7 degrees.
Bob S

 

[likephysics]

It just seems that what you are taught in class is that "inductors" cause phase lag of 90 degrees in a simple RL circuit. But realistically, inductance is everywhere and can be modeled as an "inductor". So shouldn't current lag voltage close to 90 degrees in many cases even without the presence of a true inductor?
Also, I don't really understand how an inductor, essentially a coil of wire, causes this exact phase shift. Why don't more coils cause more phase shift?

It is the property of an Inductor. current always lags the voltage by 90 degrees(ideally).
When you connect a battery to an inductor and turn on the switch, the inductor opposes the sudden flow of electrons. It gives up eventually and let's the electrons flow thru it.
Basically the inductor does not like sudden changes. Hence the lag.
Similarly the voltage lags in a capacitor, since it takes time to charge up. It is easier to understand in capacitor than inductor.

 

[HydroGuy]

It is the property of an Inductor. current always lags the voltage by 90 degrees(ideally).
When you connect a battery to an inductor and turn on the switch, the inductor opposes the sudden flow of electrons. It gives up eventually and let's the electrons flow thru it.
Basically the inductor does not like sudden changes. Hence the lag.
Similarly the voltage lags in a capacitor, since it takes time to charge up. It is easier to understand in capacitor than inductor.

Yes, but you don't seem to understand the question. I realize all of what you said, my question is WHY.

Why does an inductor - a coil of wire - oppose the flow of electrons through it?

I understand that an inductor is the shape of a coil to amplify the magnetic field, and that it is this field that resists changes in current. But what about when current is just beginning to flow, and there is no built up magnetic field?

 

[likephysics]

Yes, but you don't seem to understand the question. I realize all of what you said, my question is WHY.

Why does an inductor - a coil of wire - oppose the flow of electrons through it?

I understand that an inductor is the shape of a coil to amplify the magnetic field, and that it is this field that resists changes in current. But what about when current is just beginning to flow, and there is no built up magnetic field?

Yes, there is a build up of mag field. Here's my explanation-
Change in E-field gives rise to Mag field & change in Mag field will result in an E field.
When you flip the switch, there is a change in the E-field. This creates a magnetic field. This mag field will create an E field in the coil that opposes the battery E field.
Field is created by photons which travel at the speed of light(unlike electrons in a wire, which are slow). But this field will decrease due to finite resistance of the coil and current will not be opposed any more.