That picture is a simplified version of a DC motor. The main useful purpose of this motor is for classroom demonstrations. It does not have much practical use outside the classroom.
A working Dc motor will have multiple rotor poles and multiple rotor segments.
The north pole of the rotor is roughly halfway between the north and south poles of the stator. As the rotor turns the commutator changes the connections to maintain the center of the north pole in roughly the same position. The north pole of the rotor is both repelled by the north stator pole and attracted by the south stator pole.

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

I agree with waross, these are both simpler representations to aid understanding.

The op is comparing upper right figure with fourth-from-top figure on RHS.

Both diagrams show stationary magnets, these would in fact represent stationary field poles for industrial dc motors.

The two diagrams differ in terms of the rotor. The top one shows a mult-turn coil wrapped around each of two poles of a 2-pole rotor. The bottom one shows a single coil.

Neither one would represent an actual industrial dc motor rotor, whose construction is somewhat complicated (multiple conductors embedded in slots).

I don't think the authors are intending to convey a difference in construction. magnetic pole attraction / repulsion is another way to look at the same phenomenon as Lorentz force and most other magnetic forces. After all, the single loop conductor in fourth-from-top figure on RHS creates a 2-pole magnet pattern which we could perhaps visualize to attract/repel the stator magnets. Perhaps magnetic poles are more familiar way to show the concept to people who have played with magnets but haven't studied much magnetism. Perhaps Lorentz force is a better way to think about things in motors where the coils tend to be distributed.

That brings us to my whitepaper you mentioned which introduces another layer of complexity. It is a common and useful concept to visualize the torque producing force in terms of Lorentz force acting directly on the conductors. This approach gives the correct qualitative (which direction) and quantitative (how much) prediction of the torque producing force if we make the seemingly-simple assumptions that the conductors are exposed to the airgap flux density and the torque producing force results from Lorentz force directly on the conductors. The paper you mentioned explains that when conductors are embedded in iron slots, both these assumptions are wrong (the flux density at the location of the conductors is actually much less that airgap flux density, and the majority of torque producing force acts on the core), but surprisingly the answer obtained from combining these two wrong assumptions is correct. It is a subtle distinction that for most purposes is not important if you are just trying to visualize things. The web page you mentioned is no longer available, but I attached my whitepapers - short and long versions.

Short version: https://files.engineering.com/getfile.aspx?folder=...

Long version: https://files.engineering.com/getfile.aspx?folder=...

Section 5 of TheLongVersion describes a simple experiment to show the force acts on the core, not the conductor. The pdf link to video of the experiment results is broken, but you can see the video here: https://www.youtube.com/watch?v=Y-rTfPyyaoQ (read section 5 of the Long Version if you watch the video and don't understand the setup)


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• https://files.engineering.com/getfile.aspx?folder=69fc70f5-9822-4260-8bdf-3

Congratulations electricpete for such a wonderful analysis. Can you give such an analysis for transformers. I remember Steinmetz gave such a common theory of machines covering motors and transformers in AIEE but not covered power transfer.
https://www.eng-tips.com/viewthread.cfm?qid=426271 I enquired but could not get a complete picture.

Hi PRC. I'm pretty sure there's not much I could say about transformers that you don't already know. I just started looking at that thread. There was one thing that jumped out at me which I'll post here (since the other thread is closed):

Quote:

Let us consider a two limbed core with HV and LV separately in the two limbs ,unlike concentric arrangement, the normal norm. When we energize HV, voltage will be developed at LV terminals, but when we try to extract current from LV, the terminal voltage will drop to zero due to extremely high leakage impedance between HV and LV winding. So current will not be transferred to LV even with full induction in core. It seems current is getting transferred by the leakage flux. (mutual induction?)

Can't this be accounted for by the expected dramatic increase in leakage reactance when the coils are separated?

Why is it expected: If I wrap one turn tightly around a vertical section of a loop core, then (in addition to flux flowing in a loop through the core), there is flux that travels in the core just in the neighborhood of the turn, exits the core just below the turn, flares out through space including the tank as you mentioned, and returns to the core just above the turn. All of that flux would be leakage flux if the other winding is on the opposite leg of the core. But if I place another winding (open circuited) directly over the first, only the portion of the flux that happens to pass in the very small area between the two windings is leakage flux linking only one winding (all the other flux links both windings) and the leakage reactance is much lower.

EDIT - I see you already said it has extremely high leakage reactance. I guess you were looking at a subtler question, which I'm not quite following.


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At the risk of throwing the discussion completely off course, your post reminds me vaguely of a 1999 post that I particpated in on alt.engineering.electrical

https://groups.google.com/forum/#!topic/alt.engine...

He describes how power can be transferred in a transformer using Poynting theorem through the leakage flux and fields. It's above my head so I can't say whether it is correct, but I think the author has some pretty good credentials.

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Does anyone remember the old constant current transformers used for series street lighting?
The transformers had a tall core with the primary winding around the bottom of the core.
The secondary winding was suspended from a counterweight arrangement and free to travel up and down the core.
Depending on the design, the current and the weight of the secondary winding the counterweight may either add to or subtract from the weight of the secondary winding.
The secondary was supported by the repulsion between the primary and secondary windings.
As more lamps were added in series, the current tended to drop. The repulsion would be less and the secondary coil would drop further down the core until the repulsion again balanced the weight of the winding.
The output current was adjusted by adjusting the weight of the counterweight.

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

waross, heard about it. But no direct experience. Please see this link.

http://www.tpub.com/celec/5.htm

electricpete, thank you very much for that link. I shall bite it and come back. it may take many hours. Years back,my ex boss in ABB Mr Fogelberg (global transformer technical head) also explained to me some thing similar theorem when I posed this question to him. But it went over my head! I am looking for a simple explanation for power transfer that we can explain to an electrical engineering student!

When working with series street lighting circuits all you can depend on is Ohm's Law.

Parallel loads; Current increase with increased loading.
Series loads; Current is constant increased loading.

Parallel loads; Voltage is relatively constant with increased loading with increased loading.
Series loads; Voltage increases with increased loading with increased loading.


Parallel loads; Open circuit voltage normal, current zero.
Series loads; Open circuit voltage dangerously high, current normal.

Parallel loads; Overload or short circuit, dangerously high current. Safe by opening circuit.
Series loads; Overload or open circuit, dangerously high voltage. Safe by shorting transformer output.


In normal operation the voltage across each lamp was less than 100 Volts.
In the photograph you may see a small button between the ends of the bayonets.
This would short out at around 100 Volts and bypass a burnt out lamp.
The mogul lamp socket was special in that the center contact was spring loaded and had an extension tab.
When a lamp was removed the spring would force the center contact upwards until the tab made contact with the shell, shorting out the lamp holder.

Regulators were protected by a similar device but with a permanent shorting link. The button was about 3/4 inch in diameter and resembled the tire only from a toy car.
A small circular lead plug was pressed into one side of the center hole.
A number of mica washers were then inserted, the number dependent on the loaded circuit voltage.
In the event of an open circuit the current would flash over between the lead plugs or disks.
The arc would melt the lead that would flow together and short out the regulator.
All you ever wanted to know about series regulators and circuits.
There were a number of standard currents in use;
6.6 Amps, 7.2 Amps, 7.5 Amps and 20 Amps.
Current transformers (Not to be confused with CTs) could be and were used to transform from one current level to another.
20 Amp circuits were a special case.
On streets where street cars ran, the vibration from the passing street cars often caused rapid burnout. The voltage across a 20 Amp lamp was around 12 to 20 Volts depending on the lumens output.
The filament was massive. When disconnected, instead of going out immediately, the filament cooled down like a toaster element.
Compare a toaster element at about 6 Amps with a filament at 20 Amps.
The lower output lamps worked well on a 12 Volt car battery.
On some circuits the regulator output was 7.5 Amps and a small current transformer was installed in the base of each pole to transform the 7.5 Amps to 20 Amps.
There were also series mercury vapour ballasts available and used on some circuits.

The Point Grey area of Vancouver Canada was a separate municipality until it merged with Vancouver in 1929.
I had the privilege of working for a time on series street lighting with an old time who had started his career as an apprentice installing series street lighting in Point Grey municipality. He was about a year away from retirement when I worked with him.
It was a great experience.

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

Quote:

I am looking for a simple explanation for power transfer that we can explain to an electrical engineering student!

I'm still not sure exactly what it the subtle aspect you're trying to explain. But I'll take another stab because I'm a lot closer to a confused beginning college student than you when it comes to transformers.

I'm sure you can talk about the equivalent circuit. Apply a voltage to the primary (with secondary open circuited) and a current flows in the primary to create flux in the core whose rate of change balances the applied voltage. That flux induces a voltage in the secondary. Add a resistive load to the secondary and it draws current according to ohms law, except the voltage droops a little due to leakage reactance. The primary needs to provide additional current to balance the secondary current amp-turns (same phase) to keep the flux roughly the same in order to balance applied voltage.

So, the equivalent circuit predicts power transfer. What else remains to be said about power transfer?

Well there is of course stored energy in the magnetic field (flux). And even before we connect the secondary load, the primary winding is exchanging instantaneous circuit power with the magnetic field. If we consider the phase relationship of the magnetizing current 90 degrees behind applied voltage by Farady's law, we conclude there is instantaneous power exchanged between the primary winding and the core at a frequency twice the applied frequency, even though the average power transfer is zero (this power exchange is of course better known as reactive power).

So the primary is exchanging circuit energy with magnetic energy while the secondary is open circuited. That doesn't seem controversial or non-intuitive (does it?). I think maybe we can just extend that same idea to describe real power transfer under load in terms of energy transfer between stored magnetic energy and the primary and secondary circuits. We already know the behavior of voltages, currents and flux from equivalent circuit, we just add the bit that flux represents energy storage that can exchange with the circuits. Does that sound like it's heading in the right direction?


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"... I am looking for a simple explanation for power transfer that we can explain to an electrical engineering student!"

[Stay, OUT-of-the-WAY!]

John ; )