# Windings: basic questions.

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#### Browser

##### 100 W
Hi guys,

I'm trying to wrap my brain around some of the fundamentals of motor design.

Much of this will be trivial for those of you with the appropriate knowledge/
background/experience, but I'm trying to catch up fast, so please don't jump on me
for my misunderstandings.

Also, for the purposes of this series of questions I'm for the most part ignoring
"losses" -- induced eddy currents and the like. I know they are important to final
designs, but right now I just consewring the basics.

Starting at the beginning, the typical explanation looks something like this:
Code:
``````            ^
|
+------+ - -|- - +-------+
|      | - -|- - |       |
|      | - +|+ - |       |
|  N   | - |/| - |   S   |
|      | - +-+ - |       |
|      | - - - - |       |
+------+ - - - - +-------+``````
Given a magenetic field, and conductor carring a current (into the screen), the
conductor experiences a force (upwards). The force expereinced is proportional to
the strength of the magnetic fields, the strength of the current being carried by
the conductor, and the area of that conductor.

So, given a field strength govorned by the choice of magnet, and the current by the
power supply, to get the most torque (conductors and/or magnets constrained to move in a circle)
we need to fill the gap with as much conductor as possible.

So question 1: why not put one big-assed conductor in the gap?
Code:
``````           /^\
|
+------+ +-----+ +-------+
|      | |/////| |       |
|      | |/////| |       |
|  N   | |/////| |   S   |
|      | |/////| |       |
|      | |/////| |       |
+------+ +-----+ +-------+``````
I think the answer to this is: because a big, solid conductor would experience a
very large back-EMF,

So the typical solution is to fill the gap with lots of small insultated conductors:
Code:
``````           /^\
|
+------+ +-+-+-+ +-------+
|      | |/|/|/| |       |
|      | +-+-+-+ |       |
|  N   | |/|/|/| |   S   |
|      | +-+-+-+ |       |
|      | |/|/|/| |       |
+------+ +-+-+-+ +-------+``````
Usually, round, but with square magnet wire, you can achieve a "higher fill factor".

Also possible are "foil-wound" coils (Question 2:Though I see little mention of them here or elsewhere. Why?):
Code:
``````+------+ ||||||| +-------+       +------+ ------- +-------+
|      | ||||||| |       |       |      | ------- |       |
|      | ||||||| |       |       |      | ------- |       |
|  N   | ||||||| |   S   |       |  N   | ------- |   S   |
|      | ||||||| |       |       |      | ------- |       |
|      | ||||||| |       |       |      | ------- |       |
+------+ ||||||| +-------+   or  +------+ ------- +-------+``````
My next question 3: does it matter which way the "width" of the foil runs through the gap?

Finally, we arrive at the question that's been bugging me the most, but which I've been
unable to find an answer to despite reading dozens of articals and papers.

Typically, the individual conductors running through the gap are connected serially, as a part of a coil:
Code:
``````         +--------------------------------------+
|+------------------------------------+|
||+----------------------------------+||
|||+--------------------------------+|||
||||+------------------------------+||||
|||||+----------------------------+|||||
||||||+--------------------------+||||||
+------+ ||||||| +-------+       +------+ ||||||| +-------+
|      | ||||||| |       |       |      | ||||||| |       |
|      | ||||||| |       |       |      | ||||||| |       |
|  N   | ||||||| |   S   |       |  N   | ||||||| |   S   |
|      | ||||||| |       |       |      | ||||||| |       |
|      | ||||||| |       |       |      | ||||||| |       |
+------+ ||||||| +-------+       +------+ ||||||| +-------+
||||||-                          |||||||
|||||+---------------------------+||||||
||||+-----------------------------+|||||
|||+-------------------------------+||||
||+---------------------------------+|||
|+-----------------------------------+||
+-------------------------------------+|
+``````
With the "other side" of the coil doing duty passing through a field elsewhere in the motor, but
giving rise to losses and cost due to the "end turns".

So, question 4 is: why are they connected serially?

Why not connect the individual conductors through the field in parallel?
Code:
``````  - -----+++++++                          +++++++---- +
+------+ ||||||| +-------+       +------+ ||||||| +-------+
|      | ||||||| |       |       |      | ||||||| |       |
|      | ||||||| |       |       |      | ||||||| |       |
|  N   | ||||||| |   S   |       |  N   | ||||||| |   S   |
|      | ||||||| |       |       |      | ||||||| |       |
|      | ||||||| |       |       |      | ||||||| |       |
+------+ ||||||| +-------+       +------+ ||||||| +-------+
+++++++--------------------------+++++++``````

I'm sure there is a good reason, because no one seems to do it, I just don't see what that reason is?

Thanks for your time and expertise,

Buk

#### Browser

##### 100 W
Too simple? Too complicated? Wrong place? Wrong questions?

Anything?

#### major

##### 10 kW
Browser said:
So question 1: why not put one big-assed conductor in the gap?

I think the answer to this is: because a big, solid conductor would experience a
very large back-EMF,

Hi Buk,

It is the other way round. A single conductor, one or a half turn coil, will typically have a very low generated voltage which is cumbersome to use with available power supply potentials. So multiple turns, or series connected multiple conductors, and/or series connected coils in the armature are employed such that the armature voltage is near the supply voltage for the machine speeds desired. This term, turns per coil, or T/c, is often represented by the symbol N. See Faraday's Law.

I think if you can understand what I am saying, most of your questions from post one will clear. I found that post difficult to follow, especially your diagrams.

Regards,

major

#### spinningmagnets

##### Moderator
Staff member
I am no motor expert, but...I am of the opinion that the reason hubmotors are the way that they are is due to the low price which results from mass production, and the price sensitivity of the majority of customers.

One example might be that, last year I was quite surprised to find that upgrading a hubmotor from 0.50mm thick laminations to the more desirable 0.35mm lams was less than \$10 per hubmotor. Why isn't everyone doing that? 98% of customers will not pay \$10 extra for some feature that has a minor benefit under most circumstances, and 98% of wholesalers won't give up \$10 of their "per unit" profits...

#### Browser

##### 100 W
Major.

Thanks for the reply. I thought I'd offended the gods there for a while

However this makes no sense to me:

It is the other way round. A single conductor, one or a half turn coil, will typically have a very low generated voltage which is cumbersome to use with available power supply potentials.

Given this is a motor not a generator, isn't "a very low generated voltage" (ie. low back-EMF) exactly what you want!? And if that was what you got by using a single solid conductor, that would be the way to go.

Hence why I assume that the reason people don't use single fat conductors is because the induced current (back-EMF) is very large, due to the large area in which the eddy currents have to circulate.

This is in large part confirmed by the discussion and conclusions in this pdf I found since posting my questions: http://www.diva-portal.org/smash/get/diva2:680359/FULLTEXT01.pdf.

The discussion there also answers (assuming I'm interpreting it correctly, of which there is no guarentee), the question about why people don't use parallel conductors (or windings); ie. because parallel windings allow the eddy current to circulate.

That only leaves my question about why home builders don't use foil-wound coils? It seems that these would be ideal in slotless, ironless axial flux motors (like the one Lebowski detailed here)?

Please don't think I'm arguing with you. I'm just having a much harder time wrapping my brain around this that I'd like to admit, and if laying my thoughts open leads to someone seeing where my misunderstanding is coming from...

Cheers, Buk.

#### major

##### 10 kW
Browser said:
However this makes no sense to me:

It is the other way round. A single conductor, one or a half turn coil, will typically have a very low generated voltage which is cumbersome to use with available power supply potentials.

Given this is a motor not a generator, isn't "a very low generated voltage" (ie. low back-EMF) exactly what you want!? And if that was what you got by using a single solid conductor, that would be the way to go.

Whenever you have an armature (conductors or coils) rotating in a magnetic field you have a generated voltage. If that generated voltage opposes the applied voltage, we call the machine a motor. Calling that generated voltage BEMF is a real source for confusion IMO. That generated voltage times the armature current is the power converted from electric to mechanical in the motor. The higher the generated voltage (nearer to the applied voltage), the more efficient the power conversion. Generated voltage in the motor is a good thing. It often gets a bad rap.

As far as the size, shape, number, material, connection, etc of the armature conductors or coils; it just depends on the design, application and constraints. There are some opinions supporting low voltage motors for ebikes and some attempts to design and fabricate "low turn coils" on this board. I don't know of any success stories offhand. Most end up with medium voltage multi-turn round wire coil armatures. You're welcome to take the path least traveled. I'm sure there is interest in watching your progress. But you're likely to spend considerable effort, time and expense without realizing any significant gains in performance.

Regards,

major

#### Browser

##### 100 W
If that generated voltage opposes the applied voltage, we call the machine a motor.

Hm. If its a generator, there is no applied voltage to oppose?

Buk.

#### Punx0r

##### 1 GW
Browser said:
Hence why I assume that the reason people don't use single fat conductors is because the induced current (back-EMF) is very large, due to the large area in which the eddy currents have to circulate.

Is there a mixing-up of current and voltage here that's causing confusion?

#### crossbreak

##### 1 MW
Browser said:
If that generated voltage opposes the applied voltage, we call the machine a motor.

Hm. If its a generator, there is no applied voltage to oppose?

in a simple model, armature voltage is simply back-EMF + voltage drop over motor resistance (let inductance out of the equation, it does not matter that much here)

"Va" is the voltage source (motor controller) or armature voltage (they are equal, since they are connected), "Ra" is armature resistance, "e" is the back EMF voltage source.

Motor: Va = EMF + resistive voltage drop = e + Ra * I
Gernerator: Va = EMF - resistive voltage drop = e - Ra * I

here, the current "I" is always positive, its direction is alters. I hope i can make this clear with the "+" and "-" signs. If net current flows into the machine, it's a motor. If it runs out of the machine, it is a generator. So what determines, if a machine is a generator or motor, is current - or voltage - turn it as you like, as they both depend on each other.

the resistive voltage drop is dependent on resistance and current, described by the ohmic law: V = R * I, where V is voltage, R is resistance and I is current.

EMF Voltage is speed dependent:
e= rpm/kV, where "Kv" is the Back EMF constant, and "e" again is the back EMF

torque produced is proportional to armature current: T = I *Kt, where T is torque and Kt is the Torque constant, it can be easily derived from Kv:
Kt = 60/Kv/2pi

So why do you want a motor with great back EMF? It then has a high Kt figure, which means it will do great torque with little current

Kt tells you nothing about how much torque a motor can actually produce. It just tells you how much current it will eat for a certain torque. The only really feasible way to tell how much torque a machine can actually produce is by testing and direct measurement - on a dyno for example

#### major

##### 10 kW
Browser said:
If that generated voltage opposes the applied voltage, we call the machine a motor.

Hm. If its a generator, there is no applied voltage to oppose?

Hi Buk,

Perhaps not the best choice of words on my part. How's this? Motor when rotor torque assists rotation. Generator when rotor torque opposes rotation. As far as the generated voltage in the armature coils, it doesn't matter if it is a motor or generator. That is why I don't like calling it back emf. It isn't for the generator. Yet it is exactly the same thing; motor or generator.

As far as your solid conductor in the slots, I ran across one thread. I don't believe he ever got 'er done. https://endless-sphere.com/forums/viewtopic.php?f=30&t=70009

Regards,

major

#### Browser

##### 100 W
crossbreak said:
Kt is the Torque constant, it can be easily derived from Kv: Kt = 60/Kv/2pi

Hm. I think you mean Kt = 60 / Kv * 2pi. (I'm assuming a simple typo here

But what does that equation actually tell us?

Given that 2 of the 3 values on the right-hand side are constants ( 60 to convert RPM to RPseconds; and 2pi to convert revolutions to radians.),

Then all that equation tells us is that Torque is proportional to current. (No argument or surprise there.)

But, given the resistance of the conductor is fixed (ignoring high frequency components), then the current that flows is proportional to the voltage across it.

And, as induced voltage (aka. backEMF) is (by Lenz) in opposition to the applied voltage, the effect of back-EMF is to reduce the effective voltage across the conductor,
and thus reduce the current that flows; and consequently reduce the torque that is produced.

(Obligatory wikipedia quote from https://en.wikipedia.org/wiki/Counter-electromotive_force: "In a motor using a rotating armature in the presence of a magnetic flux, the conductors cut the magnetic field lines as they rotate. This produces a voltage in the coil; the motor is acting like a generator (Faraday's law of induction.) at the same time it is a motor. This voltage opposes the original applied voltage; therefore, it is called "back-electromotive force" (by Lenz's law). With a lower overall voltage across the armature, the current flowing into the motor is reduced")

Which shows this is a misunderstanding; or at least a misapplication.:
crossbreak said:
So why do you want a motor with great back EMF? It then has a high Kt figure, which means it will do great torque with little current

For completeness, remember that the definition of Kv (your starting point and the underlying derivation of Kt) is determined by experiment on the actual motor.

That is, they run the completed motor, without load, upto the highest speed it will achieve. As back-EMF increases with speed, you eventually reach the point where the backEMF exactly negates the applied voltage at which point no more current can flow, thus no more torque can be supplied; and the motor can go no faster.

At that point, they divide the speed the motor achieved by the (supplied) voltage the motor took and the result is the Kv in RPM/volt.

By that point, all the design choices for the motor, good, bad, and compromises, have already been made and the Kv is a measure of that; but there is no way to use Kv as an input to your design criteria because you cannot calculate it until the motor is already in existence.

#### crossbreak

##### 1 MW
you can design Kv simply by turn count of the coils.

And, as induced voltage (aka. backEMF) is (by Lenz) in opposition to the applied voltage, the effect of back-EMF is to reduce the effective voltage across the conductor,
and thus reduce the current that flows; and consequently reduce the torque that is produced.

exactly. think you got it. This is what i want to tell you by the equation Va = e + Ra * I. EMF reduces the current at speed that can flow at stall: At stall it is just limited by resistance

Kt = 60/Kv/2pi
thats right. you could also write: Kt = 60/(Kv*2pi). This is equal, maybe less misleading... Kt = 60/Kv*2pi without parenthesis is wrong though

For completeness, remember that the definition of Kv (your starting point and the underlying derivation of Kt) is determined by experiment on the actual motor.
yes, but this can be altered by coil turn count. This way, by altering the way you wind your motor, you can design Back EMF the way you want. As said, this does not alter maximum power output or torque output, which is determined by "magnetic" motor design (like size, material and slot depth... and many more)

#### major

##### 10 kW
Browser said:
........ there is no way to use Kv as an input to your design criteria because you cannot calculate it until the motor is already in existence.

Of course there is. Motor designers do it all the time. Using SI Units, Kv is equal to Kt. For PM DC motors, it is calculated this way.
PM motors essentially have a constant flux, Φ. And the motor has a machine constant (sometimes called the torque constant), Kt. The developed torque (Tem) = Kt * Φ * Ia where Ia is armature current. The generated voltage (Eg) = Kt * Φ * ω where ω = rotational velocity. The machine constant Kt is essentially the number of turns. For the particular PM motor, KtΦ is fixed and torque is proportional to current and voltage to speed.
Kt = p * N / (2 * π * a)
Where p = # of poles, N = # of armature conductors, a = # of parallel paths in the armature circuit.

The flux can be calculated from the material characteristics and machine geometry. Several of the members use a program called emetor, https://www.emetor.com/, for BLDC motors.

#### Browser

##### 100 W
you can design Back EMF the way you want.

Were that the case, the optimum "designed back-EMF" for a motor would be zero.

Because, with zero back-EMF, all of the applied voltage would contribute to producing current and thus torque. Regardless of the speed of rotation.

This would give the (famed) maximum-torque-at-standstill, at all speeds. And the speed would be unlimited, because every addition applied volt would translate into more current and more torque.

Obviously, that can't be done; but it still stand that by minimising the back-EMF -- all else being equal -- maximises torque.

#### major

##### 10 kW
Browser said:
you can design Back EMF the way you want.

Were that the case, the optimum "designed back-EMF" for a motor would be zero.

Because, with zero back-EMF, all of the applied voltage would contribute to producing current and thus torque. Regardless of the speed of rotation.

This would give the (famed) maximum-torque-at-standstill, at all speeds. And the speed would be unlimited, because every addition applied volt would translate into more current and more torque.

Obviously, that can't be done; but it still stand that by minimising the back-EMF -- all else being equal -- maximises torque.

A motor with zero generated voltage (BEMF) has all armature current producing heat in the resistance and therefore zero power output. You can get a lot of torque, but without power, you're not doing any mechanical work. That generated voltage in the motor is the best thing that ever happened to energy conversion.

major said:

TNSBATWWNS

#### Punx0r

##### 1 GW
I get the impression BEMF is in itself not a desirable thing (since, as said, it opposes current flow and torque production), but is a side effect of something that is desirable: a conductor in a rotating magnetic field, which in itself produces torque. The larger the winding (greater amp-turns) and the stronger the magnetic field, the more torque. That said, my reasoning might be circular (or at least a rephrasing of the same thing) since I've got "opposes torque" Vs. "creates torque" for essentially the same thing...

I get what Major is saying, if BEMF were zero, it would presumably be because there is no movement of the conductor through the magnetic field = potentially infinite torque, but no speed, hence no power/work. Likewise, if BEMF were infinite, torque would be zero and again, zero power/work.

Damn engineering compromises

#### crossbreak

##### 1 MW
+1 to major...this discussion is getting pointless. Low kV means high back EMF means high torque per amp. With zero back EMF CONSTANT you get ZERO TORQUE!!! That's NO MOTOR....At stall, there is no back EMF. So Torque is at its maximum. Still NO MOTOR as nothing is turning. Just dump still standing force.

#### Browser

##### 100 W
Punx0r said:
I get the impression BEMF is in itself not a desirable thing (since, as said, it opposes current flow and torque production), but is a side effect of something that is desirable: a conductor in a rotating magnetic field, which in itself produces torque.

The problem is that major is continuing to conflate -- or failing to differentiate, which amounts to the same thing -- between the (desirable) EMF that results entirely from the applied voltage. (No movement required!);

And the (undesriable) back-EMF that results from the movement that results from that application.

It is easy to demonstrate this. Lock the rotor (with a torque brake) and apply the power.

The torque brake will register the maximum torque; but there can be no back-EMF as there is no motion, so no moving magnetic field to induce the back-EMF.

But I seem to be wailing in the wind here

Buk

#### Browser

##### 100 W
crossbreak said:
With zero back EMF CONSTANT you get ZERO TORQUE!!!

Yesy, yes, yes! Exactly.

That's NO MOTOR....At stall, there is no back EMF. So Torque is at its maximum. Still NO MOTOR as nothing is turning. Just dump still standing force.

And then you threw it all away.

If you are on a hill and the motor is supplying just enough torque to stop you rolling back, but not enough to allow you to move forward, IT IS STILL DOING WORK!

Thus, it is a motor. But there can be no back-EMF because there is no moving magnetic field.

Ergo; torque production is not predicated upon the presence of back-EMF. (Indeed, as I've been saying, torque creation is OPPOSED by back-EMF!)

#### major

##### 10 kW
Browser said:
If you are on a hill and the motor is supplying just enough torque to stop you rolling back, but not enough to allow you to move forward, IT IS STILL DOING WORK!

It is not doing mechanical work. The motor may be producing torque which is used to counteract the force of gravity, but if there is no displacement, then zero work is done by the motor. There is energy conversion in the motor but it is all to the form of heat and doing no useful work. If you set the parking brake and turned off the motor, would that be doing work? Nope.

I told you this before.
major said:
A motor with zero generated voltage (BEMF) has all armature current producing heat in the resistance and therefore zero power output. You can get a lot of torque, but without power, you're not doing any mechanical work. That generated voltage in the motor is the best thing that ever happened to energy conversion.

#### major

##### 10 kW
Browser said:
The problem is that major is continuing to conflate -- or failing to differentiate, which amounts to the same thing -- between the (desirable) EMF that results entirely from the applied voltage. (No movement required!);

That is the voltage drop across the armature resistance resulting in wasted energy.

Browser said:
And the (undesriable) back-EMF that results from the movement that results from that application.

That is the potential responsible for energy conversion.

#### Browser

##### 100 W
major said:
I told you this before.

Yeah. You "told" me a lot of things; all equally wrong. Which I tried to gently attribute to typos and misunderstandings, whilst patiently correcting them with simple logic and analogy.

I came here looking for expertise, and I got YOU,

Which is a real shame, because my pre-posting lurking showed me that there are some real experts here.

So, now you've screwed my thread up by holding onto what is obviously a holy cow to you, despite that it is so obviously and patentely incorrect, I'll get branded as the noisy one.

All that's left for me to do is go find somewhere else to ask my questions and hope this time I get a more accomplished first-responder.

Thanks for nothing. Pal

#### Browser

##### 100 W
major said:
Browser said:
The problem is that major is continuing to conflate -- or failing to differentiate, which amounts to the same thing -- between the (desirable) EMF that results entirely from the applied voltage. (No movement required!);

That is the voltage drop across the armature resistance resulting in wasted energy.

Browser said:
And the (undesriable) back-EMF that results from the movement that results from that application.

That is the potential responsible for energy conversion.

How can the back-EMF, which cannot exist until the wheel moves, be responsible for it moving?

If you cannot bring yourself to see the total illogicality of what you are saying, then it is time to expand the acronym:

There are none so blind as those that will not see.

Bye

#### Punx0r

##### 1 GW
I don't think you'll find much luck elsewhere. It seems like you've got this great, simple idea to make motors much better, that everyone has somehow over-looked for the past ~150 years. I've just reread and digested the questions in your OP and I think the problem is you have a misunderstanding of how motors work and why contemporary models are designed the way they are. You're trying to shout down Major, who does knows his stuff on motors, like his an ignorant fool, while in your OP asking questions about some very fundamental aspects of electromagnetics like which way around should the foil be laid? If you're an expert why not just answer your own questions by deriving the answers from first principles?

I prefer to research, read and listen to the advice of those who have demonstrated themselves to be more knowledgeable than myself

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