Motors, torque, windings Scale Speed

[mmagliaro]

After the brief motor musings that sprouted up in my E7 project thread,
I have done some more reading and thinking about DC motors, torque, and the relationship between torque,
current, and speed.

I'm spewing this in here to elicit some more discussion.  I think I am beginning to get a feel for this
in layman's terms.   I'd appreciate someone with more of a physics and electromagnetism
prowess chiming in on all this. 

I openly claim that although I had my share of electrical engineering courses, electromagnetism
and physics are areas where I am decidely weak.  So if somebody can explain why the following
is all nonsense, feel free to explain that to me.  (but do it nicely     )

First, let's separate the terms power and torque, which are often confused.
Torque is really the rotational force the motor has.  Think of it as the "push" exerted continuously
around the center of the motor as it spins.   

Power , however, is just a measure of that force exerted over a distance, as in 

P = t x w 
where t is the torque and w is the angular velocity.
In other words, for a given torque, the faster the motor spins, the more power it is producing.

I would argue that I am not really interested in power, except perhaps as it gives me a gut
feel for what a motor can do.  I am much more interested in the torque.  I want the motor to push
very hard, but be able to do that very slowly.   If the motor has high power at low rpm,
that implies it has high torque, and that's really what we are after.

Needing to run the motor very fast to get lots of power out of it is not of much use in a locomotive.
This is what happens when you have an engine with a weak motor where you have to juice
the throttle as it climbs a hill to keep it from slowing down.  The motor cannot produce enough
power at low rpm to climb the hill, so we speed it up.   

When I put a gear reduction head in my engines, this is the problem I am solving.  The motor
can now spin faster, and produce more power, but the gearhead compensates for the excessive
speed, so that the net output of the gear-reduced shaft is lots of power at low speed

If the motor had lots of torque, it could
produce that power at low rpms and it would not slow down.

Torque is proportional to the current we are drawing in the windings.
t = I x K   
where I is the current, and K is the "torque constant" of the particular motor.

So, okay.  We draw more current at a given speed, we get more torque. 
But... what about this "K" factor?

I found several different expressions for K, but this one is easy for me to understand:

K =2 x B x N x L x R

B = strength of the magnetic field
N = number of turns of wire
L = length of the field
R = radius of the armature.

Let's assume that L and R do not change because we are not going to change out the whole armature.
We are just going to rewind it with thinner wire.  And let's assume we rewind it so that it ends up at
the same radius it was befor (which is pretty much true because you can only pack so much wire around
that armature and still have it fit within the poles).

So for the remainder of this discussion, let's say that
K=2 x B x N  because L and R aren't going to vary.  (pretend they are both 1 if that makes you
feel better)

If we rewind an armature with more turns of thinner wire, what happens?
Clearly, N goes up.  What happens to B, the magnetic field?

This page is quite illuminating:
http://www.regentsprep.org/Regents/physics/phys03/csolenoid/turns.htm

Indeed, if we double the turns, we double the strength of the field, but that's only if all other things
are equal.

Let's say we rewind the motor with twice as many turns of thinner wire.  That wire has a higher resistance
than the thicker wire.  Therefore, the motor draws less current for a given voltage.
So, at 5 volts, say, let's say it drew 100mA before.  Now it might only draw 50 mA.   

A key point here is that the diameter of the wire turns out to have very little effect
on the actual current that the motor draws!   Here's another illuminating thing I scraped from
the web:
Resistance of the armature widings has only a minor effect on armature current. Current is mostly determined by the voltage induced in the windings by their movement through the field. This induced voltage, also called "back-emf" is opposite in polarity to the applied voltage, and serves to decrease the effective value of that voltage, and thereby decreases the current in the armature.

Sooo... we may indeed be drawing less current, but we have a much longer run of wire.
and we won't be drawing that much less current.

Can we set things up so that we get 1/2 the current, but we get twice the length of wire?

Maybe.  Maybe not.   But allow me that latitude for a moment in order to express the idea...

If we did, then our magnetic field, B, would remain the same.
And if B is the same, then K would double. 
Remember K = B x N
B is the same,  and N is twice what it was before.

So... our current is cut in half, K has doubled, and therefore our torque, t = I x K, has remained the same.

Darn... no change, doctor.   BUT WAIT.

The rotational speed of the motor is NOT the same.   The motor speed is a function of voltage and current.
Indeed, with a lower current, the motor spins slower.  So we have a motor that is turning
slower, but with the same magnetic field it had before.

We have more torque!   Or, put another way, this motor can produce as much mechanical power
at, say, 1000 rpm as the heavier-winding motor could at 2000 rpm.  That's just what we want.
And I suspect this is what goes on with things like the Scale Speed Motor.

Of course, it's not "magic".  There are limits to these things.
You can only make the windings so thin.   And the more load you put on the motor, the more current
it is going to draw, and you could well exceed the capacity of the thinner wires and burn them
right up.  So you can't create a "super motor" by just putting ridiculously thin windings on it.

Also, remember how I glossed over the doubling factors?
Reducing the wire size and increasing the number of windings
doesn't work out to these awesome "doubling" relationships that I used above just to make my point.

But if I think what's going on here is that you can reduce the wire size and increase the number of windings
enough to get a stronger field, higher resistance, lower rpms and more torque.

[victor miranda]

Hi Max,

I have to ask you where you found all that info...

I found I read all that and said "but. Ummmm..."
a few times

this one is a leading example...
Resistance of the armature widings has only a minor effect on armature current.
Current is mostly determined by the voltage induced in the windings by their movement through the field.
 This induced voltage, also called "back-emf" is opposite in polarity to the applied voltage,
and serves to decrease the effective value of that voltage, and thereby decreases the current in the armature

there are aspects of this that are not true?
or are glossing over some critical pieces of the puzzle.

so slow down a bit and maybe we can piece out the puzzle.

I have a lot of practice with the usual construction of motors and what we do with them
this is seat of the pants knowlege and it may be all of what is written is true somehow
and there are aspects in how it gets said that cause me to pause with 'but, ummm...'

allow me to point out that you can use very thin wire and make it so long
that the static resistance of the coil is 240 ohms. this motor at 12 volts will only ever allow 50ma.
as the motor spins up the current will drop from back emf.

so I am a little suspicious of the sentence. It is likely true, somehow it lacks completeness to me.
iF is said the motor has to be spinning fast enough to generate back-emf and then this idea is true
then it fits in with I understand.

That leads me to the other thing that still drives me nuts
how a motor acts before it gets to spinning. 
I understand that for brushed DC motors this line in true
the motor generate max possible torque at stall.
this is easy to calculate... measure the current... or calculate the current
using the static resistance of the motor. I recall that Kato motors measure 24 ohms.
(it is a number...  you get different, post it) that means at stall and 12 volts
the motor will draw 500ma.  Ever see a kato loco draw more?

I know you want more torque.
the problem you have is that as you change the motor parameters
you have the stall current draw as a potential source of overheating the motor.
you must allow the motor to spin up enough to resist the current flow and not overheat.

so while more wraps in the coil look like the path to more torque
it is also the path to higher starting voltages.
... the loco starts moving at 3 volts and 40ma (120mW and apparent 75 ohms resistance)
and you change it to more wraps  so the starting voltage moves up to 4 volts
and the current should drop to 30ma (120mw and apparent 133 ohms)

all those calculations seem consistant.

how do we decide we have more torque available?

  we build them and test them!!!!
I have some ideas for avoiding the building part BTW....

I have to tell you that from slot car racing, the cars were faster
and came out of the starting blocks much quicker
if we used fewer wraps and thicker wire.
The thinking is that more torque is required to do the above.

so my experience with getting more torque was down the thicker wire path
which is the opposite of my understanding of what you have posted.
Now I am real curious.  Lets figure it out, cause I don't claim I know all this.

victor

[mmagliaro]

Victor...
This is a long and complicted subject.  And my post is certainly guilty of being one of the longest
and possibly eye-glazing I have written.  But I want to address one point you made and think
about the others some more...

From your slot car experience...

Interestingly, I find that that agrees with my theoretical musings, and here's why.

I think the trick to the slot car is not being torque limited OR rpm limited.

Fewer wraps of thicker wire will draw more current and will cause the motor to spin faster.
I suspect that this is good for a slot car because when you come off the blocks, you probably
tromp on the throttle and run that motor full out.  This means that you really don't care as much about
low-speed torque.   Torque matters, but what you are really after is power  In other words,
how many turns can that motor make in that first second to pull your car ahead of the others,
or torque x distance

Let's consider what happens at the high end of the speed range of our two motors.
The one with thinner windings is current limited.  At a full 12 volts, it can only draw so much current
and since the RPMs are a function of voltage and current, it cannot spin as fast as your
lower-winding, heavier-wire motor.

For a slot car race, unless the motor is too torque-limited, I would think that higher power matters more than
higher torque.   Remember my observation that power is a function of torque x distance.
Well.... if the torque is lower, but the rpms are higher, you may still end up with more power than
in the thinner-wound motor.  And in a slot car race, more rpms = covering more distance more rapidly,
matters more.  If the guy with car next to yours has double your torque, but his motor can only spin
1/2 as fast yours, it will be only a fraction of a second before your motor is spinning faster than his and you
pull ahead of him.   

The hand-waving is that the motor design has to be chosen carefully. 
If you choose the right balance, you will have a motor which trades some torque for high-end speed.

Put another way, the thin-wound motor is like an I1 - able to exert more pull, but at limited speed,
and the slot car is more like a K4 - it can move the train faster and would beat the i1 in a race
as long as the train isn't too heavy.

[Iain]

I dunno why, but this stuff really torques me! 

Interesting experiment:  Hook a motor in series with a speaker and run it at various speeds.

[victor miranda]

well...

we can measure or calculate power in.

I have to wonder if we can agree about power out...

two thoughts spring to mind after that
first is that max torque is measured at stall in a brushed DC motor.

second is that we can assume since the rotor is static at that point...
the torque generated is a direct function of the power in...
more power in... more torque...
good right up to smoke out...

[eja]

I= ER or is it I= e/R or R/IE  ....some guy named Ohm or was it Holmes. Oh wait, was it Watt?  Perhaps ergs?  You remember ... a dyne cm/ sec ²

Carry on Gents, I enjoy these discussions.


eja

[mmagliaro]

Yes, at stall, it's easier to analyze and to intuitively visualize.
An armature with thinner wire, and more of it, will have higher resistance and will draw less current.
So at stall, at maximum torque, with a constant voltage, the power in will be higher
in the motor with fewer turns of thicker wire.

At first, I thought, well, there you go.  The stall torque, which is the motor's maximum,
is highest at stall, and is proportional to the power in because it has no back emf and
no frictional losses to even worry about.  So therefore, the motor with fewer thick windings
must have more torque.

But... wait.   Power in = Power out.  The motor with the heavier windings drawing more
current is going to lose more power in heat than the motor with the thin windings.
And in fact, since the motors are stalled, all the power is in heat.   There is no
power from the rotation if the motor isn't spinning.   Now we have to worry about
the conservation of energy.  How is it converted to heat and to torque?

We cannot just assume that the heavy-wired motor produces more torque based on this.
How much energy is lost in heat?  It certainly depends on the exact materials, thickness of wire,
etc. 

This is gets more complicated with each exchange.

The torque vs speed plot of a motor is usually a straight line.  And its maximum is at zero rpm.
But that line can have a different slope.   A thin-wired motor may have less stall torque than
a thick wired motor, but when not stalled, the torque line may decline more sharply on the
thick wired motor.  I don't know the answer to that question.

EDIT:
I still think the key may be that a motor with more windings of the same gauge wire
would produce more torque because it has a stronger magnetic field.  And therefore, if we use
thinner wire, to squeeze more windings in there, and the current change due to the wire thickness
is not significant, then thinner wire would produce more torque.   That "theory" (that the thickness
of the wire is not the significant factor in the motor's current draw), is only true when the motor
is not stalled.   It may be true that the thicker-wired motor has more stall torque, but
quickly drops below the thinner-wired motor once they are moving.

[mmagliaro]

Victor,  I forgot to mention where I got some of this internet info.
http://www.micromo.com/motor-calculations    A really nice DC motor tutorial from our
friends at Faulhaber.

If you page down to the first chart of torque vs rpm vs efficiency, note how at the lowest rpms, (about 175),
where torque and current are high, the efficiency is terrible (about 1%). So therefore,
most of the output power of the motor is being wasted (I assume through heat).

[victor miranda]

Hi Max,

the micromo website is a difficult read and it requires concentration
and I am taking a break from reading it.
Thank you for finding and sharing.  I am having a lot of fun reading it.
 
I am still thinking about the goal you have of getting more torque.
the thoughts we are chasing are relative right now and we may want to
shift to a standard to help us see if we have a handle on our understanding of
the terms we kick about and to aid is seeing when we have moved toward that goal.

my off hand approach so far has been look for any way to get the overall effect
of a loco gliding on rails.
so far I have found coreless motors seem quite good ... and are not durable
and well as on the pricey side for the ones over a 6 volt rating.
another option is the spin the motor through gear reduction and add a biiiig flywheel
with the annoying gear whine as one of the trade-offs.

so lets  see what set up we can rig to check our results.

victor

[victor miranda]

Hi Max,
I realized I didn't directly talk about a few things you mentioned.

since we use our motors at stall speeds, for starting trains and for shunting,
we have to keep the stall area in our discussions.

and yes there is no doubt at stall the efficiency rating suffers
it may seem obvious... I think high percentages of efficiency are good
and the opposite is bad because heat is mostly of little use in a model loco.

onward!

victor

[rodsup9000]

Max and Victor
 This is interesting and I'm learning from it.

There is a lot of info in the link Max pointed out. It will take some time and rereading for me to digest it all.

 So Victor, are going to build a mini dyno?? That would be nice to compare motors with different windings.
 

[strummer]

Wow...

 Back when I was heavily into 2 rail O scale (where re-powering engines is a way of life), there would often be similar discussions about motors,torque,etc. In that world, we're talking the ability to move literally pounds of train weight, both in rolling stock and in the engines themselves. And, I must admit, most of it went right over my head, tho I did find it all quite fascinating, and at times helpful.

Now here we are having the same discussion in N scale, where we're talking grams and ounces; does this mean N scale has "grown up"?

Carry on,gentlemen...

Mark in Oregon

[Bill H]

Max and Victor:
Back in the sixties, I worked my way through college partly by working at a slot car track and making good money winding special armatures for the big bucks racers. While I did wind some armatures with single 26 ga for very short track work, my most popular armatures were double and triple wound armatures (wires wound in parallel), mostly double wound 30 ga or triple 32 ga that pulled incredible rpms.  Anyway, winding double or triple is a lot of work, but it produced a better performing motor on the average to longer tracks, and of course those motors had more gear reduction than the 26ga which were really torquey but had low rpms. So, for what it is worth, I agree that the higher rpm armatures, with proper gearing perform better overall than low rpm high torque armatures.

Best,
Bill

[victor miranda]

Hi Strummer,

what conclusions did the O guys reach?

the differences may be in different units, and our options may get limited by size constraints.
I suspect the end points may be close.

victor

[mmagliaro]

Max and Victor:
Back in the sixties, I worked my way through college partly by working at a slot car track and making good money winding special armatures for the big bucks racers. While I did wind some armatures with single 26 ga for very short track work, my most popular armatures were double and triple wound armatures (wires wound in parallel), mostly double wound 30 ga or triple 32 ga that pulled incredible rpms.  Anyway, winding double or triple is a lot of work, but it produced a better performing motor on the average to longer tracks, and of course those motors had more gear reduction than the 26ga which were really torquey but had low rpms. So, for what it is worth, I agree that the higher rpm armatures, with proper gearing perform better overall than low rpm high torque armatures.

Best,
Bill

Bill,
I've been reading similar accounts of what you write here on some of the slot car forums about using
higher revving rewound motors, geared down appropriately to get a good speed range and more
torque and more power.

The devil is in the phrase "with proper gearing"

Yes, if you take a higher rpm motor, and you let it run up to its higher speeds, you can get more power out of
it, but torque suffers.  So you put a gear reduction on it, which cuts the speed and boosts the torque.
I would argue that what you did buy rewinding those motors was to make a very powerful
powerplant that could only deliver at higher rpms, and then you traded that power for torque by gearing
it down. 

You achieved success!  Plenty of torque to move the car, and still enough speed to win races.
The trick was choosing the right windings and the right gear ratio so that you struck the proper balance
between torque and speed.

And now... we are trying to do that without a gearbox. 
I already know that I can take a Faulhaber motor that is capable of revving up to a ridiculous 25,000 or 30,000
rpms, and put a 4:1 gearhead on it, and get tremendous torque at a good rpm range for a model loco.
The torque is so high that even at very low speeds of just 200 rpm or so on the output shaft, I cannot
stop that thing by squeezing with my fingers.   Can we do this without a gearhead?

In other words, if I want to just drop in a different motor,
and not change the gearing, should that motor be rewound with thinner or thicker wire, and why?

The Atlas Scale Speed motor seems to imply that using more, and thinner, windings, gets you a speed reduction
and a torque increase without putting in a gearhead.  I still think this is true.  I just don't have the
mental capacity to prove it... yet 

Victor, I am still not convinced that the stall torque matters to what we are trying to figure out,
but I am willing to keep it in the back of my head.  The behavior of the motor changes so drastically
from stall to just-off-stall that I am not convinced that the characteristics have much to do with
 our locos at low speed.  Low speed is not zero speed.

What would really be cool would be to unwind an Atlas high speed and Scale speed motor, count the windings
and measure the wire gauge, and put each on a dynamometer to see what the torque is at various rpms.
I really have to wonder if Atlas has already done this, or at least has performance charts from
whoever designed those motors for them.