Q: Driver quartering - distance from center to crankpin

[mmagliaro]

I have a question for the brave among you who don't mind thinking about geometry, quartering and rotation.
This came to me as I was tinkering with a mechanism.

Consider two drivers, connected by a rod, where the crankpins are, say, 2" out from the center (the distance doesn't matter, this is just an example).  Consider that there is a slight quartering error, so we have a periodic jam or "hitch" once per rotation.

If the cranks were, instead, 4" out from the center, the rods would still be the same length for proper operation.  However, would the quartering error be less critical?   My intuition is that in one case, it would, and in one case, it would not. 

Think about what would happen if a rod were a little off in length.  That error would account for LESS degrees of rotation of the driver at 4" out from center than at 2", so  the effect of the error on the operation would be reduced the further out you go.

If the rods were correct, but one driver was just rotated a little off from 90 degrees, however, it seems to me that this error would cause MORE distance error at 4" out than at 2", so the effect on the motion would be worse the further out you go. 

Now, tell me if my thinking is correct.

[nickelplate759]

Max - you made me dust off my trig.

<never mind, this was all wrong - back to Trig refresher course!>

[peteski]

While no help on the math, I want to mention that most N scale drivers have rather sloppy axle bearings, so the drivers can move slightly in every direction, or at least vertically.  That will affect the calculations.

[Chris333]

I'm no help, but real siderods are not one piece, they hinge for each wheel so each wheel can move up and down independently. On models the siderod is usually one piece and they egg out the holes to try and make everything happy.

This page says during the first run after replacing crank pin brasses, that they are now sloppy and let the whole box rock:
http://www.catskillarchive.com/rrextra/chapt16.Html

[Chris333]

[mmagliaro]

Thank you for your thinking about this, folks...
Here's a picture to illustrate my thinking (at the end).

Where I'm going with this is that it looks to me like our N Scale models have the rods typically set further away from the center axle than the prototype, and it strikes me that this may be necessary, given the inherent error from things like Peteski mentioned: the way the drivers have to bob and wiggle around in their bearings, far more (in scale) than a prototype driver ever would.   Here's why...

Getting two wheels made the same within very close tolerance in N Scale is not hard (for a manufacturer), and getting them accurately quartered on an axle isn't hard (for a manufacturer) because they can use a specially constructed jig or key the driver holes (like Kato does), and so on.  However, there isn't much they can do about the bobbing and wobbling in the bearings, which introduce unpredictable *length* errors, it seems to me, much more than an angular rotation error.

Therefore, they have to worry more about the left-hand side of my drawing - length discrepancies, rather than the right, which is a straight-up quartering angle error. 

Perhaps placing the rods a little further out from the center makes the whole thing more forgiving of the natural slop in the driver motion?  I also imagine a rod trying to push a driver around.  If the crankhole is very close to the center, imagine how hard it is to get the wheel to turn.  But if the crankhole is out more toward the edge, you have a longer "moment" and the wheel should move more easily, no?

[nkalanaga]

On a real locomotive, farther from the center also makes balancing harder.

[mmagliaro]

On a real locomotive, farther from the center also makes balancing harder.

DEFINITELY, because the flying-around mass of the rod is further out on the wheel.  Thankfully with model trains, we don't have to worry about that.

[Cajonpassfan]

I have a question for the brave among you who don't mind thinking about geometry, quartering and rotation.
This came to me as I was tinkering with a mechanism.

Consider two drivers, connected by a rod, where the crankpins are, say, 2" out from the center (the distance doesn't matter, this is just an example).  Consider that there is a slight quartering error, so we have a periodic jam or "hitch" once per rotation.
........

Now, tell me if my thinking is correct.

Hi Max, my little brain is trying to keep up, but wouldn't the "hitch" occur twice per rotation? Tension/compression scenario?
And I'm not even thinking about what happens on the opposing side...
Maybe we better just quarter them correctly? Or run diesels
Otto

[nickelplate759]

OK, I worked out the math.

We want a formula for the distance between crankpins as the drivers rotate.   If the drivers are perfectly lined up in rotation then distance will be constant, but if they are not it will vary as the drivers rotate, hence causing binding.

First some assumptions and constant definitions:
We are working in 2 dimensions.  Locations will be represented as Cartesian coordinates (x,y)

Let the center of one driver be (0,0)
Let the distance between drivers be D, so the location of the second driver is (D, 0)
Let the distance from axle center to crankpin be R - and assume that it's the same for both drivers.
Let the rotational offset between drivers be W.  If the drivers match perfectly W = 0.

As the drivers rotate, we will represent the rotation as theta (in radians, but it doesn't actually matter)
The position of the crankpin of the first driver will be:

(-R*cos(theta), R*sin(theta))

The position of the crankpin of the second driver will be:

(D-R*cos(theta+W), R*sin(theta+W))

the distance between two points (x0,y0) and (x1,y1) is sqrt( (x0-x1)**2 + (y0-y1)**2 )
so the distance between the crankpins is:

sqrt( (D-R*cos(theta+W)+ R*cos(theta)) **2 + (R*sin(theta+W) - R*sin(theta)))**2 )

simplify a bit:

sqrt( (D-R*(cos(theta+W)-cos(theta)))**2 + (R*(sin(theta+W)-sin(theta)))**2)

You can see that if W is 0, the distance is just equal to D, but if W is not zero, the distance will vary as theta changes.   Worst case, if the crank pins are set Pi radians apart (180 degrees) the distance will vary from D+2*R to D-2*R.

[mmagliaro]

nickelplate, THANK YOU for working this out.
Yes, I understand your trig, and I believe that it is correct.  I took the liberty of running it through a rotation with the crank
at 12" from the center and 24" from the center, with a 10 degree quartering error, vs a case with no quartering error.

The results are intuitively what I expected.  Essentially, the error is a sine wave whose amplitude gets worse the further out from the center the crank pin is.  And yes, cajonpassfan, indeed the maximum error occurs at TWO points in the rotation, not one.
The plot below bears that out.  And that is one of the big reasons to resist "egging" the rod holes, because every bit of correction you do for one tight spot in the rotation will make MORE error at the opposite error point.  We get away with egging the holes to a limited extent because there are other error sources - the rod hole length, and the wobble of the bearings being the two big ones.  Often you don't actually see two bind points with a quartering error because the wobble and the other wheels help the mechanism go around at one of them.  So sometimes  you can "cheat" a little, egg a hole enough to get rid of one bind, and that isn't enough to introduce the bind at the opposite rotation point.




I am not sure what this means for a model train.  Yes, if the quartering is off, it will make things worse if the crankpin is further out from the center.  But on the other hand, the error is much easier to see, so it might be easier to rotate the driver to fix the quartering.

[garethashenden]

However, there isn't much they can do about the bobbing and wobbling in the bearings, which introduce unpredictable *length* errors, it seems to me, much more than an angular rotation error.

They could do something about the sloppiness of the bearings, if they wanted to. Eliminate them entirely and bore the frames is the best way of ensuring minimal slop. It would probably help them if they wanted to use scale coupling rods and crankpins. But the problem of course is that the slop is useful. Sloppy bearings, either holes in bearings or bearings in frames, help when the track is not perfectly laid. The slop takes the place of suspension and keeps the trains running and on the track.

Now, if we're handlaying track and scratchbuilding locomotives we can better control for these things and the overall result will be better. But the cost of doing that is it takes a lot of time and requires a lot of skill.