I completely understand the sentiment about keeping everything as it was by the original builder. It's a question I've wrestled with myself with respect to this engine, however, the crosshead and side rods at the very least need to be replaced. I'm a huge sucker for prototypical rods and valve gear, so I can't help myself but to just refresh it all. Other than that, very little will be changed. It will most definitely be recognizable as the Kollmar-built Birch NYC pacific.
James,
The combination lever and union link is where I always start when designing walschaerts, since its geometry does not necessarily depend on all the other monkey motion going on. However, everything else needs to be designed appropriately for the combination lever.
Whether you're designing from scratch or fixing erroneous valve gear on an existing model, the combination lever geometry can be calculated without worrying too much about existing fixed variables.
Really all you have to do is draw a few triangles, which I will now probably over complicate.
The variable letters I've assigned to this drawing are mostly random, so there's no need to read into it.
EDIT: Typo on the drawing. E = F + B1, not A + B1
The first thing that needs to be known is your Lap + Lead. Many existing designs should say what the lap and lead values are. If you're designing from scratch or following a prototype, it's pretty much up to you what this value should be.
As an example, the Lap + Lead on my 3/4" pacific is .1" This was determined by measuring the opening of the steam port in the liner and subtracting that from the width of one end of the piston valve. Value L in the diagram is 2x Lap + 2x Lead. This is how much travel should be introduced to the valve from the combination lever alone when the gear is in neutral (i.e. not influenced by the motion of the expansion link). On my model, that is .2"
Secondly, the stroke of the piston needs to be decided (or in my case measured to be 1.75").
And lastly, the offset of the crosshead arm (if any), needs to be taken into consideration (On my model B1 = .867, B2 = .28125).
To determine the lower segment of the combination lever (C2), a triangle can be formed between segments D, E, and C2.
On my engine, D is .755 (Stroke - L)/2 = (1.75 - .2)/2
E is 2.5545, my valve centerline height plus vertical crosshead arm offset (1.6875 + .867)
Using the friendly Pythagorean Theorem, C2 is calculated to be 2.6976 (dropped to 4 decimal places)
From this triangle, we can also calculate variable A, which is the angle of the combination lever at the end of the stroke. This is needed to calculate C1. On my little engine, the angle is 16.8807 degrees. Don't get lazy rounding off this number!
Now using this angle and L/2, we can figure out C1.
C1 = .5L/SinA
C1 = .1/Sin16.8807
C1 = .3343"
From here, the union link is a game of connect the dots. The horizontal distance of the topmost hole of the lever relative to the crosshead wristpin (at rear end of stroke) needs to be known. This location is affected primarily by the radius rod. If that is a flexible variable for you (for me it is not), then it's imperative to make sure the union link length is set so that your combination lever will not collide with the cylinders or crosshead. Then (again, if radius rod geometry is not determined) connect the dots from the top hole to wherever you decide to place your link fulcrum to find the length of your radius rod.
On my engine, I can't change the length of the radius rod for a variety of reasons. This puts the horizontal distance of my top hole to wristpin at 1.8540" when the crosshead is at the back of the stroke.
Since my combination lever is designed such that the union link is dead horizontal at either end of the stroke, the math is simple.
1.854 - S/2 - B2 = U
1.854 - 1.75/2 - .28125 = U
Union Link = .6977
It is possible to design the combination lever slightly longer or shorter. This will change how the union link swings. It can be angled slightly up or down at the end of the stroke. That is not a problem. But it needs to be taken into consideration when calculating the length of the union link. If there is a difference in height between the combination lever and crosshead arm at the end of the stroke, the Pythagorean Theorem comes into play to calculate it as a triangle, using U and height difference as the two legs, and union link length as the hypotenuse.
I hope you find these ramblings useful.
Anthony