I’m going to have to read it a few times as that math is way beyond me. Thanks for the link though!!
So the equation is just a way I developed to determine the required taper of a gib by measuring the diagonal of the gib-way-hole as a function of the position along the length of the hole. I had miss read your original post. It seems you can remove your gib and if so you can make measurements directly from the old gib. Do so. It is pretty easy compared to what I have gone through. My old gib was so bad I did not trust that it was made propertly nor that I could just take measurements for thickness from it. The most important thing about the gib is the taper or slope (rate of change of the T(z)) of the gib thickness (T(z) . The second most is the thickness of it at the opening of the large end of the hole, T(z=0). These two parameters yield an equation for the surface of the gib T(z) = T(z=0) +m*z, where m is the slope in inches per inch. (On my z-axis gib of my mill, which is the gib hole I was measuring, the gib taper is about 0.00855 inches per inch. This means that for each inch farther that the gib is inserted into the hole the dove tail gap is filled with another 0.0085 inches of thickness. So if you were to stick a 0.0085 inch thick shim on the surface of the gib then the end of the gib would stick out of the hole by another inch.) The third most important thing is the heigth of the gib-way-hole, Hs, as measured on the saddle side of the way. Of course you also must have the way dovetail angle, theta. Most US made lathes are made with a 60 degree dovetail, but it can be most any value. On my mill, made in China, is 55 degrees. There are some that are made at 45. You can easily measure this with an angle gage. If you look up dovetail cutters at places like Grainger or MSC you will find that the mostly stock 60 degree cutters in the larger sizes and some 45-48 degree. Probably will not even find 55 degree cutters. .
So if you look at my two figures you will see the dimensions defined that I just mentioned. Hs, theta, T(z). I measured the diagonal, D(z), along my gib-way-hole for several z values and then use the equation to come up with T(z).
Determining Gib dimensions from the way-gap, way-hole, gib-saddle-gap
However, Since your gib is probably still good you can just measure the thickenss of the old gib to get this equation. From this you can make a new gib on your mill. No one says your gib has to be made out of cast iron. The material should just be softer than the steel that the way is made from. This way the gib wears out and the dove tail way does not wear nearly as fast. On my old South bend lathe the gib that you are discussing is actually made from brass or copper. It two has a locking knotch, but it is at the end. Cast iron comes in many varieties of hardness and from my very limited experience with it is that some of it does not cut well, it just crumbles. One of these days I will use my equation and data that I took and make a new gib. I will either use a very soft iron or hard brass or copper. My Mill ways are suppose to be hardended and I suspect that they are, but I can scratch them. However, I may make a practice gib first out of some plastic material. I have some spare nylon that I might use.
My understanding from PM is that the gib-way-hole spacing varies from machine to machine, of the same model. However, hopefully the taper or slope is pretty consistant. For this reason it is my understanding that at the factory, they make an extra long gib rod, with the correct taper and insert it into the gib-way-hole and make it tight. They then mark the ends of the piece that is sticking out on both ends and cut them off, maybe leaving a little extra for some way systems. To do this the gib's value of height, Hs, must be a little smaller than the value that you measure at your dovetails other wise the gib jams and stops the insertion due to hitting via the D(z) dimention rather than at the T(z). Since, Hs, is a constant independent of z it does not and should not be tapered. It is ok that it is smaller provided the knotch that you are making to clamp the gib position still holds. You may want to make your gib thickness, (T(z), just a little bigger than you measure to compensate for the past wear. You can judge this by how much of the clamping screw you have left. But if your taper is like the one on my mill, at only 0.0085"/inch it cannot be much bigger and still fit.
Dave L.