A repair shop needs replacement parts on a daily basis and it won't take long before a part is needed that is no longer available. The next best choice is to find a good substitute, either a new repair part ordered from a manufacturer or supplier or from a "parts horn" hanging in the shop. In most cases it isn't very important that the part is identical to the original, especially when dealing with instruments for young students. In most repair shops and music stores, cosmetic differences are of little importance, as long as the instrument still performs its purpose well. The customer won't likely want to pay for a custom made part.
When the customer demands better or the sensibilities of the repairman won't allow less, it is almost always possible to replicate the part that is needed. You are probably already thinking that there is a wide grey area between a poor substitute and an exact replica and I completely agree. There won't be many viewers that would know the difference beyond the obvious: a mismatched button, cap etc. When replacing tuning slide tubing in cases where the correct dimensions are not available, it is most often wise to replace both inside and outside tubes with whatever is closest to the original, but there are other choices even in the most modest repair shop, if the mechanic has sufficient determination.
The focus of my work for over 40 years has been to do the best work possible and still make a living, which I've done for every one of those years. I've never had wealthy benefactors or government subsidies, so I must find ways to produce what I need with minimal expenditures for tooling and equipment. The easiest situation in this case is when you find tubing with the correct inside dimension, but too thick in the walls. You can carefully machine, file and/or sand and polish the tubing down to the correct outside diameter.
A little more determination and you can draw your own tubing to the correct size. I had been experimenting with this, making not only cylindrical tubing, but also tapered mouthpipes by hammering a steel mandrel, covered by a brass tube, through lead "doughnuts" as seen in the second photo down to the left. Keep in mind that this was the early 1980s and I had not seen any of these processes done by a maker and the internet (with great videos showing how to make everything) was a long way off. I had been told that lead was the correct material to use for this, but it became clear that to draw lengths of cylindrical tubing, I needed steel draw rings or the draw plate seen in the third photo down.
Next, I realized that by hammering on the end of the mandrels, they wouldn't last very long before they were too badly deformed. The great horn maker, Dan Rauch, showed me that he made his earliest mouthpipes on his lathe, using the tailstock screw to push the mandrel into the headstock. Legendary mouthpiece maker, Bert Herrick showed me that he spun trombone mouthpipes in his lathe. I purchased the 3 ton arbor press pictured in the top photo in order to more gently push my mandrels through the rings of steel or lead. I made up a mandrel for making keyed bugle bells (bottom photo) which was too long to push through lead using my press, so I set up an eight foot lever hinged on pins in a series of holes drilled in a central post in my shop. This worked marginally well, but was difficult to keep the base of the mandrel from slipping away from the lever.
In a conversation with Larry Frank (who had been making the Irving Bush mouthpieces for years), after repairing his trombone, I showed him my set up and described the problems. He saw my press and recommended that I drill and tap the bottom of the arbor to 1/2"-13 threads, so that I can thread the small end of my mandrels into it and pull up instead of the foolish attempts at pushing them through. A simple arbor press (without ratchet on the handle) such as this is geared so that it can pull as well as it can push and this worked very well and a large slot was cut from the mounting plate to allow pulling from beneath.
For longer mandrels, including the bells, after drawing the length of the arbor, I back it down and insert a wooden spacer between the underside of the arbor and the lead doughnut then continue drawing. You can see in the first photo, that I put a pipe over the handle of the press for more leverage. Keep in mind the forces generated with this technique and try to predict what might break or slip, causing bodily injury. Be careful and alert!!
I found that lead wasn't firm enough to draw mouthpipes tightly against the mandrels, but an annealed brass washer or plate (1/32" thick), as seen on the left of the second photo, worked well. Lead does work well for bell tails as long as the brass is already fitting fairly well on the mandrel and I usually draw these twice. The last photo shows four mandrels with adapters to fit my press arbor at 1/2"-13 (standard coarse threads). From top to bottom, they are for Eb keyed bugle bell, cornet mouthpipe, tuba mouthpipe and Bb keyed bugle bell. The top photo shows a Bb keyed bugle bell ready to be drawn. I draw the lead doughnut to within about five inches of the bell rim, then the mandrel is put on the lathe and the flare is spun against the mandrel.
I highly recommend that you watch the various videos on YouTube to see these processes being accomplished. This page will make a lot more sense after you've seen it done.
Getting back to my original premise: drawing slide tubing to match that on an instrument being repaired, you will obviously need a mandrel that matches the inside diameter of the tubing needed and a steel ring matching the outside diameter. Many instruments are standard fractional inch or standard metric sizes and steel rod can be ordered from industrial suppliers such as McMaster Carr. If not a standard size, then you will need to machine a rod to the correct diameter. The longer the mandrel, the more difficult this is to accomplish accurately.
In any shop that mass produces tubing the mandrels and rings need to hardened, straightened and ground to size to stand up to daily use, but with care, mild steel mandrels can be used many times without damage or deformation. Draw rings (plain steel, not hardened) in fractional inch sizes are available from Ferree's Tools and hardened steel draw plates in metric sizes are available from Josef Bohm. For a single size, it is not difficult to machine a draw ring from mild steel and I have had success making rings from aluminum (harder alloys), bronze and even brass for small quantities. Keep in mind that these other metals will give more than steel. The mandrels can also be made from these metals for limited use.
The next step in this lesson in making do is drawing both inside and outside tubing with only one mandrel, although two draw rings are needed. I decided to attempt this when I needed matched inside and outside tubing for an ophicleide tuning slide, which was much larger diameter than anything available. I needed to carefully calculate the inside and outside diameter of each finished tube and imagined them telescoped tightly together and on the steel mandrel. I first drew the inside tube against the mandrel and leaving it in place drew the outside tube on top of it. When finished, these tubes are very tightly stuck together and on the mandrel. Removing them is surprisingly simple. Using either a burnishing tool or, as I prefer, a rolling dent tool mounted in the vise, burnish or roll the entire length of the tubing against the mandrel until you are just able to muscle them apart. I have not used this technique very often, but it is a good example of how a little determination can solve almost any challenge.
I realize that this information is not of practical use to most of those reading it, but it is intended for those that are already fairly accomplished in brass work and want to do more. And there are certainly other methods that you might come up with that work better for your circumstances.