I've only got a micrometer and the preload measuring devices as far as the pinion preload goes.
Would it be best to start with the full stack of shims and pull them out until it's got enough drag? Or start with none and build up drag, I guess I could measure the shims and start with half and see where I'm at as well?
You have to start with the gears barely touching and move them into contact. If they're set against each other without clearance, you risk damaging them at worst or, at best, not being able to rotate them to print them.
You'll need at least an 8" caliper, vernier, dial or digital, doesn't matter. And a flat surface. An 8" square piece of glass will work; a flat steel or granite plate would be best.
Ignore backlash until you get a pattern that's somewhere near what you want. You can't set that with a spacer anyway; it's all bearing preload.
The internal bore depth is determined by measuring from the opposite side of the differential carrier casting, to the bottom of the bore. While it's empty you can reach through it and measure up, but you have to have a flat surface for the face to sit on, and to measure from. Be careful when you're doing this because there's not a lot of area to balance that big casting on.
You can measure the distance to the ring gear centerline by using any round bar that's relatively round and straight. Ideally, it should be a precision ground round bar half the size of the bore, but you're going to be adjusting distances anyway, so close is close enough. Any hot/cold rolled bar will do, as long as it's straight (shorter is better); measure from the plate supporting the carrier housing to the top of the bar and add whatever you need to in order to get to the centerline dimension. We used this method on the assembly line to get rough measurements when we were too lazy to carry the entire pile of parts into the lab and use the proper tools (BTW, that never happened). It will get you within a couple of thousandths.
You then need to measure all the other parts. Draw a picture and start stacking parts.
Once you have the theoretical dimensions, you can insert a stack of shims and see what the pattern looks like. Then it's just add/subtract thickensses until you get it right. It's not hard, it's just very tedious, although I will say that sometimes, when the moon is just right, it falls together the first time.
Fab up a crank handle to bolt onto the pinion shaft, so that you can turn the gears and get a print. It doesn't have to be fancy; you're not going to use it for anything else, ever again. Wood parts will work just fine; A dowel and a plate with a hole in both ends and a slot in one of them to clamp onto the pinion shaft is what you want. You don't need to drill a hole through the slot, you can just put a clamp on it. Again, don't get really fancy with this, it's necessary, but it's not the end goal, printed gears are.
Resist the temptation to use vise grips or a pipe wrench to turn the pinion.
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