My torque tube is disassembled, and the drive shaft with pinion and bearings is on the bench. I have watched Tom Endy's differential video, but it is based on a completely disassembled differential. I only need to deal with the drive shaft. There is a good discussion in this thread
https://www.fordbarn.com/forum/showthread.php?t=337495&highlight=pinion+preload
but there are several references to the pinion carrier. The differential carrier is pictured on p 95 of the red book, but the drawing of the drive shaft on p 94 does not identify a pinion carrier. What is the pinion carrier? Additionally, what is the best orientation of the drive shaft/pinion assembly for setting the preload? Putting the race in a bench vise will surely exert unacceptable forces on the bearings, and if the weight of the horizontal driveshaft is supported the drag will affect the reading. Sorry to make a simple task too complicated, but I would like to get it right.
Russell - you've asked several good questions here.
The pinion carrier is the pinion gear, which includes a short section of "tube" that carries the two pinion bearings and the two nuts that adjust/secure those bearings, plus the bearings, the cup and nuts. The two bearings share the pinion cup. The pinion carrier attaches to the driveshaft via a tapered and keyed fit that is secured with the nut and cotter pin that you see at the small end of the pinion gear. To remove the pinion carrier from the driveshaft you remove the nut and then press the driveshaft out of the pinion carrier. In the attached illustration (stolen from the Snyder's online catalog) the pinion gear is the short one, and the ring gear is the large round one. Picture that pinion gear with some bearings installed on the shaft.
BUT - it looks to me like your driveshaft and pinion carrier are intact. If you have not disturbed the pinion bearings and they don't feel notchy, why are you thinking of adjusting them? If they have been properly adjusted in the past you are likely better off leaving them alone. On the other hand, if you removed the forward pinion bearing adjusting nut to use the Mitchell pinion puller to pull the driveshaft out of the banjo, or if you replaced the bearings, it's good practice to check the pinion preload to be sure you haven't changed it.
If this were me, what I would do is the following:
1. Clamp the driveshaft horizontally into the vise leaving the pinion gear maybe 12" or so outside the vise.
2. Rotate the pinion cup with my fingertips. For used bearings you are looking for in the neighborhood of 15 inch-lbs (which is a force of 1 lb applied at a distance of 15" from the centerline of the driveshaft, or 2 lbs at 7.5"...) to begin the race turning. Not a whole lot. After doing a few of these you can feel this resistance pretty well in your fingertips, but if you want to measure it more precisely, you can tape a string around the outside of the pinion bearing cup and hang some weight on it. The weight you add to make it turn (I have used a plastic milk jug with water, some folks use a fishing scale) times half the diameter of the bearing cup gives you the preload.
As an example, let's say the diameter of the bearing cup is 3-1/2" (I don't remember the exact number). So half the diameter is 1.75".
Let's also say that the bearing cup begins turning when you hang a plastic milk jug with 3 quarts of water in it, and that the combined weight of those three quarts and the milk jug is 7-1/4 lbs. That is 7.25 lbs x 1.75" = 12.7 in-lb preload. Close but just a bit light. If you want to tighten it (see below) you should tighten the rear pinion bearing adjusting nut a bit tighter (you will need to open up the retaining washer if it's still installed). Measure preload ONLY with the second (forward) nut tight against the rear nut, tightening them WILL affect the preload. You will likely have to go back and forth quite a bit.
For new pinion bearings you will want a slightly higher preload, say in the 18-20 in-lb range, to give some room for things to settle in.
Keep in mind that as you reinstall the pinion into the banjo you will compress the cup a bit. That will act to increase the preload slightly. So, it is best to set your preload a little bit light when you are setting it with the pinion carrier outside of the banjo. In the example above, if this was mine, used bearings and measuring the preload outside of the banjo, I'd likely accept the 12.7 in-lb, assemble it and drive it.
Also - a final note. It is always better to err on the side of too little preload than too much. Too much risks overheating the bearing, which in turn increases the preload, which leads to more overheating, yada yada. I rebuilt one once where the bearings seized and welded themselves to the pinion shaft, and I had to turn the shaft in a lathe to get the bearing inner races off. That wasn't pretty.