Caleb, a friend of mine, set out to rebuild the rear differential for his Mustang as the whining sound was an indicator of its poor health.
Here we just finished torqueing down the new ring gear to carrier. First tightening down to 70 ft-lbs, and then to 100 ft-lbs. After that, we added the bearings to the pinion and carrier assemblies.
Assembling the pinion to the housing was interesting due to the decision to replace the crush washer with shims. This would allow for repeatable results if it were ever rebuilt again, and would allow for the shims to be reused like the shims elsewhere in this assembly.
Nailing down the shim thickness took several iterations to reach near the 15 lb-in of rolling resistance of the pinion itself. These shim stacks tested ranged from 0.010" to 0.015" of shim in 0.001" increments.
We ended up settling on a 0.013" shim stack. As 0.012" shims had negligible rolling resistance, and 0.013" had a rolling resistance of 30 lb-in. If I remember correctly.
Here are the shims in order of thickness. Where the far left was a 0.003" shim, the center four ranged around 0.004", and the far right were 0.010" & 0.015" thick.
Assembly of the carrier in the housing went well! We managed to have 0.004" of backlash in the ring gear and a textbook gear contact patch. After this check, we called it a night.
My buddy conducted the final steps the next day. Where he installed the 0.002" shim on either side of the carrier to lock the run out in place. After which, he applied the gasket, and torqued it down to finish the assembly.
When it was finally installed in his Mustang, the results were immaculate. And the car responded well to the refreshed rear diff.