98 dodge ram 1500 rear axle, setting the backlash

The only way you can get an accurate preload reading is with an in/lb torque wrench on the pinion nut with the carrier removed.

Not knowing which differential is in the truck, I'm guessing a 9.25" rear loader type.

The correct way to do it is remove the axles and ring gear carrier. Set your preload with a NEW crush sleeve and in/lb torque wrench. Re-install the ring gear carrier and check contact pattern and backlash.

That said, you probably will be alright if you re-torque the pinion nut to spec plus a hair. Look it up in a manual. EXAMPLE: if it's 210 MINIMUM ft/lb add 5-10 lbs. Preload is 10-20 in/lbs. I have seen shops do this to save the customer money (or charge them for complete disassembly and not do the work). It should take up the slack from the crush sleeve.

This is NOT the correct way, but if you are in a bind it might work. I can't guarantee the bearing won't fail in the future.

Roll a rag between the ring and pinion.Should roll right out

you can remove the axles and the drive shaft then open the differential to remove the carrier gear assembly(ring gear,side gears)then remove the pinion gear.replace these with the new gear set and get the clearance specs for the pinion depth and carrier gear clearance and adjust until within specs.you can either pickup new gear sets or one from the wreckers with the shims to start with.you will need a backlash dial gage to know if the backlash clearance is within specs as well as marking ink to know if the gear mating surface is riding in the proper area of contact.

Can't remember if your axle is set up like the ones on a Jeep (too many cars stuck in my head) but if it is, the seal is on the inboard end of the axle and easy to forget it's there. If you don't lift the axle so it goes through the center of the seal when you put it back in, it will push the seal out and cause a leak.
If that's the case, whoever did the work needs to make it right. (carrier needs to be removed as well as the axle, to replace the seal)

For the rear diff., remove the driveshaft, brake drums, diff. cover, remove pinion flange nut, move diff carrier to access side gear retainer bolt and remove bolt, slide side gear pin out and push axles in to remove axle retainers and remove axels. Mark carrier bearing retainers, spin bearing retainers to loosen carrier for removal. Remove carrier, remove pinion out of diff case, then r&r bearings. Any shims should be replaced in their original location for depth and pinion to ring contact.

it does require some special equipment. most likely have the 9.25 axle in the truck which has adjusters on both sides of the differential that are threaded in the housing. these require a special tool to adjust and set proper backlash. also helpful to have a press with bearing pullers/installers. need a dail indicator to set backlash also

The problem is almost always caused by the clips that hold the clutch disc in place on the po-si rear-ends.The clip will come lose and catch between the carrier clamp and cause metal parts to be deposited in the housing causing the front and rear pinion bearing to wear. Howling while accelerating is the rear pinion bearing. Howling while decelerating is the front pinion bearing. Sometimes you can get by with just replacing the clips and pinion bearings. Clips can be ordered out of California. For around $70.00 .The dealer will want to sell the entire assembly. Which does not include the pinion and bearings. The longer you go the more damage that will be done. If you can't do this yourself. No one is going to repair just part of the assembly and warranty.

replace the rear axle or the bearing in the one you have

Axle Preload and Backlash Specifications 8.0 Axle Preload and Backlash Specifications Application
Specification
Metric
English
Backlash
0.08-0.25 mm
0.003-0.010 in
Backlash (Preferred)
0.13-0.18 mm
0.005-0.007 in
Pinion Bearing Preload, New Bearings
1.7-3.4 N·m
15-30 lb in
Pinion Bearing Preload, Used Bearings
1.1-2.3 N·m
10-20 lb in
Pinion and Differential Case Bearing Preload, New Bearings
3.4-6.2 N·m
30-55 lb in
Pinion and Differential Case Bearing Preload, Used Bearings
2.8-5.1 N·m
25-45 lb in

The pinion depth is incorrect in the differential. This can cause excess backlash, improper bevelled gear meshing, and permanent damage to the gear set. It can be repaired most of the time by changing the shims on the pinion to allow 0.010" more penetration o the pinion into the housing.