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all differentials are all set to the same specifications as to pinion bearing preload , carrier bearing preloads and back lash between the crown wheel and pinion
the contact pattern is always the same as is the torque measurement of the drown wheel to carrier bolts
so any workshop manual that has a differential repair section will have what you want
find yourself a ford workshop manual and follow the section as to rebuilding a diff
Note --the pinion will have a + or - measurement on the end and that denotes the thickness of the spacer under the pinion between the pinion and the bearing inner race
you will have to get that right or the contact pattern will be out
3.7 ration is in utes or station wagons so it may be simpler to get one out of that vehicle and re-race it as all you will need then is new bearings and a collapsable spacer and a good tension wrench and a spring balance to get the pinion bearing preload correct
the "backlash" felt by reversing the drive shaft direction is normally the clearance in the spider gears in the diff so to get rid off that ( not necessary unless it is excessive) is to pull the diff center out and fit new thrust washers behind the spider gears
next check the diff mount bushes as the diff reaction will move the bolts in the mounts and make the noise
suggest that you talk with a diff reconditioning specialist center
if you have excessive pinion to ring gear clearance the diff will be making terrible noises not a clunk
what you have is worn side gear washers in the diff carrier and that is not essential to repair unless you get diff noise on turning corners
All diffs have play in the diffs that most people say is pinion /ring gear problems when it is not
the clunk noise comes from engaging a gear and the diff housing reacts to the load ( radius rod bushes , stabilizer bar bushes etc), the side gears take up the clearance, and the
"U " joints or cv joints take any wear
Best advice is--- if all you have is a clunk ( check everything outside the diff first) and the diff runs quiet under acceleration or deceleration, DON'T fix what ain't broken
When you say end play on the axle, how do you mean? Have you jacked the car in the air and grabbed the wheel top to bottom and side to side and felt for play in the wheel? If you did and it has play, I'd say you're looking at replacing wheel bearings and not a trans (Diff) problem.
You need to remove the bracket it goes into in order to replace the bushing, remove the nut on the raduis arm and then remove the bracket to install new bushings, some are revited on so you will need to cut the revits and replace them with bolts. also make sure that the hole that the bushing goes onto is not oval due to wear from old bushing being bad or the new bushing will not last. you will be able to see what i mean once you take it apart, the hole should be perfectly round with the lip edge.dont remove the bolt from the diff, that stays connected you will work from the rear. heres a diagram to show you what i am talking about, good day and hope this is helpful.
if you are looking for a manual for this car, try this link...
http://cgi.ebay.ph/Ford-Falcon-Ute-BA-series-Repair-Manual-2002-2005-on-CD_W0QQitemZ170423275380QQcmdZViewItemQQptZAU_Clothing_Merchandise_Media?hash=item27ae04cf74For twenty bucks you can do it all yourself
Replacing springs requires new U Bolts also
Raise and Jack stand Body then use floor jack at diff to raise rear diff and remove U Bolts Easy wat torch or Die grinder w/cutoff wheel then remove the shackle or Bushing Bolts 2 each side yank out old reverse procedure to Install 1&1/2 to 3 hours
If you have a 4x4 most likely your rear axel bushing is cracked, no big deal, just swing by your nearest Toyota dealer and order it. it goes for about $120. Easy to replace, use wd4 or nutsoff to spray inside the car body a few hours before trying to replace it. The accumulated dirt and road salt make it very hard to take the two long bolts out without a ¨fight¨. Please make sure you use a support jack to hold the rear axel in place when you get the bushing out.