Setting up the differential on my ford 8000 tractor

you have to disassemble the differential to remove the pinion gear to replace the crush sleave. to remove the pinion nut remove driveshaft then using proper size socket with an air gun remove nut then push out pinion gear from differential. to assemble check clearances of side bearings and pinion/ring gear contact clearances, and proper torque for pinion nut.

170 ft.lbs is the minimum; be aware that this differential uses a crush sleeve to set the backlash and the pinion torque is what crushes the crush sleeve. If you don't set the backlash correctly you can grind up your differential gears.
8 Inch Ford Rear End Torque Specifications eHow

Fully rebuild, or partial rebuild? Pinion, ring, spider gears, pumpkin, bearings? Rebuilding it FULLY and PROPERLY is a big story, one too big to relate here, and it takes quite a lot of special tooling (differential spreader, dial indicators, etc). Please don't attempt this unless you have a well equipped shop.

If you just need to replace the spider gears, that's easy. Drain the oil, remove the cover, rotate the pumpkin until you can unbolt the crosspin. Push/pull the crosspin out, rotate the spider gears until they come out. Remove the side gears. Remove all four thrust washers.

Replace all four thrust washers, then the new side gears, then mesh the new spider gears with the side gears & rotate them into place. If the crosspin hole won't line up, rotate one axle shaft until it does. Install the new crosspin and bolt it in. Replace the cover gasket and cover, refill.

Going further requires a LOT more work, but you'll need to remove the spider & side gears first anyway. If you're replacing bearings or the pumpkin or the ring & pinion, you'll need a bunch of new shims to work with until you can get the ring-pinion clearance exactly right. You'll also need a differential spreader to get enough space to remove/install the pumpkin with its bearings in place. If you're replacing the pinion gear, you'll need to take some painfully exact measurements or you'll NEVER get the ring/pinion clearances correct.

Thing here is that when you do change a gear in a resr diff, you need to adjust the pinion gear(this is called in mecanic's word pre-load of your pinion gear)first witch is achievable by inserting shim washers and tightennig the pinion gear bolt.

Then and only then you can adjust the backlash off your diff (witch is the distance between the pinion gear and the driven gear of your diff.).

failling to do so will either cause damage to your new driven gear or as you are aving problems here not being able to turn the diff cause the backlash doesn't have enought clearance.

Hope this will help you!!

Inspect/Test/Service/Replace

• If your testing indicates that the starter must be removed, the first step is to disconnect the negative cable at the battery.
• It may be necessary to place the vehicle on a lift to gain access to the starter. Before lifting the vehicle, disconnect all wires, fasteners, and so on that can be reached from under the hood.
• Disconnect the wires leading to the solenoid terminals.
• To avoid confusion when reinstalling the starter, it is wise to mark the wires so they can be reinstalled on their correct terminals.
• On some vehicles you may need to disconnect the exhaust system to be able to remove the starter.
• Loosen the starter mounting bolts and remove all but one.
• Support the starter while removing the remaining bolt.
• Then pull the starter out and away from the flywheel.
• Once the starter is free, remove the last bolt and the starter.
• Once the starter is out, inspect the starter drive pinion gear and the flywheel ring gear.

Starter drive and flywheel ring gear wear patterns. Courtesy of Ford Motor Company.

• When the teeth of the starter drive are abnormally worn, make sure you inspect the entire circumference of the flywheel.
• If the starter drive or the flywheel ring gear show signs of wear or damage, they must be replaced.
• Reverse the procedure to install the starter.
• Make sure all electrical connections are tight.
• If you are installing a new or remanufactured starter, sand away the paint at the mounting point before installing it. Also, make sure you have a good hold on the starter while installing it.
• Many General Motors' starters use shims between the starter and the mounting pad.

Shimming the starter to obtain proper pinion-to-ring gear clearance. Courtesy of General Motors Corporation - Service Operation.

• To check this clearance, install the starter and insert a flat blade screwdriver into the access slot on the side of the drive housing. Pry the drive pinion gear into the engaged position.
• Use a wire feeler gauge or a piece of 0.020-inch (0.5080-mm) diameter wire to check the clearance between the gears.

Checking the clearance between the pinion gear and the ring gear.

• If the clearance between the two gears is incorrect, shims will need to be added or subtracted to bring the clearance within specs.
• If the clearance is excessive, the starter will produce a high-pitched whine while it is cranking the engine.
• If the clearance is too small, the starter will make a high-pitched whine after the engine starts and the ignition switch is returned to the RUN position.
• Every starter should be bench tested after it is removed and before it is installed. to conduct a free speed or load test on a starter, see the free speed test.

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.

There is a shim adjustment on the yoke, but this is not usually the whining noise. Check the oil. Remove the plug and the oil should just come out of it. If it doesn't add some 80w90 weight till it does. Ford makes a pretty rugid differential. I have heard these screaming and still last for years. Built ford tough. Just remember to keep check on the oil.

what about it?

conventional axle or limited slip? Get axle code off door sticker.

SECTION 205-02: Rear Drive Axle/Differential - Ford 8.8-Inch Ring Gear 1998 Explorer/Mountaineer Workshop Manual
IN-VEHICLE REPAIR Rear Wheel Bearing and Axle Shaft Oil Seal -4.0L SOHC and 4.0L EI, Conventional
Special Tool(s) Axle Seal Replacer
T83T-1175-A Axle Wheel Bearing Puller
T83T-1225-A Axle Wheel Bearing Replacer
T83T-1225-B Driver Handle
T80T-4000-W Impact Slide Hammer
T50T-100-A
Removal

1. Remove the axle shaft; refer to Axle Shaft in this section.

Axle Shaft Removal

1. CAUTION: Do not use heat to loosen a seized lug nut. Heat can damage the wheel (1007) and the rear wheel bearings (1225).
   Loosen the lug nuts (1012).
   1. Remove the center cap.
   1. With the weight of the vehicle on the wheels, loosen the lug nuts.

1. Raise and support the vehicle.

1. Remove the wheel and tire assembly.
   1. Remove the lug nuts.
   1. Remove the wheel and tire assembly.

1. Remove the axle housing cover (4033).
   1. Loosen the axle housing cover bolts (4346) and drain the rear axle (4001).
   1. Remove the axle housing cover bolts.
   1. Remove the axle housing cover.

1. Remove the rear disc brake rotors (2C026); refer to Section 206-04 .

1. CAUTION: Once the differential pinion shaft (4211) has been removed, turning the differential case (4204) or an axle shaft (4234) will cause the differential pinion gears (4215) to fall out of the assembly. This could result in chipped or damaged components.
   Remove the differential pinion shaft.
   1. Remove the differential pinion shaft lock bolt.
   1. Remove the differential pinion shaft.

1. CAUTION: Do not damage the rubber O-rings in the U-washer grooves.
   Remove the U-washers (4N237).
   1. Push the axle shafts inboard.
   1. Remove the U-washers.

1. Reinstall the differential pinion shaft.
   1. Install the differential pinion shaft.
   1. Install the differential pinion shaft lock bolt finger-tight.

1. CAUTION: Do not damage the inner wheel bearing oil seal (1177).
   Remove the two axle shafts.

Installation

1. Lubricate the lip of the inner wheel bearing oil seal.
   • Use Premium Long-Life Grease XG-1-C or equivalent meeting Ford specification ESA-M1C75-B.

1. CAUTION: Once the differential pinion shaft has been removed, turning the differential case or an axle shaft will cause the differential pinion gears to fall out of the assembly. This could result in chipped or damaged components.
   Remove the differential pinion shaft.
   1. Remove the differential pinion shaft lock bolt.
   1. Remove the differential pinion shaft.

1. CAUTION: Do not damage the inner wheel bearing oil seal.
   Install the two axle shafts.

1. CAUTION: Do not damage the rubber O-rings in the U-washer grooves.
   Install the U-washers.
   1. Position the two U-washers on the button end of the axle shafts.
   1. Pull the axle shafts outward.

1. Install the differential pinion shaft.
   1. Align the hole in the differential pinion shaft with the differential pinion shaft lock bolt hole.
   1. Install the differential pinion shaft lock bolt.

1. Install the rear disc brake rotors; refer to Section 206-04 .

1. Install the axle housing cover and fill the rear axle housing (4010) with 2.4 liters (5.5 pints) of specified lubricant; refer to Axle Housing Cover in this section.

1. WARNING: Always remove any corrosion, dirt or foreign material that may be present on the mounting surfaces of the wheel or the surface of the wheel hub or rear disc brake rotor that contacts the wheel. Installing wheels without proper metal-to-metal contact at the wheel mounting surfaces can cause the lug nut to loosen and the wheel to come off while the vehicle is in motion, causing loss of control.
   Clean the wheel hub and mounting surfaces.

1. Install the tire and wheel assembly.
   1. Position the tire and wheel assembly.
   1. Install the lug nuts and lower the vehicle.
   1. Tighten the lug nuts.
   1. Install the center cap.

1. CAUTION: Never remove the axle shaft oil seal by itself. Always remove the rear wheel bearing and the axle shaft oil seal at the same time.
   NOTE: If the axle shaft oil seal is leaking, the axle housing vent may be plugged with debris.
   Use Impact Slide Hammer and Axle Wheel Bearing Puller to remove the rear wheel bearing and the axle shaft oil seal.

Installation

1. Lubricate the new rear wheel bearing.
   1. Use Thermally Stable Rear Axle Lubricant XY-80W90-QL or equivalent meeting Ford specification WSP-M2C197-A.

1. Use Axle Wheel Bearing Replacer with Driver Handle to install the rear wheel bearing.

1. Lubricate the lip of the new axle shaft oil seal.
   • Use Premium Long-Life Grease XG-1-C or equivalent meeting Ford specification ESA-M1C75-B.

1. Use Axle Seal Replacer with Driver Handle to install the axle shaft oil seal.

1. Install the axle shaft; refer to Axle Shaft in this section.

This problem can be caused by a crush sleeve that needs replaced. Proper installation of this sleeve is critical for noise free operation. If the pinion nut is loosened at any time during the adjustment process then a new sleeve must be installed.

there could be four different issues. out of oil, bearings are in need of replacement(could be also of the previous), possibly even out of time or teeth are needing adjusted for proper meshing.
I am not there to hear the howl so i cannot determine perfectly for you.
you will need to any any of these cases remove the differential cover and inspect interior of housing and oil if any remaining for metal and worn parts.
I would suggest getting the repair manual for your vehicle as this can be a difficult process and can cause serious issues if not done correctly.
If i am remembering correctly these are not a hunt/ search differential. meaning they don't have a specific setting point for gearing.
If they are set timing they will have indents on gears that must be aligned when assembled.
also check for excessive movement of pinion gear.(signs of wear and needed maintenance such as excessive oil leakage.)
also when the book states a certain amount of foot or inch pounds to tighten the pinion it does not mean to tighten it that much. it means when you spin the pinion gear that is how much force required to keep turning it.(as you are turning the pinion the gauge should read that amount)
in other words if you are turning the pinion you should be applying ## foot or inch lbs. so you would tighten the retaining nut until this point is achieved.