@“the same mountainbike”
But George suggested replacing the innards, and I don’t really like that idea 
Not on the axle in the pictures, for what it’s worth
He mentioned his own truck with a drop-in 3rd member, and how easy it was to remove the 3rd member. But OP’s axle is completely different. It’s like comparing apples and oranges, in my opinion
It’s like valve adjustments. Locknut and screw is easy, but shims are a lot more work 
@GeorgeSanJose
No offense intended
I was just stating my own preferences and opinions
“I like Ok’s idea to just swap out the innards from a junkyard unit” - George
I agree with you, db, but I understood George’s comment to mean that he understood OK’s recommendation as being to swap out the innards. I could be mistaken.
Properly shimming the carrier and pinion is way beyond the abilities of a DIYer in the driveway/garage at home. It’s a tough job the first time even when working on a lift with a 6’x6’ tool box full of Snap-On’s finest. A competor/friend specialized in rear end repairs and whevever he was not snowed under I referred customers to him and farmed out fleet work to him when possible.
The Ford removable chunk axles are quite different from other semi-floating units in that the ring to pinion and carrier bearing pre-load can be adjusted with a threaded nut while the housing is resting on a table, and while setting the pinion depth requires shimming, again that can be done resting on a table where everything is more visible and accessible. Laying on a creeper working on a greasy gear case with parts like shims getting mixed up makes for mistakes and often they are costly mistakes… When shims are properly sorted out and installed in the journals it is difficult to get the carrier in place. Very difficult when laying on your back, and that carrier is a mouthful if it falls.
If the rear of the truck is lifted and safely resting on properly placed jack stands on a level concrete drive the rubber brake hose is disconnected and then the parking brake cable. Next the shock absorber lower bolts are removed and the U-joint U-bolts removed and the driveshaft tied up out of the way after taping the cross cups onto the cross. If there is an anti-roll bar disconnect it from the axle. Next place chocks fore and aft of each rear wheel and loosen all 4 axle U-bolt nuts, then remove the rear leaf spring shackle nuts and after installing a jack under the center of the chunk remove the shackle bolts. Working from ahead of the wheels remove the axle U-bolt nuts, then lower the axle to rest on the pavement then count your blessings that you broke no fingers. With a helper move the chocks rearward incrementally, rolling the axle to the rear foot by foot until it is clear of the rear bumper then remove the wheels and set the axle aside, out of the way… This is always a fun line. Reassembly is the reverse of disassembly.
If any of you guys have done that job the “down and dirty way” and see that I have left something out please help this guy out. I often hesitate throwing out such specific advice but it is very likely that the result of attempting to repair the rear end would result in a great deal of costly, frustrating work resulting in having no alternative but to buy and install a used axle while thoroughly broke and disgusted… BTDT. I worked my way into being a professional(?) mechanic starting at the bottom. The very bottom.
edit; loosen the lug nuts while the axle is still attached to the truck.
Good coments above. I don’t have experience with modern F150’s, and if the configuration of the axel/differential is significantly different than my 9 inch Dana axel – for which the third member can be removed quite easily – then my comments of course wouldn’t apply to the OP’s problem. Another difference in what I did – even if the OP had the same axel/differential – was that I wasn’t replacing the third member, just removing it for inspection and diagnosis. Once I replaced the clutches I installed it back in. So there was no shimming involved to get the pinion matched up to the ring gear.
@GeorgeSanJose
Night and day difference
I doubt that axle in the picture even has limited slip, like yours apparently does
I have done a few axle swaps quite a few years ago, they used to be called drum to drum swaps then, I guess that would be disc to disc now. Swapping the whole thing is much easier and cheaper that replacing anyhing inside the pumpkin.
I had a friend that worked at GM’s Delevan Axle plant in Buffalo. His full time job was rebuilding noisy rear ends that came off the line. He was allowed one shot at adjusting and shimming to quiet the unit, if it was still noisy they scrapped it.
I think there are more differential failures now than years ago because when you got an oil change years ago it came with a grease job that included removing the fill plug from the differential and dipping you finger in the fluid. if you couldn’t touch the fluid, you refilled it.
Nobody is checking them now unless they are leaving puddles or getting noisy.
Interesting discussion. If anybody knows of a link w/a comparative description of the modern F150 differential/axle configuration vs. the 1970’s style, I’d be interested in looking at it.
@GeorgeSanJose
It has nothing to do with the age of the vehicle
It has everything to do about what kind of axle it is
There are still tons of axles currently being produced with drop-in 3rd members, like on your truck
I believe all of the large commercial trucks in our fleet have axles with a drop-in 3rd member
I think it’s also called a removable carrier . . . ?
Is the F150 unique then, and other modern trucks like Chevy’s Silverado – a popular one here in Northern Calif it seems – use the drop in differential?
@GeorgeSanJose
There is nothing unique about the F150 . . . or the Silverado, for that matter
As I said, it’s all about the axle type, not when the truck was designed
It seems that the “small” GM and Ford trucks in our fleet both do NOT have axles with removable carriers
here’s an interesting observation I’ve made, and it’s certainly not a blanket statement, because I know of some exceptions
Rear axles with a removable rear cover tend to NOT have removable carriers
Rear axles without a removable rear cover tend to have removable carriers
But as I said, it’s not a blanket statement, and I’ve seen some exceptions
Thanks, I understand what you mean better now. I have access to some of the F150 service data so I’ll take a look and see if I can find the rear axle diagrams there.
@codydub03 , there was plenty of warning that the rear end was dry and needed attention, but you ignored it’s pleas for assistance and just turned up the radio to drown those pleas out.
Had you noticed that there was a puddle under the rear end where it had been leaking for the last week/month, you could have gotten away with just the seal replaced for around $100 with labor, but because it was so loud and especially because it vibrated so bad…I’d say the bearings are shot.
I too would drop a used rear end into it.
Call around to other shops and see what other prices there are.
If you do want to do this yourself, get someone who knows a little more about car/trucks and have them help you. Maybe if the used replacement is cheap enough…your dear uncle might like to be flown out to help you, and for as quick visit.
You can go to any ford dealer with your Vin # and they can tell you what rear end was put in that truck from the factory. It only takes a minute and it’s easier than finding the tag on the rear end…if it’s still there.
If you do this yourself, be sure to drain the old lube and put fresh lube in, before you drive it one inch. The dealer can also tell you what fluid to fill it with.
Just look at all these untrustworthy mechanic’s that have come to help you with your problem!!!
Yosemite