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Yes damaged axle shafts can create a howl noise. If the inner hub bearing is bad and not supporting the axle it will for one eat into the axle shaft causing it to fail as well as cause the axle shaft to spin un-commanded by 4x4 use resulting in a turbulence noise from the spinning axle. Also faulty hub bearings can create this noise as well as damaged pinion and differential bearings in the axle housing. Step one is to repair the known damaged axles and the source for there damage.
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The axles seal off the front differential for leaking, this is why I needed you to install the rags, to stop the oil and stop debris from getting in. It was leaking because the vehicle leans when turned and the oil can get out of the differential housing and flow out the tubes without the axles there, but since your not using 4x4 during this test, the loss of some oil will not hurt it.
Check the hub bearings by shaking the tire while it off the ground.
Also verify the rear driveshaft U-joints are good as well as the alignment.
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Anytime the outer pinion bearing is replaced the crush collar has to be replaced. here is how to set the pinion preload from ford.
I have no clue if the yoke is good or bad, I cant see it. At the ford garage I use a photocell hooked up to the scan tool to check for an out of balance shaft or yoke, there is nothing visually you can see to determine if its good or not. I also use a vibration analyzer to get the hertz of the vibration then do some match to determine what the vibrations RPM is then do some more match to determine whats spinning this speed and the diameter of the rotation then I have it nailed down to whats causing it.
To remove an axle shaft, just remove the hub cap and the 8 bolts holding the axle on and slide it out.
Yes a transfer case can have a worn output shaft bushing causing a vibration. You can remove the driveshaft and try to wobble it as well to see if any movement occurs.
On a superduty you should be able to just pull the axle shafts out without removing the rotors by removing the 8 bolts behind the hub caps.
I'm in TN.
Due to just answer rules I cant respond to questions not pertaining to the original concern of the axle noise.