It could be the U joints from the transfer case causing the problem.
sounds like out of center u joints
Transfer case pump grinding a hole through the casing, U-Joints, bearings.
The pivot ball joint has failed. It is located between the double U-joints at the transfer case end.
Correctly phasing the u joints will prevent driveling vibration Doing it incorrectly can cause a damaging vibration that can ruin, transmission, transfer case, differential etc.
My jeep makes this noise sometimes too the only thing I can tell you is check the transfer case fluid then if it doesn't stop make sure it's not something more serious like u joints or your transfer case itself, but it's most likely the transfer case fluid
I am not 100% sure what the question is, but here is a shot at it. If you are trying to replace the u-joint, there is a video at myjeepwrangler.com under Fix-it > u-joint
Check the U joints and motor mounts. You may have also stripped teeth in your tranny, transfer case or diffs
Bad u joint Transfer case was out of fluid,
If it sounds like angry sparrows under the jeep it is the centering joint on your front drive shaft, it is where it connects to the transfer case and is between the two U joints.
Normally there are constant velocity joints not u-joints.
There are 2 U joints on a 1999 Ford expedition. There is an U joints on each end of the driveshaft.