What kind of noise does a front differential make when it's going bad?

Serpentine belt may be going bad and can make tapping/knocking sounds when they do .

You probably have a front drive splined disconnect assembly that has gone bad. This assembly engages the front differential when 4WD is selected. Below is a figure of the item, it is on the passenger side of the differential area.

It could be the CV joint on your front drive shaft. I don't feel that it would be your front differential because if that was going bad you would have one heck of a noise no matter how fast you were going. Hopefully this helps you out a little or at least gives you another place to look if you already have not checked.

The green grease is out of the CVJoint on the drive axle

That is not good,nor is a lot of heat from possibly the
front differential

Check the differential for fluid and a clear vent hose

It sounds like a problem within the front differential, possibly broken spider gears. If so broken gear shrapnel may be jamming that wheels output shaft.

chevy need to recall the trailblazer from 02 -08 and fix the front differntials. its amazing how everyone is having the same problems its not the drivers its the car

Sounds odd...Check the driveline for excessive movement and watch carefully when it's going into and out of gear. If you see any excessive movement in the differential yoke, likely there is a lot of gear lash inside. Also make sure all differential mounts are secure and that no bushings are worn. Likely if you are looking at them and someone puts it into gear, you will see a shift there if they are worn or loose. With difficult noises, I often use a long pipe, bar etc and actually place it against different olcations to narrow down the noise source.
Noise while loaded is different and can come from a bad internal shaft bushing in the transmission, a cracked flywheel or possibly a bad main or rod bearing.
Since you removed the transfer case, I'll assume you checked the universal joints for binding and excess play so that should be a non-issue. I'd also check front axle joints as well just to make sure there is nothing going on up there (sounds often travel, which is why looking is better than listening)

Maybe one idea. Going to Florida has nothing to do with the noise except makes you scared being away from home. Sometimes front wheel bearings go bad-all of a sudden. Not bad where the wheel will fall off but starting to make a noise like a airplane prop. A humming low pitch sound but almost constant. Not enough to feel it in steering wheel. If this decribes your sound-noise chances that is what it is. DON'T worry you can travel many, many miles with this noise. My mini van started doing it 20,000 miles ago. I got the parts but it's a bear to replace. I hope this helps you. If you need parts go to ebay.
burdfrenzy

could be a bad ujoint or the carrier bearing. hope this was helpful

A CV joint - when going bad - is more of a clicking sound.. Not so much a knocking sound.. And tends to get louder when turning & accelorating..

Hope this helps !!
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