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I have a 2006 with 32K miles and when I tow or take off from a stop light with a heavey foot I hear and feel a growl. Its always done this but I think I am noticeing it more lately. It just lasts a few seconds. I have changed the Differential oil.
This isn't related to your low speed growl but i've got an 06 with 23,000 on it and now i noticed at 55 at certain R's it'll growl but i think the exhaust is finally broken in cause it's like a drone under light acceleration at about 55
Mines doing it too, and this is what I've learned so far.
When you tow, if your truck squats then it may change your drive line angle. (Your diff and tranny HAVE to be at the same angle). Apparently there are shim kits you can get to deal with that, or put on air bags, load springs, wieght distributing hitch, etc.
The other thing might be the clutches in the limited slip diff. I'm not sure the best way to have that checked, but I know it will be cheaper than the "big" one: the tranny. Those of us who make bigger than stock power have to be ready for other stuff to pay the price.
Hope it works out for you....
Mines doing it too, and this is what I've learned so far.
When you tow, if your truck squats then it may change your drive line angle. (Your diff and tranny HAVE to be at the same angle). Apparently there are shim kits you can get to deal with that, or put on air bags, load springs, wieght distributing hitch, etc.....
What you just described here is called axle wrap. I am hoping it is not that, the cure for axle wrap is a traction bar.
I took it to the dealer and after testing it they they told me they will order some parts to fix it and call me when the parts get in. Aparently it is a common problem and they will fix it. When I get it done I will ask the Mechanic what he fixed.