Vibration/Rumble While Turning

Is a tire scrubbing while near or at full lock? If so, it is normal.
Rgds,
Vincenzo

 

May be a Wheel bearing.

Turn hard left and listen, then right and listen. If it gets louder when you turn one way, it is the opposite side wheel bearing.

 

Could be the limited slip is chattering slightly in turns. A very, very small amount of limited slip additive would cure that if it is the problem.

 

Not "rubbing" - but "scrubbing" - a technical term.

It is not clear to me what you mean to convey with "not in a full radius turn". If you mean wide, rather than tight turn - scrubbing is likely not an issue (assuming your ride height and toe settings are at factory spec).

See here for scrubbing info:
Frictional Interaction of Tire and Pavement - Google Books


Additionally;
The front tires' toe settings go out of whack in a tight circle (Ackerman effect) and this causes a tire to slip sideways with slip/catch/slip/catch "chugging" motion that you may be referring to as a rumble. You will feel it most greatly in a parking lot with a thin bit of loose gravel, at slow speeds and very tight circle.

Additionally,
A limited slip will cause the same thing at the rear. Each of the two tires are travelling different distances in a tight turn. When one of them slips, it gives the same type of chugging describes above when on a loose surface.

All the above issues are normal in the 360.

Automotive Service: Inspection, Maintenance and Repair - Tim Gilles - Google Books

Rgds,
Vincenzo