Whirring is such a broad term, I wouldn't know where to start. When I got engine electrical interference through my amp, a whirring noise came from my speakers. I have heard glazed brake pads make some strange noises as could a throw out or pilot shaft bearing. I would spend some free time crawling around all four corners and everything in between trying a process of elimination for the components that move. U-joints are a great place to start, the advice about the ring and pinion is sound as well. I had a bad ring and pinion and it gave off what I would describe as a howling noise. Side note: these Jeeps can be noisy buggers, but most sounds are symptoms of wear, lack of lubrication or influence of foreign substances. The good news, sooner or later, every noise gets identified, often though component failure. BTW, my NV3550 is in perfect health (for now) and it is a noisy box of growling rocks when compared to most transmissions. Don't be afraid to change your gear oil using Red Line MTL. Expensive, but it is definitely kind to the guts of your tranny. It quieted down my first tranny a lot. I found a replacement with very low miles so I swapped it, the engine and transfer at the same time. Deal was too good to pass up. Came from a RHD Japanese rig that was pampered on pavement and only saw about 25-30K miles.