BMW: Differential Noise!, ring and pinion gears, wheel bearings

Question
My car is an 87'BMW 325i, 5speed with 138,000 miles and in very good mechanical shape.

My problem is a humming noise coming from my differential and progressively getting louder over the past month. Whats the best way to discepher the problem.

***If the humming noise remains audible after you remove your foot "off" the accelerator, does this indicate WORN BEARINGS!

***Compared to humming noise "NOT" remaining audible when you remove your foot "off" the accelerator, does this indicate WORN RING&PINION

It is best to simply have a competent shop replace all bearing & seals first, and see if this fixes the problem.....

or

Have the ring and pinion gears done as well @ the same time! To make sure 100% the problem to fixed.

Is it likely to have extenive wear in the ring and pinion of differential with 138,000 Miles?

Should it be simply bearings Vs. Ring and Pinion how long can one drive the car in this state! I drive about 250 miles a week..

Look Forward to your help!


Answer
Vaughan,
 I wish it was really that simple, but unfortunately you cant just say "well if THIS happens then the problem is with this part", or atleast not with listening to the differential.

 This is a problem because if the car is rolling, the wheel bearings, differential bearings, and ring and pinion are ALL turning.  Whether you are acellerating or not, these parts are turning.  You may notice a difference in pitch of the sound because there is obviously more force on the parts than if you are just coasting.

 Its really hard to say what your problem is, because wheel bearings wear out most often, and make a noise.  This noise is more like a "whine" than a humming noise though.  So that makes me think the R&P are worn.  Your other problem is that if you have a shop replace the bearings only, they will still have to tear the whole diff apart to get them, and this labor is not cheap.  If they replace the R&P they will basically have to do the exact same thing over again.

 I suppose you should have a TRUSTED mechanic (one that isn't going to rob you) take a look at the car just to see if he can decipher where the noise is actually coming from.

 Its hard to say how long a car in this condition would last... but I would think you could drive on it for a few more days until you can get it fixed.  By saying this I am not telling you to put off fixing this problem, it could be dangerous as a rear-end failure at the wrong time could be catastrophic (i.e. pulling out in front of someone).

 I would take it easy on the car and drive it as little as possible until you can have it checked.

 Good luck,
 Josh