Yes, unfortunately the GM 5L40-E (BMW call it the A5S390R) transmission fitted to your 3.0 d suffers badly from issues relating to reduced hydraulic pressures caused by increased leakage in the valve block due to wear.
One significant consequence is that the lock-up clutch in the torque converter wears through its lining and deposits huge quantities of metallic debris into the fluid



The noise you’re hearing may therefore be the lock-up clutch giving up the ghost (and not absorbing the engine’s torsional vibrations). You can sometimes see the engine revs on the rev. counter bouncing up and down by a couple of hundred rpm during the vibration.

The lock-up clutch operates on a different shift map in the ‘D’ and ‘S’ modes.

Another possibility is that the screens on the PWM solenoid that activates the lock-up clutch have become blocked or damaged





I think as a starting point you need to have the fluid drained and checked to see if there’s metallic debris in there (or stuck to the sump magnet). If the LUC has worn through its lining then, as the BMW specialist has said, it’s just a matter of time before the hydraulic circuitry becomes affected and the transmission starts to drop into failsafe mode.

Sorry, that didn’t sound very optimistic did it?

Phil