BMW F10 xDrive transfer case jerks or grinds

Usually the cause is transfer case oil that has lost its properties, or the condition of the friction plates, i.e. the clutch pack. It is worth changing the oil first. If the symptom does not go away, the clutch plates or the drum are dirty or worn.

It often helps, but one change is not always enough: old oil remains in the case, so the change is done twice if needed. When changing the oil, the transfer case adaptations, i.e. learned values, must be reset, otherwise the symptom may remain or get worse.

Grinding, especially under engine braking, usually indicates broken bearings, and an oil change does not help then. A reconditioned unit is often the best solution, and replacing it is about four hours of work. If one axle does not drive, the cause may be worn splines or coupling sleeves.

Yes. Driveshaft joints, propshaft cross joints, rear subframe bushings and the engine mount can cause jerks or shaking. The transfer case's share can be separated by unplugging the transfer case connector for a test drive, in which case the car drives as rear-wheel drive.