Method and apparatus for damping/absorbing rotational vibrations/oscillations

1. A passive vibration damping device for use with a downhole tool, the downhole tool having a tool axis, the vibration damping device comprising:

a device housing mechanically coupled to the downhole tool, wherein the device housing includes a receptacle having a volume and an inner surface; and

an inertia element movably supported in the receptacle and having a volume, a mass, and a non-zero moment of inertia about the tool axis;

at least one of a longitudinal bearing and a radial bearing positioned between the inertia element and the inner surface of the receptacle

wherein the volume of the inertia element is less than the volume of the receptacle so that an interstitial volume is defined between the inertia element and the receptacle, and wherein the interstitial volume is occupied by a fluid or an elastomer; and

wherein the inertia element is supported within the receptacle in a manner that allows the inertia element to move relative to the device housing.

2. The device of claim 1 , and further including:

a cartridge mechanically coupled to the downhole tool, wherein cartridge defines the receptacle.

3. The device of claim 2 , further including positioned between the inertia element and the inner surface of the receptacle, at least one of:

a longitudinal biasing means and longitudinal friction pad combination; and

a radial biasing means and radial friction pad combination.

4. The device of claim 1 , further including positioned between the inertia element and the inner surface of the receptacle, at least one of a longitudinal biasing means and longitudinal friction pad combination or a radial biasing means and radial friction pad combination.

5. The device of claim 1 wherein the device housing and receptacle are configured such that movement of the inertia element relative to the device housing can comprise rotation through 360 degrees about the tool axis.

6. The device of claim 1 wherein the device housing comprises a collar configured to be part of a drill string.

7. The device of claim 1 wherein the device housing is affixed to or integral with a drill bit.

8. The device of claim 1 wherein the housing comprises an annular wall having a central bore therethrough, wherein the inertia element has an outer radius less than the outer radius of the housing, wherein the inertia element has an inner radius substantially equal to the radius of the central bore, and wherein the receptacle is in fluid communication with the central bore.

9. The device of claim 1 wherein the housing comprises an annular wall having a central bore and an outer radius, wherein the inertia element has an outer radius substantially equal to the outer radius of the housing, wherein the inertia element has an inner radius greater than the radius of the central bore, and wherein the receptacle is in fluid communication with the environment surrounding the housing.

10. The device of claim 1 wherein the inertia element has a shape selected from the group consisting of square toroids, tori, and azimuthally-spaced segments.

11. The device of claim 1 , further comprising a pressure compensation feature adapted to adjust the pressure inside the device housing to the pressure in a wellbore.

12. The device of claim 11 wherein the pressure compensation housing is formed separately from the device housing and the pressure compensation housing and the cartridge are both received within the device housing.

13. The device of claim 11 wherein the pressure compensation housing comprises the device housing.

14. The device of claim 11 wherein the pressure compensation housing is formed separately from the device housing and is received within the device housing.