Enter the offset (in) and the bar diameter (in) into the Eccentric Turning Packing Calculator. The calculator will evaluate the Eccentric Turning Packing.
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Eccentric Turning Packing Formula
To turn an eccentric feature on a round bar, you offset the bar in the chuck by shimming one jaw with packing. The packing thickness needed for a given offset is:
P = 1.5 * e * (1 - 0.125 * e / D)
- P = packing thickness placed under one chuck jaw
- e = required offset (eccentricity) between original and new axis
- D = bar diameter
The leading factor of 1.5 comes from the geometry of a 3-jaw chuck: shimming one jaw shifts the bar axis by roughly two-thirds of the shim thickness, so the shim must be 1.5 times the desired offset. The (1 - 0.125 e/D) term is the second-order correction that matters once the offset becomes a noticeable fraction of the radius. For small offsets (e/D below about 0.05) the correction is under 1% and you can use the simpler P ≈ 1.5e.
To go the other direction (find the offset produced by a known packing), the calculator solves the quadratic 0.1875 e² − 1.5 D e + P D = 0 and returns the smaller positive root.
Assumes a 3-jaw self-centering chuck, packing placed against the jaw opposite the desired offset direction, and that the packing material does not compress significantly under clamping load.
Reference Tables
Quick-reference packing thickness for common bar sizes (inches), using the full formula:
| Bar Dia. | Offset 1/32″ | Offset 1/16″ | Offset 1/8″ | Offset 1/4″ |
|---|---|---|---|---|
| 0.75″ | 0.0467 | 0.0931 | 0.1844 | 0.3594 |
| 1.00″ | 0.0468 | 0.0934 | 0.1855 | 0.3633 |
| 1.50″ | 0.0468 | 0.0936 | 0.1863 | 0.3672 |
| 2.00″ | 0.0469 | 0.0937 | 0.1867 | 0.3691 |
| 3.00″ | 0.0469 | 0.0938 | 0.1870 | 0.3711 |
How to read the offset-to-diameter ratio the calculator reports:
| e/D Ratio | Interpretation |
|---|---|
| below 0.05 | Small offset. The simple P = 1.5e estimate is accurate. |
| 0.05 to 0.20 | Typical eccentric turning range. Use the full formula. |
| 0.20 to 0.40 | Large offset. Check chuck jaw travel and clearance carefully. |
| above 0.40 | Extreme. Consider a 4-jaw independent chuck or a fixture instead. |
Example
You need a 0.125″ eccentric on a 1.500″ diameter bar.
- e/D = 0.125 / 1.500 = 0.0833
- Correction = 1 − 0.125 × 0.0833 = 0.9896
- P = 1.5 × 0.125 × 0.9896 = 0.1856″
Place a 0.186″ shim against the jaw opposite the side you want the new axis to shift toward, then re-clamp and indicate the new center before cutting.
FAQ
Why isn’t the packing just equal to the offset? Shimming one jaw of a 3-jaw chuck moves the bar axis by about two-thirds the shim thickness, because the other two jaws constrain it. You need 1.5× the offset in shim, plus a small correction.
Does this work on a 4-jaw chuck? No. With an independent 4-jaw, you set the offset directly by moving one jaw. This formula is only for shimming a self-centering 3-jaw chuck.
What should the packing be made of? Use a hard, non-compressible material such as steel shim stock or gauge plate. Soft packing crushes under clamp load and changes the offset.
