KEVOS® MAKEOS · Quality
Machine Axis Error Budget (Positioning, Abbe, Thermal, Fixture)
Can this machine axis hold my tolerance once positioning error, repeatability, Abbe error, thermal growth of the screw and fixture error are added up?
Error budget for a dimension made or measured along one machine axis: positioning accuracy and repeatability from the machine test, the Abbe error from the offset between the work and the scale and the axis tilt (as the Abbe error tool), the uncompensated part of the screw or scale thermal growth (as the thermal growth tool), and the fixture or set-up error, combined by worst-case sum and by root-sum-square, against the share of the tolerance you allow the machine.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Tolerance band on the dimension | mm | Total tolerance band (upper minus lower limit). |
| Share of the tolerance allowed for the machine | % | Part of the tolerance you allow for machine errors, leaving the rest for tool wear, deflection and measurement. |
| Positioning accuracy (from the axis test) | µm | Positioning accuracy over the travel from an ISO 230-2 or similar test. |
| Repeatability | µm | Repeatability from the same test. |
| Abbe offset | mm | Distance between the work point and the axis scale or screw line. |
| Axis pitch or yaw over the travel | arcsec | Angular error (pitch or yaw) of the axis over the travel. |
| Screw or scale length in use | mm | Length of screw between the fixed bearing and the working position (or scale length). |
| Screw expansion coefficient | µm/m·K | Expansion coefficient of the screw or scale. |
| Screw temperature rise | K | Temperature rise of the screw in running. |
| Share of thermal growth compensated | % | Share of the thermal growth the control compensates (0 if none). |
| Fixture and set-up error | µm | Error from locating and clamping the part. |
Method and formulas
- Abbe error = offset × tan(tilt) (as the Abbe error tool).
- Thermal error = L α ΔT × (1 − compensation) (as the thermal growth tool).
- Worst case = sum of all contributions; RSS = √(sum of squares); compare with the allowed share of the tolerance band.
- Example: worst case 24.174 µm, RSS 11.702 µm, against 25 µm allowed; the largest source is Positioning accuracy.
Limitations
- Treats contributions as independent for RSS; correlated thermal errors add directly.
- One axis only; multi-axis features need volumetric errors.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Decide whether a machine can hold a tight tolerance
- Find the largest error source on an axis
- Justify thermal compensation or a better fixture
Who it is for
- Manufacturing engineers
- Quality engineers
- Machine tool engineers
What you get
- Each error contribution
- Worst-case and root-sum-square totals
- Total against the allowed share of tolerance
Interpreting the result
- Thermal growth is often the largest error on long screws: compensation or a scale feedback removes most of it.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 709–735, 375–376. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Machine Axis Error Budget (Positioning, Abbe, Thermal, Fixture) calculator
