BIZOMAT MAKEOS · Quality
CNC Axis Positioning Accuracy and Repeatability
What positioning accuracy and repeatability does this axis have from repeated runs to target points?
Machine tool positioning accuracy by the AMT method described in the handbook: for each target point the mean positional deviation and standard deviation of repeated unidirectional runs, the ±3σ repeatability spread, and the axis accuracy as the spread from the lowest (mean − 3σ) to the highest (mean + 3σ) across all targets.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Target points used | How many target points along the axis you measured (up to four here). | |
| Target 1: deviations of five runs | ||
| Target 1, run 1 | µm | Positional deviation (measured − target) of run 1 to target 1. |
| Target 1, run 2 | µm | Positional deviation (measured − target) of run 2 to target 1. |
| Target 1, run 3 | µm | Positional deviation (measured − target) of run 3 to target 1. |
| Target 1, run 4 | µm | Positional deviation (measured − target) of run 4 to target 1. |
| Target 1, run 5 | µm | Positional deviation (measured − target) of run 5 to target 1. |
| Target 2: deviations of five runs | ||
| Target 2, run 1 | µm | Positional deviation (measured − target) of run 1 to target 2. |
| Target 2, run 2 | µm | Positional deviation (measured − target) of run 2 to target 2. |
| Target 2, run 3 | µm | Positional deviation (measured − target) of run 3 to target 2. |
| Target 2, run 4 | µm | Positional deviation (measured − target) of run 4 to target 2. |
| Target 2, run 5 | µm | Positional deviation (measured − target) of run 5 to target 2. |
| Target 3: deviations of five runs | ||
| Target 3, run 1 | µm | Positional deviation (measured − target) of run 1 to target 3. |
| Target 3, run 2 | µm | Positional deviation (measured − target) of run 2 to target 3. |
| Target 3, run 3 | µm | Positional deviation (measured − target) of run 3 to target 3. |
| Target 3, run 4 | µm | Positional deviation (measured − target) of run 4 to target 3. |
| Target 3, run 5 | µm | Positional deviation (measured − target) of run 5 to target 3. |
| Target 4: deviations of five runs | ||
| Target 4, run 1 | µm | Positional deviation (measured − target) of run 1 to target 4. |
| Target 4, run 2 | µm | Positional deviation (measured − target) of run 2 to target 4. |
| Target 4, run 3 | µm | Positional deviation (measured − target) of run 3 to target 4. |
| Target 4, run 4 | µm | Positional deviation (measured − target) of run 4 to target 4. |
| Target 4, run 5 | µm | Positional deviation (measured − target) of run 5 to target 4. |
| Required accuracy (total spread) | µm | Accuracy the work requires, as a total spread. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Target points used
- What it is
- How many target positions along the axis were measured, each approached five times; only targets up to this number are evaluated.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 4. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Runs entered for targets above this number are ignored.
Target 1: deviations of five runs
What this means: Target 1, run 1
- What it is
- The signed positioning error of run 1 to target point 1: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -5.08 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 1 from the same direction on every run.
What this means: Target 1, run 2
- What it is
- The signed positioning error of run 2 to target point 1: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5.08 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 1 from the same direction on every run.
What this means: Target 1, run 3
- What it is
- The signed positioning error of run 3 to target point 1: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12.7 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 1 from the same direction on every run.
What this means: Target 1, run 4
- What it is
- The signed positioning error of run 4 to target point 1: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 17.78 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 1 from the same direction on every run.
What this means: Target 1, run 5
- What it is
- The signed positioning error of run 5 to target point 1: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20.32 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 1 from the same direction on every run.
Target 2: deviations of five runs
What this means: Target 2, run 1
- What it is
- The signed positioning error of run 1 to target point 2: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 2 from the same direction on every run.
What this means: Target 2, run 2
- What it is
- The signed positioning error of run 2 to target point 2: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 6 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 2 from the same direction on every run.
What this means: Target 2, run 3
- What it is
- The signed positioning error of run 3 to target point 2: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 2 from the same direction on every run.
What this means: Target 2, run 4
- What it is
- The signed positioning error of run 4 to target point 2: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 2 from the same direction on every run.
What this means: Target 2, run 5
- What it is
- The signed positioning error of run 5 to target point 2: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 2 from the same direction on every run.
Target 3: deviations of five runs
What this means: Target 3, run 1
- What it is
- The signed positioning error of run 1 to target point 3: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -3 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 3 from the same direction on every run.
What this means: Target 3, run 2
- What it is
- The signed positioning error of run 2 to target point 3: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 3 from the same direction on every run.
What this means: Target 3, run 3
- What it is
- The signed positioning error of run 3 to target point 3: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 3 from the same direction on every run.
What this means: Target 3, run 4
- What it is
- The signed positioning error of run 4 to target point 3: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 3 from the same direction on every run.
What this means: Target 3, run 5
- What it is
- The signed positioning error of run 5 to target point 3: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with -1 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 3 from the same direction on every run.
Target 4: deviations of five runs
What this means: Target 4, run 1
- What it is
- The signed positioning error of run 1 to target point 4: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 4 from the same direction on every run.
What this means: Target 4, run 2
- What it is
- The signed positioning error of run 2 to target point 4: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 4 from the same direction on every run.
What this means: Target 4, run 3
- What it is
- The signed positioning error of run 3 to target point 4: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 4 from the same direction on every run.
What this means: Target 4, run 4
- What it is
- The signed positioning error of run 4 to target point 4: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 4 from the same direction on every run.
What this means: Target 4, run 5
- What it is
- The signed positioning error of run 5 to target point 4: the position the axis actually reached minus the commanded position, read from the laser interferometer or gauge.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts -100000 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Keep the sign (negative when the axis stops short) and approach target 4 from the same direction on every run.
What this means: Required accuracy (total spread)
- What it is
- The positioning accuracy the work needs from this axis, as a total spread from the lowest to the highest expected position rather than a ± value.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0.000001 µm to 100000 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 75 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It does not change the measured accuracy; it sets the pass or fail verdict.
- Get it right
- Double a ± tolerance: ±a µm is a spread of 2a µm.
Method and formulas
- Mean positional deviation X̄ = Σ x ÷ n at each target.
- σ = √[Σ (x − X̄)² ÷ (n − 1)]; repeatability at a target is the ±3σ spread (6σ).
- Axis accuracy = max(X̄ + 3σ) − min(X̄ − 3σ) over all targets (handbook example: deviations −0.0002 to +0.0008 in. give X̄ = 0.0004 in. and 3σ = 0.0012 in.).
- Example: the default runs give an axis accuracy of 61.905 µm.
Limitations
- Unidirectional approach only; bidirectional tests add backlash and give larger spreads.
- Five runs per target is a small sample; standards specify the number of runs and targets.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Evaluate a laser or gauge check of a CNC axis
- Compare machines against a required accuracy
- Track axis accuracy before and after compensation
Who it is for
- Quality engineers
- Maintenance engineers
- Machine tool technicians
What you get
- Mean deviation and sigma at each target
- Repeatability (±3σ) at the worst target
- Axis accuracy spread
Interpreting the result
- Repeatability is usually about half the accuracy; compensation improves accuracy more than repeatability.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 1319–1322. Topic reference; no source tables or recommended settings are reproduced.
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