BIZOMAT MAKEOS · Quality
Sine-Bar Set-up (Stack Height, Rounding and Angle Error)
What gauge-block stack sets this sine bar to the angle, how much angle error do block rounding and tolerance add, and is it within my angle tolerance?
Set-up of a sine bar or sine plate: the height difference between the rollers for the angle (as the sine bar tool), the stack rounded to the resolution of the gauge-block set (and checked as buildable by the gauge block stack tool), the angle actually set by the rounded stack, the angle change per micrometre of height, the total angle error from rounding plus your stack tolerance, and the check against the angle tolerance, with a warning above 45° where sine bars lose sensitivity.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Sine bar length (roller centres) | mm | Distance between the roller centres of the sine bar or plate (common sizes 100, 200, 250 mm or 5, 10 in). |
| Angle wanted | ° | Angle the work must be set to. |
| Gauge-block set resolution | mm | Smallest step the gauge-block set can build (0.0005 mm for an 88-piece metric set). |
| Stack tolerance (sum of block tolerances) | µm | Combined length tolerance of the blocks in the stack (from the block grade; your value). |
| Angle tolerance (±) | arcsec | Tolerance on the angle being inspected or ground. |
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: Sine bar length (roller centres)
- What it is
- The nominal distance between the centres of the two rollers of the sine bar or sine plate, usually engraved on it. The gauge-block height is this length times the sine of the angle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer bar makes each micrometre of stack error a smaller angle error.
- Get it right
- Use the roller centre distance, not the overall length of the bar.
What this means: Angle wanted
- What it is
- The angle the work must be set to, measured between the top face of the sine bar and the surface plate.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.01° to 80°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger angle raises the angle change per micrometre of height, so set-up error grows; it rises steeply above 45°.
- Get it right
- Enter decimal degrees: 30° 15′ is 30.25.
What this means: Gauge-block set resolution
- What it is
- The smallest height step your gauge-block set can build. The exact height is rounded to a multiple of it, which causes the rounding error.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.0001 mm to 0.01 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.0005 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A coarser step can leave a larger rounding error.
- Get it right
- Check the set’s contents; a set without the finest series has a coarser step.
What this means: Stack tolerance (sum of block tolerances)
- What it is
- The combined length tolerance of all the blocks wrung together in the stack, from the block grade and calibration certificate.
- Units and format
- Enter a number in µm: micrometres (µm, microns). The form accepts 0 µm to 50 µm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.25 µm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Each micrometre adds the angle change per micrometre to the total error.
- Get it right
- Add the tolerances of every block in the stack, not just one block.
What this means: Angle tolerance (±)
- What it is
- The plus-or-minus tolerance on the angle being inspected or ground, from the drawing. The total set-up error is compared with it.
- Units and format
- Enter a number in arcsec: arcsec. The form accepts 0.1 arcsec to 3600 arcsec. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 arcsec as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter seconds of arc: 1′ = 60″ and 1° = 3600″.
Method and formulas
- Height H = L sin θ (as the sine bar tool); stack = H rounded to the set resolution.
- Angle set θ′ = sin⁻¹(stack ÷ L); rounding error = θ′ − θ.
- Sensitivity = 0.001 ÷ (L cos θ) radians per micrometre; total error = |rounding error| + stack tolerance × sensitivity.
- Example: 30° on a 200 mm bar needs a 100 mm stack; the set-up error is about 0.29772″ against ±10″.
Limitations
- Roller and bar errors and the surface plate flatness add to the error.
- Above about 45° a small height error gives a large angle error: use an angle block or a compound set-up.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set a sine bar to inspect or grind an angle
- Find how accurately an angle can be set
- Check whether a longer sine bar is needed
Who it is for
- Inspectors
- Toolmakers
- Machinists
What you get
- Exact and rounded stack height
- Angle set and the error from rounding
- Total angle error against the tolerance
Interpreting the result
- A longer sine bar lowers the angle error per micrometre in proportion to its length.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 676–682, 705–708. Topic reference; no source tables or recommended settings are reproduced.
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Open the Sine-Bar Set-up (Stack Height, Rounding and Angle Error) calculator