BIZOMAT MAKEOS · Quality
Internal Taper Inspection with Two Balls (Accept or Reject)
From my two-ball depth readings, what is this internal taper’s included angle and top diameter, and are they within the drawing limits?
Inspection of an internal taper (ring gauge, socket or bore) with a small and a large precision ball: the included angle, diametral taper and diameter at the top face from the two depth readings (as the taper balls tool), the depth difference expected at the nominal angle, and accept or reject against the angle and top-diameter tolerances.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Small ball diameter | mm | Diameter of the small ball (it sits deeper). |
| Large ball diameter | mm | Diameter of the large ball. |
| Depth from the top face to the top of the small ball | mm | Measured depth from the top face down to the top of the small ball. |
| Depth from the top face to the top of the large ball | mm | Measured depth from the top face down to the top of the large ball (negative if it stands above the face). |
| Drawing limits | ||
| Nominal included angle | ° | Included angle on the drawing. |
| Included angle tolerance (±) | ° | Plus-or-minus tolerance on the included angle. |
| Nominal diameter at the top face | mm | Diameter at the top face on the drawing. |
| Top diameter tolerance (±) | mm | Plus-or-minus tolerance on that diameter. |
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: Small ball diameter
- What it is
- The diameter of the smaller precision ball, which drops deeper into the taper bore. Use the calibrated size of the ball.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be smaller than the large ball, or the tool stops.
What this means: Large ball diameter
- What it is
- The diameter of the larger precision ball, which sits higher in the taper bore nearer the top face. Use the calibrated size of the ball.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Depth from the top face to the top of the small…
- What it is
- The measured depth from the top face of the part down to the top of the small ball sitting in the taper, taken with a depth micrometer or height gauge.
- Units and format
- Enter a number in mm: millimetres. The form accepts -500 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger difference between the two depths gives a smaller included angle.
- Get it right
- Measure to the top of the ball, not its centre.
What this means: Depth from the top face to the top of the large…
- What it is
- The measured depth from the top face of the part down to the top of the large ball sitting in the taper.
- Units and format
- Enter a number in mm: millimetres. The form accepts -500 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- If the ball stands proud of the face, enter the height above the face as a negative value.
Drawing limits
What this means: Nominal included angle
- What it is
- The nominal included angle of the internal taper on the drawing: the full angle between opposite sides of the cone.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.1° to 120°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter the included angle, not the half angle; it is twice the angle to the axis.
What this means: Included angle tolerance (±)
- What it is
- The plus-or-minus tolerance on the included angle from the drawing. The measured angle is accepted when its deviation from nominal is within it.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 0.0001° to 10°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter decimal degrees: 6′ is 0.1°.
What this means: Nominal diameter at the top face
- What it is
- The nominal diameter of the taper where it meets the top face of the part, from the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 28.6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the diameter at the face the depths are measured from.
What this means: Top diameter tolerance (±)
- What it is
- The plus-or-minus tolerance on the diameter at the top face, from the drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.0001 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- sin(α ÷ 2) = (R₂ − R₁) ÷ [(h₁ − h₂) − (R₂ − R₁)] (as the taper balls tool).
- Diametral taper = 2 tan(α ÷ 2); top diameter from the large ball’s contact position.
- Expected depth difference at the nominal angle = (R₂ − R₁) ÷ sin(α_N ÷ 2) + (R₂ − R₁).
- Example: the readings give 23.074° and 28.577 mm at the top against 23° and 28.6 mm.
Limitations
- Ball diameter errors and depth-gauge squareness affect the result.
- Assumes a straight (conical) bore; check bellmouth with more balls.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect a taper socket or ring gauge
- Check a machine spindle taper
- Set limits for a two-ball taper check
Who it is for
- Inspectors
- Toolmakers
- Quality engineers
What you get
- Included angle, taper and top diameter from the readings
- Depth difference expected at the nominal angle
- Accept or reject
Interpreting the result
- If the angle is right but the top diameter is off, the taper sits too deep or too shallow rather than being the wrong shape.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 682–691. Topic reference; no source tables or recommended settings are reproduced.
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Open the Internal Taper Inspection with Two Balls (Accept or Reject) calculator