KEVOS® 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. |
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.
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 Internal Taper Inspection with Two Balls (Accept or Reject) calculator
