BIZOMAT MAKEOS · Quality
Taper Disc Gauge Check (Centre Distance for a Taper, Taper from the Measured Setting)
For a disc-type taper gauge set to a taper per foot, what centre distance and reading over the discs should it have, and what taper does my measured setting actually give?
Set-up and check of a two-disc taper gauge: the centre distance of the discs for a taper per foot along the centre line (as the taper discs tool), the reading over the outsides of the discs at that distance, the actual taper and included angle from a measured reading over the discs (as the same tool from diameters and centre distance), and the error against your tolerance on the taper.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Large disc diameter | in | Diameter of the large disc. |
| Small disc diameter | in | Diameter of the small disc. |
| Taper per foot wanted (on diameter) | in/ft | Taper per foot on diameter the gauge is to represent. |
| Taper tolerance (±) | in/ft | Plus-or-minus tolerance on the taper per foot. |
| Measured reading over the discs (along their centre line) | in | Measurement over the outsides of the two discs along the line of centres. |
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: Large disc diameter
- What it is
- The diameter of the larger of the two precision discs of the taper gauge.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 10000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the measured or certified size of the disc; its error goes straight into the taper.
What this means: Small disc diameter
- What it is
- The diameter of the smaller of the two discs of the taper gauge.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 10000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 in 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 disc.
What this means: Taper per foot wanted (on diameter)
- What it is
- The taper the gauge is to represent, as the change in diameter over one foot of length measured along the centre line.
- Units and format
- Enter a number in in/ft: in/ft. The form accepts 0.0001 in/ft to 1000 in/ft. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.75 in/ft as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A steeper taper needs the discs closer together.
- Get it right
- Enter taper per foot on diameter, not per side and not per inch: multiply a taper per inch by 12.
What this means: Taper tolerance (±)
- What it is
- The plus-or-minus tolerance on the taper per foot, used to accept or reject the setting and to give the readings over the discs at the taper limits.
- Units and format
- Enter a number in in/ft: in/ft. The form accepts 0 in/ft to 10 in/ft. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.002 in/ft as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the same units as the taper: inches per foot on diameter.
What this means: Measured reading over the discs (along their ce…
- What it is
- The measurement taken over the outside edges of both discs along the line through their centres, from which the actual centre distance and taper are worked out.
- Units and format
- Enter a number in in: inches. The form accepts 0.000001 in to 100000 in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 9.255 in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger reading means the discs are further apart, so the taper from the setting is smaller.
- Get it right
- Measure along the line of centres, not across the discs at an angle.
Method and formulas
- Centre distance for a taper T: C = (D − d) ÷ 2 × √(1 + (T ÷ 24)²) ÷ (T ÷ 24) (as the taper discs tool).
- Reading over the discs = C + (D + d) ÷ 2; measured centre distance = reading − (D + d) ÷ 2.
- K = (D − d) ÷ 2C; taper = 24K ÷ √(1 − K²); angle = 2 asin K (as the taper discs tool).
- Example: set the discs 8.0039 in apart (9.2539 in over them); 9.255 in gives 0.7499 in/ft.
Limitations
- Discs touching straight edges tangent to both; disc roundness and edge straightness are not included.
- Taper measured along the centre line, not from one side.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set a disc gauge for a Morse or other taper
- Check a disc gauge setting before use
- Convert a measured setting to taper and angle
Who it is for
- Toolmakers
- Inspectors
- Machinists
What you get
- Centre distance and reading for the taper
- Taper and angle from the measured setting
- Decision
Interpreting the result
- A small error in centre distance moves the taper very little: disc gauges are forgiving to set but need accurate discs.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 684–685. Topic reference; no source tables or recommended settings are reproduced.
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