Machining
Tapers
In short
Taper ratio, angle, compound setting and tailstock offset; Morse, metric and chuck tapers. Example with the default values: Compound setting α/2 = 1.4377°.
Calculation
Example calculated with the tool’s default values.
Inputs
- Input
- Standard taper (Morse, metric, chuck)
- Taper
- CM3
Results
- Compound setting α/2
- 1.4377°1°26′16″
- Taper
- 1:19.922Self-holding (small angle)
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Included angle α
- 2.8754°2°52′31″
- Large Ø D
- 23.825 mm
- Small Ø d
- 19.761 mm
- Taper length
- 80.96 mm
- Taper in mm/m
- 50.200.6023 in per foot
- Tailstock offset
- 2.032 mm
- Axial shift per 0.01 mm on Ø
- 0.199 mmRing gauge check: gauge plane shift = Ø error / C.
- Morse: d and L are the ASME B5.10 values (ISO 296 gives rounded L: 50 / 53.5 / 64 / 81 / 102.5 / 129.5 / 182).
- Tailstock offset above 1/50 of the length: centres bear badly, use the compound or a taper attachment.
Step-by-step calculation
Taper
C = (D − d) / L
(23.825 − 19.761) / 80.96 = 0.05020 = 1:19.922
Half-angle
tan(α/2) = (D − d) / (2 L)
α/2 = 1.4377° = 1°26′16″
Tailstock offset
e = (D − d) · Lt / (2 L)
(4.064) × 81.0 / (2 × 80.96) = 2.032 mm
Standard tapers
| Taper | Taper | α/2 | D (mm) | L (mm) |
|---|---|---|---|---|
| CM0 | 1:19.212 | 1°29′27″ | 9.045 | 50.80 |
| CM1 | 1:20.047 | 1°25′43″ | 12.065 | 53.98 |
| CM2 | 1:20.020 | 1°25′50″ | 17.780 | 65.09 |
| CM3 | 1:19.922 | 1°26′16″ | 23.825 | 80.96 |
| CM4 | 1:19.254 | 1°29′15″ | 31.267 | 103.19 |
| CM5 | 1:19.002 | 1°30′26″ | 44.399 | 131.76 |
| CM6 | 1:19.180 | 1°29′36″ | 63.348 | 184.15 |
| Métrique 4 | 1:20.000 | 1°25′56″ | 4.000 | 23.00 |
| Métrique 6 | 1:20.000 | 1°25′56″ | 6.000 | 32.00 |
| Métrique 80 | 1:20.000 | 1°25′56″ | 80.000 | 196.00 |
| Métrique 100 | 1:20.000 | 1°25′56″ | 100.000 | 232.00 |
| Métrique 120 | 1:20.000 | 1°25′56″ | 120.000 | 268.00 |
| Métrique 160 | 1:20.000 | 1°25′56″ | 160.000 | 340.00 |
| Métrique 200 | 1:20.000 | 1°25′56″ | 200.000 | 412.00 |
| B10 | 1:20.047 | 1°25′43″ | 10.094 | 14.50 |
| B12 | 1:20.047 | 1°25′43″ | 12.065 | 18.50 |
| B16 | 1:20.020 | 1°25′50″ | 15.733 | 24.00 |
| B18 | 1:20.020 | 1°25′50″ | 17.780 | 32.00 |
| B22 | 1:19.922 | 1°26′16″ | 21.793 | 40.50 |
| JT1 | 1:12.973 | 2°12′26″ | 9.754 | 16.67 |
| JT2 | 1:12.261 | 2°20′06″ | 14.199 | 22.23 |
| JT3 | 1:18.786 | 1°31′28″ | 20.599 | 30.96 |
| JT33 | 1:15.747 | 1°49′07″ | 15.850 | 25.40 |
| JT6 | 1:19.272 | 1°29′10″ | 17.170 | 25.40 |
Common tapers (ISO 1119)
| Taper | α/2 | Use |
|---|---|---|
| 1:3 | 9°27′44″ | Parts taken apart often |
| 1:5 | 5°42′38″ | Cone clutches |
| 1:10 | 2°51′45″ | Tapered shaft ends (ISO 775), handwheels, propellers |
| 1:12 | 2°23′09″ | Tapered-bore bearings (K), adapter sleeves |
| 1:16 | 1°47′24″ | NPT and BSPT taper pipe threads |
| 1:20 | 1°25′56″ | ISO 296 metric tapers |
| 1:30 | 0°57′17″ | Spherical bearings with tapered bore (K30) |
| 1:50 | 0°34′23″ | ISO 2339 taper pins |
| 7:24 | 8°17′50″ | ISO 30/40/50 spindle tapers (not self-holding) |
Limits
Indicative results: they replace neither the applicable standards nor the job drawings and instructions. Check the values entered and the result before doing the work.
Sources
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