Notes on Tapers


Tailstock Chuck for a metal lathe,
showing #3 Morse Taper and #33 Jacobs Taper

Tapers are used in machine tools because they provide both accurate alignment and a firm seat for driving the tool.

Self-holding tapers or slow tapers have a very shallow angle, typically only 2 or 3 degrees, and wedge themselves in the socket so firmly that no locking device is required. Self-releasing or fast tapers do not do this.

All of the following are self-holding tapers.

Morse Tapers

Different numbers of Morse Tapers have slightly different tapers, but all approximate 5/8 inch per foot (0.05208 inch per inch). Morse taper shanks are used on a variety of tools, and exclusively on the shanks of twist drills. Old twist drills are, in fact, an inexpensive source for Morse tapers.
Morse
Number
Taper* Minor
Diameter
Major
Diameter
Length
0 0.05205 0.252 0.3561 2.000
1 0.04988 0.369 0.4750 2.126
2 0.04995 0.572 0.700 2.562
3 0.05019 0.778 0.938 3.188
4 0.05193 1.020 1.231 4.064
5 0.05262 1.475 1.748 5.188
6 0.05213 2.116 2.494 7.252
7 0.05200 2.750 3.270 10.00

*Inches diameter per inch of length.

Jacobs Tapers

Jacobs tapers are used for drill chucks.
Jacobs
Number
Taper* Minor
Diameter
Major
Diameter
Length
0 0.04930 0.22844 0.25000 0.43750
1 0.07710 0.33341 0.3840 0.65625
2 0.08160 0.48764 0.5590 0.87500
2 short 0.08160 0.48784 0.5490 0.97861
3 0.05320 0.74610 0.8110 1.21875
4 0.05240 1.0372 1.1240 1.6563
5 0.05170 1.3161 1.4130 1.8750
6 0.05190 0.6241 0.6760 1.0000
33 0.06349 0.5605 0.6240 1.0000

*Inches diameter per inch of length.

Brown & Sharpe Tapers

Brown & Sharpe tapers are used for taper shanks on tools such as end mills and reamers, arbors, collets and machine tool spindles, especially milling machines and grinding machines.

The taper is approximately 1/2 inch per foot (0.04167 inch per inch) for all sizes except for taper No. 10, where the taper is 0.5161 inch per foot (0.04301 inch per inch). In many cases there are a number of different lengths of sockets corresponding to the same number of taper; all these tapers, however, are of the same diameter at the small end.
B&S
Number
Taper* Minor
Diameter
Major
Diameter
Length
1 0.04160 0.200 0.239 0.9375
2 0.04126 0.250 0.299 1.1875
3 0.04200 0.312 0.375 1.5000
3 0.04171 0.312 0.385 1.7500
3 0.04150 0.312 0.395 2.0000
4 0.04160 0.350 0.402 1.2500
4 0.04148 0.350 0.420 1.6875
5 0.04171 0.450 0.523 1.7500
5 0.04150 0.450 0.533 2.0000
5 0.04188 0.450 0.539 2.1250
6 0.04168 0.500 0.599 2.3750
6 0.04154 0.500 0.635 3.2500
7 0.04167 0.600 0.725 3.0000
8 0.04154 0.750 0.898 3.5625
8 0.04175 0.750 0.917 4.0000
9 0.04175 0.900 1.067 4.0000
9 0.04165 0.900 1.077 4.2500
10 0.04167 1.0446 1.260 5.0000
10 0.04167 1.0446 1.289 5.6875
10 0.04167 1.0446 1.312 6.2188

*Inches diameter per inch of length.

Jarno Tapers

Originally proposed by Oscar J. Beale of Brown & Sharpe, the Jarno tapers are based on a mathematical relationship to the taper number. The major diameter is one-eighth inch per taper number, the minor diameter is one-tenth inch per taper number, and the length is one-half inch per taper number. For example, a #7 Jarno taper is 7/8" at the big end, 0.7000" at the small end, and is 3½" long. All Jarno tapers taper at a rate of 0.6000 inches per foot (0.0500 inch per inch).

References

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© 2003 W. E. Johns