Tc 9-524 fundamentals of machine tools

TPF = D - d x 
12
L
TPF = taper per foot,
D = large diameter (in inches),
d = small diameter (in inches),
L = length of taper
7-41

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TC 9-524
After the TPF is determined, the approximate angle can be
set on the graduated TPF scale of the taper attachment. Use a
dial indicator and a test bar to set up for the exact taper.
Check the taper in the same manner as cutting the taper by
allowing for backlash and moving the dial indicator along
the test bar from the tailstock end of the head stock end.
Check the TPI by using the thread-chasing dial, or using
layout lines of 1-inch size, and multiply by 12 to check the
TPF. Make any adjustments needed, set up the work to be
tapered, and take a trial cut. After checking the trial cut and
making final adjustments, continue to cut the taper to
required dimensions as in straight turning. Some lathes are
set up in metric measurement instead of inch measurement.
The taper attachment has a scale graduated in degrees, and
the guide bar can be set over for the angle of the desired
taper. If the angle of the taper is not given, use the following
formula to determine the amount of the guide bar set over:
Guide Bar Set Over (in millimeters) = 
D = large diameter of taper (mm)
d = small diameter of taper (mm)
I = length of taper (mm)
L = length of guide bar (mm)
Reference lines must be marked on the guide bar an equal
distance from the center for best results.
A metric dial indicator can be used to measure the guide bar
set over, or the values can be changed to inch values and an
inch dial indicator used.
Checking Tapers for Accuracy
Tapers must be checked for uniformity after cutting a trial
cut. Lay a good straight edge along the length of the taper and
look for any deviation of the angle or surface. Deviation is
caused by backlash or a lathe with loose or worn parts. A
bored taper may be checked with a plug gage (Figure 7-71) by
marking the gage with chalk or Prussian blue pigment. Insert
the gage into the taper and turn it one revolution. If the
marking on the gage has been rubbed evenly, the angle of
taper is correct. The angle of taper must be increased when
there is not enough contact at the small end of the plug gage,
and it must be decreased when there is not enough contact at
the large end of the gage. After the correct taper has been
obtained but the gage does not enter the workpiece far
enough, additional cuts must be taken to increase the diameter
of the bore.
An external taper may be checked with a ring gage
(Figure 7-71). This is achieved by the same method as for
checking internal tapers, except that the workpiece will be
marked with the chalk or Prussian blue pigment rather than
the gage. Also, the angle of taper must be decreased when
there is not enough contact at the small end of the ring gage
and it must be increased when there is not enough contact at
the large end of the gage. If no gage is available, the
workpiece should be tested in the hole it is to fit. When even
contact has been obtained, but the tapered portion does not
enter the gage or hole far enough, the diameter of the piece is
too large and must be decreased by additional depth of cut
Another good method of checking external tapers is to
scribe lines on the workpiece 1 inch apart (Figure 7-72);
then, take measurements with an
outside micrometer.
Subtracting the small reading from the large reading will
give the taper per inch.