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1 
Tapers and 
Taper Turning 
Session 10
2 
Taper 
• Uniform change in diameter of workpiece 
measured along its axis 
• Inch system expressed in taper per foot, taper 
per inch, or degrees 
• Metric system expressed as ratio of 1 mm per 
unit of length 
• Provides rapid and accurate method of aligning 
machine parts and easy method of holding tools
3 
Machine Tapers 
• Classified by American Standards Association 
• Self-holding tapers 
• Steep or self-releasing tapers
4 
Self-Holding Tapers 
• Remain in position because of the wedging action 
of the small taper angle 
• Most common forms 
• Morse, the Brown & Sharpe, .750-in.-per-ft taper 
• Smaller sizes provided with tang to help drive the 
cutting tool 
• Larger sizes employ tang drive with shank held in 
by key or key drive with shank held draw bolt
Steep Tapers 
• 3.500 in. taper per foot (tpf) 
• Formerly called standard milling machine 
taper 
• Used mainly for alignment of milling machine 
arbors and accessories 
• Has key drive and uses draw-in bolt to hold it 
securely in milling machine spindle 
5
6 
Standard Tapers 
• Morse taper 
• Approximaely .625-in tpf, eight sizes #0 to #7 
• Used for drills, reamers, and lathe center shanks 
• Brown & Sharpe taper 
• .502-in. tpf, sizes from #4 to #12 
• Used on Brown and Sharpe machines 
• Jarno taper 
• .600-in. tpf, sizes from #2 to #20 
• Standard taper pins 
• Used for positioning and holding parts together 
• ¼ tpf, standard sizes range from #6/0 to #10
Table 54.1: Basic dimensions of 
self-holding tapers 
7 
Taper 
Number per Diameter at Diameter at 
of Taper Foot Gage Line (A) Small End (D) Length (P) 
1 .502 .2392 .200 15⁄16 
2 .502 .2997 .250 13⁄16 
3 .502 .3752 .3125 11⁄2 
0* .624 .3561 .252 2 
1 .5986 .475 .369 21⁄8 
2 .5994 Portion .700 of table .572 shown 
29⁄16 
3 .6023 .938 .778 33⁄16 
in textbook
Two Types of Lathe 
Spindle Nose Tapers 
• Type D-1 
8 
• Short tapered section and used on 
cam-lock spindles 
• Type L 
– Taper of 3.500-in./ft 
– Longer taper than Type D-1 
– Chuck held on by treaded lock 
ring fitted on spindle 
– Key drive used
Taper Calculations: TPF 
tpf = 1.250 - 1 = 
9 
x 12 
Example: tpf = D - d 
l 
x 12 1 
3
To Calculate the Tailstock 
Offset 
Must know the tpf and the total length of work (L) 
Tailstock offset = tpf x length of work 
10 
24 
Example: 
Copyright Š The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Taper per inch = 
taper per foot 
Tailstock offset taper per inch x overall length (OL) 
11 
Simplified Formula 
Simplified formula can be used to calculate 
tailstock offset if taper per inch t/in. known: 
2 
12 
= 
In cases where not necessary to find tpf: 
( ) 
2 
x D - d 
Tailstock offset = OL 
TL 
OL = overall length 
TL = length of tapered section 
D = diameter of large end 
d = diameter at small end
Inch Taper Attachment 
Offset Calculations 
• Most tapers cut on lathe with taper 
attachment are expressed in tpf 
• If tpf not given, it may be calculated: 
( ) 
= 1.375 - .9375 x 12 
12 
( ) 
tpf = D - d x 12 
TL 
7 
Calculate the tpf for a taper with the following dimensions: 
large diameter (D), 1.375; small diameter (d), .9375; 
length of tapered section (TL), 7 in.
Metric Tapers 
• Expressed as ratio of 1 mm per unit of 
length Work would taper 1 mm 
in a distance of 20 mm 
ratio of 1:20 
13
Metric Taper Calculations 
If know d, k, and l, D may be calculated. D 
equal to small dia + amount of taper. 
Amount of taper is equal to 1¸k, so total 
taper equals l¸k. 
D = d + total taper 
D = d + l/k 
d = small diameter 
k = unit length of taper 
l = total length of taper 
D = large diameter 
14
Metric Tailstock Offset 
Calculations 
• If taper turned by offsetting tailstock, 
amount of offset O is calculated as 
follows: 
15 
x L 
Offset D - d 
2 x 
l 
= 
where D = large diameter 
d = small diameter 
l = length of taper 
L = length of work
Example: Metric Tailstock 
Offset 
Calculate tailstock offset required to turn a 
1:30 taper X 60 mm long on a workpiece 300 mm 
long. The small diameter of tapered section is 
20 mm. 
Solution: 
x L 
Offset D - d 
2 x 
= 
22 - 20 
5 mm 
16 
x 300 
2 x 60 
= 
= 
l 
D = d + 
l 
20 60 
= + = + 
22mm 
20 2 
30 
k 
=
Metric Taper Attachment 
Offset Calculations 
1. When taper attachment used to turn 
taper, amount guide bar set over is one-half 
17 
angle given on drawing.
2. If angle of taper not given on drawing, 
use following formula to find amount of 
guide bar 
setover: 
where D = large diameter of taper 
d = small diameter of taper 
l = length of taper 
GL = length of taper attachment guide bar 
18 
x GL 
l 
Guide bar setover = D - d 
2
Taper Turning 
• Performed on work held between centers of in 
lathe chuck 
• Three methods of producing taper 
19 
• Offsetting tailstock 
• Taper attachment set to proper tpf 
• Metric by calculating guide bar offset 
• Adjusting compound rest to angle of taper 
• Method used depends on work length, taper 
length, taper angle and number of pieces
Tailstock Offset Method 
• Generally used to cut taper when no 
taper attachment available 
• Involves moving tailstock center out of 
line with headstock center 
• Amount tailstock may be offset limited 
• Will not permit steep tapers to be 
turned or standard tapers turned on 
end of long piece of work 
20
Tailstock Offset Method 
21
Three Methods of 
Offsetting the Tailstock 
• By using graduations on end of the tailstock 
(visual method) 
• By means of the graduated collar and 
feeler gage 
• By means of a dial indicator 
22
Procedure to Offset Tailstock 
by the Visual Method 
• Loosen the tailstock clamp nut 
• Offset upper part of tailstock by loosening one 
setscrew and tightening the other until required 
amount is indicated on graduated scale at end 
of tailstock 
Note: Make sure both setscrews snugged 
up to prevent any lateral movement of 
tailstock 
23
Procedure to Offset the 
Tailstock Accurately 
1. Adjust tailstock spindle to distance it 
24 
will be used in machining setup and 
lock tailstock spindle clamp 
2. Mount a dial indicator in toolpost with plunger in 
horizontal position and on center 
3. Using crossfeed handle, move indicator so 
registers ~.020 in on work, and set indicator and 
crossfeed graduated collars to zero
4. Loosen tailstock clamp nut 
5. With tailstock adjusting setscrews, 
move tailstock until required offset 
shown on dial indicator 
6. Tighten tailstock setscrew that was 
loosened, making sure indicator reading 
does not change 
7. Tighten tailstock clamp nut 
Note: Tailstock may also be offset by using feeler 
gage between toolpost and tailstock spindle in 
conjunction with crossfeed graduated collar 
25
Advantages of Using 
Taper Attachment for 
Tapers 
1. Lathe centers remain in alignment, 
preventing distortion of centers on 
work 
2. Setup is simple and permits changing 
from taper to parallel turning with no 
time lost to align centers 
3. Length of workpiece does not matter, 
since duplicate tapers may be turned 
on any length of work 
26
4. Tapers may be produced on work held 
between centers, in chuck or in collet 
5. Internal tapers can be produced by this 
27 
method 
6. Metric taper attachments are graduated 
in millimeters and degrees, while inch 
attachments are graduated in both 
degrees and inches of tpf 
• Eliminates need for lengthy 
calculations and setup 
4. Wider range of tapers may be produced
28 
Two Types of Taper 
Attachments 
• Plain taper 
• Remove binding screw that holds cross-slide 
to crossfeed screw nut 
• Binding screw used to connect sliding block to 
slide of taper attachment 
• Depth of cut made by using compound 
rest feed handle 
• Telescopic taper 
• Crossfeed screw not disengaged and 
depth of cut set by crossfeed handle
Plain Taper Attachment 
29
To Cut a Taper Using a 
Taper Attachment 
1. Clean and oil guide bar 
2. Loosen lock screws and offset end of 
guide bar the required amount or, for 
inch attachments, set bar to required 
taper in degrees or tpf 
3. Tighten lock screws 
4. With compound rest set at 90Âş, set up 
30 
cutting tool on center
Telescopic Taper 
Attachment 
5. Set workpiece in lathe and mark 
31 
length of taper 
6. Tighten connecting screw on sliding 
block 
7. Move carriage until center of 
attachment opposite length to be 
tapered 
8. Lock anchor bracket to lathe bed
Telescopic Taper 
Attachment 
9. Take cut .060 in. long, stop lathe, 
32 
check end of taper for size 
10.Set depth of roughing cut to .050 to . 
060 in. oversize, and machine taper 
11.Readjust taper attachment, if 
necessary, take light cut, and recheck 
taper fit 
12.Finish-turn and fit taper to gage
33 
• Standard tapers 
– Taper plug gage mounted between centers and 
taper attachment adjusted to angle by using dial 
indicator mounted on center 
• Internal taper 
– Same procedure, except guide bar set to side of 
centerline 
• Mating external and internal tapers 
– Machine internal taper to plug gage then external
Taper Turning Using the 
Compound Rest 
• Used to produce short or steep tapers 
34 
stated in degrees 
• Tool fed by hand, using compound rest 
feed handle
Taper Turning Using the 
Compound Rest 
Procedure 
1. Refer to drawing for amount of taper 
or tpi 
35 
required in degrees (not given: 
calculate) 
2 
angle tpf 
2 
24 
Tan 1 =
2. Loosen compound rest lock screws 
3. Swivel compound rest as follows: 
36 
Copyright Š The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
4. Tighten compound rest lock screws 
5. Set cutting tool to center with 
toolholder at right angles to taper to be 
cut 
6. Tighten toolpost securely 
7. Back off top slide of compound rest so 
there will be enough travel to machine 
length of taper 
37
8. Move carriage to position cutting tool 
near start of taper and then lock 
carriage 
9. Rough turn taper by feeding cutting 
tool using compound rest feed handle 
10.Check taper for accuracy and readjust 
compound rest setting if necessary 
11.Finish-turn and check taper for size 
38 
and fit
Checking a Taper 
• Scribing two lines exactly 1 in. apart on 
inch taper and measuring taper at these 
points with micrometer (difference is tpi) 
• Using a sine bar 
• Using taper ring gage for external tapers 
• Using a taper plug gage for internal 
tapers 
39
Taper Micrometer 
• Measures tapers quickly and accurately while 
work still in machine 
• Includes adjustable anvil and 1-in. sine bar 
attached to frame 
• Adjusted by micrometer thimble 
• Reading indicates tpi, which converts to tpf 
• Available in various model for measuring internal 
tapers and dovetails 
40
Advantages of Taper 
Micrometers 
• Taper accuracy can be checked while 
workpiece still in machine 
• Provide quick and accurate means of checking 
tapers 
• Simple to operate 
• Need for costly gaging equipment eliminated 
• Can be used for measuring external tapers, 
internal tapers, and dovetails 
41
To Fit an External Taper 
1. Make three equally spaced lines with chalk or 
42 
mechanics blue along taper 
2. Insert taper into ring gage and turn counterclockwise 
for one-half turn 
3. Remove workpiece and examine chalk marks 
• Correct if chalk spread along whole length of taper 
• Adjust if chalk lines rubbed from only one end 
4. Make slight adjustment to taper attachment and taking 
trial cuts, machine taper until fit is correct
To Check a Metric Taper 
1. Check drawing for taper required 
2. Clean tapered section of work; apply layout dye 
3. Lay out two lines on taper that are same distance 
43 
apart as second number in taper ratio 
4. Measure diameters with metric micrometer at the two 
lines. Difference between should be 1 mm for each 
unit of length 
5. If necessary, adjust taper attachment setting to correct 
taper
44
45
46
47
48
49
50
51

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Tapers and taper_turning

  • 1. 1 Tapers and Taper Turning Session 10
  • 2. 2 Taper • Uniform change in diameter of workpiece measured along its axis • Inch system expressed in taper per foot, taper per inch, or degrees • Metric system expressed as ratio of 1 mm per unit of length • Provides rapid and accurate method of aligning machine parts and easy method of holding tools
  • 3. 3 Machine Tapers • Classified by American Standards Association • Self-holding tapers • Steep or self-releasing tapers
  • 4. 4 Self-Holding Tapers • Remain in position because of the wedging action of the small taper angle • Most common forms • Morse, the Brown & Sharpe, .750-in.-per-ft taper • Smaller sizes provided with tang to help drive the cutting tool • Larger sizes employ tang drive with shank held in by key or key drive with shank held draw bolt
  • 5. Steep Tapers • 3.500 in. taper per foot (tpf) • Formerly called standard milling machine taper • Used mainly for alignment of milling machine arbors and accessories • Has key drive and uses draw-in bolt to hold it securely in milling machine spindle 5
  • 6. 6 Standard Tapers • Morse taper • Approximaely .625-in tpf, eight sizes #0 to #7 • Used for drills, reamers, and lathe center shanks • Brown & Sharpe taper • .502-in. tpf, sizes from #4 to #12 • Used on Brown and Sharpe machines • Jarno taper • .600-in. tpf, sizes from #2 to #20 • Standard taper pins • Used for positioning and holding parts together • Âź tpf, standard sizes range from #6/0 to #10
  • 7. Table 54.1: Basic dimensions of self-holding tapers 7 Taper Number per Diameter at Diameter at of Taper Foot Gage Line (A) Small End (D) Length (P) 1 .502 .2392 .200 15⁄16 2 .502 .2997 .250 13⁄16 3 .502 .3752 .3125 11⁄2 0* .624 .3561 .252 2 1 .5986 .475 .369 21⁄8 2 .5994 Portion .700 of table .572 shown 29⁄16 3 .6023 .938 .778 33⁄16 in textbook
  • 8. Two Types of Lathe Spindle Nose Tapers • Type D-1 8 • Short tapered section and used on cam-lock spindles • Type L – Taper of 3.500-in./ft – Longer taper than Type D-1 – Chuck held on by treaded lock ring fitted on spindle – Key drive used
  • 9. Taper Calculations: TPF tpf = 1.250 - 1 = 9 x 12 Example: tpf = D - d l x 12 1 3
  • 10. To Calculate the Tailstock Offset Must know the tpf and the total length of work (L) Tailstock offset = tpf x length of work 10 24 Example: Copyright Š The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
  • 11. Taper per inch = taper per foot Tailstock offset taper per inch x overall length (OL) 11 Simplified Formula Simplified formula can be used to calculate tailstock offset if taper per inch t/in. known: 2 12 = In cases where not necessary to find tpf: ( ) 2 x D - d Tailstock offset = OL TL OL = overall length TL = length of tapered section D = diameter of large end d = diameter at small end
  • 12. Inch Taper Attachment Offset Calculations • Most tapers cut on lathe with taper attachment are expressed in tpf • If tpf not given, it may be calculated: ( ) = 1.375 - .9375 x 12 12 ( ) tpf = D - d x 12 TL 7 Calculate the tpf for a taper with the following dimensions: large diameter (D), 1.375; small diameter (d), .9375; length of tapered section (TL), 7 in.
  • 13. Metric Tapers • Expressed as ratio of 1 mm per unit of length Work would taper 1 mm in a distance of 20 mm ratio of 1:20 13
  • 14. Metric Taper Calculations If know d, k, and l, D may be calculated. D equal to small dia + amount of taper. Amount of taper is equal to 1¸k, so total taper equals l¸k. D = d + total taper D = d + l/k d = small diameter k = unit length of taper l = total length of taper D = large diameter 14
  • 15. Metric Tailstock Offset Calculations • If taper turned by offsetting tailstock, amount of offset O is calculated as follows: 15 x L Offset D - d 2 x l = where D = large diameter d = small diameter l = length of taper L = length of work
  • 16. Example: Metric Tailstock Offset Calculate tailstock offset required to turn a 1:30 taper X 60 mm long on a workpiece 300 mm long. The small diameter of tapered section is 20 mm. Solution: x L Offset D - d 2 x = 22 - 20 5 mm 16 x 300 2 x 60 = = l D = d + l 20 60 = + = + 22mm 20 2 30 k =
  • 17. Metric Taper Attachment Offset Calculations 1. When taper attachment used to turn taper, amount guide bar set over is one-half 17 angle given on drawing.
  • 18. 2. If angle of taper not given on drawing, use following formula to find amount of guide bar setover: where D = large diameter of taper d = small diameter of taper l = length of taper GL = length of taper attachment guide bar 18 x GL l Guide bar setover = D - d 2
  • 19. Taper Turning • Performed on work held between centers of in lathe chuck • Three methods of producing taper 19 • Offsetting tailstock • Taper attachment set to proper tpf • Metric by calculating guide bar offset • Adjusting compound rest to angle of taper • Method used depends on work length, taper length, taper angle and number of pieces
  • 20. Tailstock Offset Method • Generally used to cut taper when no taper attachment available • Involves moving tailstock center out of line with headstock center • Amount tailstock may be offset limited • Will not permit steep tapers to be turned or standard tapers turned on end of long piece of work 20
  • 22. Three Methods of Offsetting the Tailstock • By using graduations on end of the tailstock (visual method) • By means of the graduated collar and feeler gage • By means of a dial indicator 22
  • 23. Procedure to Offset Tailstock by the Visual Method • Loosen the tailstock clamp nut • Offset upper part of tailstock by loosening one setscrew and tightening the other until required amount is indicated on graduated scale at end of tailstock Note: Make sure both setscrews snugged up to prevent any lateral movement of tailstock 23
  • 24. Procedure to Offset the Tailstock Accurately 1. Adjust tailstock spindle to distance it 24 will be used in machining setup and lock tailstock spindle clamp 2. Mount a dial indicator in toolpost with plunger in horizontal position and on center 3. Using crossfeed handle, move indicator so registers ~.020 in on work, and set indicator and crossfeed graduated collars to zero
  • 25. 4. Loosen tailstock clamp nut 5. With tailstock adjusting setscrews, move tailstock until required offset shown on dial indicator 6. Tighten tailstock setscrew that was loosened, making sure indicator reading does not change 7. Tighten tailstock clamp nut Note: Tailstock may also be offset by using feeler gage between toolpost and tailstock spindle in conjunction with crossfeed graduated collar 25
  • 26. Advantages of Using Taper Attachment for Tapers 1. Lathe centers remain in alignment, preventing distortion of centers on work 2. Setup is simple and permits changing from taper to parallel turning with no time lost to align centers 3. Length of workpiece does not matter, since duplicate tapers may be turned on any length of work 26
  • 27. 4. Tapers may be produced on work held between centers, in chuck or in collet 5. Internal tapers can be produced by this 27 method 6. Metric taper attachments are graduated in millimeters and degrees, while inch attachments are graduated in both degrees and inches of tpf • Eliminates need for lengthy calculations and setup 4. Wider range of tapers may be produced
  • 28. 28 Two Types of Taper Attachments • Plain taper • Remove binding screw that holds cross-slide to crossfeed screw nut • Binding screw used to connect sliding block to slide of taper attachment • Depth of cut made by using compound rest feed handle • Telescopic taper • Crossfeed screw not disengaged and depth of cut set by crossfeed handle
  • 30. To Cut a Taper Using a Taper Attachment 1. Clean and oil guide bar 2. Loosen lock screws and offset end of guide bar the required amount or, for inch attachments, set bar to required taper in degrees or tpf 3. Tighten lock screws 4. With compound rest set at 90Âş, set up 30 cutting tool on center
  • 31. Telescopic Taper Attachment 5. Set workpiece in lathe and mark 31 length of taper 6. Tighten connecting screw on sliding block 7. Move carriage until center of attachment opposite length to be tapered 8. Lock anchor bracket to lathe bed
  • 32. Telescopic Taper Attachment 9. Take cut .060 in. long, stop lathe, 32 check end of taper for size 10.Set depth of roughing cut to .050 to . 060 in. oversize, and machine taper 11.Readjust taper attachment, if necessary, take light cut, and recheck taper fit 12.Finish-turn and fit taper to gage
  • 33. 33 • Standard tapers – Taper plug gage mounted between centers and taper attachment adjusted to angle by using dial indicator mounted on center • Internal taper – Same procedure, except guide bar set to side of centerline • Mating external and internal tapers – Machine internal taper to plug gage then external
  • 34. Taper Turning Using the Compound Rest • Used to produce short or steep tapers 34 stated in degrees • Tool fed by hand, using compound rest feed handle
  • 35. Taper Turning Using the Compound Rest Procedure 1. Refer to drawing for amount of taper or tpi 35 required in degrees (not given: calculate) 2 angle tpf 2 24 Tan 1 =
  • 36. 2. Loosen compound rest lock screws 3. Swivel compound rest as follows: 36 Copyright Š The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
  • 37. 4. Tighten compound rest lock screws 5. Set cutting tool to center with toolholder at right angles to taper to be cut 6. Tighten toolpost securely 7. Back off top slide of compound rest so there will be enough travel to machine length of taper 37
  • 38. 8. Move carriage to position cutting tool near start of taper and then lock carriage 9. Rough turn taper by feeding cutting tool using compound rest feed handle 10.Check taper for accuracy and readjust compound rest setting if necessary 11.Finish-turn and check taper for size 38 and fit
  • 39. Checking a Taper • Scribing two lines exactly 1 in. apart on inch taper and measuring taper at these points with micrometer (difference is tpi) • Using a sine bar • Using taper ring gage for external tapers • Using a taper plug gage for internal tapers 39
  • 40. Taper Micrometer • Measures tapers quickly and accurately while work still in machine • Includes adjustable anvil and 1-in. sine bar attached to frame • Adjusted by micrometer thimble • Reading indicates tpi, which converts to tpf • Available in various model for measuring internal tapers and dovetails 40
  • 41. Advantages of Taper Micrometers • Taper accuracy can be checked while workpiece still in machine • Provide quick and accurate means of checking tapers • Simple to operate • Need for costly gaging equipment eliminated • Can be used for measuring external tapers, internal tapers, and dovetails 41
  • 42. To Fit an External Taper 1. Make three equally spaced lines with chalk or 42 mechanics blue along taper 2. Insert taper into ring gage and turn counterclockwise for one-half turn 3. Remove workpiece and examine chalk marks • Correct if chalk spread along whole length of taper • Adjust if chalk lines rubbed from only one end 4. Make slight adjustment to taper attachment and taking trial cuts, machine taper until fit is correct
  • 43. To Check a Metric Taper 1. Check drawing for taper required 2. Clean tapered section of work; apply layout dye 3. Lay out two lines on taper that are same distance 43 apart as second number in taper ratio 4. Measure diameters with metric micrometer at the two lines. Difference between should be 1 mm for each unit of length 5. If necessary, adjust taper attachment setting to correct taper
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