# Tables For Making Involute Gear Cutter Cutters



## ProfessorGuy

If you want to make an involute gear, you'll need an involute gear cutter.  Buy a set, or make them according to the formulas in Ivan Law's _Gear and Gear Cutting_ (Workshop Practice Series #17).  Basically make a button cutter and use the distance between centers and infeed to make the profile of the gear cutter.

Law gives the values for making a set of 6 cutters from 17-20 teeth to 135-rack for pressure angle of 20 degrees and a set of 9 cutters from 10-11 teeth to 135-rack for pressure angle of 30 degrees.

I did some math that let me look at what theoretically perfect teeth would look like for every tooth count.  Here are my findings:

Law's cutter -------------- Values are actually for
135-rack --------------------  150 teeth
55-134  ---------------------  94 teeth
26-34  ----------------------  30 teeth
21-25   ---------------------   25 teeth
*17-20  --------------------   23 teeth*

Here are the full results for Pressure Angle of 30*
Law's Cutter  -------------  Values are actually for
135-rack --------------------  135 teeth
55-134 ----------------------  55 teeth
35-54  ----------------------  35 teeth
26-34   ---------------------  26 teeth
21-25  ----------------------   21 teeth
17-20  ---------------------   17 teeth
14-16 ----------------------   14 teeth
12 & 13 --------------------  12 teeth
10 & 11 --------------------   10 teeth

Notice that the 20* values start to deviate from ideal as the tooth count goes down.   The bold values above show that as you get down there, you have to cut bigger and bigger relative spaces--creating thinner and thinner teeth forms--so the teeth have enough room to "turn" in the spaces since the diameters become quite small.

Also, Law states the tooth should be 0.48 of the circular pitch while the space should be 0.52 to add a little backlash as clearance.  I did enough math to find his chart values do indeed include this adjustment.

I was able to make an entire chart with every tooth count (from 6 to 150) for 20*, 30*, and 14.5*.  However, if you want to make custom cutters, you'll have to "slide up" the scale some amount for clearance as Law did for his low numbered gears.  I don't know how he picked his actual tooth numbers.  Anyone know?

I'll post the charts in one of the forums here if someone tells me which one.


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## drom68

Nice.  I would be interested in the chart for 14.5*.  That is the majority of gears I cut.  

As for Law picking his numbers. I think the tolerances work out that way.  A cutter for 55 teeth can cut up to 134 accurate enough that you don't need a special cutter.  But if you want a truly accurate gear using a cutter of this type, you would need to do the math for the specific tooth count.  Once you make that cutter you will find that it will cut a range effectively and it will look a lot like what you posted.  

My question is, can you make a button cutter specifically for a 72 tooth gear that is within the tolerancess?


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## bcall2043

I also would like to see the 14.5* gear information also. I have an old Southbend lathe that needs some gear repair at some point in the future.

Thanks, Benny


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## ProfessorGuy

drom68 said:


> My question is, can you make a button cutter specifically for a 72 tooth gear that is within the tolerances?



You be the judge.  Here's some numbers for a typical 20 DP at 30* pressure angle:
------------------------  71 teeth -------- 72 teeth -------  73 teeth
Cutter dia.  -----------   1.775 ---------- 1.8 ------------- 1.825
Between ctrs -------- 1.596882 ----- 1.618538 ------- 1.640194
Infeed ---------------- 0.483918 ----- 0.490173 ------ 0.496427

Seems like those are different enough to make it possible.


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## ProfessorGuy

bcall2043 said:


> I also would like to see the 14.5* gear information also.


NOTE: I am not totally convinced that cutting teeth that are perfectly positioned and shaped to fill 0.48 of the pitch will actually work at lower tooth counts.  Notice there is little deviation for usable cutters at a pressure angle of 30*, but a deviation of theory to practice begins at lower numbers for 20*.  I guess the tooth count cutter you actually should use would deviate even more at 14.5* and starting at even larger tooth counts.  But how much?  That I do not know.

To make involute gear cutters, use this chart to make a hardened, relieved circular cutter ("cutter-cutter" dia.) and infeed it on both sides of the edge of a spinning disk or fly cutting blank (between ctrs & infeed).  The edge will take on the profile of a tooth space and it becomes the gear cutter.  Hence, the circular cutter described here is a gear cutter-cutter.

To use the tables in metric, the table values are in millimeters (mm) for modulus 1.0.  Multiply the table values by the actual modulus you need.  To use the tables in English, the table values are in inches (in) for DP=1.  Divide the table values by the actual DP you need.

Here's 20-100 teeth for pressure angle of 14.5*.   There seems to be some art to sizing cutters, so for any given tooth count you need, you may have to choose a larger count in the table.  This is especially true for the low end of the table.  These cutter-cutter settings are for theoretically perfect 96% wide teeth.

TABLE FOR MAKING AND USING INVOLUTE CUTTER-CUTTERS
DP=1 (read chart values in inches) or M=1 (values in mm), PRESSURE ANGLE = 14.5*
TOOTH_COUNT ,   cutter-cutter dia. ,  between centers ,  infeed
20, 5.00760, 6.33271, 2.80985
21, 5.25798, 6.57600, 2.90511
22, 5.50836, 6.81921, 3.00024
23, 5.75874, 7.06234, 3.09526
24, 6.00912, 7.30541, 3.19018
25, 6.25950, 7.54842, 3.28501
26, 6.50988, 7.79138, 3.37977
27, 6.76026, 8.03430, 3.47446
28, 7.01064, 8.27718, 3.56909
29, 7.26102, 8.52002, 3.66367
30, 7.51140, 8.76283, 3.75820
31, 7.76178, 9.00562, 3.85269
32, 8.01216, 9.24837, 3.94713
33, 8.26254, 9.49111, 4.04154
34, 8.51292, 9.73383, 4.13592
35, 8.76330, 9.97653, 4.23026
36, 9.01368, 10.21921, 4.32458
37, 9.26406, 10.46187, 4.41888
38, 9.51444, 10.70452, 4.51315
39, 9.76482, 10.94716, 4.60739
40, 10.01520, 11.18978, 4.70162
41, 10.26558, 11.43240, 4.79583
42, 10.51596, 11.67500, 4.89002
43, 10.76634, 11.91759, 4.98420
44, 11.01672, 12.16018, 5.07836
45, 11.26710, 12.40276, 5.17250
46, 11.51748, 12.64532, 5.26664
47, 11.76786, 12.88789, 5.36076
48, 12.01824, 13.13044, 5.45487
49, 12.26862, 13.37299, 5.54897
50, 12.51900, 13.61553, 5.64306
51, 12.76938, 13.85807, 5.73714
52, 13.01976, 14.10060, 5.83121
53, 13.27014, 14.34313, 5.92527
54, 13.52052, 14.58565, 6.01932
55, 13.77090, 14.82816, 6.11337
56, 14.02128, 15.07068, 6.20741
57, 14.27166, 15.31319, 6.30144
58, 14.52204, 15.55569, 6.39547
59, 14.77242, 15.79820, 6.48949
60, 15.02280, 16.04069, 6.58350
61, 15.27318, 16.28319, 6.67751
62, 15.52356, 16.52568, 6.77151
63, 15.77394, 16.76817, 6.86551
64, 16.02432, 17.01066, 6.95951
65, 16.27470, 17.25314, 7.05349
66, 16.52508, 17.49563, 7.14748
67, 16.77546, 17.73810, 7.24146
68, 17.02584, 17.98058, 7.33544
69, 17.27622, 18.22306, 7.42941
70, 17.52660, 18.46553, 7.52338
71, 17.77698, 18.70800, 7.61734
72, 18.02736, 18.95047, 7.71130
73, 18.27774, 19.19294, 7.80526
74, 18.52812, 19.43540, 7.89922
75, 18.77850, 19.67787, 7.99317
76, 19.02888, 19.92033, 8.08712
77, 19.27926, 20.16279, 8.18107
78, 19.52964, 20.40525, 8.27501
79, 19.78002, 20.64771, 8.36896
80, 20.03040, 20.89016, 8.46290
81, 20.28078, 21.13262, 8.55683
82, 20.53116, 21.37507, 8.65077
83, 20.78154, 21.61753, 8.74470
84, 21.03192, 21.85998, 8.83863
85, 21.28230, 22.10243, 8.93256
86, 21.53268, 22.34488, 9.02649
87, 21.78306, 22.58733, 9.12041
88, 22.03344, 22.82977, 9.21434
89, 22.28382, 23.07222, 9.30826
90, 22.53420, 23.31467, 9.40218
91, 22.78458, 23.55711, 9.49610
92, 23.03496, 23.79955, 9.59001
93, 23.28534, 24.04200, 9.68393
94, 23.53572, 24.28444, 9.77784
95, 23.78610, 24.52688, 9.87175
96, 24.03648, 24.76932, 9.96566
97, 24.28686, 25.01176, 10.05957
98, 24.53724, 25.25420, 10.15348
99, 24.78762, 25.49664, 10.24739
100, 25.03800, 25.73907, 10.34129


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## ProfessorGuy

Here's the table for 20* pressure angle.   Again, use with the caveats as above.

TABLE FOR MAKING AND USING INVOLUTE CUTTER-CUTTERS
DP=1 (read chart values in inches) or M=1 (values in mm), PRESSURE ANGLE = 20*
TOOTH_COUNT , cutter-cutter dia. , between centers , infeed
20, 6.84040, 7.82054, 3.12191
21, 7.18242, 8.14305, 3.23575
22, 7.52444, 8.46546, 3.34948
23, 7.86646, 8.78777, 3.46310
24, 8.20848, 9.11001, 3.57663
25, 8.55050, 9.43217, 3.69008
26, 8.89252, 9.75427, 3.80345
27, 9.23454, 10.07632, 3.91677
28, 9.57656, 10.39831, 4.03003
29, 9.91858, 10.72027, 4.14324
30, 10.26060, 11.04218, 4.25640
31, 10.60262, 11.36406, 4.36952
32, 10.94464, 11.68591, 4.48261
33, 11.28666, 12.00773, 4.59566
34, 11.62868, 12.32952, 4.70868
35, 11.97071, 12.65129, 4.82167
36, 12.31273, 12.97304, 4.93464
37, 12.65475, 13.29477, 5.04758
38, 12.99677, 13.61648, 5.16050
39, 13.33879, 13.93817, 5.27340
40, 13.68081, 14.25985, 5.38628
41, 14.02283, 14.58151, 5.49914
42, 14.36485, 14.90316, 5.61199
43, 14.70687, 15.22480, 5.72482
44, 15.04889, 15.54643, 5.83764
45, 15.39091, 15.86805, 5.95045
46, 15.73293, 16.18965, 6.06324
47, 16.07495, 16.51125, 6.17602
48, 16.41697, 16.83284, 6.28879
49, 16.75899, 17.15442, 6.40155
50, 17.10101, 17.47599, 6.51430
51, 17.44303, 17.79755, 6.62704
52, 17.78505, 18.11911, 6.73977
53, 18.12707, 18.44066, 6.85250
54, 18.46909, 18.76221, 6.96522
55, 18.81111, 19.08375, 7.07793
56, 19.15313, 19.40528, 7.19063
57, 19.49515, 19.72681, 7.30333
58, 19.83717, 20.04834, 7.41602
59, 20.17919, 20.36986, 7.52871
60, 20.52121, 20.69137, 7.64139
61, 20.86323, 21.01289, 7.75406
62, 21.20525, 21.33439, 7.86673
63, 21.54727, 21.65590, 7.97940
64, 21.88929, 21.97740, 8.09206
65, 22.23131, 22.29890, 8.20471
66, 22.57333, 22.62039, 8.31737
67, 22.91535, 22.94188, 8.43002
68, 23.25737, 23.26337, 8.54266
69, 23.59939, 23.58486, 8.65530
70, 23.94141, 23.90634, 8.76794
71, 24.28343, 24.22782, 8.88057
72, 24.62545, 24.54930, 8.99321
73, 24.96747, 24.87077, 9.10583
74, 25.30949, 25.19225, 9.21846
75, 25.65151, 25.51372, 9.33108
76, 25.99353, 25.83519, 9.44370
77, 26.33555, 26.15665, 9.55632
78, 26.67757, 26.47812, 9.66893
79, 27.01959, 26.79958, 9.78155
80, 27.36161, 27.12104, 9.89416
81, 27.70363, 27.44250, 10.00677
82, 28.04565, 27.76396, 10.11937
83, 28.38767, 28.08542, 10.23198
84, 28.72969, 28.40687, 10.34458
85, 29.07171, 28.72833, 10.45718
86, 29.41373, 29.04978, 10.56978
87, 29.75575, 29.37123, 10.68237
88, 30.09777, 29.69268, 10.79497
89, 30.43979, 30.01413, 10.90756
90, 30.78181, 30.33557, 11.02015
91, 31.12383, 30.65702, 11.13274
92, 31.46585, 30.97846, 11.24533
93, 31.80787, 31.29991, 11.35792
94, 32.14989, 31.62135, 11.47050
95, 32.49191, 31.94279, 11.58309
96, 32.83393, 32.26423, 11.69567
97, 33.17595, 32.58567, 11.80825
98, 33.51797, 32.90711, 11.92083
99, 33.85999, 33.22855, 12.03341
100, 34.20201, 33.54998, 12.14599


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## Uglydog

How do I measure a gear to learn if it is a 14.5* or a 20*.
I've read gear books which talk about the angles.
Is it possible to actually measure the * without an optical comparator?

Daryl
MN


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## ProfessorGuy

Here's the table for 30* pressure angle. Here I start at only 10 teeth since 30* pressure angles are usually used because of the small diameters of low tooth-numbered gears.  Again, use with the caveats as above.

TABLE FOR MAKING AND USING INVOLUTE CUTTER-CUTTERS
DP=1 (read chart values in inches) or M=1 (values in mm), PRESSURE ANGLE = 30*
TOOTH_COUNT , cutter-cutter dia. , between centers , infeed
10, 5.00000, 5.47119, 2.01356
11, 5.50000, 5.91012, 2.14266
12, 6.00000, 6.34800, 2.27109
13, 6.50000, 6.78509, 2.39901
14, 7.00000, 7.22156, 2.52652
15, 7.50000, 7.65755, 2.65371
16, 8.00000, 8.09315, 2.78063
17, 8.50000, 8.52843, 2.90733
18, 9.00000, 8.96344, 3.03385
19, 9.50000, 9.39824, 3.16020
20, 10.00000, 9.83285, 3.28643
21, 10.50000, 10.26731, 3.41254
22, 11.00000, 10.70162, 3.53855
23, 11.50000, 11.13582, 3.66447
24, 12.00000, 11.56992, 3.79032
25, 12.50000, 12.00393, 3.91610
26, 13.00000, 12.43786, 4.04182
27, 13.50000, 12.87172, 4.16749
28, 14.00000, 13.30551, 4.29311
29, 14.50000, 13.73926, 4.41869
30, 15.00000, 14.17295, 4.54424
31, 15.50000, 14.60659, 4.66974
32, 16.00000, 15.04020, 4.79522
33, 16.50000, 15.47377, 4.92066
34, 17.00000, 15.90730, 5.04609
35, 17.50000, 16.34081, 5.17148
36, 18.00000, 16.77428, 5.29686
37, 18.50000, 17.20773, 5.42221
38, 19.00000, 17.64116, 5.54755
39, 19.50000, 18.07457, 5.67287
40, 20.00000, 18.50795, 5.79817
41, 20.50000, 18.94132, 5.92346
42, 21.00000, 19.37467, 6.04874
43, 21.50000, 19.80800, 6.17400
44, 22.00000, 20.24132, 6.29925
45, 22.50000, 20.67463, 6.42449
46, 23.00000, 21.10792, 6.54972
47, 23.50000, 21.54120, 6.67494
48, 24.00000, 21.97447, 6.80015
49, 24.50000, 22.40773, 6.92535
50, 25.00000, 22.84097, 7.05054
51, 25.50000, 23.27421, 7.17573
52, 26.00000, 23.70744, 7.30091
53, 26.50000, 24.14066, 7.42608
54, 27.00000, 24.57388, 7.55125
55, 27.50000, 25.00708, 7.67641
56, 28.00000, 25.44028, 7.80156
57, 28.50000, 25.87347, 7.92671
58, 29.00000, 26.30666, 8.05186
59, 29.50000, 26.73984, 8.17700
60, 30.00000, 27.17302, 8.30213
61, 30.50000, 27.60619, 8.42726
62, 31.00000, 28.03935, 8.55239
63, 31.50000, 28.47251, 8.67751
64, 32.00000, 28.90566, 8.80263
65, 32.50000, 29.33881, 8.92774
66, 33.00000, 29.77196, 9.05285
67, 33.50000, 30.20510, 9.17796
68, 34.00000, 30.63824, 9.30306
69, 34.50000, 31.07137, 9.42817
70, 35.00000, 31.50450, 9.55327
71, 35.50000, 31.93763, 9.67836
72, 36.00000, 32.37076, 9.80345
73, 36.50000, 32.80388, 9.92855
74, 37.00000, 33.23699, 10.05363
75, 37.50000, 33.67011, 10.17872
76, 38.00000, 34.10322, 10.30380
77, 38.50000, 34.53633, 10.42889
78, 39.00000, 34.96944, 10.55396
79, 39.50000, 35.40255, 10.67904
80, 40.00000, 35.83565, 10.80412
81, 40.50000, 36.26875, 10.92919
82, 41.00000, 36.70185, 11.05426
83, 41.50000, 37.13494, 11.17933
84, 42.00000, 37.56804, 11.30440
85, 42.50000, 38.00113, 11.42947
86, 43.00000, 38.43422, 11.55453
87, 43.50000, 38.86731, 11.67960
88, 44.00000, 39.30039, 11.80466
89, 44.50000, 39.73348, 11.92972
90, 45.00000, 40.16656, 12.05478
91, 45.50000, 40.59965, 12.17984
92, 46.00000, 41.03273, 12.30490
93, 46.50000, 41.46580, 12.42995
94, 47.00000, 41.89888, 12.55501
95, 47.50000, 42.33196, 12.68006
96, 48.00000, 42.76503, 12.80511
97, 48.50000, 43.19811, 12.93016
98, 49.00000, 43.63118, 13.05521
99, 49.50000, 44.06425, 13.18026
100, 50.00000, 44.49732, 13.30531


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## ProfessorGuy

Uglydog said:


> How do I measure a gear to learn if it is a 14.5* or a 20*.
> Is it possible to actually measure the * without an optical comparator?



When at least 2 or 3 involute teeth are in contact at the meshing point, look carefully at where they are actually touching.  The angle of the line of the touch points compared to a line tangent to the gears is the pressure angle.  A careful look should distinguish a 20 from a 30, but the 14.5 might be harder.  Good luck.


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## ProfessorGuy

*Involute Gear-Cutter Cutter Calculator*

If anyone wants some exotic tooth count or pitch angle, you can use my Excel worksheet.  You input Modulus and Pitch Angle, it calculates the entire table.  You can also input whatever tooth count you want.  And I've used Excel's "goal seek" to have it tell me what the tooth count is, given a particular cutter-cutter diameter (so you can figure out unmarked tools or see what size gears you can make with a circular tool you already have).

Get it here:  InvoluteCutterCutters.xlsx (link downloads Excel spreadsheet from my website).  There are two color diagrams on the worksheet to explain the 29 separate calculation steps required to come up with each tooth count spec.


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