Machinery's Handbook, 31st Edition
2284
HELICAL GEARING Factors for Selecting Cutters for Milling Helical Gears
Helix Angle, α
Helix Angle, α
Helix Angle, α
Helix Angle, α
K K ′
K K ′
K K ′ 1.640 0.390 1.695 0.422 1.755 0.455 1.819 0.490 1.889 0.528 1.963 0.568 2.044 0.610 2.130 0.656 2.225 0.704 2.326 0.756 2.436 0.811 2.557 0.870 2.687 0.933 2.983 1.072 3.152 1.150 2.828 1
K K ′ 3.336 1.233 3.540 1.323 3.767 1.420 4.012 1.525 4.284 1.638 4.586 1.761 4.925 1.894 5.295 2.039 5.710 2.198 6.190 2.371 6.720 2.561 7.321 2.770 8.000 3.000 8.780 3.254 9.658 3.537
0 1 2 3 4 5 6 7 8 9
1.000 1.001
0 0
16 1.127 0.082 17 1.145 0.093 18 1.163 0.106 19 1.182 0.119 20 1.204 0.132 21 1.228 0.147 22 1.254 0.163 23 1.282 0.180 24 1.312 0.198 25 1.344 0.217 26 1.377 0.238 27 1.414 0.260 28 1.454 0.283 29 1.495 0.307 30 1.540 0.333 31 1.588 0.361
32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47
48 49 50 51 52 53 54 55 56 57 58 59 60 61 62
1.002 0.001 1.004 0.003 1.007 0.005 1.011 0.008 1.016 0.011 1.022 0.015 1.030 0.020 1.038 0.025
10 1.047 0.031 11 1.057 0.038 12 1.068 0.045 13 1.080 0.053 14 1.094 0.062 15 1.110 0.072
63 10.687 3.852
K = 1 ÷ cos 3 α = sec 3 α ; K ′ = tan 2 α Outside and Pitch Diameters of Standard Involute-form Milling Cutters Nor mal Dia metral Pitch, P n Out side Dia., D o Pitch Dia., D c Q = P n D c Nor mal Dia metral Pitch, P n Out side Dia., D o Pitch Dia., D c Q = P n D c Nor mal Dia metral Pitch, P n Out side Dia., D o Pitch Dia., D c
Q = P n D c
1
8.500 6.18 6.18 7.750 5.70 7.12 7.000 5.46 8.19 6.500 5.04 8.82 5.750 4.60 9.20 5.750 4.83 12.08 4.750 3.98 11.94 4.250 3.67 14.68 3.750 3.29 16.45
6 7 8 9
3.125 2.76 16.56 2.875 2.54 17.78 2.875 2.61 20.88 2.750 2.50 22.50 2.375 2.14 21.40 2.250 2.06 24.72 2.125 1.96 27.44
20 24 28 32 36 40 48
2.000 1.89 37.80 1.750 1.65 39.60 1.750 1.67 46.76 1.750 1.68 53.76 1.750 1.69 60.84 1.750 1.70 68.00 1.750 1.70 81.60 … … …
1 1 ∕ 1 1 ∕ 1 3 ∕
4
2
4
2
10 12 14 16
2 1 ∕
2
3 4 5
2.125 1.98 31.68 .. 2.000 1.87 33.66 ..
18 … … … Pitch diameters shown in the table are computed from the formula: D c = D o − 2(1.57 ÷ P n ). This same formula may be used to compute the pitch diameter of a non-standard outside diameter cutter when the normal diametral pitch P n and the outside diameter D o are known. Milling the Helical Teeth.— The teeth of a helical gear are proportioned from the normal pitch and not the circular pitch. The whole depth of the tooth can be found by dividing 2.157 by the normal diametral pitch of the gear, which corresponds to the pitch of the
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