Machinery's Handbook, 31st Edition
COUPLINGS and Clutches 2533 case, the two clutch members would not mesh completely: the engagement of the teeth cut as shown at D and E would be as indicated at D 1 and E 1 respectively. As will be seen, when the outer points of the teeth at D 1 are at the bottom of the grooves in the opposite member, the inner ends are not together, the contact area being represented by the dotted lines. At E 1 the inner ends of the teeth strike first and spaces are left between the teeth around the outside of the clutch. To overcome this objectionable feature, the clutch teeth should be cut as indicated at B , or so that the bottoms and tops of the teeth have the same inclination, con- verging at a central point x . The teeth of both members will then engage across the entire width as shown at C . The angle α required for cutting a clutch as at B can be determined by the following formula in which α equals the required angle, N = number of teeth, θ = cutter angle, and 360 ° / N = angle between teeth: cos 2 # α = tan (360° ⁄ N ) cot θ The angles α for various numbers of teeth and for 60-, 70- or 80-degree single-angle cutters are given in the table on page 2532. The following table is for double-angle cutters used to cut V-shaped teeth. Angle of Dividing-Head for Milling V-Shaped Teeth with Double-Angle Cutter
180°/ N
cos N ) cot ( θ ⁄ 2) This is the angle ( α , Fig. 4) shown by graduations on the dividing-head. θ is the included angle of a double-angle cutter, see Fig. 1. 2 # α = tan (180° ⁄
Included Angle of Cutter, θ
Included Angle of Cutter, θ
60 °
90 °
60 °
90 °
No. of Teeth, N
No. of Teeth, N
Dividing Head Angle, α
Dividing Head Angle, α
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
39.4'
39'
56.9' 6.42 15.4 23.8 31.8 39.3 46.4 53.1 59.5 5.51 11.3 16.7 26.9 31.7 36.2 40.6 22 44.8 48.8 52.6 56.3
5.13' 10.6 15.8 20.7 25.2 29.6 33.7 37.5 41.2 44.7 51.2 54.2 48 59.8 2.4 4.91 7.32 9.63 11.8 57
73 °
80 °
84 ° 85 85 85
87 ° 87 87 87
75 16.1 76 34.9 77 40.5 78 36 79 23.6 80 4.83 80 41 81 13 81 41.5 82 6.97 82 30 82 50.8 83 9.82 83 27.2 83 43.1 83 57.8 84 11.4 84 24 84 35.7 84 46.7
81 33.5 82 18 82 55.3 83 26.8 83 54 84 17.5 84 38.2 84 56.5 85 12.8 85 27.5 85 40.7 85 52.6 86 3.56 86 13.5 86 22.7 26 31.2 86 39 86 46.2 86 53 86 59.3
85 85 85 85 85 86 86 86 86 86 86 86 86 86 86 86
87 87 87 87 87 87 87 87 87 87 87 88 88 88 88 88
30 14 The angles given in the table above are applicable to the milling of V-shaped grooves in brackets, etc., which must have toothed surfaces to prevent the two members from turning relative to each other, except when unclamped for angular adjustment 86 88
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