Machinery's Handbook, 31st Edition
896 Milling Cutters Setting Angles for Milling Straight Teeth of Uniform Land Width in End Mills, Angu- lar Cutters, and Taper Reamers.— The accompanying tables give setting angles for the dividing head when straight teeth, having a land of uniform width throughout their length, are to be milled using single-angle fluting cutters. These setting angles depend upon three factors: the number of teeth to be cut; the angle of the blank in which the teeth are to be cut; and the angle of the fluting cutter. Setting angles for various combinations of these three factors are given in the tables. For example, assume that 12 teeth are to be cut on the end of an end mill using a 60-degree cutter. By following the horizontal line from 12 teeth, read in the column under 60 degrees that the dividing head should be set to an angle of 70 degrees and 32 minutes.
C
A
B
The following formulas, which were used to compile these tables, may be used to calcu late the setting-angles for combinations of number of teeth, blank angle, and cutter angle not covered by the tables. In these formulas, A = setting-angle for dividing head, B = angle of blank in which teeth are to be cut, C = angle of fluting cutter, N = number of teeth to be cut, and D and E are angles not shown on the accompanying diagram that are used only to simplify calculations. (1) (2) (3) Example: Suppose 9 teeth are to be cut in a 35-degree blank using a 55-degree single- angle fluting cutter. Then, N = 9, B = 35 ° , and C = 55 ° . tan D cos 360 9 cot35 0.76604 1.4281 1.0940; and D 47 34 sin E tan cot55 sin47 34 0.83910 0.70021 0.73806 0.43365; and E 25 42 # # # # # # ° ° ° ′ ° ° ′ ° ′ = = = = = = = = ⁄ 360 9 °⁄ ( ) ( ) Setting angle A 47 34 25 42 21 52 ° ′ ° ′ ° ′ = − = For end mills and side mills, the angle of the blank B is 0 degrees, and the following sim plified formula may be used to find the setting angle A: (4) Example: If in the previous example the blank angle was 0 degrees, cos A = tan (360 ° /9) × cot 55 ° = 0.83910 × 0.70021 = 0.58755 and setting-angle A = 54 ° 1 ′. tan D cos = N 360 cot B # ° ) ⁄ ( sin E tan = cot C sin D # # N 360 ° ⁄ ( ) Setting-angle A D E = − cos A tan = N 360 cot C # ° a k ⁄
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