Machinery's Handbook, 31st Edition
COuNTeR MILLING 907 Counter Milling.— Changing the direction of a linear milling operation by a specific angle requires a linear offset before changing the angle of cut. This compensates for the radius of the milling cutters, as illustrated in Fig. 1a and Fig. 1b.
Radius
x
Cutter Path
Radius
x
r
Cutter Path
r
Inside Angle θ
θ
Outside Angle
Fig. 1a. Inside Milling Fig. 1b. Outside Milling For inside cuts the offset is subtracted from the point at which the cutting direction changes (Fig. 1a), and for outside cuts the offset is added to the point at which the cutting direction changes (Fig. 1b). The formula for the offset is x rM = where x = offset distance; r = radius of the milling cutter; and, M = the multiplication factor ( M = tan θ ∕ 2 ). The value of M for certain angles can be found in Table 5. Table 5. Offset Multiplication Factors Deg ° M Deg ° M Deg ° M Deg ° M Deg ° M 1 ° 0.00873 19 ° 0.16734 37 ° 0.33460 55 ° 0.52057 73 ° 0.73996 2 ° 0.01746 20 ° 0.17633 38 ° 0.34433 56 ° 0.53171 74 ° 0.75355 3 ° 0.02619 21 ° 0.18534 39 ° 0.35412 57 ° 0.54296 75 ° 0.76733 4 ° 0.03492 22 ° 0.19438 40 ° 0.36397 58 ° 0.55431 76 ° 0.78129 5 ° 0.04366 23 ° 0.20345 41 ° 0.37388 59 ° 0.56577 77 ° 0.79544 6 ° 0.05241 24 ° 0.21256 42 ° 0.38386 60 ° 0.57735 78 ° 0.80978 7 ° 0.06116 25 ° 0.22169 43 ° 0.39391 61 ° 0.58905 79 ° 0.82434 8 ° 0.06993 26 ° 0.23087 44 ° 0.40403 62 ° 0.60086 80 ° 0.83910 9 ° 0.07870 27 ° 0.24008 45 ° 0.41421 63 ° 0.61280 81 ° 0.85408 10 ° 0.08749 28 ° 0.24933 46 ° 0.42447 64 ° 0.62487 82 ° 0.86929 11 ° 0.09629 29 ° 0.25862 47 ° 0.43481 65 ° 0.63707 83 ° 0.88473 12 ° 0.10510 30 ° 0.26795 48 ° 0.44523 66 ° 0.64941 84 ° 0.90040 13 ° 0.11394 31 ° 0.27732 49 ° 0.45573 67 ° 0.66189 85 ° 0.91633 14 ° 0.12278 32 ° 0.28675 50 ° 0.46631 68 ° 0.67451 86 ° 0.93252 15 ° 0.13165 33 ° 0.29621 51 ° 0.47698 69 ° 0.68728 87 ° 0.94896 16 ° 0.14054 34 ° 0.30573 52 ° 0.48773 70 ° 0.70021 88 ° 0.96569 17 ° 0.14945 35 ° 0.31530 53 ° 0.49858 71 ° 0.71329 89 ° 0.98270 18 ° 0.15838 36 ° 0.32492 54 ° 0.50953 72 ° 0.72654 90 ° 1.00000 Multiply factor M by the tool radius r to determine the offset dimension
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