Machinery's Handbook 27th Edition JIG BORING 997 Table 13 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles (English or Metric Units) The diagram shows a type “B” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 17 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 0.40813 0.00851 0.23678 0.07489 0.10099 0.19868 0.01909 0.36317 0.00213 0.54613 0.05242 0.72287 0.16315 0.86950 0.31938 0.96624 0.50000 1.00000 0.68062 0.96624 0.83685 0.86950 0.94758 0.72287 0.99787 0.54613 0.98091 0.36317 0.89901 0.19868 0.76322 0.07489 0.59187 0.00851 18 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 24 Holes 0.41318 0.00760 0.25000 0.06699 0.11698 0.17861 0.03015 0.32899 0.00000 0.50000 0.03015 0.67101 0.11698 0.82139 0.25000 0.93301 0.41318 0.99240 0.58682 0.99240 0.75000 0.93301 0.88302 0.82139 0.96985 0.67101 1.00000 0.50000 0.96985 0.32899 0.88302 0.17861 0.75000 0.06699 0.58682 0.00760 19 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 25 Holes 0.41770 0.00682 0.26203 0.06026 0.13214 0.16136 0.04211 0.29915 0.00171 0.45871 0.01530 0.62274 0.08142 0.77347 0.19289 0.89457 0.33765 0.97291 0.50000 1.00000 0.66235 0.97291 0.80711 0.89457 0.91858 0.77347 0.98470 0.62274 0.99829 0.45871 0.95789 0.29915 0.86786 0.16136 0.73797 0.06026 0.58230 0.00682 20 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 26 Holes 0.42178 0.00616 0.27300 0.05450 0.14645 0.14645 0.05450 0.27300 0.00616 0.42178 0.00616 0.57822 0.05450 0.72700 0.14645 0.85355 0.27300 0.94550 0.42178 0.99384 0.57822 0.99384 0.72700 0.94550 0.85355 0.85355 0.94550 0.72700 0.99384 0.57822 0.99384 0.42178 0.94550 0.27300 0.85355 0.14645 0.72700 0.05450 0.57822 0.00616 21 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 27 Holes 0.42548 0.00558 0.28306 0.04952 0.15991 0.13347 0.06699 0.25000 0.01254 0.38874 0.00140 0.53737 0.03456 0.68267 0.10908 0.81174 0.21834 0.91312 0.35262 0.97779 0.50000 1.00000 0.64738 0.97779 0.78166 0.91312 0.89092 0.81174 0.96544 0.68267 0.99860 0.53737 0.98746 0.38874 0.93301 0.25000 0.84009 0.13347 0.71694 0.04952 0.57452 0.00558 22 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 0.42884 0.00509 0.29229 0.04518 0.17257 0.12213 0.07937 0.22968 0.02025 0.35913 0.00000 0.50000 0.02025 0.64087 0.07937 0.77032 0.17257 0.87787 0.29229 0.95482 0.42884 0.99491 0.57116 0.99491 0.70771 0.95482 0.82743 0.87787 0.92063 0.77032 0.97975 0.64087 1.00000 0.50000 0.97975 0.35913 0.92063 0.22968 0.82743 0.12213 0.70771 0.04518 0.57116 0.00509 28 Holes x1 y1 x2 y2 x3 0.43474 0.00428 0.30866 0.03806 0.19562 x1 y1 x2 y2 x3 0.43733 0.00394 0.31594 0.03511 0.20611 x1 y1 x2 y2 x3 0.43973 0.00365 0.32270 0.03249 0.21597 x1 y1 x2 y2 x3 0.44195 0.00338 0.32899 0.03015 0.22525 x1 y1 x2 y2 x3 0.44402 0.00314 0.33486 0.02806 0.23398 y3 0.10332 y3 0.09549 y3 0.08851 y3 0.08226 y3 0.07664 Copyright 2004, Industrial Press, Inc., New York, NY 23 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 0.43192 0.00466 0.30080 0.04139 0.18446 0.11214 0.09152 0.21166 0.02887 0.33256 0.00117 0.46588 0.01046 0.60173 0.05606 0.73003 0.13458 0.84128 0.24021 0.92721 0.36510 0.98146 0.50000 1.00000 0.63490 0.98146 0.75979 0.92721 0.86542 0.84128 0.94394 0.73003 0.98954 0.60173 0.99883 0.46588 0.97113 0.33256 0.90848 0.21166 0.81554 0.11214 0.69920 0.04139 0.56808 0.00466 Machinery's Handbook 27th Edition 998 JIG BORING Table 13 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles (English or Metric Units) The diagram shows a type “B” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 24 Holes 0.10332 0.19562 0.03806 0.30866 0.00428 0.43474 0.00428 0.56526 0.03806 0.69134 0.10332 0.80438 0.19562 0.89668 0.30866 0.96194 0.43474 0.99572 0.56526 0.99572 0.69134 0.96194 0.80438 0.89668 0.89668 0.80438 0.96194 0.69134 0.99572 0.56526 0.99572 0.43474 0.96194 0.30866 0.89668 0.19562 0.80438 0.10332 0.69134 0.03806 0.56526 0.00428 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 25 Holes 0.11474 0.18129 0.04759 0.28711 0.00886 0.40631 0.00099 0.53140 0.02447 0.65451 0.07784 0.76791 0.15773 0.86448 0.25912 0.93815 0.37566 0.98429 0.50000 1.00000 0.62434 0.98429 0.74088 0.93815 0.84227 0.86448 0.92216 0.76791 0.97553 0.65451 0.99901 0.53140 0.99114 0.40631 0.95241 0.28711 0.88526 0.18129 0.79389 0.09549 0.68406 0.03511 0.56267 0.00394 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 26 Holes 0.12574 0.16844 0.05727 0.26764 0.01453 0.38034 0.00000 0.50000 0.01453 0.61966 0.05727 0.73236 0.12574 0.83156 0.21597 0.91149 0.32270 0.96751 0.43973 0.99635 0.56027 0.99635 0.67730 0.96751 0.78403 0.91149 0.87426 0.83156 0.94273 0.73236 0.98547 0.61966 1.00000 0.50000 0.98547 0.38034 0.94273 0.26764 0.87426 0.16844 0.78403 0.08851 0.67730 0.03249 0.56027 0.00365 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 27 Holes 0.13631 0.15688 0.06699 0.25000 0.02101 0.35660 0.00085 0.47093 0.00760 0.58682 0.04089 0.69804 0.09894 0.79858 0.17861 0.88302 0.27560 0.94682 0.38469 0.98652 0.50000 1.00000 0.61531 0.98652 0.72440 0.94682 0.82139 0.88302 0.90106 0.79858 0.95911 0.69804 0.99240 0.58682 0.99915 0.47093 0.97899 0.35660 0.93301 0.25000 0.86369 0.15688 0.77475 0.08226 0.67101 0.03015 0.55805 0.00338 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 x28 y28 28 Holes 0.14645 0.14645 0.07664 0.23398 0.02806 0.33486 0.00314 0.44402 0.00314 0.55598 0.02806 0.66514 0.07664 0.76602 0.14645 0.85355 0.23398 0.92336 0.33486 0.97194 0.44402 0.99686 0.55598 0.99686 0.66514 0.97194 0.76602 0.92336 0.85355 0.85355 0.92336 0.76602 0.97194 0.66514 0.99686 0.55598 0.99686 0.44402 0.97194 0.33486 0.92336 0.23398 0.85355 0.14645 0.76602 0.07664 0.66514 0.02806 0.55598 0.00314 Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition JIG BORING 999 Table 14 Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units) The diagram shows a type “A” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 3 Holes x1 y1 x2 y2 x3 y3 0.00000 −0.50000 −0.43301 +0.25000 +0.43301 +0.25000 Holes x1 y1 x2 y2 x3 y3 x4 y4 0.00000 −0.50000 −0.50000 0.00000 0.00000 +0.50000 +0.50000 0.00000 10 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 0.00000 −0.50000 −0.29389 −0.40451 −0.47553 −0.15451 −0.47553 +0.15451 −0.29389 +0.40451 0.00000 +0.50000 +0.29389 +0.40451 +0.47553 +0.15451 +0.47553 −0.15451 +0.29389 −0.40451 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 11 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 0.00000 −0.5000 −0.27032 −0.42063 −0.45482 −0.20771 −0.49491 +0.07116 −0.37787 +0.32743 −0.14087 +0.47975 +0.14087 +0.47975 +0.37787 +0.32743 +0.49491 +0.07116 +0.45482 −0.20771 +0.27032 −0.42063 0.00000 −0.50000 −0.47553 −0.15451 −0.29389 +0.40451 +0.29389 +0.40451 +0.47553 −0.15451 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 12 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 0.00000 −0.50000 −0.25000 −0.43301 −0.43301 −0.25000 −0.50000 0.00000 −0.43301 +0.25000 −0.25000 +0.43301 0.00000 +0.50000 +0.25000 +0.43301 +0.43301 +0.25000 +0.50000 0.00000 +0.43301 −0.25000 +0.25000 −0.43301 0.00000 −0.50000 −0.43301 −0.25000 −0.43301 +0.25000 0.00000 +0.50000 +0.43301 +0.25000 +0.43301 −0.25000 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 13 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 0.00000 −0.50000 −0.23236 −0.44273 −0.41149 −2.28403 −0.49635 −0.06027 −0.46751 +0.17730 − 0.33156 +0.37426 −0.11966 +0.48547 +0.11966 +0.48547 +0.33156 +0.37426 +0.46751 +0.17730 +0.49635 −0.06027 +0.41149 −0.28403 +0.23236 −0.44273 0.00000 −0.50000 −0.39092 −0.31174 −0.48746 +0.11126 −0.21694 +0.45048 +0.21694 +0.45048 +0.48746 +0.11126 +0.39092 −0.31174 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 14 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 0.00000 −0.50000 −0.21694 −0.45048 −0.39092 −0.31174 −0.48746 −0.11126 −0.48746 +0.11126 −0.39092 +0.31174 −0.21694 +0.45048 0.00000 +0.50000 +0.21694 +0.45048 +0.39092 +0.31174 +0.48746 +0.11126 +0.48746 −0.11126 +0.39092 −0.31174 +0.21694 −0.45048 0.00000 −0.50000 −0.35355 −0.35355 −0.50000 0.00000 −0.35355 +0.35355 0.00000 +0.50000 +0.35355 +0.35355 +0.50000 0.00000 +0.35355 −0.35355 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 15 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 0.00000 −0.50000 −0.20337 −0.45677 −0.37157 −0.33457 −0.47553 −0.15451 −0.49726 y5 +0.05226 x6 −0.43301 y6 +0.25000 x7 −0.29389 y7 +0.40451 x8 −0.10396 y8 +0.48907 x9 +0.10396 y9 +0.48907 x10 +0.29389 y10 +0.40451 x11 +0.43301 y11 +0.25000 x12 +0.49726 y12 +0.05226 x13 +0.47553 y13 −0.15451 x14 +0.37157 y14 −0.33457 x15 +0.20337 y15 −0.45677 Copyright 2004, Industrial Press, Inc., New York, NY x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 0.00000 −0.50000 −0.32139 −0.38302 −0.49240 −0.08682 −0.43301 +0.25000 −0.17101 +0.46985 +0.17101 +0.46985 +0.43301 +0.25000 +0.49240 −0.08682 +0.32139 −0.38302 16 Holes 0.00000 −0.50000 −0.19134 −0.46194 −0.35355 −0.35355 −0.46194 −0.19134 −0.50000 0.00000 −0.46194 +0.19134 −0.35355 +0.35355 −0.19134 +0.46194 0.00000 +0.50000 +0.19134 +0.46194 +0.35355 +0.35355 +0.46194 +0.19134 +0.50000 0.00000 +0.46194 −0.19134 +0.35355 −0.35355 +0.19134 −0.46194 Machinery's Handbook 27th Edition 1000 JIG BORING Table 14 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units) The diagram shows a type “A” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 17 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 0.00000 −0.50000 −0.18062 −0.46624 −0.33685 −0.36950 −0.44758 −0.22287 −0.49787 −0.04613 −0.48091 +0.13683 −0.39901 +0.30132 −0.26322 +0.42511 −0.09187 +0.49149 +0.09187 +0.49149 +0.26322 +0.42511 +0.39901 +0.30132 +0.48091 +0.13683 +0.49787 −0.04613 +0.44758 −0.22287 +0.33685 −0.36950 +0.18062 −0.46624 18 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 24 Holes 0.00000 −0.50000 −0.17101 −0.46985 +0.32139 −0.38302 −0.43301 −0.25000 −0.49240 −0.08682 −0.49420 +0.08682 −0.43301 +0.25000 −0.32139 +0.38302 −0.17101 +0.46985 0.00000 +0.50000 +0.17101 +0.46985 +0.32139 +0.38302 +0.43301 +0.25000 +0.49240 +0.08682 +0.49240 −0.08682 +0.43301 −0.25000 +0.32139 −0.38302 +0.17101 −0.46985 19 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 25 Holes x1 y1 x2 y2 x3 0.00000 −0.50000 −0.12941 −0.48296 −0.25000 x1 y1 x2 y2 x3 y3 − 0.43301 y3 0.00000 −0.50000 −0.12434 −0.48429 −0.24088 0.00000 −0.50000 −0.16235 −0.47291 −0.30711 −0.39457 −0.41858 −0.27347 −0.48470 −0.12274 −0.49829 +0.04129 −0.45789 +0.20085 −0.36786 +0.33864 −0.23797 +0.43974 −0.08230 +0.49318 +0.08230 +0.49318 +0.23797 +0.43974 +0.36786 +0.33864 +0.45789 +0.20085 +0.49829 +0.04129 +0.48470 −0.12274 +0.41858 −0.27347 +0.30711 −0.39457 + 0.16235 −0.47291 20 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 26 Holes x1 y1 x2 y2 x3 −0.43815 y3 0.00000 −0.50000 −0.11966 −0.48547 −0.23236 0.000000 −0.50000 −0.15451 −0.47553 −0.29389 −0.40451 −0.40451 −0.29389 −0.47553 −0.15451 −0.50000 0.00000 −0.47553 +0.15451 −0.40451 +0.29389 −0.29389 +0.40451 −0.15451 +0.47553 0.00000 +0.50000 +0.15451 +0.47553 +0.29389 +0.40451 +0.40451 +0.29389 +0.47553 +0.15451 +0.50000 0.00000 +0.47553 −0.15451 +0.40451 −0.29389 +0.29389 −0.40451 +0.15451 −0.47553 21 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 27 Holes x1 y1 x2 y2 x3 −0.44273 y3 0.00000 −0.50000 −0.11531 −0.48652 −0.22440 0.00000 −0.50000 −0.14738 −0.47779 −0.28166 −0.41312 −0.39092 −0.31174 −.046544 −0.18267 −0.49860 −0.03737 −0.48746 +0.11126 −0.43301 +0.25000 −0.34009 +0.36653 −0.21694 +0.45048 −0.07452 +0.49442 +0.07452 +0.49442 +0.21694 +0.45048 +0.34009 +0.36653 +0.43301 +0.25000 +0.48746 +0.11126 +0.49860 −0.03737 +0.46544 −0.18267 +0.39092 −0.31174 +0.28166 −0.41312 +0.14738 −0.47779 22 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 0.00000 −0.50000 −0.14087 −0.47975 −0.27032 −0.42063 −0.37787 −0.32743 −0.45482 −0.20771 −0.49491 −0.07116 −0.49491 +0.07116 −0.45482 +0.20771 −0.37787 +0.32743 −0.27032 +0.42063 −0.14087 +0.47975 0.00000 +0.50000 +0.14087 +0.47975 +0.27032 +0.42063 +0.37787 +0.32743 +0.45482 +0.20771 +0.49491 +0.07116 +0.49491 −0.07116 +0.45482 −0.20771 +0.37787 −0.32743 +0.27032 −0.42063 +0.14087 −0.47975 28 Holes x1 y1 x2 y2 x3 0.00000 −0.50000 −0.11126 −0.48746 −0.21694 −0.44682 y3 −0.45048 Copyright 2004, Industrial Press, Inc., New York, NY 23 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 0.00000 −0.50000 −0.13490 −0.48146 −0.25979 −0.42721 −0.36542 −0.34128 −0.44394 −0.23003 −0.48954 −0.10173 −0.49883 +0.03412 −0.47113 +0.16744 −0.40848 +0.28834 −0.31554 +0.38786 −0.19920 +0.45861 −0.06808 +0.49534 +0.06808 +0.49534 +0.19920 +0.45861 +0.31554 +0.38786 +0.40848 +0.28834 +0.47113 +0.16744 +0.49883 +0.03412 +0.48954 −0.10173 +0.44394 −0.23003 +0.36542 −0.34128 +0.25979 −0.42721 +0.13490 −0.48146 Machinery's Handbook 27th Edition JIG BORING 1001 Table 14 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units) The diagram shows a type “A” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 24 Holes −0.35355 −0.35355 −0.43301 −0.25000 −0.48296 −0.12941 −0.50000 0.00000 −0.48296 +0.12941 −0.43301 +0.25000 −0.35355 +0.35355 −0.25000 +0.43301 −0.12941 +0.48296 0.00000 +0.50000 +0.12941 +0.48296 +0.25000 +0.43301 +0.35355 +0.35355 +0.43301 +0.25000 +0.48296 +0.12941 +0.50000 0.00000 +0.48296 −0.12941 +0.43301 −0.25000 +0.35355 −0.35355 +0.25000 −0.43301 +0.12941 −0.48296 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 25 Holes −0.34227 −0.36448 −0.42216 −0.26791 −0.47553 −0.15451 −0.49901 −0.03140 −0.49114 +0.09369 −0.45241 +0.21289 −0.38526 +0.31871 −0.29389 +0.40451 −0.18406 +0.46489 −0.06267 +0.49606 +0.06267 +0.49606 +0.18406 +0.46489 +0.29389 +0.40451 + 0.38526 +0.31871 +0.45241 +0.21289 +0.49114 +0.09369 +0.49901 −0.03140 +0.47553 −0.15451 +0.42216 −0.26791 +0.34227 −0.36448 +0.24088 −0.43815 +0.12434 −0.48429 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 26 Holes −0.33156 −0.37426 −0.41149 −0.28403 −0.46751 −0.17730 −0.49635 −0.06027 −0.49635 +0.06027 −0.46751 +0.17730 −0.41149 +0.28403 −0.33156 +0.37426 −0.23236 +0.44273 −0.11966 +0.48547 0.00000 +0.50000 +0.11966 +0.48547 +0.23236 +0.44273 +0.33156 +0.37426 +0.41149 +0.28403 +0.46751 +0.17730 +0.49635 +0.06027 +0.49635 −0.06027 +0.46751 −0.17730 +0.41149 −0.28403 +0.33156 −0.37426 +0.23236 −0.44273 +0.11966 −0.48547 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 27 Holes −0.32139 −0.38302 −0.40106 −0.29858 −0.45911 −0.19804 −0.49240 −0.08682 −0.49915 +0.02907 −0.47899 +0.14340 −0.43301 +0.25000 −0.36369 +0.34312 −0.27475 +0.41774 −0.17101 +0.46985 −0.05805 +0.49662 +0.05805 +0.49662 +0.17101 +0.46985 +0.27475 +0.41774 +0.36369 +0.34312 +0.43301 +0.25000 +0.47899 +0.14340 +0.49915 +0.02907 +0.49240 −0.08682 +0.45911 −0.19804 +0.40106 −0.29858 +0.32139 −0.38302 +0.22440 −0.44682 +0.11531 −0.48652 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 x28 y28 28 Holes −0.31174 −0.39092 −0.39092 −0.31174 −0.45048 −0.21694 −0.48746 −0.11126 −0.50000 0.00000 −0.48746 +0.11126 −0.45048 +0.21694 −0.39092 +0.31174 −0.31174 +0.39092 −0.21694 +0.45048 −0.11126 +0.48746 0.00000 +0.50000 +0.11126 +0.48746 +0.21694 +0.45048 +0.31174 +0.39092 +0.39092 +0.31174 +0.45048 +0.21694 +0.48746 +0.11126 +0.50000 0.00000 +0.48746 −0.11126 +0.45048 −0.21694 +0.39092 −0.31174 +0.31174 −0.39092 +0.21694 −0.45048 +0.11126 −0.48746 Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1002 JIG BORING Table 15 Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units) The diagram shows a type “B” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 3 Holes x1 y1 x2 y2 x3 y3 −0.43301 −0.25000 0.00000 +0.50000 +0.43301 −0.25000 10 Holes x1 −0.15451 y1 −0.47553 x2 −0.40451 y2 −0.29389 x3 −0.50000 y3 0.00000 x4 −0.40451 y4 +0.29389 x5 −0.15451 y5 +0.47553 x6 +0.15451 y6 +0.47553 x7 +0.40451 y7 +0.29389 x8 +0.50000 y8 0.00000 x9 +0.40451 y9 −0.29389 x10 +0.15451 y10 −0.47553 Holes x1 y1 x2 y2 x3 y3 x4 y4 −0.35355 −0.35355 −0.35355 +0.35355 +0.35355 +0.35355 +0.35355 −0.35355 11 Holes x1 −0.14087 y1 −0.47975 x2 −0.37787 y2 −0.32743 x3 −0.49491 y3 −0.07116 x4 −0.45482 y4 +0.20771 x5 −0.27032 y5 +0.42063 x6 0.00000 y6 +0.50000 x7 +0.27032 y7 +0.42063 x8 +0.45482 y8 +0.20771 x9 +0.49491 y9 −0.07116 x10 +0.37787 y10 −0.32743 x11 +0.14087 y11 −0.47975 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 −0.29389 −0.40451 −0.47553 +0.15451 0.00000 +0.50000 +0.47553 +0.15451 +0.29389 −0.40451 12 Holes x1 −0.12941 y1 −0.48296 x2 −0.35355 y2 −0.35355 x3 −0.48296 y3 −0.12941 x4 −0.48296 y4 +0.12941 x5 −0.35355 y5 +0.35355 x6 −0.12941 y6 +0.48296 x7 +0.12941 y7 +0.48296 x8 +0.35355 y8 +0.35355 x9 +0.48296 y9 +0.12941 x10 +0.48296 y10 −0.12941 x11 +0.35355 y11 −0.35355 x12 +0.12941 y12 −0.48296 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 −0.25000 −0.43301 −0.50000 0.00000 −0.25000 +0.43301 +0.25000 +0.43301 +0.50000 0.00000 +0.25000 −0.43301 13 Holes x1 −0.11966 y1 −0.48547 x2 −0.33156 y2 −0.37426 x3 −0.46751 y3 −0.17730 x4 −0.49635 y4 +0.06027 x5 −0.41149 y5 +0.28403 x6 −0.23236 y6 +0.44273 x7 0.00000 y7 + 0.50000 x8 +0.23236 y8 +0.44273 x9 +0.41149 y9 +0.28403 x10 +0.49635 y10 +0.06027 x11 +0.46751 y11 −0.17730 x12 +0.33156 y12 −0.37426 x13 +0.11966 y13 −0.48547 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 −0.21694 −0.45048 −0.48746 −0.11126 −0.39092 +0.31174 0.00000 +0.50000 +0.39092 +0.31174 +0.48746 −0.11126 +0.21694 −0.45048 14 Holes x1 −0.11126 y1 −0.48746 x2 −0.31174 y2 −0.39092 x3 −0.45048 y3 −0.21694 x4 −0.50000 y4 0.00000 x5 −0.45048 y5 +0.21694 x6 −0.31174 y6 +0.39092 x7 −0.11126 y7 +0.48746 x8 +0.11126 y8 +0.48746 x9 +0.31174 y9 +0.39092 x10 +0.45048 y10 +0.21694 x11 +0.50000 y11 0.00000 x12 +0.45048 y12 −0.21694 x13 +0.31174 y13 −0.39092 x14 +0.11126 y14 − 0.48746 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 −0.19134 −0.46194 −0.46194 −0.19134 −0.46194 +0.19134 −0.19134 +0.46194 +0.19134 +0.46194 +0.46194 +0.19134 +0.46194 −0.19134 +0.19134 −0.46194 15 Holes x1 −0.10396 y1 −0.48907 x2 −0.29389 y2 −0.40451 x3 −0.43301 y3 −0.25000 x4 −0.49726 y4 −0.05226 x5 −0.47553 y5 +0.15451 x6 −0.37157 y6 +0.33457 x7 −0.20337 y7 +0.45677 x8 0.00000 y8 +0.50000 x9 +0.20337 y9 +0.45677 x10 +0.37157 y10 +0.33457 x11 +0.47553 y11 +0.15451 x12 +0.49726 y12 −0.05226 x13 +0.43301 y13 −0.25000 x14 +0.29389 y14 −0.40451 x15 +0.10396 y15 −0.48907 Copyright 2004, Industrial Press, Inc., New York, NY Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 −0.17101 −0.46985 −0.43301 −0.25000 −0.49240 +0.08682 −0.32139 +0.38302 0.00000 +0.50000 +0.32139 +0.38302 +0.49240 +0.08682 +0.43301 −0.25000 +0.17101 −0.46985 16 Holes x1 −0.09755 y1 −0.49039 x2 −0.27779 y2 −0.41573 x3 −0.41573 y3 −0.27779 x4 −0.49039 y4 −0.09755 x5 −0.49039 y5 +0.09755 x6 −0.41573 y6 +0.27779 x7 −0.27779 y7 +0.41573 x8 −0.09755 y8 +0.49039 x9 +0.09755 y9 +0.49039 x10 +0.27779 y10 +0.41573 x11 +0.41573 y11 +0.27779 x12 +0.49039 y12 +0.09755 x13 +0.49039 y13 −0.09755 x14 +0.41573 y14 −0.27779 x15 +0.27779 y15 −0.41573 x16 +0.09755 y16 −0.49039 Machinery's Handbook 27th Edition JIG BORING 1003 Table 15 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units) The diagram shows a type “B” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 17 Holes x1 −0.09187 y1 − 0.49149 x2 −0.26322 y2 −0.42511 x3 − 0.39901 y3 −0.30132 x4 −0.48091 y4 −0.13683 x5 −0.49787 y5 +0.04613 x6 −0.44758 y6 +0.22287 x7 −0.33685 y7 +0.36950 x8 −0.18062 y8 +0.46624 x9 0.00000 y9 +0.50000 x10 +0.18062 y10 +0.46624 x11 +0.33685 y11 +0.36950 x12 +0.44758 y12 +0.22287 x13 +0.49787 y13 +0.04613 x14 +0.48091 y14 −0.13683 x15 +0.39901 y15 −0.30132 x16 +0.26322 y16 −0.42511 x17 +0.09187 y17 − 0.49149 18 Holes x1 −0.08682 y1 −0.49240 x2 −0.25000 y2 −0.43301 x3 −0.38302 y3 −0.32139 x4 −0.46985 y4 −0.17101 x5 −0.50000 y5 0.00000 x6 −0.46985 y6 +0.17101 x7 −0.38302 y7 +0.32139 x8 −0.25000 y8 +0.43301 x9 −0.08682 y9 +0.49240 x10 +0.08682 y10 +0.49240 x11 +0.25000 y11 +0.43301 x12 +0.38302 y12 +0.32139 x13 +0.46985 y13 +0.17101 x14 +0.50000 y14 0.00000 x15 +0.46985 y15 −0.17101 x16 +0.38302 y16 −0.32139 x17 +0.25000 y17 −0.43301 x18 +0.08682 y18 −0.49240 24 Holes x1 −0.06526 y1 −0.49572 x2 −0.19134 y2 −0.46194 x3 −0.30438 y3 −0.39668 19 Holes x1 −0.08230 y1 −0.49318 x2 −0.23797 y2 −0.43974 x3 −0.36786 y3 −0.33864 x4 −0.45789 y4 −0.20085 x5 −0.49829 y5 −0.04129 x6 −0.48470 y6 +0.12274 x7 −0.41858 y7 +0.27347 x8 −0.30711 y8 +0.39457 x9 −0.16235 y9 +0.47291 x10 0.00000 y10 +0.50000 x11 +0.16235 y11 +0.47291 x12 +0.30711 y12 +0.39457 x13 +0.41858 y13 +0.27347 x14 +0.48470 y14 +0.12274 x15 +0.49829 y15 −0.04129 x16 +0.45789 y16 −0.20085 x17 +0.36786 y17 −0.33864 x18 +0.23797 y18 −0.43974 x19 +0.08230 y19 −0.49318 25 Holes 20 Holes x1 −0.07822 y1 −0.49384 x2 −0.22700 y2 −0.44550 x3 −0.35355 y3 −0.35355 x4 −0.44550 y4 −0.22700 x5 −0.49384 y5 −0.07822 x6 −0.49384 y6 +0.07822 x7 −0.44550 y7 +0.22700 x8 −0.35355 y8 +0.35355 x9 −0.22700 y9 +0.44550 x10 −0.07822 y10 +0.49384 x11 +0.07822 y11 +0.49384 x12 +0.22700 y12 +0.44550 x13 +0.35355 y13 +0.35355 x14 +0.44550 y14 +0.22700 x15 +0.49384 y15 +0.07822 x16 +0.49384 y16 −0.07822 x17 +0.44550 y17 −0.22700 x18 +0.35355 y18 −0.35355 x19 +0.22700 y19 −0.44550 x20 +0.07822 y20 −0.49384 26 Holes 21 Holes x1 −0.07452 y1 −0.49442 x2 −0.21694 y2 −0.45048 x3 −0.34009 y3 −0.36653 x4 −0.43301 y4 −0.25000 x5 −0.48746 y5 −0.11126 x6 −0.49860 y6 +0.03737 x7 −0.46544 y7 +0.18267 x8 −0.39092 y8 +0.31174 x9 −0.28166 y9 +0.41312 x10 −0.14738 y10 +0.47779 x11 0.00000 y11 +0.50000 x12 +0.14738 y12 +0.47779 x13 +0.28166 y13 +0.41312 x14 +0.39092 y14 +0.31174 x15 +0.46544 y15 +0.18267 x16 +0.49860 y16 +0.03737 x17 +0.48746 y17 −0.11126 x18 +0.43301 y18 −0.25000 x19 +0.34009 y19 −0.36653 x20 +0.21694 y20 −0.45048 x21 +0.07452 y21 −0.49442 27 Holes 22 Holes x1 −0.07116 y1 −0.49491 x2 −0.20771 y2 −0.45482 x3 −0.32743 y3 −0.37787 x4 −0.42063 y4 −0.27032 x5 −0.47975 y5 −0.14087 x6 −0.50000 y6 0.00000 x7 −0.47975 y7 +0.14087 x8 −0.42063 y8 +0.27032 x9 −0.32743 y9 +0.37787 x10 −0.20771 y10 +0.45482 x11 −0.07116 y11 +0.49491 x12 + 0.07116 y12 +0.49491 x13 +0.20771 y13 +0.45482 x14 +0.32743 y14 +0.37787 x15 +0.42063 y15 +0.27032 x16 +0.47975 y16 +0.14087 x17 +0.50000 y17 0.00000 x18 +0.47975 y18 −0.14087 x19 +0.42063 y19 −0.27032 x20 +0.32743 y20 −0.37787 x21 +0.20771 y21 −0.45482 x22 +0.07116 y22 −0.49491 28 Holes −0.06267 −0.49606 −0.18406 −0.46489 −0.29389 x1 y1 x2 y2 x3 −0.06027 −0.49635 −0.17730 −0.46751 −0.28403 x1 y1 x2 y2 x3 −0.05805 −0.49662 −0.17101 −0.46985 −0.27475 x1 y1 x2 y2 x3 y3 −0.40451 y3 −0.41149 y3 −0.41774 y3 −0.42336 x1 y1 x2 y2 x3 −0.05598 −0.49686 −0.16514 −0.47194 −0.26602 Copyright 2004, Industrial Press, Inc., New York, NY 23 Holes x1 −0.06808 y1 −0.49534 x2 −0.19920 y2 −0.45861 x3 −0.31554 y3 −0.38786 x4 −0.40848 y4 −0.28834 x5 −0.47113 y5 −0.16744 x6 −0.49883 y6 −0.03412 x7 −0.48954 y7 +0.10173 x8 −0.44394 y8 +0.23003 x9 −0.36542 y9 +0.34128 x10 −0.25979 y10 +0.42721 x11 −0.13490 y11 +0.48146 x12 0.00000 y12 +0.50000 x13 +0.13490 y13 +0.48146 x14 +0.25979 y14 +0.42721 x15 +0.36542 y15 +0.34128 x16 +0.44394 y16 +0.23003 x17 +0.48954 y17 +0.10173 x18 +0.49883 y18 −0.03412 x19 +0.47113 y19 −0.16744 x20 +0.40848 y20 −0.28834 x21 +0.31554 y21 −0.38786 x22 +0.19920 y22 −0.45861 x23 +0.06808 y23 −0.49534 Machinery's Handbook 27th Edition 1004 JIG BORING Table 15 (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units) The diagram shows a type “B” circle for a 5-hole circle Coordinates x, y are given in the table for hole circles of from to 28 holes Dimensions are for holes numbered in a counterclockwise direction (as shown) Dimensions given are based upon a hole circle of unit diameter For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 24 Holes x4 −0.39668 y4 −0.30438 x5 −0.46194 y5 −0.19134 x6 −0.49572 y6 −0.06526 x7 −0.49572 y7 +0.06526 x8 −0.46194 y8 +0.19134 x9 −0.39668 y9 +0.30438 x10 −0.30438 y10 +0.39668 x11 −0.19134 y11 +0.46194 x12 −0.06526 y12 +0.49572 x13 +0.06526 y13 +0.49572 x14 +0.19134 y14 +0.46194 x15 +0.30438 y15 +0.39668 x16 +0.39668 y16 +0.30438 x17 +0.46194 y17 +0.19134 x18 +0.49572 y18 +0.06526 x19 +0.49572 y19 −0.06526 x20 +0.46194 y20 −0.19134 x21 +0.39668 y21 −0.30438 x22 +0.30438 y22 −0.39668 x23 +0.19134 y23 −0.46194 x24 +0.06526 y24 −0.49572 25 Holes x4 −0.38526 y4 −0.31871 x5 −0.45241 y5 −0.21289 x6 −0.49114 y6 −0.09369 x7 −0.49901 y7 +0.03140 x8 −0.47553 y8 +0.15451 x9 −0.42216 y9 +0.26791 x10 −0.34227 y10 + 0.36448 x11 −0.24088 y11 +0.43815 x12 −0.12434 y12 +0.48429 x13 0.00000 y13 +0.50000 x14 +0.12434 y14 +0.48429 x15 +0.24088 y15 +0.43815 x16 +0.34227 y16 +0.36448 x17 +0.42216 y17 +0.26791 x18 +0.47553 y18 +0.15451 x19 +0.49901 y19 +0.03140 x20 +0.49114 y20 −0.09369 x21 +0.45241 y21 −0.21289 x22 +0.38526 y22 −0.31871 x23 +0.29389 y23 −0.40451 x24 +0.18406 y24 −0.46489 x25 +0.06267 y25 −0.49606 26 Holes x4 −0.37426 y4 −0.33156 x5 −0.44273 y5 −0.23236 x6 −0.48547 y6 −0.11966 x7 −0.50000 y7 0.00000 x8 −0.48547 y8 +0.11966 x9 −0.44273 y9 +0.23236 x10 −0.37426 y10 +0.33156 x11 −0.28403 y11 +0.41149 x12 −0.17730 y12 +0.46751 x13 −0.06027 y13 +0.49635 x14 +0.06027 y14 +0.49635 x15 +0.17730 y15 +0.46751 x16 +0.28403 y16 +0.41149 x17 +0.37426 y17 +0.33156 x18 +0.44273 y18 +0.23236 x19 +0.48547 y19 +0.11966 x20 +0.50000 y20 0.00000 x21 + 0.48547 y21 −0.11966 x22 +0.44273 y22 −0.23236 x23 +0.37426 y23 −0.33156 x24 +0.28403 y24 −0.41149 x25 +0.17730 y25 −0.46751 x26 +0.06027 y26 −0.49635 27 Holes x4 −0.36369 y4 −0.34312 x5 −0.43301 y5 − 0.25000 x6 −0.47899 y6 −0.14340 x7 −0.49915 y7 − 0.02907 x8 −0.49240 y8 +0.08682 x9 −0.45911 y9 +0.19804 x10 −0.40106 y10 +0.29858 x11 −0.32139 y11 +0.38302 x12 −0.22440 y12 +0.44682 x13 −0.11531 y13 +0.48652 x14 0.00000 y14 +0.50000 x15 +0.11531 y15 +0.48652 x16 +0.22440 y16 +0.44682 x17 +0.32139 y17 +0.38302 x18 +0.40106 y18 + 0.29858 x19 +0.45911 y19 +0.19804 x20 +0.49240 y20 +0.08682 x21 +0.49915 y21 −0.02907 x22 +0.47899 y22 − 0.14340 x23 +0.43301 y23 −0.25000 x24 +0.36369 y24 −0.34312 x25 +0.27475 y25 −0.41774 x26 +0.17101 y26 −0.46985 x27 +0.05805 y27 −0.49662 28 Holes x4 −0.35355 y4 −0.35355 x5 −0.42336 y5 −0.26602 x6 −0.47194 y6 −0.16514 x7 −0.49686 y7 −0.05598 x8 −0.49686 y8 +0.05598 x9 −0.47194 y9 +0.16514 x10 −0.42336 y10 +0.26602 x11 −0.35355 y11 +0.35355 x12 −0.26602 y12 +0.42336 x13 −0.16514 y13 +0.47194 x14 −0.05598 y14 +0.49686 x15 +0.05598 y15 +0.49686 x16 +0.16514 y16 +0.47194 x17 +0.26602 y17 +0.42336 x18 +0.35355 y18 +0.35355 x19 +0.42336 y19 +0.26602 x20 +0.47194 y20 +0.16514 x21 +0.49686 y21 +0.05598 x22 +0.49686 y22 −0.05598 x23 +0.47194 y23 −0.16514 x24 +0.42336 y24 −0.26602 x25 +0.35355 y25 −0.35355 x26 +0.26602 y26 −0.42336 x27 +0.16514 y27 −0.47194 x28 +0.05598 y28 −0.49686 Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition TABLE OF CONTENTS MACHINING OPERATIONS CUTTING SPEEDS AND FEEDS 1009 Indroduction to Speeds and Feeds 1009 Cutting Tool Materials 1013 Cutting Speeds 1014 Cutting Conditions 1014 Selecting Cutting Conditions 1014 Tool Troubleshooting 1016 Cutting Speed Formulas 1018 RPM for Various Cutting Speeds and Diameter SPEED AND FEED TABLES 1022 1022 1026 1027 1031 1032 1033 1035 1037 1038 1039 1040 1043 1044 1045 1049 1050 1052 1054 1056 1057 1059 1060 1061 1066 1067 1068 1070 1071 1072 1072 1074 1075 1075 1077 1079 1080 1081 How to Use the Tables Principal Speed andFeed Tables Speed and Feed Tables for Turning Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals Speed and Tool Life Adjustments Copper Alloys Titanium and Titanium Alloys Superalloys Speed and Feed Tables for Milling Slit Milling Aluminium Alloys Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals High Speed Steel Cutters Speed Adjustment Factors Radial Depth of Cut Adjustments Tool Life Adjustments Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals Light Metals Adjustment Factors for HSS Copper Alloys Tapping and Threading Cutting Speed for Broaching Spade Drills Spade Drill Geometry Spade Drilling Feed Rates Power Consumption Trepanning ESTIMATING SPEEDS AND MACHINING POWER 1082 1082 1082 1082 1082 1084 1084 1085 1085 1088 1090 1090 1091 1091 1091 Planer Cutting Speeds Cutting Speed and Time Planing Time Speeds for Metal-Cutting Saws Turning Unusual Material Estimating Machining Power Power Constants Feed Factors Tool Wear Factors Metal Removal Rates Estimating Drilling Thrust, Torque, and Power Work Material Factor Chisel Edge Factors Feed Factors Drill Diameter Factors MACHINING ECONOMETRICS 1093 Tool Wear And Tool Life Relationships 1093 Equivalent Chip Thickness (ECT) 1094 Tool-life Relationships 1098 The G- and H-curves 1099 Tool-life Envelope 1102 Forces and Tool-life 1104 Surface Finish and Tool-life 1106 Shape of Tool-life Relationships 1107 Minimum Cost 1108 Production Rate 1108 The Cost Function 1109 Global Optimum 1110 Economic Tool-life 1113 Machine Settings and Cost Calculations 1113 Nomenclature 1114 Cutting Formulas 1118 Tooling And Total Cost 1119 Optimized Data 1122 High-speed Machining Econometrics 1123 Chip Geometry in Milling 1125 Chip Thickness 1127 Forces and Tool-life 1128 High-speed Milling 1129 Econometrics Comparison 1005 Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1112 MACHINING ECONOMETRICS In the V–ECT graph, Fig 21, 45-degree lines have been drawn tangent to each tool-life curve: T=1, 5, 15, 30, 60, 100 and 300 minutes The tangential points define the G-curve, and the 45-degree lines represent different constant cutting times: 1, 2, 3, 10 minutes, etc Following one of these lines and noting the intersection points with the tool-life curves T = 1, 5, etc., many different speed and feed combinations can be found that will give the same cutting time As tool-life gets longer (tooling cost is reduced), ECT (feed) increases but the cutting speed has to be reduced LIVE GRAPH Click here to view 1000 Constant cutting time increasing going down 45 Degrees V, m/min G-CURVE T=1 T=5 T=15 T=30 T=60 100 0.1 ECT, mm Fig 21 Constant cutting time in the V-ECT plane, tool-life constant Global Optimum, Mathematical Method.—Global optimization is the search for extremum of CTOT for the three parameters: T, ECT, and V The results, in terms of the tool-life equation constants, are: Optimum tool-life: 1T O = T V × ⎛ - – 1⎞ ⎝n ⎠ O n O = 2M × ( L × lnT O ) + – N + L × ( 2M + H ) where nO = slope at optimum ECT The same approach is used when searching for maximum production rate, but without the term containing tooling cost Optimum cutting speed: VO = e – M + K + ( H × L – N ) × lnT O + M × L × ( lnT O ) Optimum ECT: ECT O = e H + 2M × ( L × ln ( T O ) + ) Global optimum is not reached when face milling for very large feeds, and CTOT decreases continually with increasing feed/tooth, but can be reached for a cutter with many teeth, say 20 to 30 In end milling, global optimum can often be achieved for big feeds and for to teeth Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition MACHINING ECONOMETRICS 1115 Number of parts before tool change = Nch = 90/3 = 30 parts Cycle time before tool change = TCYC = 30 × (3 + 3) = 180 minutes Example 5: Given cutting time, tc = minute, idle time ti = minute, Nch = 100 parts, calculate the tool-life T required to complete the job without a tool change, and the cycle time before a tool change is required Tool-life = T = Nch × tc = 100 × = 100 minutes Cycle time before tool change = TCYC = 100 × (1 + 1) = 200 minutes Calculation of Cost of Cutting and Grinding Operations.—When machining data varies, the cost of cutting, tool changing, and tooling will change, but the costs of idle and slack time are considered constant Cost of Cutting per Batch: CC = HR × TC/60 TC = cutting time per batch = (number of parts) × tc, minutes, or when determining time for tool change TCch = Nch × tc minutes = cutting time before tool change tc = Cutting time/part, minutes HR = Hourly Rate Cost of Tool Changes per Batch: HR T RPL $ C CH = × T C × - ⋅ = $ 60 T where T = tool-life, minutes, and TRPL = time for replacing a worn edge(s), or tool for regrinding, minutes Cost of Tooling per Batch: Including cutting tools and holders, but without tool changing costs, 60C E ⋅ $ ⋅ hr HR HR hr $$ C TOOL = × T C × ⋅ ⋅ - = $ 60 T min Cost of Tooling + Tool Changes per Batch: Including cutting tools, holders, and tool changing costs, 60C E T RPL + -HR HR ( C TOOL + C CH ) = × T C × T 60 Total Cost of Cutting per Batch: 60C E ⎛ T RPL + ⎞ ⎜ HR HR ⎟ C TOT = × T C ⎜ + - ⎟ 60 T ⎜ ⎟ ⎝ ⎠ Equivalent Tooling-cost Time, TV: 60C E The two previous expressions can be simplified by using T V = T RPL + -HR thus: HR TV ( C TOOL + C CH ) = × T C × 60 T Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1116 MACHINING ECONOMETRICS TV HR C TOT = × T C ⎛ + - ⎞ ⎝ T⎠ 60 CE = cost per edge(s) is determined using two alternate formulas, depending on whether tools are reground or inserts are replaced: Cost per Edge, Tools for Regrinding cost of tool + ( number of regrinds × cost/regrind ) C E = -1 + number of regrinds Cost per Edge, Tools with Inserts: cost of insert(s) cost of cutter body C E = - + number of edges per insert cutter body life in number of edges Note: In practice allow for insert failures by multiplying the insert cost by 4/3, that is, assuming only out of edges can be effectively used Example 6, Cost per Edge–Tools for Regrinding:Use the data in the table below to calculate the cost per edge(s) CE, and the equivalent tooling-cost time TV, for a drill Time for cutter replacement TRPL, minute Cutter Price, $ Cost per regrind, $ Number of regrinds Hourly shop rate, $ Batch size Taylor slope, n Economic cutting time, tcE minute 40 50 1000 0.25 1.5 Using the cost per edge formula for reground tools, CE = (40 + × 6) ÷ (1 + 5) = $6.80 60C E 60 ( 6.8 ) When the hourly rate is $50/hr, T V = T RPL + = + = 9.16minutes HR 50 Calculate economic tool-life using T E = T V × ⎛ – 1⎞ thus, TE = 9.17 × (1/0.25 – 1) = ⎝n ⎠ 9.16 × = 27.48 minutes Having determined, elsewhere, the economic cutting time per piece to be tcE = 1.5 minutes, for a batch size = 1000 calculate: Cost of Tooling + Tool Change per Batch: HR TV 9.16( C TOOL + C CH ) = × T C × - = 50 × 1000 × 1.5 × = $ 417 60 T 60 27.48 Total Cost of Cutting per Batch: HR TV 9.16C TOT = × T C ⎛ + - ⎞ = 50 × 1000 × 1.5 × ⎛ + ⎞ = $ 1617 ⎝ ⎝ T⎠ 27.48⎠ 60 60 Example 7, Cost per Edge–Tools with Inserts: Use data from the table below to calculate the cost of tooling and tool changes, and the total cost of cutting For face milling, multiply insert price by safety factor 4/3 then calculate the cost per edge: CE =10 × (5/3) × (4/3) + 750/500 = 23.72 per set of edges When the hourly rate is $50, equivalent tooling-cost time is TV = + 23.72 × 60/50 = 30.466 minutes (first line in table below) The economic tool-life for Taylor slope n = 0.333 would be TE = 30.466 × (1/0.333 –1) = 30.466 × = 61 minutes When the hourly rate is $25, equivalent tooling-cost time is TV = + 23.72 × 60/25 = 58.928 minutes (second line in table below) The economic tool-life for Taylor slope n = 0.333 would be TE = 58.928 × (1/0.333 –1) =58.928 × = 118 minutes Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition MACHINING ECONOMETRICS Time for replacement of inserts TRPL, minutes Number of inserts Price per insert 2 10 10 5 1 Edges per insert Cutter Price Face mill 750 750 End mill 75 Turning 50 3 1117 Edges per cutter Cost per set of edges, CE Hourly shop rate TV minutes 500 500 23.72 23.72 50 25 30.466 58.928 200 4.375 50 6.25 100 2.72 30 6.44 With above data for the face mill, and after having determined the economic cutting time as tcE = 1.5 minutes, calculate for a batch size = 1000 and $50 per hour rate: Cost of Tooling + Tool Change per Batch: HR TV 50 30.466 ( C TOOL + C CH ) = × T C × - = - × 1000 × 1.5 × - = $ 624 60 T 60 61 Total Cost of Cutting per Batch: HR TV 30.466 C TOT = × T C ⎛ + - ⎞ = 50 × 1000 × 1.5 × ⎛ + - ⎞ = $ 1874 ⎝ ⎝ 60 T⎠ 60 61 ⎠ Similarly, at the $25/hour shop rate, (CTOOL + CCH) and CTOT are $312 and $937, respectively Example 8, Turning: Production parts were run in the shop at feed/rev = 0.25 mm One series was run with speed V1 = 200 m/min and tool-life was T1 = 45 minutes Another was run with speed V2 = 263 m/min and tool-life was T2 = 15 minutes Given idle time ti = minute, cutting distance Dist =1000 mm, work diameter D = 50 mm First, calculate Taylor slope, n, using Taylor’s equation V1 × T1n = V2 × T2n, as follows: V1 T2 n = ln - ÷ ln - = ln 200 ÷ ln 15 = 0.25 -V2 T1 263 45 Economic tool-life TE is next calculated using the equivalent tooling-cost time TV, as described previously Assuming a calculated value of TV = minutes, then TE can be calculated from 1T E = T V × ⎛ – 1⎞ = × ⎛ - – 1⎞ = 12 minutes -⎝n ⎠ ⎝ 0.25 ⎠ Economic cutting speed, VE can be found using Taylor’s equation again, this time using the economic tool-life, as follows, V E1 × ( T E ) n = V × ( T ) n 0.25 T2 n V E1 = V × ⎛ - ⎞ = 263 × ⎛ 15⎞ = 278 m/min ⎝T ⎠ ⎝ 12⎠ E Using the process data, the remaining economic parameters can be calculated as follows: Economic spindle rpm, rpmE = (1000VE)/(πD) = (1000 × 278)/(3.1416 × 50) = 1770 rpm Economic feed rate, FRE = f × rpmE = 0.25 × 1770 = 443 mm/min Economic cutting time, tcE = Dist/ FRE =1000/ 443 = 2.259 minutes Economic number of parts before tool change, NchE = TE ÷ tcE =12 ÷ 2.259 = 5.31 parts Economic cycle time before tool change, TCYCE = NchE × (tc + ti) = 5.31 × (2.259 + 1) = 17.3 minutes Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1120 MACHINING ECONOMETRICS 5) Determine cost of tooling per batch (cutting tools, holders and tool changing) then total cost of cutting per batch: CTOOL = HR × TC × (CE/T)/60 (CTOOL+CCH) = HR × TC × ((TRPL+CE/T)/60 CTOT = HR × TC (1 + (TRPL+CE)/T) Example 12, Face Milling – Minimum Cost : This example demonstrates how a modern firm, using the formulas previously described, can determine optimal data It is here applied to a face mill with 10 teeth, milling a 1045 type steel, and the radial depth versus the cutter diameter is 0.8 The V–ECT–T curves for tool-lives 5, 22, and 120 minutes for this operation are shown in Fig 23a LIVE GRAPH Click here to view 1000 V, m/min G-CURVE 100 T=5 T = 22 T = 120 10 0.1 10 ECT, mm Fig 23a Cutting speed vs ECT, tool-life constant The global cost minimum occurs along the G-curve, see Fig 6c and Fig 23a, where the 45-degree lines defines this curve Optimum ECT is in the range 1.5 to mm For face and end milling operations, ECT = z ì fz ì ar/D ì aa/CEL ữ The ratio aa/CEL = 0.95 for lead angle LA = 0, and for ar/D = 0.8 and 10 teeth, using the formula to calculate the feed/tooth range gives for ECT = 1.5, fz = 0.62 mm and for ECT = 2, fz = 0.83 mm LIVE GRAPH Click here to view 0.6 T=5 T = 22 T = 120 0.5 0.4 tc 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 fz Fig 23b Cutting time per part vs feed per tooth Using computer simulation, the minimum cost occurs approximately where Fig 23a indicates it should be Total cost has a global minimum at fz around 0.6 to 0.7 mm and a speed of around 110 m/min ECT is about 1.9 mm and the optimal cutter life is TO = 22 minutes Because it may be impossible to reach the optimum feed value due to tool breakage, Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition MACHINING ECONOMETRICS 1121 the maximum practical feed fmax is used as the optimal value The difference in costs between a global optimum and a practical minimum cost condition is negligible, as shown in Figs 23c and 23e A summary of the results are shown in Figs 23a through 23e, and Table 0.31 T = 120 T = 22 0.26 T=5 CTOT, $ 0.21 0.16 0.11 0.06 0.01 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 fz, mm Fig 23c Total cost vs feed/tooth When plotting cutting time/part, tc, versus feed/tooth, fz, at T = 5, 22, 120 in Figs 23b, tool-life T = minutes yields the shortest cutting time, but total cost is the highest; the minimum occurs for fz about 0.75 mm, see Figs 23c The minimum for T = 120 minutes is about 0.6 mm and for TO = 22 minutes around 0.7 mm 0.1 T=5 0.09 T = 22 0.08 T =120 Unit Tooling Cost, $ 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 fz, mm Fig 23d Tooling cost versus feed/tooth Fig 23d shows that tooling cost drop off quickly when increasing feed from 0.1 to 0.3 to 0.4 mm, and then diminishes slowly and is almost constant up to 0.7 to 0.8 mm/tooth It is generally very high at the short tool-life minutes, while tooling cost of optimal tool-life 22 minutes is about times higher than when going slow at T =120 minutes Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1124 MACHINING ECONOMETRICS Face Milling End Milling AE hmax ar hmax ar hm hm AE fz ar cos AE = – × ⎛ -⎝ D⎞ ⎠ fz ar cos AE = – × ⎛ -⎝ D⎞ ⎠ Fig 24 Comparison of face milling and end milling geometry High-speed end milling refers to values of ar/D that are less than 0.5, in particular to ar/D ratios which are considerably smaller When ar/D = 0.5 (AE = 90 degrees) and diminishing in end milling, the chip thickness gets so small that poor cutting action develops, including plowing or scratching This situation is remedied by increasing the feed/tooth, as shown in Table 2a as an increasing fz/fz0 ratio with decreasing ar/D For end milling, the fz/fz0 feed ratio is 1.0 for ar/D = and also for ar/D = 0.5 In order to maintain the same hm as at ar/D = 1, the feed/tooth should be increased, by a factor of 6.38 when ar/D is 0.01 and by more than 10 when ar/D is less than 0.01 Hence high-speed end milling could be said to begin when ar/D is less than 0.5 In end milling, the ratio fz/fz0 = is set at ar/D = 1.0 (full slot), a common value in vendor catalogs and handbooks, for hm = 0.108 mm The face milling chip making process is exactly the same as end milling when face milling the side of a work piece and ar/D = 0.5 or less However, when face milling close to and along the work centerline (eccentricity is close to zero) chip making is quite different, as shown in Fig 24 When ar/D = 0.74 (AE = 95 degrees) in face milling, the fz/fz0 ratio = and increases up to 1.4 when the work width is equal to the cutter diameter (ar/D = 1) The face milling fz/fz0 ratio continues to diminish when the ar/D ratio decreases below ar/D = 0.74, but very insignificantly, only about 11 percent when ar/D = 0.01 In face milling fz/fz0 = is set at ar/D = 0.74, a common value recommended in vendor catalogs and handbooks, for hm = 0.151 mm Fig 25 shows the variation of the feed/tooth-ratio in a graph for end and face milling LIVE GRAPH Click here to view 6.5 fz/fz0 , Face Milling 5.5 fz/fz0 , End Milling 4.5 fz/fz0 3.5 2.5 1.5 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ar/D Fig 25 Feed/tooth versus ar/D for face and end milling Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1126 MACHINING ECONOMETRICS Table 2b Variation of ECT, Chip Thickness and fz/fz0 with ar/D Face Milling ar/D 1.0000 0.9000 0.8080 0.7360 0.6137 0.5900 0.5000 0.2170 0.1250 0.0625 0.0300 0.0100 0.0010 hm 0.108 0.137 0.146 0.151 0.158 0.159 0.162 0.169 0.170 0.170 0.170 0.170 0.170 fz/fz0 1.398 1.107 1.036 1.000 0.958 0.952 0.932 0.897 0.892 0.891 0.890 0.890 0.890 ECT 0.411 0.370 0.332 0.303 0.252 0.243 0.206 0.089 0.051 0.026 0.012 0.004 0.002 End Milling (straight) ECT0 corrected for fz/fz0 0.575 0.410 0.344 0.303 0.242 0.231 0.192 0.080 0.046 0.023 0.011 0.004 0.002 hm 0.108 0.122 0.123 0.121 0.116 0.115 0.108 0.076 0.059 0.042 0.029 0.017 0.005 fz/fz0 1.000 0.884 0.880 0.892 0.934 0.945 1.000 1.422 1.840 2.574 3.694 6.377 20.135 ECT 0.103 0.093 0.083 0.076 0.063 0.061 0.051 0.022 0.013 0.006 0.003 0.001 0.001 ECT0 corrected for fz/fz0 0.103 0.082 0.073 0.067 0.059 0.057 0.051 0.032 0.024 0.017 0.011 0.007 0.005 In face milling, the approximate values of aa/CEL = 0.95 for lead angle LA = 0° (90° in the metric system); for other values of LA, aa/CEL = 0.95 × sin (LA), and 0.95 × cos (LA) in the metric system Example, Face Milling: For a cutter with D = 250 mm and ar = 125 mm, calculate ECTF for fz = 0.1, z = 12, and LA = 30 degrees First calculate ar/D = 0.5, and then use Table 2b and find ECT0F = 0.2 Calculate ECTF with above formula: ECTF = 0.2 × (12/8) × (0.1/0.17) × 0.95 × sin 30 = 0.084 mm End milling: ECTE = ECT0E × (z/2) × (fz/0.17) × (aa/CEL), or if ECTE is known calculate fz from: fz = 0.17 × (ECTE/ECT0E) × (2/z)) × (CEL/aa) The approximate values of aa/CEL = 0.95 for lead angle LA = 0° (90° in the metric system) Example, High-speed End Milling:For a cutter with D = 25 mm and ar = 3.125 mm, calculate ECTE for fz = 0.1 and z = First calculate ar/D = 0.125, and then use Table 2b and find ECT0E = 0.0249 Calculate ECTE with above formula: ECTE = 0.0249 × (6/2) × (0.1/0.17) × 0.95 × = 0.042 mm Example, High-speed End Milling: For a cutter with D = 25 mm and ar = 0.75 mm, calculate ECTE for fz = 0.17 and z = and First calculate ar/D = 0.03, and then use Table 2b and find fz/fz0 = 3.694 Then, fz = 3.694 × 0.17 = 0.58 mm/tooth and ECTE = 0.0119 × 0.95 = 0.0113 mm and 0.0357 × 0.95 = 0.0339 mm for and teeth respectively These cutters are marked HS2 and HS6 in Figs 26a, 26d, and 26e Example, High-speed End Milling: For a cutter with D = 25 mm and ar = 0.25 mm, calculate ECTE for fz = 0.17 and z = and First calculate ar/D = 0.01, and then use Table 2b and find ECT0E = 0.0069 and 0.0207 for and teeth respectively When obtaining such small values of ECT, there is a great danger to be far on the left side of the H-curve, at least when there are only teeth Doubling the feed would be the solution if cutter design and material permit Example, Full Slot Milling:For a cutter with D = 25 mm and ar = 25 mm, calculate ECTE for fz = 0.17 and z = and First calculate ar/D =1, and then use Table 2b and find ECTE = Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1130 MACHINING ECONOMETRICS Fig 27 compares total cost ctot, using the end milling cutters of the previous examples, for full slot milling with high-speed milling at ar/D =0.03, and versus ECT at T =45 minutes H-CURVE minutes 2,4,6 teeth marked SL2 SL4 SL6 ctot , $ HS2 0.1 HS4 T = 45, z = 4, SL HS6 T = 45, z = 6, SL T = 45, z = 2, HS T = 45, z = 4, H T = 45, z = 6, HS 0.01 0.01 0.1 ECT, mm Fig 27 Cost comparison of slot milling (ar/D = 1) and high-speed milling at (ar/D = 0.03) for 2, 4, and teeth at T = 45 minutes The feed/tooth for slot milling is fz0 = 0.17 and for high-speed milling at ar/D = 0.03 the feed is fz = 3.69 × fz0 = 0.628 mm The calculations for total cost are done according to above formula using tooling cost at TV = 6, 10, and 14 minutes, for z = 2, 4, and teeth respectively The distance cut is Dist = 1000 mm Full slot milling costs are, at feed rate FR = 3230 and z = ctot = 50 × (1000/3230) × (1 + 14/45)/60 = $0.338 per part at feed rate FR =1480 and z = ctot = 50 × (1000/1480) × (1 + 6/45)/60 = $0.638 per part High-speed milling costs, at FR=18000, z = ctot = 50 × (1000/18000) × (1 + 14/45)/60 = $0.0606 per part at FR= 5250, z = ctot = 50 × (1000/5250) × (1 + 6/45)/60 = $0.180 per part The cost reduction using high-speed milling compared to slotting is enormous For highspeed milling with teeth, the cost for high-speed milling with teeth is 61 percent (0.208/0.338) of full slot milling with teeth (z = 6) The cost for high-speed milling with teeth is 19 percent (0.0638/0.338) of full slot for z = Aluminium end milling can be run at to times lower costs than when cutting steel Costs of idle (non-machining) and slack time (waste) are not considered in the example These data hold for perfect milling conditions such as zero run-out and accurate sharpening of all teeth and edges Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition Approximate Cutting Speeds and Feeds for Standard Automatic Screw Machine Tools—Brown and Sharpe (Continued) Cut Tool Turned diam under 5⁄32 in { Turned diam over 5⁄32 in { Turret { Knee tools Knurling tools { Side or swing { Top { End cut { Pointing and facing tools Reamers and bits Recessing tools { Inside cut Swing tools, forming Turning, straight and taperb Taps 1⁄ –1⁄ 16 1⁄ 1⁄ 3⁄ 1⁄ 1⁄ 32 1⁄ 16 1⁄ 3⁄ 16 … Dia of Hole, Inches … … … … … … … … … … … … … … … … 1⁄ or less 1⁄ or over … … … … … … … … … … … … … Brassa { { Feed, Inches per Rev 0.012 0.010 0.017 0.015 0.012 0.010 0.009 … 0.020 0.040 0.004 0.006 0.005 0.008 0.001 0.0025 0.010 – 0.007 0.010 0.001 0.005 0.0025 0.0008 0.002 0.0012 0.001 0.0008 0.008 0.006 0.005 0.004 … Feed, Inches per Rev 0.010 0.009 0.014 0.012 0.010 0.008 0.007 0.010 0.015 0.030 0.002 0.004 0.003 0.006 0.0008 0.002 0.008 – 0.006 0.010 0.0006 0.003 0.002 0.0006 0.0007 0.0005 0.0004 0.0003 0.006 0.004 0.003 0.0025 … Material to be Machined Mild or Soft Steel Tool Steel, 0.80–1.00% C Surface Speed, Feet per Min Surface Speed, Feet per Min Feed, Carbon H.S.S Carbon H.S.S Inches Tools Tools Tools Tools per Rev 70 150 0.008 40 85 70 150 0.006 40 85 70 150 0.010 40 85 70 150 0.008 40 85 70 150 0.008 40 85 70 150 0.006 40 85 70 150 0.0045 40 85 70 150 0.008 40 85 150 … 0.010 105 … 150 … 0.025 105 … 150 … 0.002 105 … 150 … 0.003 105 … 150 … 0.002 105 … 150 … 0.004 105 … 70 150 0.0005 40 80 70 150 0.0008 40 80 70 105 0.006 – 0.004 40 60 70 105 0.006 – 0.008 40 60 70 150 0.0004 40 75 70 150 0.002 40 75 70 105 0.0015 40 60 70 105 0.0004 40 60 70 150 0.0005 40 85 70 150 0.0003 40 85 70 150 0.0002 40 85 70 150 0.0002 40 85 70 150 0.0035 40 85 70 150 0.003 40 85 70 150 0.002 40 85 70 150 0.0015 40 85 25 30 … 12 15 b For taper turning use feed slow enough for greatest depth depth of cut Copyright 2004, Industrial Press, Inc., New York, NY 1133 a Use maximum spindle speed on machine SCREW MACHINE SPEEDS AND FEEDS Hollow mills and balance turning tools { Width or Depth, Inches 1⁄ 32 1⁄ 16 1⁄ 32 1⁄ 16 1⁄ 3⁄ 16 1⁄ 1⁄ 32 On Off … … … … … … 0.003 – 0.004 0.004 – 0.008 … … Machinery's Handbook 27th Edition STOCK FOR SCREW MACHINES 1137 Stock Required for Screw Machine Products The table gives the amount of stock, in feet, required for 1000 pieces, when the length of the finished part plus the thickness of the cut-off tool blade is known Allowance has been made for chucking To illustrate, if length of cut-off tool and work equals 0.140 inch, 11.8 feet of stock is required for the production of 1000 parts Length of Piece and Cut-Off Tool Feet per 1000 Parts Length of Piece and Cut-Off Tool Feet per 1000 Parts Length of Piece and Cut-Off Tool 0.050 0.060 0.070 0.080 0.090 0.100 0.110 0.120 0.130 0.140 0.150 0.160 0.170 0.180 0.190 0.200 0.210 0.220 0.230 0.240 0.250 0.260 0.270 0.280 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410 0.420 4.2 5.0 5.9 6.7 7.6 8.4 9.2 10.1 10.9 11.8 12.6 13.4 14.3 15.1 16.0 16.8 17.6 18.5 19.3 20.2 21.0 21.8 22.7 23.5 24.4 25.2 26.1 26.9 27.7 28.6 29.4 30.3 31.1 31.9 32.8 33.6 34.5 35.3 0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800 36.1 37.0 37.8 38.7 39.5 40.3 41.2 42.0 42.9 43.7 44.5 45.4 46.2 47.1 47.9 48.7 49.6 50.4 51.3 52.1 52.9 53.8 54.6 55.5 56.3 57.1 58.0 58.8 59.7 60.5 61.3 62.2 63.0 63.9 64.7 65.5 66.4 67.2 0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910 0.920 0.930 0.940 0.950 0.960 0.970 0.980 0.990 1.000 1.020 1.040 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 1.220 1.240 1.260 1.280 1.300 1.320 1.340 1.360 Feet per 1000 Parts 68.1 68.9 69.7 70.6 71.4 72.3 73.1 73.9 74.8 75.6 76.5 77.3 78.2 79.0 79.8 80.7 81.5 82.4 83.2 84.0 85.7 87.4 89.1 90.8 92.4 94.1 95.8 97.5 99.2 100.8 102.5 104.2 105.9 107.6 109.2 110.9 112.6 114.3 Length of Piece and Cut-Off Tool Feet per 1000 Parts 1.380 1.400 1.420 1.440 1.460 1.480 1.500 1.520 1.540 1.560 1.580 1.600 1.620 1.640 1.660 1.680 1.700 1.720 1.740 1.760 1.780 1.800 1.820 1.840 1.860 1.880 1.900 1.920 1.940 1.960 1.980 2.000 2.100 2.200 2.300 2.400 2.500 2.600 116.0 117.6 119.3 121.0 122.7 124.4 126.1 127.7 129.4 131.1 132.8 134.5 136.1 137.8 139.5 141.2 142.9 144.5 146.2 147.9 149.6 151.3 152.9 154.6 156.3 158.0 159.7 161.3 163.0 164.7 166.4 168.1 176.5 184.9 193.3 201.7 210.1 218.5 Copyright 2004, Industrial Press, Inc., New York, NY Previous page Machinery's Handbook 27th Edition 1158 GRINDING FEEDS AND SPEEDS GRINDING FEEDS AND SPEEDS Grinding data are scarcely available in handbooks, which usually recommend a small range of depths and work speeds at constant wheel speed, including small variations in wheel and work material composition Wheel life or grinding stiffness are seldom considered Grinding parameter recommendations typically range as follows: • Wheel speeds are usually recommended in the 1200 to 1800 m/min (4000 to 6000 fpm) range, or in rare cases up to 3600 m/min (12000 fpm) • Work speeds are in the range 20 to 40 m/min (70 to 140 fpm); and, depths of cut of 0.01 to 0.025 mm (0.0004 to 0.001 inch) for roughing, and around 0.005 mm (.0002 in.) for finish grinding • Grit sizes for roughing are around 46 to 60 for easy-to-grind materials, and for difficult-to-grind materials higher such as 80 grit In finishing, a smaller grit size (higher grit number) is recommended Internal grinding grit sizes for small holes are approximately 100 to 320 • Specific metal removal rate, SMRR, represents the rate of material removal per unit of wheel contact width and are commonly recommended from 200 to 500 mm3/mm width/min (0.3 to 0.75 in3/inch width/min) • Grinding stiffness is a major variable in determining wheel-life and spark-out time A typical value of system stiffness in outside-diameter grinding, for 10:1 length/diameter ratio, is approximately KST = 30–50 N/µm System stiffness KST is calculated from the stiffness of the part, Kw and the machine and fixtures, Km Machine values can be obtained from manufacturers, or can be measured using simple equipment along with the part stiffness • Generally a lower wheel hardness (soft wheel) is recommended when the system stiffness is poor or when a better finish is desired Basic Rules The wheel speed V and equivalent chip thickness ECT = SMRR ÷ V ÷ 1000 are the primary parameters that determine wheel-life, forces and surface finish in grinding The following general rules and recommendations, using ECT, are based on extensive laboratory and industry tests both in Europe and USA The relationships and shapes of curves pertaining to grinding tool-life, grinding time, and cost are similar to those of any metal cutting operation such as turning, milling and drilling In turning and milling, the ECT theory says that if the product of feed times depth of cut is constant, the tool-life is constant no matter how the depth of cut or feed is varied, provided that the cutting speed and cutting edge length are maintained constant In grinding, wheel-life T remains constant for constant cutting speed V, regardless of how depth of cut ar or work speed Vw are selected as long as the specific metal removal rate SMMR = Vw × ar is held constant (neglecting the influence of grinding contact width) ECT is much smaller in grinding than in milling, ranging from about 0.0001 to 0.001 mm (0.000004 to 0.00004 inch) See the section MACHINING ECONOMETRICS starting on page 1093 for a detailed explanation of the role of ECT in conventional machining Wheel life T and Grinding Ratio.—A commonly used measure of relative wheel-life in grinding is the grinding ratio that is used to compare grindability when varying grinding wheel composition and work material properties under otherwise constant cutting conditions The grinding ratio is defined as the slope of the wear curve versus metal removal rate: grinding ratio = MRR ÷ W*, where MRR is the metal removal rate, and W* is the volume wheel wear at which the wheel has to be dressed The grinding ratio is not a measure of wheel-life, but a relationship between grinding ratio and wheel-life T can be obtained from Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition GRINDING FEEDS AND SPEEDS 1159 the formula grinding ratio = SMRR ì T ữ W*, where SMRR (specific metal removal rate) is determined from MRR = SMRR ì T or from ECT = SMRR ữ V ÷ 1000 Thus, grinding ratio = 1000 × ECT × V ì T ữ W*, and T = grinding ratio × W* ÷ (1000 × ECT × V), provided that the wheel wear criterion W* is valid for all data combinations Example 1:If W* in one test is found to be 500 mm3 for ECT = 0.00033 mm and V = 3600 m/min, and grinding ratio = 10, then wheel-life will vary with measured grinding ratios, wheel speed, and ECT as follows: T =500 ì grinding ratio ữ (V ì ECT) = 4.2 minutes In the remainder of this section the grinding ratio will not used, and wheel-life is expressed in terms of ECT or SMRR and wheel speed V ECT in Grinding.—In turning and milling, ECT is defined as the volume of chips removed per unit cutting edge length per revolution of the work or cutter In milling specifically, ECT is defined as the ratio of (number of teeth z × feed per tooth fz × radial depth of cut ar × and axial depth of cut aa) and (cutting edge length CEL divided by πD), where D is the cutter diameter, thus, πDzf z a r a a ECT = CEL In grinding, the same definition of ECT applies if we replace the number of teeth with the average number of grits along the wheel periphery, and replace the feed per tooth by the average feed per grit This definition is not very practical, however, and ECT is better defined by the ratio of the specific metal removal rate SMMR, and the wheel speed V Thus, ECT = 1000 ì SMRR ữ V Keeping ECT constant when varying SMRR requires that the wheel speed must be changed proportionally In milling and turning ECT can also be redefined in terms of SMRR divided by the work and the cutter speeds, respectively, because SMRR is proportional to the feed rate FR Work Speed and Depth of Cut Selection: Work speed V w is determined by dividing SMMR by the depth of cut ar , or by using the graph in Fig LIVE GRAPH Click here to view 1000 SMRR = 100 SMRR = 200 SMRR = 500 SMRR = 750 SMRR = 1000 SMRR = 1500 SMRR = 2000 Vw, m/min 100 10 0.001 0.01 0.1 ar, mm Fig Work speed Vw vs depth of cut ar Referring to Fig 1, for depths of cuts of 0.01 and 0.0025 mm, a specific metal removal rate SMMR = 1000 mm3/mm width/min is achieved at work speeds of 100 and 400 m/min, respectively, and for SMMR =100 mm3/mm width/min at work speeds of 10 and 40 m/min, respectively Unfortunately, the common use of low values of work speed (20 to 40 m/min) in finishing cause thermal surface damage, disastrous in critical parts such as aircraft components As the grains slide across the work they generate surface heat and fatigue-type loading may cause residual tensile stresses and severe surface cracks Proper finish grinding conditions Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1160 GRINDING FEEDS AND SPEEDS are obtained by increasing the work speed to 10 times higher than the above recommendations indicate These higher work speeds will create compressive stresses that are not detrimental to the surface The by-product of higher work speeds is much higher SMRR values and thereby much shorter grinding times Compressive stresses are also obtained by reducing the depth of cut ar Wheel Life Relationships and Optimum Grinding Data.—Figs 2a, 2b, and 2c show, in three planes, the 3-dimensional variation of wheel-life T with wheel speed V and ECT when grinding a hardened tool steel Fig 2a depicts wheel-life versus wheel speed (the T– V plane) with constant ECT appearing as approximately straight lines when plotted in loglog coordinates In grinding, the wheel-life variation follows curves similar to those obtained for conventional metal cutting processes, including a bend-off of the Taylor lines (T–V graph) towards shorter life and lower cutting speeds when a certain maximum life is achieved for each value of ECT In the two other planes (T–ECT, and V–ECT) we usually find smooth curves in which the maximum values of wheel-life are defined by points along a curve called the H–curve LIVE GRAPH Click here to view 100 ECT × 10−5 T, minutes ECT = 17 ECT = 33 ECT = 50 ECT = 75 10 10000 00 00 13 1000 V m/min 19 100 Fig 2a Taylor lines: T vs V, ECT plotted for grinding M4 tool steel, hardness Rc 64 Example 2: The variation of SMRR = V × ECT × 1000 and wheel-life at various wheel speeds can be obtained from Fig 2a Using sample values of ECT = 33 × 10−5 mm and V = 1300 and 1900 m/min, SMRR = 1300 × 33 × 10−5 × 1000= 429, and 1900 × 33 × 10−5 × 1000 = 627 mm3/mm width/min, respectively; the corresponding wheel lives are read off as approximately 70 and 30 minutes, respectively LIVE GRAPH Click here to view 1000 H-CURVE G-CURVE T, 100 V = 4600 V = 3600 V = 2907 V = 2220 V = 1800 V = 1500 10 0.00001 0.0001 0.001 ECT, mm Fig 2b T vs ECT, V plotted Fig 2b depicts wheel-life T versus ECT with constant wheel speed V shown as curves plotted in log-log coordinates, similar to those for the other cutting operations Copyright 2004, Industrial Press, Inc., New York, NY Machinery's Handbook 27th Edition 1162 GRINDING FEEDS AND SPEEDS branch attains a maximum SMRR along the G-curve (compare with the same curve in the V–ECT graph, Fig 2c) and a maximum speed region along the H-curve When the SMRRvalues are lower than the H-curve the ECT values for each branch decrease towards the bottom of the graph, then the speed for constant wheel-life must be reduced due to the fact that the ECT values are to the left of their respective H-curves in V–ECT graphs LIVE GRAPH Click here to view SMRR mm3/mm/min 10000 Vw × a, T = 30, IncX Vw × a, T = 10, IncX Vw × a, T = 30, M4 Vw × a, T = 10, M4 Vw × a, T = 30, T-15 Vw × a, T = 10, T-15 Vw × a, T = 30, 1020 Unh Vw × a, T = 10, 1020 Unh Optimum = G-CURVE 1000 H-CURVE 100 100 1000 10000 V m/min Fig Specific metal removal rate vs cutting speed at T=10 and 30 minutes wheel life In the figure, IncX is Inconel; M4, and T-15 are tool steels; and 1020 Unh is unhardened 1020 steel Surface Finish, Ra.—The finish is improved by decreasing the value of ECT as shown in Fig 4, where Ra is plotted versus ECT at different wheel lives 1,10 and 30 minutes at constant wheel speed Because ECT is proportional to the depth of cut, a smaller depth of cut is favorable for reducing surface roughness when the work speed is constant LIVE GRAPH Ra, mm 10 Click here to view T=1 T=5 T = 15 T = 45 T = 100 0.1 0.00001 0.0001 0.001 ECT, mm Fig Surface finish, Ra vs ECT, wheel-life T plotted In Fig 5, Ra is plotted versus wheel-life at different ECT’s Both Figs and illustrate that a shorter life improves the surface finish, which means that either an increased wheel speed (wheel-life decreases) at constant ECT, or a smaller ECT at constant speed (wheellife increases), will result in an improved finish For a required surface finish, ECT and wheel-life have to be selected appropriately in order to also achieve an optimum grinding time or cost In cylindrical grinding a reduction of side feed fs improves Ra as well In terms of specific metal removal rate, reducing SMRR will improve the surface finish RA Copyright 2004, Industrial Press, Inc., New York, NY ... −0.50000 −0.140 87 −0. 479 75 −0. 270 32 −0.42063 −0. 377 87 −0.3 274 3 −0.45482 −0.2 077 1 −0.49491 −0. 071 16 −0.49491 +0. 071 16 −0.45482 +0.2 077 1 −0. 377 87 +0.3 274 3 −0. 270 32 +0.42063 −0.140 87 +0. 479 75 0.00000... +0.50000 +0.140 87 +0. 479 75 +0. 270 32 +0.42063 +0. 377 87 +0.3 274 3 +0.45482 +0.2 077 1 +0.49491 +0. 071 16 +0.49491 −0. 071 16 +0.45482 −0.2 077 1 +0. 377 87 −0.3 274 3 +0. 270 32 −0.42063 +0.140 87 −0. 479 75 28 Holes... Holes x1 −0.0 975 5 y1 −0.49039 x2 −0. 277 79 y2 −0.41 573 x3 −0.41 573 y3 −0. 277 79 x4 −0.49039 y4 −0.0 975 5 x5 −0.49039 y5 +0.0 975 5 x6 −0.41 573 y6 +0. 277 79 x7 −0. 277 79 y7 +0.41 573 x8 −0.0 975 5 y8 +0.49039