Machinery's Handbook, 31st Edition
1212 MACHINING ECONOMETRICS The cutting time for minimum cost varies with the ratio of tooling cost and H R . Minimum cost moves towards a longer cutting time (longer tool life) when either the price of the tooling increases, or when several tools cut simultaneously on the same part. In Fig. 18b , this is exemplified by running 2 and 4 cutters simultaneously on the same work piece, at the same feed and depth of cut, and with a similar tool as in Fig. 18a. As the tooling cost goes up 2 and 4 times, respectively, and H R is the same, the total costs curves move up, but also moves to the right, as do the points of minimum cost and optimal cutting times. This means that going somewhat slower, with more simultaneously cutting tools, is advantageous. Global Optimum.— Usually, global optimum occurs for large values of feed, heavy roughing, and in many cases the cutting edge will break trying to apply the large feeds required. Therefore, true optima cannot generally be achieved when roughing, in particu lar when using coated and wear resistant grades; instead, use the maximum values of feed, ECT max , along the tool life envelope, see Fig. 7. As will be shown in the following, the first step is to determine the optimal tool life T O , and then determine the optimum values of speeds and feeds. Optimum Tool Life T O = 22 minutes
f z V 22 t c , sec. C TOOL C TOT 0.03 416 28.067 0.1067 0.4965 0.08 397 11.017 0.0419 0.1949 0.10 374 9.357 0.0356 0.1655 0.17 301 6.831 0.0260 0.1208 0.20 276 6.334 0.0241 0.1120 0.40 171 5.117 0.0194 0.0905 Minimum Cost 0.60 119 4.903 0.0186 0.0867
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CTOOL T = 22 CTOOL T varies CTOT T = 22 CTOT T varies
0.55
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0.70 91 4.924 0.0187 0.0871 Maximum Production Rate, T = 5 minutes f z V 5 t c C TOOL C TOT 0.7 163 3.569 0.059 0.109 T varies between 1 and 240 minutes f z = 0.10 ECT = 0.26 t c sec. C TOOL C TOT T V 5.850 0.487 0.569 1 598 6.914 0.192 0.288 3 506 7.473 0.125 0.228 5 468 8.304 0.069 0.185 10 421 8.832 0.049 0.172 15 396
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Cutting Time, seconds Fig. 19. Variation of Tooling and Total
Cost with Cutting Time, Comparing Global Optimum with Minimum Cost at f z = 0.1 mm
Minimum Cost 9.815 0.027 0.164 30
357 321
10.906 0.015 0.167 60 11.600 0.011 0.172 90
302 12.119 0.008 0.177 120 289 13.467 0.005 0.192 240 260 The example in Fig. 19 assumes that T O = 22 minutes and the speed and feed optima were calculated as f O = 0.6 mm/tooth, V O = 119 m/min, and cutting time t cO = 4.9 sec. The point of maximum production rate corresponds to f O = 0.7 mm/tooth, V O = 163 m/min, at tool life T O = 5 minutes, and cutting time t cO = 3.6 sec. The tooling cost is approximately three times higher than at minimum cost (0.059 versus 0.0186), while the piece cost is only slightly higher: $0.109 versus $0.087. When comparing the global optimum cost with the minimum at feed = 0.1 mm/tooth the graph shows it to be less than half (0.087 versus 0.164), but also the tooling cost is about 1⁄3 lower (0.0186 versus 0.027). The reason why tooling cost is lower depends on the tooling cost term t c 3 C E / T (see Calculation of Cost of Cutting and Grinding Operations
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