Machinery's Handbook, 31st Edition
MACHINING ECONOMETRICS 1213 on page 1218). In this example, cutting times t c = 4.9 and 9.81 seconds, at T = 22 and 30 minutes respectively, and the ratios are proportional to 4.9⁄22 = 0.222 and 9.81⁄30 = 0.327 respectively. The portions of the total cost curve for shorter cutting times than minimum correspond to using speeds and feeds to the right of the G -curve, and those on the other side are left of this curve. Optimization Models, Economic Tool Life when Feed is Constant.— Usually, optimi zation is performed versus the parameters tool life and cutting speed, keeping feed at a constant value. The cost of cutting as function of cutting time is a straight line with the slope = H R = hourly rate. This cost is independent of the values of tool change and tooling. Adding the cost of tool change and tooling, gives the variation of total cutting cost which shows a minimum with cutting time that corresponds to an economic tool life, T E . Eco nomic tool life represents a local optima (minimum cost) at a given constant value of feed, feed/tooth, or ECT . Using the Taylor Equation: V 3 T = C and differentiating C TOT with respect to T yields: Economic tool life: T E = T V 3 (1/ n − 1), minutes Economic cutting speed: V E = C/ T E n , m/min, or sfm In these equations, n and C are constants in the Taylor equation for the given value of feed. Values of Taylor slopes, n, are estimated using the speed and feed Table 1 through Table 23 starting on page 1095 and Handbook Table 5b on page 1103 for turning, and Table 15e on page 1127 for milling and drilling; T V is the equivalent tooling-cost time. T V = T RPL + 60 3 C E ÷ H R , minutes, where T RPL = time for replacing a worn insert, or a set of inserts in a milling cutter or inserted drill, or a twist drill, reamer, thread chaser, or tap. T V is described in detail, later; C E = cost per edge, or set of edges, or cost per regrind including amortized price of tool; and H R = hourly shop rate, or that rate that is impacted by the changes of cutting conditions . In two dimensions, Fig. 20a shows how economic tool life varies with feed per tooth. In this figure, the equivalent tooling-cost time T V is constant, however the Taylor constant n varies with the feed per tooth.
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Fig. 20a. Economic Tool Life, T E versus Feed per Tooth, f z
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