Machinery's Handbook, 31st Edition
1214 MACHINING ECONOMETRICS Economic tool life increases with greater values of T V , either when T RPL is longer, or when cost per edge C E is larger for constant H R , or when H R is smaller and T RPL and C E are unchanged. For example, when using an expensive machine (which makes H R bigger) the value of T V gets smaller, as does the economic tool life, T E = T V 3 (1/ n - 1). Reducing T E results in an increase in the economic cutting speed, V E . This means raising the cutting speed and illustrates the importance, in an expensive system, of utilizing the equipment better by using more aggressive machining data.
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ECT = 1.54 ECT = 0.51 ECT = 0.8
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Fig. 20b. Tool Life versus Cutting Speed, Constant ECT As shown in Fig. 20a for a face milling operation, economic tool life T E varies consider ably with feed/tooth f z , in spite of the fact that the Taylor lines have only slightly different slopes ( ECT = 0.51, 0.6, 1.54), as shown in Fig. 20b. The calculation is based on the follow ing cost data: T V = 6, hourly shop rate H R = $60/hour, cutter diameter D = 125 mm with number of teeth z = 10, and radial depth of cut ar = 40 mm. The conclusion relating to the determination of economic tool life is that both hourly rate H R and slope n must be evaluated with reasonable accuracy in order to arrive at good values. However, the method shown will aid in setting the trend for general machining economics evaluations. Global Optimum, Graphical Method.— There are several ways to demonstrate in graphs how cost varies with the production parameters including optimal conditions. In all cases, tool life is a crucial parameter. Cutting time t c is inversely proportional to the specific metal removal rate, SMRR = V 3 ECT , thus, 1/ t c = V 3 ECT . Taking the log of both sides, (7) where C is a constant. Equation (7) is a straight line with slope (–1) in the V - ECT graph when plotted in a log-log graph. This means that a constant cutting time is a straight 45-degree line in the V - ECT graph, when plotted in log-log coordinates with the same scale on both axis (a square graph). The points at which the constant cutting time lines (at 45-degree slope) are tangent to the tool life curves define the G -curve, along which global optimum cutting occurs. Note: If the ratio a / CEL is not constant when ECT varies, the constant cutting time lines are not straight, but the cutting time deviation is quite small in most cases. ln ln ln V ECT t C c =− − +
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