Machinery's Handbook, 31st Edition
MACHINING ECONOMETRICS 1211 Production Rate.— The production rate is defined as the cutting time or the metal re - moval rate, corrected for the time required for tool changes, but neglecting the cost of tools. The result of optimizing production rate is a shorter tool life, higher cutting speed, and a higher feed compared to minimum cost optimization, and the tooling cost is considerably higher. Production rate optima also occur along the G -curve. The Cost Function.— There are a number of ways the total machining cost C TOT can be plotted, for example, versus feed, ECT , tool life, cutting speed or other parameter. In Fig. 18a, cost for a face milling operation is plotted versus cutting time, holding feed con- stant, and using a range of tool-lives, T , varying from 1 to 240 minutes. t c C TOOL C TOT T V 0.3
5.85 0.487 0.569 1 598 6.91 0.192 0.288 3 506 7.47 0.125 0.228 5 468 8.30 0.069 0.185 10 421 8.83 0.049 0.172 15 396 Minimum cost 9.81 0.027 0.164 30 356
C TOOL T varies C TOT T varies
0.25
Total Cost
0.2
Cutting Time Cost of
10.91 0.015 0.167 60 321 11.60 0.011 0.172 90 302 12.12 0.008 0.177 120 289 13.47 0.005 0.192 240 260
0.15
Hourly Rate = 60$/hour
0.1
0.05
Tooling Cost
0
5
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9
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15
Cutting Time, seconds
Fig. 18a. Variation of Tooling Cost C TOOL , and Total Cost C C , with Cutting Time t c , Including Minimum Cost Cutting Time
The tabulated values show the corresponding cutting speeds determined from the tool life equation, and the influence of tooling on total cost. Tooling cost, C TOOL = sum of tool cost + cost of replacing worn tools, decreases the longer the cutting time, while the total cost, C TOT , has a minimum at around 10 seconds of cutting time. The dashed line in the graph represents the cost of machining time: the product of hourly rate H R , and the cutting time t c divided by 60. The slope of the line defines the value of H R .
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
C TOT 1 Tool C TOT 2 Tools C TOT 4 Tools
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9
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11
12
13
14 15
Cutting time, seconds
Fig. 18b. Total Cost versus Cutting Time for Simultaneously Cutting with 1, 2, and 4 Tools
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