Machinery's Handbook, 31st Edition
MACHINING ECONOMETRICS 1215 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.
1000
45 Degrees Constant cutting time increasing going down
G-CURVE
T =1 T =5 T =15 T =30 T =60
100
0.1
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 C TOT for the three parameters: T , ECT , and V . The results, in terms of the tool life equation constants, are: Optimum tool life:
ln T T n n M L T 1 1 2 O V O # # # = = − ^ c m
2
1
N L M H 2 # + ^
h
h
+ − +
0
O
O
where n O = 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: V e O = – M + K + ( H # L – N 0 ) # ln T O + M # L 2 # (ln T O ) 2 Optimum ECT : ECT e O = H + 2 M # ( L # ln( T O ) + 1) Global optimum is not reached when face milling for very large feeds, and C TOT 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 3 to 8 teeth.
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