MACHINING ECONOMETRICS Machinery's Handbook, 31st Edition
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40
V B = 0.2 mm V B = 0.15 mm V B = 0.05 mm V B = 0.1 mm
30
30
20
20
10
10
VB 0.15 mm VB 0.1 mm VB 0.05 mm
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0
VC (cutting speed), m/min 200 250 300 350 400 450 500
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0.05
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0.2
F z (feed per tooth), mm
Fig. 2. Influence of Feed per Tooth on Cutting Time Fig. 3. Influence of Cutting Speed on Tool Life Tool life has a maximum value at a particular setting of speed and feed. Economic and productive cutting speeds always occur on the right side of the curves in Fig. 2 and Fig. 4, which are called Taylor curves, represented by the so called Taylor’s equation. The variation of tool life with speed and feed constitute complicated relationships, illus trated in Fig. 6a, Fig. 6b, and Fig. 6c. Taylor’s Equation.— Taylor’s equation is the most commonly used relationship between tool life T , and cutting speed V . It constitutes a straight line in a log-log plot, one line for each feed, nose radius, lead angle, or depth of cut, mathematically represented by: (1a) where n = slope of the line C = constant equal to the cutting speed for T = 1 minute By transforming the equation to logarithmic axes, the Taylor lines become straight lines with slope = n . The constant C is the cutting speed on the horizontal ( V ) axis at tool life T = 1 minute, expressed as follows (1b) For different values of feed or ECT , log-log plots of Equation (1a) form approximately straight lines in which the slope decreases slightly with a larger value of feed or ECT . In practice, the Taylor lines are usually drawn parallel to each other, i.e., the slope n is assumed to be constant. Fig. 4 illustrates the Taylor equation, tool life T versus cutting speed V, plotted in log-log coordinates, for four values of ECT = 0.1, 0.25, 0.5 and 0.7 mm. In Fig. 4, starting from the right, each T - V line forms a generally straight line that bends off and reaches its maximum tool life, then drops off with decreasing speed (see also Fig. 2 and Fig. 3. When operating at short tool-lives, approximately when T is less than 5 minutes, each line bends a little so that the cutting speed for 1 minute life becomes less than the value calculated by constant C. The Taylor equation is a very good approximation of the right hand side of the real tool life curve (slightly bent). The portion of the curve to the left of the maximum tool life gives shorter and shorter tool lives when decreasing the cutting speed starting from the point of maximum tool life. Operating at the maximum point of maximum tool life, or to the left of it, causes poor surface finish, high cutting forces, and sometimes vibrations. V T C n # = ln ln ln V n T C # + =
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