MACHINING ECONOMETRICS Machinery's Handbook, 31st Edition
1199
100
T max
ECT = 0.1 ECT = 0.25 ECT = 0.5 ECT = 0.7
T 2 ,V 2
b
10
n = a/b
a
T 1 ,V 1
1
C
10
100
1000
V m/min
Fig. 4. Definition of Slope n and Constant C in Taylor’s Equation Evaluation of Slope n , and Constant C.— When evaluating the value of the Taylor slope based on wear tests, care must be taken in selecting the tool life range over which the slope is measured, as the lines are slightly curved. The slope n can be found in three ways: • Calculate n from the formula n = (ln C—ln V )/ln T , reading the values of C and V for any value of T in the graph. • Alternatively, using two points on the line, ( V 1 , T 1 ) and ( V 2 , T 2 ), calculate n using the relationship V 1 3 T 1 n = V 2 3 T 2 n . Then, solving for n , n = ln ( V 1 ⁄ V 2 ) ln ( T 2 ⁄ T 1 ) • Graphically, n may be determined from the graph by measuring distances a and b using a mm scale, and n is the ratio of a and b , thus, n = a / b Example: Using Fig. 4 and a given value of ECT = 0.7 mm, calculate the slope and con stant of the Taylor line. On the Taylor line for ECT = 0.7, locate points corresponding to tool-lives T 1 = 15 min utes and T 2 = 60 minutes. Read off the associated cutting speeds as, approximately, V 1 = 110 m/min and V 2 = 65 m/min. The slope n is then found to be n = ln (110⁄65)/ln (60⁄15) = 0.38 The constant C can be then determined using the Taylor equation and either point ( T 1 , V 1 ) or point ( T 2 , V 2 ), with equivalent results, as follows: C = V 3 T n = 110 3 15 0.38 = 65 3 60 0.38 = 308 m/min (1027 fpm) The Generalized Taylor Equation.— The above calculated slope and constant C define tool life at one particular value of feed f , depth of cut a , lead angle LA , nose radius r , and other relevant factors. The generalized Taylor equation includes these parameters and is written (2) where A = area; and, n, m, p, q, and s = constants. There are two problems with the generalized equation: 1) a great number of tests have to be run in order to establish the constants n, m, p, q, s, etc.; and 2) the accuracy is not very good because Equation (2) yields straight lines when plotted versus f, a, LA, and r, when in reality, they are parabolic curves. T A f a LA r n m p q s # # # # =
Copyright 2020, Industrial Press, Inc.
ebooks.industrialpress.com
Made with FlippingBook - Share PDF online