Machinery's Handbook, 31st Edition
MACHINING ECONOMETRICS 1205 derived from the ratio F H / F C , which varies with ECT and speed in a fashion similar to Kc . Fig. 10 shows how this relationship may vary. As seen in Fig. 10, F H / F C is in the range 0.3 to 0.6 when ECT varies from 0.1 to 1 mm, and speed varies from 200 to 250 m/min using modern insert designs and grades. Hence, using reasonable large feeds F H / F C is around 0.3–0.4 and when finishing about 0.5–0.6. Example: Determine F A and F R , based on the chip flow angle CFA and the cutting force F C , in turning. Using a value of Kc = 1500 N/mm 2 for roughing, when ECT = 0.4, and the cutting edge length CEL = 5 mm, first calculate the area A = 0.4 3 5 = 2 mm 2 . Then, determine the cut ting force F C = 2 3 1500 = 3000 N, and an approximate value of F H = 0.5 3 3000 = 1500 N. Using a value of Kc = 1700 N/mm 2 for finishing, when ECT = 0.2, and the cutting edge length CEL = 2 mm, calculate the area A = 0.2 3 2 = 0.4 mm 2 . The cutting force F C = 0.4 3 1700 = 680 N and an approximate value of F H = 0.35 3 680 = 238 N. Fig. 8 can be used to estimate CFA for rough and finish turning. When the lead angle LA is 15 degrees and the nose radius is relatively large, an estimated value of the chip flow angle becomes about 30 degrees when roughing, and about 60 degrees in finishing. Using the formulas for F A and F R relative to F H gives: Roughing:
F A = F H 3 cos ( CFA ) = 1500 3 cos 30 = 1299 N F R = F H 3 sin ( CFA ) = 1500 3 sin 30 = 750 N Finishing: F A = F H 3 cos ( CFA ) = 238 3 cos 60 = 119 N F R = F H 3 sin ( CFA ) = 238 3 sin 60 = 206 N
The force ratio F H / F C also varies with the tool rake angle and increases with negative rakes. In grinding, F H is much larger than the grinding cutting force F C ; generally F H / F C is approximately 2 to 4, because grinding grits have negative rakes of the order –35 to –45 degrees. Forces and Tool Life.— Forces and tool life are closely linked. The ratio F H / F C is of par ticular interest because of the unique relationship of F H / F C with tool life.
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Fig. 11a. F H / F C versus ECT The results of extensive tests at Ford Motor Company are shown in Fig. 11a and Fig. 11b, where F H / F C and tool life T are plotted versus ECT at different values of cutting speed V . For any constant speed, tool life has a maximum at approximately the same values of ECT as has the function F H / F C .
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