Machinery's Handbook, 31st Edition
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MACHINING ECONOMETRICS Table 2a. Variation of Chip Thickness and f z / f z 0 with ar / D
Face Milling
End Milling (straight)
ecentricity e = 0 z = 8
z = 2 f z 0 = 0.17 cos AE = 1 − 2 3 ( ar / D )
f z 0 = 0.17 cos AE = 1 − 2 3 ( ar / D ) 2
ar / D hm ECT / hm f z / f z 0 1.0000 180.000 0.637 0.108 5.000 1.398 180.000 0.637 0.108 1.000 1.000 0.9000 128.316 0.804 0.137 3.564 1.107 143.130 0.721 0.122 0.795 0.884 0.8000 106.260 0.863 0.147 2.952 1.032 126.870 0.723 0.123 0.711 0.881 0.7355 94.702 0.890 0.151 2.631 1.000 118.102 0.714 0.122 0.667 0.892 0.6137 75.715 0.929 0.158 1.683 0.958 103.144 0.682 0.116 0.573 0.934 0.5000 60.000 1.025 0.162 1.267 0.932 90.000 0.674 0.115 0.558 1.000 0.3930 46.282 0.973 0.165 1.028 0.915 77.643 0.580 0.099 0.431 1.098 0.2170 25.066 0.992 0.169 0.557 0.897 55.528 0.448 0.076 0.308 1.422 0.1250 14.361 0.997 0.170 0.319 0.892 41.410 0.346 0.059 0.230 1.840 0.0625 7.167 0.999 0.170 0.159 0.891 28.955 0.247 0.042 0.161 2.574 0.0300 3.438 1.000 0.170 0.076 0.890 19.948 0.172 0.029 0.111 3.694 0.0100 1.146 1.000 0.170 0.025 0.890 11.478 0.100 0.017 0.064 6.377 0.0010 0.115 1.000 0.000 0.000 0.890 3.624 0.000 0.000 0.000 20.135 AE hm / f z hm ECT / hm f z / f z 0 AE hm / f z In Table 2a, a standard value f z 0 = 0.17 mm/tooth (commonly recommended average feed) was used, but the f z / f z 0 values are independent of the value of feed/tooth, and the pre viously mentioned relationships are valid whether f z 0 = 0.17 or any other value. In both end and face milling, hm = 0.108 mm for f z 0 = 0.17 mm when ar / D =1. When the f z / f z 0 ratio = 1, hm = 0.15 for face milling, and 0.108 in end milling both at ar / D = 1 and 0.5. The tabulated data hold for perfect milling conditions, such as, zero run-out and accurate sharpening of all teeth and edges. Mean Chip Thickness hm and Equivalent Chip Thickness ECT.— The basic formula for equivalent chip thickness ECT for any milling process is: ECT = f z 3 z / π 3 ( ar / D ) 3 aa / CEL , where f z = feed/tooth, z = number of teeth, D = cutter diameter, ar = radial depth of cut, aa = axial depth of cut, and CEL = cutting edge length. As a function of mean chip thickness hm : ECT = hm 3 ( z ⁄2) 3 ( AE ⁄180), where AE = angle of engagement. Both terms are exactly equal when one tooth engages as soon as the preceding tooth leaves the cutting section. Mathematically, hm = ECT when z = 360/ AE ; thus: Calculation of Equivalent Chip Thickness (ECT) versus Feed/tooth and Number of Teeth: Table 2b is a continuation of Table 2a, showing the values of ECT for face and end milling for decreasing values ar / D , and the resulting ECT when multiplied by the f z / f z 0 ratio f z 0 = 0.17 (based on hm = 0.108). Small ar / D ratios produce too small mean chip thickness for cutting chips. In practice, minimum values of hm are approximately 0.02 through 0.04 mm for both end and face milling. Formulas.— Equivalent chip thickness can be calculated for other values of f z and z by means of the following formulas: Face milling: ECT F = ECT 0 F 3 ( z ⁄8) 3 ( f z ⁄0.17) 3 ( aa / CEL ) or, if ECT F is known calculate f z using: f z = 0.17 3 ( ECT F / ECT 0 F ) 3 (8/ z ) 3 ( CEL / aa ) for face milling, AE = arccos (1—2 3 ( ar / D ) 2 ) for end milling, AE = arccos (1—2 3 ( ar / D ))
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