Machinery's Handbook, 31st Edition
MACHINING ECONOMETRICS 1203 than approximately 0.03 mm should not be allowed. In Fig. 7, the ECT MIN boundary is indicated by contour line A ' E ' . In milling, the minimum feed/tooth depends on the ratio ar / D , of radial depth of cut ar , and cutter diameter D . For small ar / D ratios, the chip thickness becomes so small that it is necessary to compensate by increasing the feed/tooth. See High-Speed Machining Econometrics starting on page 1225 for more on this topic. Fig. 7 demonstrates, in principle, minimum cost conditions for roughing at point O R , and for finishing at point O F , where surface finish or tolerances have set a limit. Maintaining the speed at O R , 125 m/min, and decreasing feed reaches a maximum tool life = 300 min utes at ECT = 0.2, and a further decrease of feed will result in shorter lives. Similarly, starting at point X ( V = 150, ECT = 0.5, T = 15) and reducing feed, the H -curve will be reached at point E ( ECT = 0.075, T = 300). Continuing to the left, tool life will decrease and serious troubles occur at point E' ( ECT = 0.03). Starting at point O F ( V = 300, ECT = 0.2, T = 15) and reducing feed, the H -curve will be reached at point E ( ECT = 0.08, T = 15). Continuing to the left, life will decrease and seri ous troubles occur at ECT = 0.03. Starting at point X ( V = 400, ECT = 0.2, T = 5) and reducing feed, the H -curve will be reached at point E ( ECT = 0.09, T = 7). Continuing to the left, life will decrease and serious troubles occur at point A' ( ECT =0.03), where T = 1 minute. Cutting Forces and Chip Flow Angle.— There are three cutting forces, illustrated in Fig. 8, that are associated with the cutting edge with its nose radius r , depth of cut a , lead angle LA , and feed per revolution f , or in milling feed per tooth f z . There is one drawing for roughing and one for finishing operations. Roughing: a r 1 LA ( –sin( )) ≥ f 2 -- ECT Finishing: a < r (1 – sin( LA )) c
f / 2
feed
S
s
x
x
a
r (1 – sin( LA ))
a – x
u
O
r
r – a
r
CEL
a LA (US)
CFA
LA (US)
90 – CFA z =
90 – u= CFA
b f - 2-- r LA ( ) LA ( ) a r × sin( LA )) ( – tan = + ×cos +
r 2 – f
2
x r = –
z
4 ---
O
c f =- 2 -+ r – ( r – a ) 2
F
b
a x – b ------
H
a x – c ------ atan
CFA = 90 – atan
F H
F R
CFA = 90 –
F R
CFA
Axial Force = F A = F H × cos( CFA ) Radial Force = F R = F H × sin( CFA )
F A
F A
ISO LA = 90 – LA (US)
Fig. 8. Definitions of Equivalent Chip Thickness, ECT , and Chip Flow Angle, CFA . The cutting force F C , or tangential force, is perpendicular to the paper plane. The other two forces are the feed or axial force F A , and the radial force F R directed towards the work piece. The resultant of F A and F R is called F H . When finishing, F R is bigger than F A , while in roughing F A is usually bigger than F R . The direction of F H , measured by the chip flow angle CFA , is perpendicular to the rectangle formed by the cutting edge length CEL and ECT (the product of ECT and CEL constitutes the cross sectional area of cut, A ). The important task of determining the direction of F H , and calculation of F A and F R , are shown in the formulas given in the Fig. 8. The method for calculating the magnitudes of F H , F A , and F R is described in the following. The first thing is to determine the value of the cutting force F C . Approximate formulas to
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