Machinery's Handbook, 31st Edition
1426 Drawing Sheet Metal Diameters of drawing workpiece for the first and succeeding operations are given by d m D d m d d m d i i i 1 1 2 2 1 1 f = = = − However, diameter D f needs to be accomplished in the first drawing operation if possible. Diameters of Shell Blanks: The diameters of blanks for drawing plain cylindrical shells can be obtained from Table 17, which gives a very close approximation for thin stock. The blank diameters given in this table are for sharp-cornered shells and are found by the following formula (39) where D = diameter of flat blank (inch or mm); d = diameter of finished shell (inch or mm); and, h = height of finished shell (inch or mm). Example 1 : If the diameter of the finished shell d , is to be 1.5 inches (mm), and the height h , 2 inches (mm), the trial diameter of the blank D , would be found as follows: Table 16. Values of Ratio m for Drawing a Cylindrical Cup With Flange D f D d dh 4 2 = +
R d
h
R p
d
T D T 100 r =
(%)
Relative thickness of the material
Drawing ratio m
d D f 1.1 1.3 1.5 1.8 2.0 2.5 3.0
2.0–1.5
1.5–1.0
1.0–0.6
0.6–0.3
0.3–0.15
0.51 0.49 0.47 0.45 0.42 0.37 0.32
0.53 0.51 0.49 0.46 0.43 0.38 0.33 0.75 0.78 0.80 0.82
0.55 0.53 0.50 0.47 0.44 0.38 0.33 0.76 0.79 0.82 0.84
0.57 0.54 0.51 0.48 0.45 0.38 0.33 0.78 0.80 0.83 0.85
0.59 0.55 0.52 0.48 0.45 0.38 0.33 0.80 0.82 0.84 0.86
m 1
… 0.73 … 0.75 … 0.78 … 0.80
m 2 m 3 m 4 m 5
. D 15 4 15 2 1425 378inches (mm) 2 # # = + = = . . .
For a round-cornered cup, the following formula, in which r equals the radius of the cor ner, will give fairly accurate diameters, provided the radius does not exceed, say, 1 ∕ 4 the height of the shell: (40) These formulas are based on the assumption that the thickness of the drawn shell is to be the same as the original thickness of the stock and that the blank is so proportioned that its area will equal the area of the drawn shell. This method of calculating the blank diameter is quite accurate for thin material, when there is only a slight reduction in the thickness of the metal incident to drawing; but when heavy stock is drawn and the thickness of the finished shell is much less than the original thickness of the stock, the blank diameter obtained from Formulas (39) or (40) will be too large, because when the stock is drawn thinner, there is an increase in area. When an appreciable reduction in thickness is to be made, the blank diameter can be obtained by first determining the “mean height” of the drawn shell by the following formula, which is only approximately correct, but will give results sufficiently accurate for most work: (41) M T ht = D d dh r 4 2 = + −
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