Machinery's Handbook, 31st Edition
Drawing Sheet Metal 1425 bottom of the cup is subjected to radial and tangential tensile stress. From the bottom, the punch transmits the force through the walls of the cup to the flange. In this stressed state, the walls tend to elongate in a longitudinal direction. Elongation causes the cup wall to become thinner, which can cause the workpiece to tear. If a drawing die radius in a deep drawing operation is too small, it will cause fracture of the cup in the zone between the wall and the flange. If a punch corner radius is too small, it may cause fracture in the zone between a wall and the bottom of a cup. Fracture can also result from high longitudinal tensile stresses in the bottom cup, due to a high ratio between the blank diameter and the punch diameter. Parts made by deep drawing usually require several successive draws. One or more annealing operations may be required to reduce work hardening by restoring the ductile grain structure. Number of Draws: The number of successive draws n required is a function of the ratio of the part height h to the part diameter d , and is given by this formula: (38) n d h =
where n = number of draws; h = part height; and, d = part diameter. The value of n for the cylindrical cup draw is given in Table 14.
Table 14. Number of Draws ( n ) for a Cylindrical Cup Draw
h / d
< 0.6
0.6 to1.4
1.4 to 2.5
2.5 to 4.0
4.0 to 7.0
7.0 to 12.0
n 6 Deep Drawability : Deep drawability is the ability of a sheet metal to be formed, or drawn, into a cupped or cavity shape without cracking or otherwise failing. The depth to which metal can be drawn in one operation depends upon the quality and kind of material, its thickness, and the amount that the work material is thinned in drawing. 1 2 3 4 5 Drawing a Cylindrical Cup Without a Flange: A general rule for determining the depth to which a cylindrical cup without a flange can be drawn in one operation is defined as the ratio of the mean diameter d m of the drawn cup to the blank diameter D . This relation is known as the drawing ratio m . The value of the drawing ratio for the first and succeeding operations is given by: m D d m D d m D d m D d m m m m m n m m 1 2 3 n n 1 1 2 2 3 1 f = = = = − The magnitude of these ratios determines the following parameters: 1) the stresses and forces of the deep drawing processes 2) the number of successive draws 3) the blank holder force 4) the quality of the final drawn parts. Table 15 shows optimal drawing ratios for cylindrical cups of sheet steel and brass with out a flange. Table 15. Optimal Ratios M for Drawing a Cylindrical Cup Without Flanges Relative Thickness of the Material (%) T D T 100 r = Drawing ratio m 2.0–1.5 1.5–1.0 1.0–0.6 0.6–0.3 0.3–0.15 0.15–0.08 m 1 0.48–0.50 0.50–0.53 0.53–0.55 0.55–0.58 0.58–0.60 0.60–0.63 m 2 0.73–0.75 0.75–0.76 0.76–0.78 0.78–0.79 0.79–0.80 0.80–0.82 m 3 0.76–0.78 0.78–0.79 0.79–0.80 0.81–0.82 0.81–0.82 0.82–0.84 m 4 0.78–0.80 0.80–0.81 0.81–0.82 0.82–0.83 0.83–0.85 0.85–0.86 m 5 0.80–0.82 0.82 - 0.84 0.84–0.85 0.85–0.86 0.86–0.87 0.78–0.90 Diameters of drawing workpieces 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 = = = − Drawing a Cylindrical Cup With a Flange: Table 16 gives values of the drawing ratio m for the first and succeeding operations for drawing a cylindrical cup with flange.
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