Peter Ulintz
Technical Director

# Drawing, Conical, Spherical and Parabolic Shapes

June 14, 2021

When deep drawing a cylindrical cup with a flat bottom and vertical walls, a punch force applied to a sheet metal blank causes the material to bend over the punch and create the cup bottom. The force subsequently transmits from the cup bottom to the walls, then to the deformation zone (flange area). Deep drawing cylindrical cups without a flat bottom or vertical walls, such as conical, spherical and parabolic shapes, proves considerably more difficult.

A primary reason for this difficulty: Deformation is not restricted to the flange area (Fig. 1, point a). For these shapes, deformation also occurs in the unsupported region between the die and punch face where compressive stresses can cause puckers (area between Fig. 1, points b and c). Puckering describes the stretch-forming wrinkles that form on the body of the blank, in contrast to drawing wrinkles that occur at the blank edge.
Puckering must be avoided as these wrinkles usually cannot be removed. Avoid puckering by raising blankholder pressure or increasing the blank diameter—both will increase radial tension and reduce compressive stresses—or by using draw beads.

Another reason for difficulty: The drawing loads must be transmitted by a smaller cross-sectional area under the punch face (Fig. 1, point c). This holds particularly true at the beginning of the drawing process where the risk of splitting is very high, even for small drawing ratios.

Conical Shapes

The ratio of the largest to smallest cone diameter and the cone angle (α) influence the limiting draw ratio (LDR) for most conical draws (Fig. 2).

When α measures < 20 deg., the cone can usually be processed in the same manner as a cup draw.

Shallow cones, with a ratio of h/d2 < 0.30 and a measures > 45 deg., usually can be drawn in a single step.

For deeper cones, with h/d2 between 0.30 and 0.70 and α measures between 15 and 45 deg., the relative sheet-thickness-to-blank-diameter ratio (t/D) influences LDR to a greater extent than for cup drawing. For example:

• With t/D > 0.25, a single draw can be attained with nominal blankholder pressure.
• With t/D between 0.15 and 0.25, a single draw may still be feasible but requires much higher blankholder pressure.
• A t/D < 0.15 makes the blank very susceptible to wrinkling, and requires multiple draw reductions.

Successfully drawing highly tapered shells, with h/d2 > 0.70 and α measures approximately 20-30 deg., requires a stepped-cup approach (Fig. 3).

Deep drawing stepped cups basically mimics cylindrical cup drawing, with draw reduction for the adjacent steps equivalent to the corresponding cup diameters. The redraw operation stops part-way to establish the corresponding step, with the step shell then drawn into a cone in the final redraw steps. Due to elastic recovery, the step-like shoulders cannot be completely removed in the final redraw, and impressions made by the punch radii will remain in the finished part.

Spherical Shapes

Difficulty drawing spherical shapes arises due to high drawing loads applied to a very small contact area under the punch, especially early in the process. If edge movement of the blank begins too early, thin materials will easily pucker. The severity of puckering is determined by dividing the cup-wall ID by the sheet thickness. Results greater than 150 to 200 indicate severe puckering and the need for multiple draws or a product redesign.

As the cup bottom approaches a full hemispherical shape, the stretch-forming and blankholding requirements become greater. Additional bending and straightening loads provided by draw beads can help retard sheet metal flow. The biggest challenge: Metal flow toward the punch must begin immediately after dome stretching completes; otherwise, excessive thinning in the dome bottom will cause tearing of the metal (splits) instead of drawing in the blank flange. Because this process combines stretch forming and cup drawing, the percentage reduction will be less for spherical cups.
The t/D ratio also will influence the die design.

• With t/D > 0.03, use a simple bottoming die without a blankholder.
• With t/D from 0.005 to 0.03, use a simple blankholder.
• A t/D < 0.005 often requires reverse redrawing (Fig. 4).

Parabolic Shapes

Shallow paraboloids with a height-to-diameter ratio (h/d) of approximately 0.55 or less are nearly spherical, making the drawing method similar to that for spherical parts.

Deeper paraboloids (h/d >0.55) prove much more difficult to draw due to wrinkling under the punch, and often require multiple draws, variable blankholder force and lock beads.

Not much technical data nor a large knowledge base exist for drawing deep, large-diameter parabolic shapes because these products usually can be produced more cost effectively via other processes, such as metal spinning or hydroforming. MF

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