Blank Diameter Calculation in Drawing Dies

When drawing cylindrical cups, the blank diameter of the material to be drawn is calculated first. During drawing, the cup material undergoes bending, compressive, and tensile stresses. However, for cups with a flat base, only the base itself is not subjected to bending, compressive, or tensile stresses.

The following methods are used to calculate the blank diameter:

Area method
Length and center-of-gravity method
Graphical method

Finding the Blank Diameter with the Area Method

The area of the part before drawing is set equal to the area of the cup after drawing. The figure below shows the blank diameter of a straight cylindrical cup and its dimensions after drawing.

Flat-bottom cylindrical cup drawing die blank diameter — Flat-bottom cylindrical cup

Area of the part to be drawn: π . D²/ 4
Area of the drawn cup: π . d²/ 4 + d . h mm²

Setting both areas equal to each other;
π . D²/ 4 = π . d²/ 4 + d . h

Rounded-base cylindrical cup drawing die blank diameter — Cylindrical cup with a rounded base edge

The blank diameter of the cylindrical cup with a rounded base, shown in the image above, is also calculated the same way:

Another example is the flat-bottomed flanged cylindrical cup shown in the figure below. For this type of flanged cup as well, the area of the part to be drawn is set equal to the area of the drawn cup to find the blank diameter.

blank diameter calculation in drawing dies

D = Blank diameter of the cup to be drawn, mm
S = Area of the drawn cup, mm²

table of drawn cups and their areas in drawing dies — Table of drawn cups and their areas

table of drawn cups and their blank diameters in drawing dies — Table of drawn cups and their blank diameters

Finding the Blank Diameter with the Length and Center-of-Gravity Method

To find the blank diameter using the length and center-of-gravity method, a symmetric cross-section of the drawn cup is taken, and the lengths of all the edges subject to drawing are found individually. Then, the sum of the products of all the lengths and the distances of their centers of gravity from the axis of symmetry is set equal to the area of the part to be drawn.

For this method to be applied;

The cross-sectioned cup is divided into symmetric segments.
The lengths l₁, l₂,l₃… ln, representing each of the symmetric segments, are found.
The distances r₁, r₂, r₃,. . , r_n of the center of gravity of each length from the cup’s axis are found, and the blank diameter is calculated using the formula below.