A deep drawing operation is performed on a sheet-metal blank that is 1/8 in thick. The height of the cup = 3.8 in and its diameter = 5.0 in (both inside dimensions). (a) Assuming the punch radius = 0, compute the starting diameter of the blank to complete the operation with no material left in the flange. (b) Is the operation feasible (ignoring the fact that the punch radius is too small) ?

a) Db = 10.05 in

b) The operation is not feasible

Explanation:

Let's begin by listing out the given variables:

Thickness = 1/8 in, Height (h) = 3.8 in,

Diameter (Dp) = 5 in ⇒ rp = Dp : 2 = 5 : 2 = 2.5 in

a) Area of cup = Area of wall + Area of base

A = 2πh (rp) + π (rp) ²

A = (2π * 2.5 * 3.8) + (π * 2.5²)

A = 59.69 + 19.635 = 79.325 in²

A ≈ 79.33 in²

But π (rb) ² = 79.33 ⇒ rb² = 79.33 : π

rb² = 25.25

rb = 5.025 ⇒ Db = 2 * rb = 2 * 5.025 = 10.05 in

Db = 10.05 in

b) To calculate for feasibility, we use the formula, draw ratio equals diameter of the blank divided by diameter of the punch

Mathematically,

DR = Db : Dp

DR = 10.05 : 5 = 2.01

DR = 2.01

DR > 2 ⇒ the operation is not feasible

For an operation to be feasible, it must have a drawing ratio limit of 2 or lesser