Question

A square of side length 50 mm is to be blanked from a strip of 2 mm thickness. The sheet metal has a shear strength of 200 MPa.

To enable a single step blanking operation, the theoretical minimum blanking force required is ______ \( \times 10^3 \) N (in integer).

Note: Neglect the effect of clearances and friction.

Hint:

Blanking force equals shear strength times cutting perimeter times sheet thickness.

Answer 1

Correct Answer: 80

Step 1: Recall the formula for blanking force:
Blanking is a shearing operation where a punch cuts a blank out of a sheet along the entire boundary at once.
The theoretical force needed equals the shear strength of the material times the area being sheared, and that sheared area is the perimeter of the cut multiplied by the sheet thickness.
\[ F = L \times t \times \tau \]
Here L is the total length of the cut edge, t is the sheet thickness, and \( \tau \) is the shear strength of the material.

Step 2: Work out the cutting perimeter of the square blank:
The blank is a square with each side 50 mm long, and a square has four equal sides.
\[ L = 4 \times 50 = 200 \text{ mm} \]

Step 3: Substitute all values into the force formula:
The thickness is given as \( t = 2 \) mm, and the shear strength is \( \tau = 200 \) MPa, which is the same as 200 N per square mm.
\[ F = 200 \times 2 \times 200 = 80000 \text{ N} \]

Step 4: Convert to the units asked in the question:
The question wants the force expressed as a multiple of \( 10^3 \) N.
\[ F = 80000 \text{ N} = 80 \times 10^3 \text{ N} \]

Final Answer:
The theoretical minimum blanking force works out to 80, in units of \( 10^3 \) N, and this matches the official answer range of 80 to 80. \[ \boxed{80} \]