Question

The shear strength of a sheet metal is 300 MPa. The blanking force required to produce a blank of 100 mm diameter from a 2 mm thick sheet is close to

• A. 190 kN
• B. 150 kN
• C. 120 kN
• D. 90 kN

Hint:

Blanking force is calculated as \( F = \tau \times \text{shear area} \), where the shear area for a circular blank is the circumference times the sheet thickness.

Answer 1

The Correct Option is A

Step 1: Understand the blanking process.
Blanking is a sheet metal cutting process where a punch shears a blank (a circular piece in this case) from a sheet. The blanking force depends on the shear strength of the material and the area over which the shear occurs. Step 2: Identify the given values.
Shear strength of the sheet metal: \( \tau = 300 \, \text{MPa} = 300 \times 10^6 \, \text{Pa} \),
Diameter of the blank: \( d = 100 \, \text{mm} = 0.1 \, \text{m} \),
Thickness of the sheet: \( t = 2 \, \text{mm} = 0.002 \, \text{m} \).
Step 3: Calculate the blanking force.
The blanking force \( F \) is given by: \[ F = \tau \times \text{shear area}, \] where the shear area for a circular blank is the circumference of the blank times the thickness of the sheet (the area along the shear perimeter):
Circumference of the blank: \( \pi d = \pi \times 0.1 = 0.1 \pi \, \text{m} \),
Shear area: \( \text{Circumference} \times \text{thickness} = 0.1 \pi \times 0.002 = 0.0002 \pi \, \text{m}^2 \), Blanking force: \[ F = 300 \times 10^6 \times 0.0002 \pi, \] \[ F = 300 \times 10^6 \times 0.0002 \times 3.1416, \] \[ F = 300 \times 0.0002 \times 3.1416 \times 10^6, \] \[ F = 60 \times 3.1416 \times 10^3, \] \[ F \approx 188,496 \, \text{N} = 188.5 \, \text{kN}. \] Step 4: Compare with the options.
The calculated force is approximately 188.5 kN, which is closest to 190 kN. The problem states the force is "close to" a value, so 190 kN is a reasonable match. Step 5: Evaluate the options.
(1) 190 kN: Closest to the calculated value of 188.5 kN. Correct.
(2) 150 kN: Too low compared to 188.5 kN. Incorrect.
(3) 120 kN: Too low. Incorrect.
(4) 90 kN: Too low. Incorrect.
Step 6: Select the correct answer.
The blanking force required is approximately 188.5 kN, which is closest to 190 kN, matching option (1).