# Calculating Required Press Tonnage for Blanking We are given: - **Blank diameter (\(d\))**: 30 mm - **Sheet thickness (\(t\))**: 2 mm - **Shear strength of material (\(\tau\))**: 300 MPa Let's solve step by step. --- ## 1. **Determine the Force Required (Shear Force Formula)** The force required to blank a circular sheet (assuming the material is sheared along the circumference) is: \[ F = \text{Perimeter} \times \text{Thickness} \times \text{Shear Strength} \] Where: - **Perimeter of the blank** (\(P\)): \(P = \pi d\) - **Thickness** (\(t\)): sheet thickness - **Shear Strength** (\(\tau\)): as given Plug in values: - \(d = 30\,\text{mm} = .03\,\text{m}\) - \(t = 2\,\text{mm} = .002\,\text{m}\) - \(\tau = 300\,\text{MPa} = 300 \times 10^6\,\text{N/m}^2\) First, calculate the perimeter: \[ P = \pi d = \pi \times 30\,\text{mm} = \pi \times .03\,\text{m} \approx .0942\,\text{m} \] Now, calculate the force: \[ F = P \times t \times \tau \] \[ F = .0942\,\text{m} \times .002\,\text{m} \times 300 \times 10^6\,\text{N/m}^2 \] \[ F = .0942 \times .002 \times 300 \times 10^6 \] \[ F = .0001884 \times 300 \times 10^6 \] \[ F = 56,520\,\text{N} \] --- ## 2. **Convert Force to Tonnes (Press Tonnage)** 1 tonne-force (\(\text{tf}\)) \(= 9,806\,\text{N}\) (approx 10,000 N for rough calculations, but use precise value for accuracy). \[ \text{Tonnage} = \frac{F}{9,806} \] \[ \text{Tonnage} = \frac{56,520}{9,806} \] \[ \text{Tonnage} \approx 5.76\,\text{tonnes} \] --- ## 3. **Summary Table** | Parameter | Value | |-------------------|-------------------| | Diameter (\(d\)) | 30 mm | | Thickness (\(t\)) | 2 mm | | Shear Strength (\(\tau\)) | 300 MPa | | Shear Force (\(F\)) | 56,520 N | | Required Tonnage | 5.76 tonnes | --- ## 4. **Conclusion** **The required press tonnage to blank a 30 mm diameter circle from 2 mm thick mild steel sheet with a shear strength of 300 MPa is approximately 5.8 tonnes.** --- ### Diagram (for reference)  *Alt text: Diagram showing blanking of a circular disc from a metal sheet, indicating punch diameter and thickness.* --- ## **Notes** - Always round up the tonnage slightly for safety. In practice, a 6-ton or 10-ton press would be chosen. - If material properties or actual cutting conditions differ, recalculate accordingly. - Add a safety factor as per industry standards (commonly 1.2–1.5 times calculated force).