# Solution to Question 1 --- ## **1.1. Four Operations Performed with Metal Tooling** 1. **Shearing:** Cutting sheet metal into pieces using a punch and die. 2. **Bending:** Deforming sheet metal along a straight axis (e.g., V-bending, U-bending). 3. **Drawing:** Forming sheet metal into a desired shape by stretching it over a die. 4. **Punching:** Creating holes in sheet metal by driving a punch through the material. --- ## **1.2. Bending Operation on Cold-Rolled Steel** **Given Data:** - Thickness of steel, \( t = 8.00\, \text{mm} \) - Bend radius, \( R = 10.5\, \text{mm} \) - Bend angle, \( \alpha' = 60^\circ \) - Tensile strength, \( \sigma_t = 434\, \text{MPa} \) - Shear strength, \( \tau = 350\, \text{MPa} \) - Die opening, \( V = 50\, \text{mm} \) --- ### **1.2.1. (a) Blank Size Required** The blank length for a bent section is calculated using the formula for the **bend allowance (BA)**: \[ \text{BA} = \theta \left( R + K \cdot t \right) \] Where: - \( \theta \) = bend angle in radians = \( 60^\circ \times \frac{\pi}{180^\circ} = 1.047\, \text{rad} \) - \( R \) = inside bend radius = \( 10.5\, \text{mm} \) - \( t \) = thickness = \( 8.00\, \text{mm} \) - \( K \) = K-factor (typically .33 for V-bending) \[ \text{BA} = 1.047 \times (10.5 + .33 \times 8) \] \[ \text{BA} = 1.047 \times (10.5 + 2.64) \] \[ \text{BA} = 1.047 \times 13.14 \] \[ \text{BA} \approx 13.76\, \text{mm} \] **If you have straight legs before and after the bend, add those lengths to BA. For only a single bend, the blank size is the bend allowance.** --- ### **1.2.1. (b) Bending Force Required** The bending force (\( F \)) for a V-die is calculated as: \[ F = \frac{k \cdot \sigma_t \cdot t^2 \cdot L}{V} \] Where: - \( k \) = constant (typically 1.33 for V-die bending) - \( \sigma_t \) = tensile strength (MPa) - \( t \) = thickness (mm) - \( L \) = length of bend (assume 1 mm for per mm calculation, unless given) - \( V \) = die opening (mm) Assume \( L = 1\, \text{mm} \) (for per mm calculation): \[ F = \frac{1.33 \times 434 \times 8^2 \times 1}{50} \] Calculate \( 8^2 = 64 \): \[ F = \frac{1.33 \times 434 \times 64}{50} \] \[ F = \frac{1.33 \times 277760}{50} \] \[ F = \frac{369420.8}{50} \] \[ F = 7388.4\, \text{N} \quad \text{(per mm of bend length)} \] --- ## **Final Answers** ### **1.1. Four Operations with Metal Tooling** - Shearing - Bending - Drawing - Punching ### **1.2.1.** #### **(a) Blank size required (bend allowance)** \[ \boxed{13.76\, \text{mm}} \] #### **(b) Bending force required per mm of bend length** \[ \boxed{7388.4\, \text{N/mm}} \] **Note:** If the total length of the bend is given, multiply the bending force per mm by the total length.