Question

In a wire drawing operation, diameter of a steel wire is reduced from 10 mm to 8 mm. The mean flow stress of the material is 400 MPa. The ideal force requied for drawing (ignoring friction and redundant work) is:
1. 4.48 kN
2. 8.97 kN
3. 20.11 kN
4. 31.41 kN

Answer 1

Correct Answer - Option 2 : 8.97 kN

Given D_i = 10 mm, D_f = 8 mm , σ₀ = 400 MPa

Ignoring friction & reduntant work means , μ = 0; β = 0

Hence \({\sigma _d} = 2{\sigma _0}{\rm{ln}}\ \left( {\frac{{{d_i}}}{{{d_f}}}} \right) \Rightarrow {\sigma _d} = 2{\sigma _0}{\rm{ln}}\ \left( {\frac{{{r_i}}}{{{r_f}}}} \right) \)

\(= 2 \times 400\ln \left( {\frac{5}{4}} \right) = 178.51\ MPa\)

Ideal force \(= 178.51 \times {10^6}\ \pi r_f^2\)

= 8968 N = 8.97 kN