Manufacturing Processes I · Metal Forming · 2 marks · Numerical answer
A wire is drawn from 5 mm to 4 mm diameter through a conical die at pulling speed 5 m/s. Neglect friction/redundant work. Drawing stress is $\sigma_d=\bar\sigma\ln[1/(1-r)]$, with r fractional area reduction and mean flow strength 600 MPa. Find power in kW to two decimals.
Area ratio $1/(1-r)=A_0/A_f=25/16$. Thus σ_d = 600 ln(25/16) = 267.772 MPa. Final area is π4²/4 = 4π mm², so force = σ_d A_f ≈ 3364.93 N. Power = Fv = 16824.6 W = **16.82 kW**.
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