GATE 2018 ME (ME2) – Question 57
A steel wire is drawn from diameter $d_i=10$ mm to $d_f=7.5$ mm. Die half-angle α = 5°, friction coefficient μ = 0.1 and average yield stress is 350 MPa. Drawing stress is $$\sigma_f=(\sigma_Y)_{\rm avg}\left(1+\frac1{\mu\cot\alpha}\right)\left[1-\left(\frac{d_f}{d_i}\right)^{2\mu\cot\alpha}\right].$$ Find the required drawing stress (MPa), to two decimal places.
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Correct answer: 315.00 to 317.00
Explanation
Compute $b=\mu\cot\alpha=0.1\cot5^\circ=1.143005$ and $d_f/d_i=0.75$. Substitute in the supplied equation: $$\sigma_f=350(1+1/b)[1-0.75^{2b}]=316.2472\ \mathrm{MPa}.$$ Answer **316.25 MPa**.