Discussion
A plate of 30 mm thickness is fed through a rolling mill with two powered rolls. Each roll has a diameter of 500 mm. The plate thickness is to be reduced to 27 mm in a single pass. Assume no change in width. The process feasibility and the maximum draft (in mm) can be represented, respectively, as
Use the coefficient of friction as 0.12
Answer: A
The pass is feasible, with maximum draft 3.6 mm.
In flat rolling, the maximum draft that friction can drag into the roll gap is \(\Delta h_{max} = \mu^{2}R\), with roll radius \(R = 250\) mm:
\[ \begin{aligned} \Delta h_{max} &= 0.12^{2}\times 250 \\ &= 0.0144\times 250 = 3.6\ \text{mm} \end{aligned} \]
The required draft is \(30 - 27 = 3\) mm, which is less than 3.6 mm, so the pass is feasible. 3.0 mm is the required draft, not the maximum; 6.0 and 2.6 mm do not follow from \(\mu^{2}R\), and the pass is not infeasible.
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