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# GATE Mechanical 1991 Question

A strip of thickness $T$ $mm$ is rolled in a $2$ high single pass rolling mill, having roll diameter $D$ $mm,$ to a final thickness of $\left( {T - 2\Delta T} \right)mm.$ If the friction coefficient between the roll and strip is $\mu ,$ calculate the maximum reduction $2\Delta T$ possible in this operation. Using this relation, for $D=300mm,$ $T=40mm$ and friction coefficient is $0.3,$ calculate the outgoing thickness of the strip. If the inlet velocity is $5m/s,$ what is the outgoing strip velocity?.
A metal strip is to be rolled from an initial wrought thickness of $3.5$ $mm$ to a final rolled thickness of $2.5$ $mm$ in a single pass rolling mill having rolls of $250$ $mm$ diameter. The strip is $450$ $mm$ wide. The average coefficient of friction in the roll gap is $0.08$. Taking plane strain low stress of $140$ $MPa,$ for the metal and assuming negligible spreading, the roll separating force is . . . . . . . . .
A cylindrical billet of $100$ $mm$ diameter is forged from $50$ $mm$ height to $40$ $mm$ at ${1000^0}$$C$. The material has constant flow stress of $80$ $MPa.$ Find the work of deformation. If a $10$ $kN$ drop hamper is used to complete the reduction in one blow. What will be the height of fall.