GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which gives a coefficient of friction, μ = 0.1. The flow stress (σ) of the material in MPa is σ = 207 + 414 𝜀, where 𝜀 is the true strain. Assuming rolling to be a plane strain deformation process, the roll separation force (F) for maximum permissible draft (thickness reduction) is _________ kN (round off to the nearest integer).
Use:
 $\mathit{F}=1.15\overline{\mathit{\sigma }}\left(1+\frac{\mathit{\mu }\mathit{L}}{2\overline{\mathit{h}}}\right)$ wL, where $\overline{\mathit{\sigma }}$ is average flow stress, L is roll-workpiece contact length, and $\overline{\mathit{h}}$ is the average sheet thickness