A $4$ $\text{mm}$ thick aluminum sheet of width $w = 100$ $\text{mm}$ is rolled in a two-roll mill of roll diameter $200$ $\text{mm}$ each. The workpiece is lubricated with a mineral oil, which gives a coefficient of friction, $\mu = 0.1$. The flow stress ($\sigma$) of the material in $\text{MPa}$ is $\sigma = 207 + 414\; \varepsilon$, where $\varepsilon$ 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 _______________ $\text{kN}$ (round off to the nearest integer).

Use:

$F = 1.15\bar{\sigma }\left ( 1 + \dfrac{\mu L}{2\bar{h}} \right )wL$, where $\bar{\sigma}$ is average flow stress, $L$ is roll-workpiece contact length, and $\bar{h}$ is the average sheet thickness.

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