Question

A 4 mm thick sheet is rolled with 300 mm diameter rolls to reduce thickness without any change in its width. The friction coefficient at the work-roll interface is 0.1. The minimum possible thickness of the sheet that can be produced in a single pass is

• A. 1.0 mm
• B. 1.5 mm
• C. 2.5 mm
• D. 3.7 mm

Answer 1

The correct option is C 2.5 mm

Given,

Initial thickness of sheet,

$t_i=4mm=4\times {10}^{-3}m$

Diameter of roll,

D = 300 mm = 0.3 m

Frictional coefficient at work-roll interface,

$\mu =0.1$

Let $t_f=$ Final thickness of sheet after rolling

For single pass without slipping minimum possible

thickness,

$t_i-t_f={\mu }^{2}R$

$\mu =\sqrt{\frac{t_i-t_f}{R}}$

0.1 = $\sqrt{\frac{4\times {10}^{-3}-t_f}{0.15}}$

or $t_f=2.5mm$