Question

A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively are

• A. 0.45 and 44.72
• B. 0.45 and 38.84
• C. 0.39 and 38.84
• D. 0.39 and 44.72

Answer 1

The correct option is A 0.45 and 44.72

$h_0=40mm,h_f=20mm$

$\Delta h=40-20=20mm,D=200mm$

R = 100 mm

Projected length,

$L=\sqrt{R\Delta h}=\sqrt{100\times 20}$

$=\sqrt{2000}=44.7213mm$

$\Delta h={\mu }^{2}R$

$\therefore 20={\mu }^2\times 100$

$\therefore 0.2={\mu }^2$

or, $\mu =0.4472$