$476$

Chapter $18/$Bulk Deformation Processes in Metalworking

the plate $=77\frac{m}{m}in.$ Roll radius $=300mm,$ and rotational speed $=45re\frac{v}{m}in.$ Determine $($a$)$ the minimum required coefficient of friction that would make this rolling operation possible, $($b$)$ exit velocity of the plate, and $($c$)$ forward slip.

$18\mathrm{.}2($USCS units$)$ A $3-$in$-$thick slab is $12$ in wide and $15ft$ long. Thickness of the slab is reduced in three steps in a hot rolling operation. In each step, thickness is reduced by $20\%$ and width increases by $3\%.$ If the entry speed of the slab in the first step is $40f\frac{t}{m}in,$ and roll speed is the same for the three steps, determine $($a$)$ length and $($b$)$ exit velocity of the slab after the final reduction.

$18\mathrm{.}3($SI units$)$ A series of cold rolling operations are to be used to reduce the thickness of a metal plate from $50mm$ to $20mm$ in a reversing two$-$high mill. Roll diameter $=600mm,$ and coefficient of friction between rolls and work $=0\mathrm{.}15.$ The specification is that the draft is to be equal on each pass. Determine $($a$)$ minimum number of passes required, and $($b$)$ draft for each pass?

$18\mathrm{.}4($SI units$)$ In the previous problem, suppose that the percent reduction rather than the draft were specified to be equal for each pass. $($a$)$ What is the minimum number of passes required? $($b$)$ What is the draft and exiting stock thickness for each pass?