An orthogonal cutting operation is performed using a rake

angle of $18$ on a work material whose shear strength is

$280$ MPa $.$ The chip thickness before the cut $=0\mathrm{.}31mm$ and

width of cut $=2\mathrm{.}5mm.$ if the chip thickness ratio is measured

after the cut to be $0\mathrm{.}59.$ Determine

$($a$)$ the chip thickness after the cut,

$($b$)$ shear angle,

$($c$)$ friction angle,

$($d$)$ Coefficient of friction, and

$($e$)$ shear strain.

$($f$)$ the shear force,

$($g$)$ cutting force,

$($h$)$ thrust force,

$($i$)$ friction force.