Problem $1$

The following data are available from orthogonal cutting experiment.

Depth of cut $t_o=0\mathrm{.}13mm,$ width of cut $w=2\mathrm{.}5mm,$ rake angle $=-5,$ cutting speed $V=2\frac{m}{s},$ Chip thickness, $t_c,0\mathrm{.}23mm,$ Cutting force, $F_c,430N,$ Thrust force, $F_t,280N,$

Determine:

$($a$)$ The shear angle $,$

$($b$)$ friction coefficient $($Hint: $F=F_{c}sin+F_{t}cos$ and $N=F_{c}cos-F_{t}sin)$

$($c$)$ shear stress $,$

$($d$)$ shear strain $$ on the shear plane,

$($e$)$ chip velocity $V_c,$

$($f$)$ shear velocity $V_s,$

$($g$)$ total specific energy, $u_t$