QUESTION $3$

The following data were obtained from a cutting test: $=20,k=90,$ depth of cut $6\mathrm{.}4$ mm $,$ feed

$0\mathrm{.}25m\frac{m}{r}ev,$ chip length before cutting $29\mathrm{.}4$ mm $,$ chip length after cutting $12\mathrm{.}9$ mm $.$ The cutting

forces were axial force $427$ N $,$ vertical force $1050$ N $.$

Use Merchant's analysis to calculate:

$($a$)$ The direction and magnitude of the resultant force.

$[5$ marks$]$

$($b$)$ The shear plane angle.

$[5$ marks$]$

$($c$)$ The frictional force.

$[5$ marks$]$

$($d$)$ The friction angle.

$[5$ marks$]$