Problem $16$: In a face$-$milling operation, the back engagement $($depth of cut$)$ is $5$ mm$,$ the work feed speed is $0\mathrm{.}65$ mm$/$s$,$ and the work engagement $($width of workpiece$)$ is $50$ mm$.$ The cutter has a diameter of $100$ mm and has $20$ teeth. If the cutting speed is to be $1$ m$/$s$,$ calculate

a$.$ The rotational frequency of the cutter

b$.$ The maximum metal removal rate

c$.$ The time taken to machine $1000$ workpieces of length $150$ mm if it takes $180$ s to load and unload a workpiece and return the

cutter to the beginning of the cut

d$.$ The maximum un$-$deformed chip thickness