In a face milling operation, the cutting tool has a diameter of $\backslash (\backslash$mathbf$\{60$ ~ m m$\}\backslash )$ with $\backslash (\backslash$mathbf$\{15\}\backslash )$ tungsten carbide $($WC$)$ inserts and the spindle speed is $\backslash (260+\backslash )$ A rpm$.$ Given that the feed rate is $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~mm$\}/\backslash$mathrm$\{$rev$\}\backslash )$ and the life of the cutting edge of each insert is given by Taylor's Tool Life equation VT $\backslash (\{\}^\{0\mathrm{.}25\}=140\backslash ).$

Notes: $\backslash ($ A$=\backslash$underline$\{$l a s t$\}\backslash )$ digit of your student ID $\backslash ($ A$=9\backslash )$

Determine:

$($a$)$ The time in minutes before each insert needs to be changed to a new edge.

$($b$)$ The number of workpieces that can be completed during the time calculated in $($a$),$ if this face milling operation involves only one pass for each $\backslash (\backslash$mathbf$\{400\}\backslash$mathrm$\{$mm$\}\backslash )$ long by $\backslash (\backslash$mathbf$\{50$ ~ m m$\}\backslash )$ wide workpiece. Assume that for the pass $\backslash (\backslash$mathbf$\{25$ ~ m m$\}\backslash )$ is machined off the width of the workpiece as shown in Figure $2.$ The approach distance at the start is equal to the tool radius, and the return speed of the tool is $3$ times the feed rate.

In Taylor's Tool Life equation: $\backslash (\backslash$mathrm$\{$V$\}=\backslash )$ cutting speed in $\backslash (\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$min$\}\backslash$& $\backslash$mathrm$\{$~T$\}=\backslash )$ tool life in minutes

Figure $2$: Top view of face milling operation.