$3.)$ Milling.

You are going to mill a pocket as shown in the Figure below.

You will start with a block of $6061-$T$6$ aluminum that is already milled to the dimensions of $100$ mm X $100$ mm X $100$ mm and use a diamond coated high speed steel ball mill cutter with a $10$ mm diameter. The bottom of the pocket should have a peak to valley surface finish $\backslash (\backslash$left$(\backslash$mathrm$\{$R$\}\_\{\backslash$mathrm$\{$t$\}\}\backslash$right$)\backslash )$ of no more than $\backslash (1\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash ).$ You should minimize the machining time for this operation. Please provide the following information for the pocket milling operation:

a$)$ The feed speed, rotational velocity $($RPM$),$ surface speed and depth of cut for the ball mill cutter. $(30$ points$)$

b$)$ The smallest and largest value of the radii $\backslash ($ R$\_\{1\}\backslash )$ and $\backslash ($ R$\_\{2\}\backslash )$ that you can produce on this part. $(20$ points$)$

c$)$ The machining time for your part. $(10$ points$)$

d$)$ If we now change the part material to $1017$ steel hardened to $50$ RC $,$ how would you change the process. Just describe what would be different in your answers to parts A$-$C$,$ there is no need to redo the calculations. $(20$ Points$)$

e$)$ For both the aluminum and steel parts, please provide any recommendations for a substitute tool material, if you think that a better material should be used. Make sure to fully explain your answer. $(20$ points$)$