Problem $16$: In a face$-$milling operation, the back engagement $($depth of cut$)$ is $5$ mm $,$ the work feed speed is $0\mathrm{.}65m\frac{m}{s},$ 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

$1\frac{m}{s},$ 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

Table $1\mathrm{.}4$: Summary of Equations for Cutting Operations

Key: $\{\begin{array}{ccc}\text{:}[a_e=& \text{w}\text{o}\text{r}\text{k}\text{i}\text{n}\text{g}\text{e}\text{n}\text{g}\text{a}\text{g}\text{e}\text{m}\text{e}\text{n}\text{t}& ]\\ a_p=& \text{b}\text{a}\text{c}\text{k}\text{e}\text{n}\text{g}\text{a}\text{g}\text{e}\text{m}\text{e}\text{n}\text{t}& \\ b_w=& \text{w}\text{i}\text{d}\text{t}\text{h}of\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}tobe\text{m}\text{a}\text{c}\text{h}\text{i}\text{n}\text{e}\text{d}& \\ d_m=& \text{d}\text{i}\text{a}\text{m}\text{e}\text{t}\text{e}\text{r}of\text{m}\text{a}\text{c}\text{h}\text{i}\text{n}\text{e}\text{d}\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}& \\ d_t=& \text{d}\text{i}\text{a}\text{m}\text{e}\text{t}\text{e}\text{r}of\text{t}\text{o}\text{o}\text{l}& \\ f=& \text{f}\text{e}\text{e}\text{d}& \\ l_t=& \text{l}\text{e}\text{n}\text{g}\text{t}\text{h}of\text{t}\text{o}\text{o}\text{l}& \\ l_w=& \text{l}\text{e}\text{n}\text{g}\text{t}\text{h}of\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}or\text{h}\text{o}\text{l}\text{e}to& be\\ & \text{m}\text{a}\text{c}\text{h}\text{i}\text{n}\text{e}\text{d}& \\ n_r=& \text{f}\text{r}\text{e}\text{q}\text{u}\text{e}\text{n}\text{c}\text{y}of\text{r}\text{e}\text{c}\text{i}\text{p}\text{r}\text{o}\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}& \\ n_t=& \text{r}\text{o}\text{t}\text{a}\text{t}\text{i}\text{o}\text{n}\text{a}\text{l}\text{f}\text{r}\text{e}\text{q}\text{u}\text{e}\text{n}\text{c}\text{y}of\text{t}\text{o}\text{o}\text{l}& \\ n_w=& \text{r}\text{o}\text{t}\text{a}\text{t}\text{i}\text{o}\text{n}\text{a}\text{l}\text{f}\text{r}\text{e}\text{q}\text{u}\text{e}\text{n}\text{c}\text{y}of\text{w}\text{o}\text{r}\text{k}\text{p}\text{i}\text{e}\text{c}\text{e}& \\ N=& \text{n}\text{u}\text{m}\text{b}\text{e}\text{r}of\text{t}\text{e}\text{e}\text{t}\text{h}on\text{c}\text{u}\text{t}\text{t}\text{e}\text{r}& \\ v=& \text{c}\text{u}\text{t}\text{t}\text{i}\text{n}\text{g}\text{s}\text{p}\text{e}\text{e}\text{d}& \\ v_f=& \text{f}\text{e}\text{e}\text{d}\text{s}\text{p}\text{e}\text{e}\text{d}& \\ {}_r=& \text{m}\text{a}\text{j}\text{o}\text{r}\text{c}\text{u}\text{t}\text{t}\text{i}\text{n}\text{g}\text{e}\text{d}\text{g}\text{e}\text{a}\text{n}\text{g}\text{l}\text{e}& \end{array}$