A cutting tool is designated in 'Orthogonal Rake System' as: $$${0^ \circ } - {0^ \circ } - {6^ \circ } - {6^ \circ } - {25^ \circ } - {75^ \circ } - 0.8\,\,mm.$$$
The following data were given
$${S_0} = $$ feed $$=0.12$$ $$mm/rev$$
$$T=$$ depth of cut $$=2.0$$ $$mm$$
$${a_2} = $$ chip thickness $$=0.22$$ $$mm$$
$${V_f} = $$ chip velocity $$=52.6$$ $$m/min$$
$${\tau _s} = $$ dynamic yield shear strength $$=400$$ $$MPa$$
$${P_z} = $$ main cutting force $$ = {S_0}\,t\,{\tau _s}\left( {\zeta \,\sec y - \tan \gamma + 1} \right)$$

Where $$\zeta = $$ chip reduction coefficient and $$\gamma = $$ orthogonal rake.
The main cutting force $$\left( {{P_z}} \right)$$ and cutting power assuming orthogonal machining are

Tool life in drilling steel using $$HSS$$ drill is expressed as $${T^{0.2}} = 9.8\,\,{D^{0.4}}\,\,/\,\,V\,{s^{0.5}}$$ where $$D$$ is the drill diameter (in $$mm$$), $$T$$ is the tool life (in minutes), $$V$$ is the cutting speed (in $$m/min$$) and $$s$$ is the feed ($$mm/rev$$). The feed is set at maximum possible value of $$0.4$$ $$mm/rev$$ for a given drill diameter of $$30mm.$$ The length of drilling is $$50mm.$$ The machine hour rate Rs $$60$$ and the cost of drill is Rs. $$400.$$

$$i)$$ For the given conditions, the tailor's exponent and constant are .............
$$ii)$$ The optimum cutting speed, $${V_{opt}},$$ neglecting the work-piece and tool changing times is

In certain machining operation with a cutting speed of $$50$$ $$m/min,$$ tool life of $$45$$ minutes was observed, when the cutting speed was increased to $$100$$ $$m/min,$$ the tool life decreased to $$10$$ minutes. The cutting speed for maximum productivity, if tool change time is $$2$$ minutes is

In a single pass turning operation the cutting speed is the only variable Based on the cutting time cost and the cutting edge cost. The tool life for minimum cost given that cost of $$1$$ cutting edge is Rs.$$5$$, operator wages including the machine tool cost is Rs. $$75$$/hour and tool life equation is $$V{T^{0.1}}$$ is $$100.$$