Determine the Merchants constant $$'C'$$ (shear angle relation) for aluminium from the following orthogonal machining data. Rake angle $${35^ \circ }$$ and an uncut chip thickness $$0.15mm,$$ the values of $${F_c}$$ and $${F_t}$$ are found to be $$200$$ and $$90$$ $$N$$ respectively. The average chip thickness is also measured and found to be $$0.3$$ $$mm,$$ width of cut $$2.5mm$$ and cutting velocity $$30m/min.$$

Find the percentage change in cutting speed required to give a $$50\% $$ reduction in tool life (that is required tool life is half of the original tool life ) when the value of the tool life exponent $$n=0.125$$ or $$1/8$$.

A tube is orthogonally machined in lathe to reduce its length under the following conditions.
Outside diameter of the tube : $$100mm,$$
Inside diameter of the tube $$=96$$ $$mm$$
$$RPM$$ of the work piece $$=120,$$
Longitudinal feed $$=0.5mm/rev$$
Cutting ratio $$=0.3,$$
Tangential force $$=800N,$$
Axial force $$=600N$$
Calculate the chip velocity in $$m/min$$ and the total power consumption in $$KW$$

In an orthogonal cutting test on the following data were obtained
Uncut chip thickness $$=0.25mm,$$ Cutting speed: $$60m/min,$$ Tool rake angle: $$0$$ Chip thickness $$0.75mm,$$ Cutting force : $$900$$ $$N$$, Thrust force : $$450$$ $$N$$

Calculate the shear angle, total power in making the cut and coefficient of friction between the chip tool interface.