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 $$1/8$$.

Most of the metal cutting heat goes into the