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 $$KW$$

The following data is available for machining a component on a turret or center lathe: find out the total number of components to be machined to justify the use of turret lathe

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.