In a single point turning operation with cemented carbide tool and steel work piece, it is found that the Taylor's exponent is $$0.25.$$ If the cutting speed is reduced by $$50\% $$ then the tool life changes by ____________ times.

An orthogonal turning operation is carried out under the following conditions; rake angle $$ = {5^ \circ },$$ spindle rotational speed $$=400$$ $$rpm,$$ axial feed $$=0.4$$ $$m/min$$ and radial depth of $$cut = 5mm$$. The chip thickness, $${t_c},$$ is found to be $$3mm.$$ The shear angle (in degrees) in this turning process is ________________

Orthogonal turning of a mild steel tube with a tool of rake angle $${10^0}$$ is carried out at a feed of $$0.14$$ $$mm/rev.$$ If the thickness of the chip produced is $$0.28mm,$$ the values of shear angle and shear strain will be respectively.

A single point cutting tool with $${0^0}$$ rake angle is used in an orthogonal machining process. At a cutting speed of $$180$$ $$m/min$$ the thrust force is $$490N.$$ If the coefficient of friction between the tool and the chip is $$0.7.$$ Then the power consumption (in $$kW$$) for the machining operation is ____________