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.

For an orthogonal cutting operation, tool material is $$HSS,$$ rake angle is $${22^ \circ },$$ chip thickness is $$0.8$$ $$mm,$$ speed is $$48$$ $$m/min$$ and feed is $$0.4$$ $$mm/rev$$. The shear plane angle (in degrees) is

For a certain job, the cost of metal cutting is $$Rs.18C/V$$ and the cost of tooling is Rs.$$270C/(TV).$$ Where $$C$$ is a constant, $$V$$ is the cutting speed in $$m/min$$ and $$T$$ is the tool life in minutes. The Taylor's tool life equation is $$V{T^{0.25}} = 150.$$ The cutting speed (in $$m/min$$) for the minimum total cost is ___________

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 ____________