Orthogonal machining of a steel work-piece is done with a $$HSS$$ tool of zero rake angle. The ratio of the cutting force and the thrust force on the tool is $$1:0.372.$$ The length of cut chip is $$4.71$$ $$mm$$ while the uncut chip length is $$10$$ $$mm.$$ What are the shear plane angle $$\phi $$ and friction angle $$\beta $$ in deg.? Use Merchant's theory.

A single point cutting tool with a nose radius of $$0.4$$ $$mm$$ was used to turn a component in a lathe employing a feed rate of $$0.3$$ $$mm/rev.$$ If the feed-rate is doubled, the ideal surface roughness (peak-to-valley height) produced on the component will increase by a factor of

A cylinder of $$25mm$$ diameter and $$100mm$$ length is turned with a tool, for which the relation $$V{T^{0.25}} = 55$$ is applicable. The cutting velocity is $$22m/min.$$ For a tool feed of $$0.046$$ $$mm/rev,$$ the number of tool regrinds required to produce $$425$$ cylinders is

The following data refers to an orthogonal machining of mild steel with a single point $$HSS$$ tool. Rake angle of tool $$ = {10^ \circ },$$ uncut chip thickness $$=0.3mm,$$ width of cut $$=2.0mm,$$ single plane shear angle $$ = {36^ \circ },$$ shear strength of mild steel $$=450$$ $$MPa,$$ using Merchants analysis

The coefficient of friction between the chip and tool will be