In a turning trail using orthogonal tool geometry, a chip length of $$84mm$$ was obtained for an uncut chip length of $$200mm.$$ The cutting conditions were $$V=30m/min,$$ $${t_1} = 0.5mm,$$ rake angle $$=20deg,$$ cutting tool is $$HSS.$$ Estimate shear plane angle, chip thickness and the shear plane angle for minimum chip strain.

A Throwaway carbide insert was used to machine a steel work pieces with a cutting speed of $$60$$ $$m/min,$$ tool life of $$40$$ minutes was observed, when the cutting speed was increased to $$100$$ $$m/min,$$ the tool life decreased to $$10$$ minutes. The cutting speed for maximum productivity, if tool change time is $$2$$ minutes is

Tool life of a $$10$$ hours is obtained when cutting with a single point tool at $$63m/min.$$ If Taylor's constant $$C=257.35,$$ tool life on doubling the velocity will be

While turning a $$C15$$ steel of $$160mm$$ diameter at $$215rpm,$$ $$2.5mm$$ depth of cut and feed of $$0.16mm/rev$$ by a tool of geometry $$0-10-8-9-15-75-0mm,$$ the following observations were made. Tangential component of the cutting force $$=500N,$$ axial component of the cutting force $$=200N,$$ chip thickness $$=0.48mm.$$ Determine the dynamic shear strength of the work piece material.