For tool $$A,$$ Taylor’s tool life exponent $$(n)$$ is $$0.45$$ and constant $$(K)$$ is $$90.$$ Similarly for tool $$B,$$ $$n=0.3$$ and $$K=60.$$ The cutting speed (in $$m/min$$) above which tool $$A$$ will have a higher tool life than tool $$B$$ is

In a shear cutting operation, a sheet of $$5mm$$ thickness is cut along a length of $$200mm.$$ The cutting blade is $$400mm$$ long and zero-shear $$(S=0)$$ is provided on the edge. The ultimate shear strength of the sheet is $$100$$ $$MPa$$ and penetration to thickness ratio is $$0.2.$$ Neglect friction

Assuming force $$Vs$$ displacement curve to be rectangular, the work done in $$J$$ is

In a shear cutting operation, a sheet of $$5mm$$ thickness is cut along a length of $$200mm.$$ The cutting blade is $$400mm$$ long and zero-shear $$(S=0)$$ is provided on the edge. The ultimate shear strength of the sheet is $$100$$ $$MPa$$ and penetration to thickness ratio is $$0.2.$$ Neglect friction

A shear of $$20mm$$ $$(S=20mm)$$ is now provided on the blade. Assuming force $$Vs$$ displacement curve to be trapezoidal, the maximum force (in $$kN$$) exerted is

A shaft has a dimension $$\phi $$ $${35^{\matrix{ { - 0.009} \cr { - 0.025} \cr } }}$$. The respective values of fundamental deviation and tolerance are