Calculate the punch size in $$mm,$$ for a circular blanking operation for which details are given below.

Size of the blank $$25$$ $$mm$$
Thickness of the sheet $$2$$ $$mm$$
Radial clearance between punch and die $$0.06$$ $$mm,$$ Die allowance $$0.05$$ $$mm$$

In an interchangeable assembly, shafts of size $${25.000^{\matrix{ { + 0.040} \cr { - 0.010} \cr } }}\,\,mm$$ mate with holes of size $${25.000^{\matrix{ { + 0.030} \cr { + 0.020} \cr } }}\,\,mm.$$

The maximum interference (in microns) in the assembly is

A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(100, 100)$$ on the $$XY$$ plane (dimensions in $$mm$$). The feed rate used for milling is $$50$$ $$mm/min.$$ Milling time for the slot (in seconds) is

A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $$\Delta T.$$ If the thermal coefficient of the material is $$\alpha $$, young's modulus is $$E$$ and the Poisson's ratio is $$\upsilon $$, the thermal stress developed in the cube due to heating is