A cup is to be drawn to a diameter of $$70mm$$ with $$35mm$$ depth from a $$0.5mm$$ thick sheet metal. The cup is drawn in one operation. Assume $${\sigma _u} = 430\,\,MPa.$$

The maximum drawing force is

It is required to punch a hole of diameter $$10mm$$ on a sheet of thickness $$3mm.$$ The shear strength of the work material is $$420MPa.$$ The required punch force is

A gear with $$84$$ teeth is to be machined using a milling process with indexing. The index plate has the following four hole circles: $$36,38, 42., 48.$$ The change gear ratio required is

A copper strip of $$200$$ $$mm$$ width and $$30$$ $$mm$$ thickness is to be rolled to a thickness of $$25$$ $$mm.$$ The roll of radius $$300$$ $$mm$$ rotates at $$100$$ $$rpm.$$ The average shear strength of the work material is $$180$$ $$MPa.$$ The roll strip contact length and the roll force are