Calculate the minimum number of hot rolling passes necessary to reduce an ingot of $$200mm$$ thickness to $$100mm$$ thickness in two high reversible rolling mill with roll diameter is $$500$$ $$mm.$$ The coefficient of friction between the rolls and the hot material is assumed as $$0.20.$$

A steel wire of length $$100$$ $$m$$ and diameter $$12.214$$ $$mm$$ is drawn to a final diameter of $$10mm.$$ Tensile tests of specimen made before and after the drawing operation gave yield stress as $$200$$ $$MPa$$ and $$400$$ $$MPa$$ respectively,

The yield stress of the steel at a true stain $$0.2,$$ by assuming linear strain hardening law.

A steel wire of length $$100$$ $$m$$ and diameter $$12.214$$ $$mm$$ is drawn to a final diameter of $$10mm.$$ Tensile tests of specimen made before and after the drawing operation gave yield stress as $$200$$ $$MPa$$ and $$400$$ $$MPa$$ respectively,

The length of drawn wire is

In a wire drawing operation diameter of $$6mm$$ is reduced in stages to a diameter of $$1.34mm.$$ Assuming ideally rigid plastic material and ideally lubricant condition,
$$i)$$$$\,\,\,\,\,\,\,$$ The minimum number of passes required by assuming max reduction per pass
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ is obtained with $$\mu = 0.2$$ and half die angle as $${6^0}$$. If the flow strength of the
$$\,\,\,\,\,\,\,\,\,\,\,\,$$ material is $$60$$ $$MPa.$$

$$ii)$$$$\,\,\,\,\,$$ The diameter of wire after $${2^{nd}}$$ stage