A steel wire is drawn from an initial diameter (di) of 10 mm to a final diameter (df) of 7.5 mm. The half cone angle (α) of the die is 5∘ and the coefficient of friction (μ) between the die and the wire is 0.1. The average of the initial and final yield stress [(σy)avg] is 350 MPa. The equation for drawing stress σf. (in MPa) is given as:σf=(σy)avg{1+1μcotα}[1−(dfdi)2μcotα]The drawing stress (in MPa) required to carry out this operation is (correct to two decimal places).

A steel wire is drawn from an initial diameter (di) of 10 mm to a fina

1.	A steel wire is drawn from an initial diameter (di) of 10 mm to a final diameter (df) of 7.5 mm. The half cone angle (α) of the die is 5∘ and the coefficient of friction (μ) between the die and the wire is 0.1. The average of the initial and final yield stress [(σy)avg] is 350 MPa. The equation for drawing stress σf. (in MPa) is given as:σf=(σy)avg{1+1μcotα}[1−(dfdi)2μcotα]The drawing stress (in MPa) required to carry out this operation is (correct to two decimal places).
Answer» A steel wire is drawn from an initial diameter $(d_{i})$ of 10 mm to a final diameter $(d_{f})$ of 7.5 mm. The half cone angle $(α)$ of the die is $5^{\circ}$ and the coefficient of friction $(μ)$ between the die and the wire is 0.1. The average of the initial and final yield stress $[(σ_{y})_{a v g}]$ is 350 MPa. The equation for drawing stress $σ_{f}$ . (in MPa) is given as: $σ_{f} = (σ_{y})_{a v g} {1 + \frac{1}{μ c o t α}} [1 - {(\frac{d_{f}}{d_{i}})}^{2 μ c o t α}]$ The drawing stress (in MPa) required to carry out this operation is (correct to two decimal places).

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