How to Analyze Drawing of Non-Circular Wires? | Metallurgy

In this analysis, it is assumed that plane sections remain plane during deformation. Die has cross-section similar to that of the wire. The size of wire reduces proportionately from entry to the exit.

Let us consider a small section of slab of width dx at a distance x from the exit of conical portion of die. The different stresses acting on the slab are shown in the Fig. 9.23. It is assumed that the die pressure and frictional stress do not vary around the circumference, the variation is only with respect to x.

Let A_x and A_x + dA_x be the areas of cross sections of the two faces of the slab and let C_x be the mean circumference of the slab. Resolving all the forces acting on the slab along the axis of wire we get the following equation-

Neglecting the product of two differential terms dσ_x and dA_x, we can simplify the above equation as follows-

In the above formulation the increase in drawing stress due to shear at the entry and exit is not included. For its calculation the particular shape of cross section has to be considered. As an approximation we may take the average value of semi-cone angle of die as below-

Particular Cases:

(1) Circular Wire:

For circular wire the different constants in Eqn. (9.70) are calculated below-

(ii) Polygonal Wire/Bar:

For an n sided regular polygonal bar the value of M is given by

Here α denotes the angle that the plane containing one of the faces of polygonal bar in the die makes with the central axis. ‘R_x‘ denotes the distance from the axis to the mid-point of the side of polygonal section at a distance x from exit. R₁ and R₂ are the values of R_x at the entry section and exit section respectively. Now

Substituting these values in Eqn. (9.77) and integrating the resultant equation we get

The drawing stress may be calculated by substituting these factors in Eqn. (9.70).

Example:

A square wire of side 10 mm is drawn through a similar shaped die to a square wire of side 8mm. Determine the pull required if the flat square side in the die makes an angle of 8 degrees with the wire axis. The yield strength of material in tension is 250 N/mm² and µ = 0.1. Compare the pull with that required for drawing of circular wire of 10 mm diameter to 8 mm diameter under similar conditions.

Solution: