Drawing Process. Drawing is a metalworking process which uses tensile forces to stretch metal. It is broken up into two types: sheet metal drawing and wire, bar, and tube drawing.
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A wide strip is being drawn through a frictionless die with a total included angle of 2α
Plane strain condition is applied (no strain in the width direction.)
The equilibrium of forces in the x direction is made up of two components
1. Due to the change in longitudinal stress with x increasing positively to the left.
2. Due to the die pressure at the two interfaces.
Taking equilibrium of force in the x direction and neglecting dσx dh
We shall now consider the problem of strip drawing where a Coulomb friction coefficient exists between the strip and the die.
The equilibrium now includes 2µpdx
Taking equilibrium of forces in the x direction eq.2 becomes
Since h = 2x tan α, and dh = 2dx tanα, then 2dx = dh/tan α
We now have
Since the yield condition for plane strain is σx + p = σ’0 and B = µ cot α, the differential equation for strip drawing is
If B and σ’0 are both constant, Eq.4 can be integrated directly to give the draw stress σxa
For wire drawing conducted with conical dies,
The surface area of contact between the wire and the die is given by
Balancing the horizontal components of the frictional force and the normal pressure.
In the asence of friction, B = 0 and
The draw stress with friction is given by
If redundant work is included in Eq. 9, the expression becomes
Where Ф is a factor for the influence of redundant work, which can be defined as
Where ε* = the enhanced strain corresponding to the yield stress of the metal, which has been homogeneously deformed to a strain ε
There are three basic types of tube-drawing processes
2. Plug drawing
- Fixed plug
- Floating plug
3. Mandrel drawing