7.5.1 Formulation of the Problem

In the present text the geometry of the floating plug is studied in order to optimize the tube drawing process, i.e., in order to increase the drawing speed, to increase the reduction per pass, to reduce the consumption of energy used, etc. For this purpose the theory of fast tube drawing with floating plug is formulated and a formula is given expressing the drawing stress as function of various parameters involved in the drawing process (drawing speed, semi-cone die angle ?, tube geometry, mechanical properties of the material, friction coefficients and plug geometry).

Some data, mainly of experimental character and of industrial practice can be found in Bisk and Shveikin [1963] and Perlin [1957]. From the experiments described in these books it results that when the drawing speed is increased from 20 m/min to 60 m/min the drawing force increases several times (two or even three times). The significant influence of the speed on the wire drawing process was mentioned. Since the rates of strains are higher than 10 ² s ^?1, one has to describe theoretically this process with a viscoplastic constitutive equation (Cleja and Cristescu [1979]).

Due to the geometrical symmetry of the die, plug and of the tube the problem can be considered to be axisymmetrical. For this reason the geometry of the deformation process was represented in Fig. 7.5.1 in a symmetry plane. The tube of initial thickness R ₁ ?R ₃ enter...