In tube sinking the change in tube thickness is rather small compared to the change in diameter of tube. Therefore, in this analysis we neglect the change in tube thickness. Figure 9.20 shows the different stresses acting on a slab of thickness dx located at x from the end of conical portion of the tube. The mean radius of tube is r on the smaller side and r + dr on the bigger side of the slab. Here ‘h’ denotes the thickness of tube.
Work of Shear Deformation at Entry and Exit:
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The shear deformation at the entry to die and at exit from die increases the drawing stress. In tube sinking the tube thickness remains nearly same. Therefore, throughout the thickness the material suffers a shear deformation equal to α. This gives rise to an axial stress at the entry to die, which is given by the following equation.
where α is in radians. A similar stress σs2 develops due to shear deformation at the exit from the die. We may take σs1 along with back tension and σs2 is just added to get σd.
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Effect of Thickness Change:
The other factor that may affect the drawing stress in tube sinking is the slight thickening/ thinning that occurs during drawing. Experiments by Rajnish and Juneja have shown that during tube sinking thin tubes become thick and thick tubes become thin. Let h1 be the thickness of tube and R the radius of tube before drawing.
For h1/R < 0.33 the tube becomes thicker during drawing, while for h1/R > 0.33 the tube becomes thinner during drawing. For h1/R ≅ 0.33 the tube thickness does not change. In order to allow for slight changes in diameter we may take yield strength as λ. σ0 where λ varies between 1 to 2/√3. Generally λ is taken equal to 1.1.
Example 1:
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In a tube sinking process a steel tube of 20 mm outer diameter and 2 mm thick is reduced to 16 mm outer diameter. There is no change in thickness. The semi-die-angle is 8 degrees, coefficient of friction µ = 0.1 and average value of yield strength σ0 = 300 N/mm2. Determine the drawing stress after the conical portion of die and pull required to draw the tube if the land length of die = 4 mm.
Solution:
