Experimental research regarding the hydraulic forming of revolution shape parts.

Coman, Liviu ; Hamat, Codruta ; Pittner, Ana 等

1. INTRODUCTION

The forming process involves deformation of a metal sheet using an increasing hydraulic pressure applied to the lower side of sheet. The metal sheet is clamping between two dies, the upper die having a circular hole. Under the action of hydraulic pressure, the metal sheet will take approximately a spherical shape. The same process performed under standardized condition is known as viscous pressure bulging test (VPB). This test is used to determinate deformability of various metals.

Hitherto, the predictive solutions of the equations (that describe this forming process) are obtained using various assumptions about shape of part or stress-strain relation existing inside of material (Anon, 1997). In this paper, no predictive theory is attempted. Instead of this, a study is made of some experimental results and some conclusions are drawn, conclusions which are applicable to metal sheets having revolution shapes formed in this way.

2. EXPERIMENTAL RESEARCH AND INITIAL CONSIDERATION

The principle of the experimental stand is already known from other studies made in the past (Altan, 2000).

The experiments analyzed in present paper were made on parts with flange, from copper sheet Cu 99,9 with the nominal thickness g = 1,2 mm, tensile strength [R.sub.m] = min 200 MPa, rupture constriction A = min 30% and a diameter [phi]> = 200 mm.

The upper die-block opening had a diameter of 150 mm with a die entrance radius of 13 mm. The forming rate was 10 cm/min. How the geometrical parameters of the part are measured is briefly described in fig.1.

In a part with revolution shape, the directions of the principal stresses are in the circumferential and the meridional tangential directions. If [sigma] stands for stress, [delta] for radius of curvature, p for the hydraulic pressure, g for the local thickness and subscripts [theta] and m for the circumferential respectively the tangential direction, then the equation for the sheet stress is (Hsu&Shang,1977) :

[[sigma].sub.[theta]]/[[delta].sub.[theta]] + [[sigma].sub.m]/[[delta].sub.m] = p/g (1)

Next steep implies to determinate the variable K value.

[FIGURE 1 OMITTED]

The ratio of the principal curvatures [[delta].sub.[theta]]/ [[delta].sub.m]] (called K--value) is of fundamental geometrical significance, because it provides a quantitative measure of the deviation from the spherical shape (Yang&Oh, 2001). For determining the K value at different points in the shape is used the radius of curvature of the meridional section [[delta].sub.m]:

[[delta].sub.m] = 1/cos[theta] x dr/d[theta] (2)

After are made some mathematical operations like integrating and differentiating, finally are obtained:

[[sigma].sub.m] = 1/K sin [theta] 1 - K/K (3)

r = sin [[theta].sup.1/K] (4)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

where [gamma] is the running value of the angle [theta]. The integration of this equation is possible only by graphical or numerical methods (Hsu&Chu,1995). Equations (4) and (5) are the parametric equations for l and r, with 9 as the parameter.

3. EXPERIMENTAL RESULTS AND COMMENTS

The dependence of the K value in the part shape at various stages of the forming process are shown in fig. 2 and 3. The correspondence between the curves in figures, the part height H and the pressurep respectively, is given in table 1.

The seven curves in fig. 2 and 3 may be divided into three groups: curve 1 in the first group, representing the initial stage of the process; curves 2,3,4 in the second group, for the main part of the process under stable conditions; curves 5,6,7 in the last group, the third one, when the conditions are unstable, the oil pressure being maintained at a constant value.

In the both fig. 2 respectively 3 the discussion are made around the line corresponding to K = 1.

[TABLE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

As can be seen, until the process becomes unstable, the shape is perfectly spherical only at the pole (K=1, r = 0), and along a circle, represented by the intersection of a curve and the line K=1. The difference between curves 1 and 2 illustrates the distinction between prolateness and curvature. Also, it can be seen that, in the region near the flange, the prolateness decreases (meaning that K increases) when passing from curve 1 to curve 2.

The stresses in the part are to be expressed in a nondimensional form, in order to show the effect of the shape of the part on the stresses in it. For this, we have:

[[sigma].sub.m] x g/R x p = [delta].sub.[theta]/2R (6)

[[sigma].sub.[theta]] x g/R x p = (2 - K) x [[delta].sub.[theta]]/2R (7)

where R is the radius of curvature at the top of the part (pole). The left term of equation (6) and (7) are thus the nondimensional meridional tangential and circumferential stresses, respectively.

Expressed in this form, the effects of thickness, pressure and general curvature are eliminated and only the effect of prolateness on the stresses is revealed. The two nondimensional stresses in equations (8) and (9) are plotted against each other in fig. 4 and 5.

In these two figures, the state of stress is represented by a vector drawn from the origin point (0,0) to a point on the curves. If the shape is a perfect sphere, the end of the vector is at the point with the coordinates (1/2, 1/2).

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

4. CONCLUSIONS

The experiments reveal that, from theoretical studies point of view the assumption of a spherical shape obtained in the forming process is often inadequate. So far as engineering applications are concerned, these results are useful for improve the geometric parameters (for example for a better distribution of the thickness, etc.). The knowledge about stress distribution and the control of it through the prolateness of the shape are also very important for tool's designers.

5. REFERENCES

Anon, C. (1997). Hydroforming technology, Advanced Material Process, Vol. 151 No.5, pp. 50-53

Altan, T. (2000). Practical determination of formability using the viscous pressure bulging test, Stamping Journal, May

Hsu, T.C. & Shang, H.M.(1977). Mechanics of sheet metal formed by hydraulic pressure into asymmetrical shells, Experimental Mechanics, October

Hsu, T.C. & Chu, C.H. (1995). A finite element analysis of sheet metal forming process, J. Mater. Process. Tech., Vol. 54, pp. 70-75

Yang, G.; Jeon, B. & Oh, S. (2001). Design sensitivity analysis and optimization of hydroforming process, Journal of Material Processing Techmology, 113, pp. 666-672