Analysis of shape variation during hydro-forming of ellipsoidal shells with double generating lines

• Geometric criteria of double generating lines changing into single generating line is derived.
• Mathematical model between shell volume and axis length ratio is developed.
• The needed shell shape can be controlled by inputting pressured wate.

In order to obtain an ideal ellipsoidal shell by the controlling of inputting pressured water volume, the curvature and volume variation have been analyzed for hydro-forming of ellipsoidal shell with double generating lines. The geometric criteria of double generating lines changing into single generating line was derived, and the mathematical model between shell volume and axis length ratio was developed. It is shown that the volume variation is only associated with the initial and final axial length ratios, and can be theoretically predicted. An experiment was conducted on hydro-forming of the ellipsoidal shells with the axis length ratio 1.5, 1.7 and 2.2, respectively, and the effect of internal pressure was discussed on the deformation of the shell shape, curvature and volume variation. It is experimentally shown that the short axis is linearly increased, the long axis is slightly changed and the shell volume is exponentially increased. It is proved that the theoretical prediction of the volume variation has a good agreement with the experimental results, which indicates that the needed ideal ellipsoidal shell can be successfully formed by controlled of inputting pressured water volume.