Research On Hydro-forming Of Ellisoidal Shell With Double Generating Lines

Ellipsoidal shells have been usually used as water tanks due to the advantages of the small wind area and lower centriod, and it can be also used as bottom of fuel tank in the rockets. There is a latitudinal compressive stress in the equatorial zone when the initial axis length ratio exceeding 2^1/2, which would lead to wrinkling in the equatorial zone. In order to avoid the wrinkling occurrence during hydro-forming, an ellipsoidal shell with double generating lines has been designed as the pre-form shell. Theoretical analysis, numerical simulation and experiments have been carried out to deeply analyze hydro-forming process of ellipsoidal shell. This study provides theory foundation and technology support to manufacture the large-size ellipsoidal shells.The influence of axis length ratio was discussed on stress distribution by theoretical analysis, and the reason of wrinkling occurrence was pointed out. To avoid the latitudinal compressive stress, this shell segment from the equatorial line to the dividing line is replaced by another ellipsoidal shell with axis length ratio less than 2^1/2, so that an ellipsoidal shell with double generating lines can be obtained. Stress analysis on the ellipsoidal shell with double generating lines subjected to internal pressure was carried out. According to Tresca yield criterion, yield pressure was derived for the ellipsoidal shell with double generating lines.In order to analyze the axis lengths variation during hydro-forming of ellipsoidal shell with double generating lines, experiments for ellipsoidal shell with the axis length ratio 1.5, 1.7 and 2.2 respectively were conducted. The wrinkling does not occur, and the sound ellipsoidal shells are obtained. The internal pressure were discussed on axis lengths variation. It is shown that the short axis is significantly elongated, and elongation is linearly increased with the internal pressure. The bigger the initial axis length ratio is, the larger the elongation of short axis is. The long axis is slightly changed with the internal pressure. When the forming pressure is 1.5sp, the variation of short axis is 16.6%,26.1% and 41.0% respectively, and the variation of long axis is 1.3%,1.9% and 2.7%.Stress locus obtained by strain gauge measurement were illustrated on the yield surface, and the initial yield pressure sp was obtained. Experimental results show that the initial yield pressure sp is 3.0MPa for all the three shells. To analyze the variation of generating equation, the critical pressure that the double generating lines is changed to single generating line was given, and the internal pressure was discussed on variation of curvature radius on the dividing angle. It is shown that the curvature radius for the first ellipsoidal shell is decreased with internal pressure, while the curvature radius for the second ellipsoidal shell（ l（27）2） is first increased and then decreased with the internal pressure. When the internal pressure is 1.1sp, an ellipsoidal shell with single generating line is obtai ned.In order to obtain needed ellipsoidal shell by volume flow control, the variation of shell volume was discussed on the internal pressure, and the mathematical model between shell volume and axis length ratio was developed. It is shown that the shell volume is exponentially increased with the internal pressure, and the bigger the initial axis length ratio is, the larger the volume variation is. When the internal pressure is 1.5sp, the variation of shell volume is 16.6%, 26.1% and 41.0%, respectively. The maximum thinning is located on the pole, while the minimum thinning is located on the equatorial plane. Accordingly the maximum thinning is 10.4%,16.3% and 21.0% respectively.In order to reverse an optimum pre-form structure according to needed ellipsoidal shell, a mathematical response model between axis lengths and structural parameters was developed on the basis of the Box-Behnken design method. For needed ellipsoidal shell with axis length ratio λ=1.5, the optimum initial axis length ratio of pre-form shell is λ=2.0².2. By comparison with the experimental results, it is indicated that the predicted axis lengths calculated by reverse design are in good agreement with the experimental data, and the deviation is less than 1%.Mechanism of avoiding wrinkling for the ellipsoidal shell with double generating lines was carried out by simulation, and the stress distribution during hydro-forming is given. It is shown that the stress state on the center of lateral petals are double tensile all the time, while the stress state on weld seam is tensile-compressive at an early stage of deformation. The latitudinal compressive stress is caused by spreading out of the initial dihedral angle between lateral petals, which brings a moment and additional compressive stress on the weld seam. However, the magnitude of latitudinal compressive stress is not sufficient for causing wrinkling. The results show that the stress state is changed by desining pre-form shape with double generating lines when the initial axis length ratio is exceeding 2^1/2, hence the wrinkling can be avoided.Occurring and expanding of plastic deformation for the ellipsoidal shell with double generating lines was conducted by simulation. It is shown that the dividing angle is first yielded and expanded towards to temperate zone and equatorial zone, and then the pole is yielded and expanded towards to equatorial zone. The center of the lateral petals is easily yielded than the vicition of weld seams.The prolate ellipsoidal shell is more suitable for using as storage of volatile oil such as gasoline due to the advantage of the smaller cross-sectional area under the condition the same height compared with the oblate ellipsoidal shell and spherical shell. In order to resolve the problem that the polar zone is not deformed during hydro-forming of prolate ellipsoidal shell, a prolate ellipsoidal shell with double generating lines is proposed to decrease the yield pressure. An experiment of hydro-forming of the prolate ellipsoidal shell with the axia length ratio λ=0.7 was carried out, and the internal pressure was discussed on the variation of axis lengths and shell volume. It is shown that the short axis and long axis are both slightly elongated, and the shell volume is slightly increased. When the internal pressure is 5.5MPa, the variation of long axis and short axis are 2.1% and 8.7%, the shell volume variation is 7.3%, and the maximum thinning is 12.7%.