【正文】 ess in the expanding area is about , which shows MPa is the upper limitation of internal pressure for this tube forming. It proves that the wrinkle quantities decrease following the increase of internal pressure in the preforming stage. Before calibration, it cannot be determined which parameters are available.. In the calibration stageFollowing the first stage, the preforming stage, es the next stage, the calibration stage. The final results are illustrated as in Fig. 10. Following different internal pressures and punch strokes in the preforming stage, the different shapes of wave can be obtained. In the calibration stage, the internal pressure increases at the very high pressure of 40 MPa to flatten the wrinkles inherited from the preforming stage and the punch stroke is fixed.When the internal pressure is MPa in the preforming stage, in the calibration stage, heavy wrinkling is formed when the punch strokes are 15 and 20mm. At the same time, in the expanding zone of the formed tube, the wall thickness is very small and the maximum value is only mm, which predicts that the tube will fracture possibly at this position in an experiment. From Fig. 10(a)–(c), it can be concluded directly that the punch stroke of 20mm is too large for the forming of this tube, which can also be concluded from (d) and (e) because they show that the wrinkles still exist even after the calibration stage. In Fig. 10, it is also proven that the internal pressures of and MPa are not suitable in the forming of the tube and the punch stroke of 20 mm is too large. Here, the concepts of useful wrinkles and harmful wrinkles can be drawn out depending on whether the wrinkles formed in the preforming stage can be flattened in the calibration stage. If the wrinkles formed in the preforming stage can be flattened and no fracture occurs in the calibration stage, the wrinkles are called useful wrinkles, and contrarily, they are called harmful wrinkles.. Wall thickness distributionsThe wall thickness distributions of the formed tubes are shown in Fig. 11. In this figure, the final results are shown only when the internal pressures in the preforming stage are , , and MPa because it is impossible to obtain successful parts depending on the prescribed above when the internal pressures in the preforming stage are and MPa.Based on the wall thickness distribution, the formed part can be divided into three zones: Zone 1 is the tube end area, Zone 2 is the transferring area and Zone 3 is the main expanding area, which is shown clearly in Fig. 11(c). It proves that in the preforming stage, when punch stroke is set at 10 mm, the average wall thickness is larger and more uniform than when the punch stroke is set at 15 mm. On the contrary, after the calibration stage, the average wall thickness when the punch stroke is set at 10 mm is smaller than when the punch stroke is 15 mm. In Zone 3, the differences of the average wall thickness between the preforming stage and the calibration stage decrease when the internal pressures increase, which is shown in Fig. 12. As shown in Fig. 11, wave crest and wave trough also exist in the distributions of the tube wall thickness. It can be found that following the increase of internal pressure in the preforming stage, the distance between wave crest and wave trough bees smaller and smaller, which is also shown in Fig. 13.Fig. 13(a) shows that when punch strokes are 10 and 15 mm, respectively, following the increases of internal pressure in the preform stage, both values in wave crest and wave trough decrease and bee more similar. And Fig. 13(b) shows that following the increases of internal pressure, thedifferences between the wave crest and the wave trough bee smaller, which means the wall thickness distribution will be more uniform. If the difference between the wave crest and the wave trough is too large, small wrinkles will be formed possibly on the tube blank surface, which can beproved in experiment.Fig. 11 shows that if the internal pressure is higher, the wall thickness in the Zone 1 is thicker. And at the same time, following the increase of punch stroke, the wall thickness in Zone 1 also gets thicker. This is mainly because the frictional force between the blank and the die bees higher by the increases of internal pressure and the punch stroke.In Fig. 11, the wall thickness distribution looks like a wave, which leads to the effects of bending and unbending during forming. Fig. 14 shows the stress distributions in the preform stage and the calibration stage. In the preforming stage (at the time of s), pression stress appears in the outside of the wave trough and tensile stress inside the wave trough. On the contrary, different stress conditions appear in the wave crest. There is a big difference between the maximum tensile stress (152 MPa) and the maximum pression stress (230 MPa). In the calibration stage (at the time of s), it shows the totally different stress distribution at the same position as the time of s. Because of the large pression stress at s, the amount of spring back can be very large, which proves it is very important to control the surface quality in this process.. DiscussionsFrom the prescribed above, for the purpose of forming a tube with large expanding area, it is very important to get a suitable wave shape firstly in the preform stage. In the preforming stage, the method to control the preforming wave shape is mainly depending on the selection of suitablepunch stroke and internal pressure. Based on different parameters, different results can be obtained. For the forming of this variablediameter tube union, according to the above discussion, the optimal process window is shown in Fig. 15. And the most possible area is when the punch stroke is between 10 and 15mm and the internal pressure is between and MPa. To obtain a part with more uniform wall thickness, an internal pressure between and MPa is preferred.