Magnetic Medium-Assisted Inverse Bulge Pre-Forming and Deep Drawing Composite Forming Process for Improving Forming Performance of the Cylindrical Parts

Due to the poor plasticity of aluminum alloy at room temperature, it is dicult to form thin-walled and complex curved parts. This paper proposes a composite method of inverse bulge pre-forming deep drawing based on intelligent magnetorheological (MR) uid materials. Through the experiments and nite element modeling of cylindrical parts with drawing ratios of K 1 =2.125 and K 2 =2.25 were carried out under different forming conditions. The effect of soft mold medium on the drawing forming of cylindrical parts was studied. The research results show that the uniformity of the wall thickness of the parts is enhanced after using the soft mold medium. When the inverse bulge height is about 9mm and 5mm, the wall thickness variance of the cylindrical part is 0.0023 and 0.0025 pectively, which is reduced by 86.31% and 82.8% respectively. In the pre-forming stage, as the height of inverse bulge is increased, the maximum equivalent stress moves from the llet area of the blank holder to the outer surface of the highest point of the bulging area. Taking drawing ratio of K 1 =2.125 as an example, the circumferential compressive stress in the ange area decreases and is distributed unifomly under the back pressure and soft drawbeads, the radial stress gradient and equivalent stress gradient at the llet of die are reduced; For cylindrical parts with drawing ratios of K 1 =2.125 and K 2 =2.25, when the inverse bulge height is 9mm and 5mm, the forming effect of the part is the best.

In recent years, the uid pressure forming process has become one of the important forming technology methods for complex deep drawing parts [6]. Professor Yuan SJ et al. [7,8] proposed a new uid hydroforming process for the di culty of forming thin-walled curved parts, and established a theoretical model of uid pressure forming. The loading path was changed by using uid pressure for bulging in the early stage of deep drawing, and formed a 3m-level integral thin-walled curved surface component successfully. Liu W et al. [9] used the method of combining bulge pre-forming and hydroforming technology to study the stress distribution and deformation mechanism of the parts. The results showed that the pre-bulging process can change the stress state of the material and improve the uniformity of deformation. Li WD et al. [10] studied the in uence of changing the pre-forming parameters and process path on the deformation sequence of aluminum alloy tapered deep-drawn parts, and analyzed the results of numerical simulations to produce the tapered parts with uniform thickness distribution and high dimensional accuracy. Liu W et al. [11] studied the in uence of pre-bulging pressure and cavity pressure on the forming of parts in combination with numerical simulation and experiment. The study found that reducing the tangential compressive stress of the deformed material in unsupported wall region and increasing the contact area between the material and the punch can eliminate wrinkle defects effectively. Lang LH et al. [12] studied the in uence of the pre-forming effect on the forming of the box-shaped parts during the hydroforming process. The research results showed that too high and too low pre-bulging height are not conducive to forming, and too large pre-bulging pressure will cause obvious cracks and wrinkles in the punch part. Furthermore, the in uencing factors of the pre-forming effect in the hydroforming process of tapered parts are explored, they found that a reasonable initial inverse bulge height and pressure can make the wall thickness of the part uniform and effectively reduce the wall thickness reduction rate [13].Chen BG et al. [14] quantitatively described the in uence of the amount of pre-bulging on the hydraulic deep drawing of cylindrical parts through a combination of experiment and numerical simulation, and a certain amount of pre-bulging can increase the deformation and the hardness of the bottom of the cylindrical part.
MR uid is a new type of intelligent material, its rheological properties will change under the action of an external magnetic eld. The magnetic particles are regularly arranged along the direction of the magnetic eld to form a chain-like structure. With the increase of squeezing force, the chain of magnetic particles will break and reorganize continuously to form more stable stone clusters. Professor Merklein et al. [15] studied the application of MR uid in the eld of sheet metal forming for the rst time, and MR uid was used in the hydraulic deep drawing process as a sealing ring to increase the forming limit of the sheet.
Professor Wang ZJ [16,17] of Harbin Institute of Technology has conducted a series of researches on the forming process of MR uid soft mold. MR uid is used as a punch for bulging, which is different from other soft mold medium, MR uid has a magnetorheological effect and can change the stress state of the sheet metal in the deformation area by controlling the intensity of the external magnetic eld. Wang PY et al. [18] studied the mechanism of the in uence of variable magnetic eld conditions on the bulge forming performance of metal sheets, and the research indicated that under the external magnetic eld conditions, the forming properties of the sheet metal were signi cantly improved. Wen Tong et al. [19] used MR uid to form high-precision tubular parts. With the increase of the magnetic eld strength, the uniformity of the wall thickness distribution of the pipe parts increased, and the overall forming quality was signi cantly improved. Xu Peng [20] and others further studied the application of MR uid in the sheet deep drawing process. The study showed that under the conditions of MR uid assisted deep drawing, the forming performance of the part was signi cantly improved and the transitional thinning of the wall thickness at the corners of the punch is suppressed, which broadens the way for the application of magnetic medium in the eld of sheet metal forming. Therefore, this article uses MR uid as a exible forming medium in the deep drawing process of sheet metal. Under the action of an external magnetic eld, the in uence of the pre-forming process on the forming performance of the cylindrical part is studied by changing the height of the inverse bulge preforming, and inverse bulge deep drawing composite experiments were conducted under different pre-forming conditions. The experimental results are veri ed by nite element numerical simulation, and the mechanism of the in uence of MR uid inverse bulge pre-forming effect on the forming quality of cylindrical parts under different forming conditions is further analyzed.

Experimental Materials
The blank for the research is an Al5052 circular sheet with a thickness of 1mm, and the uniaxial tensile test experiment was nished by the electronic universal material testing machine. The tensile samples were taken at 0°, 45°, and 90° along the rolling direction of the plate, and the true stress-strain curves of the plates with different orientations were measured as shown in Fig. 1. Assuming that the true stressstrain curve of 5052 aluminum alloy conforms to the relationship , where is the strength factor and is the strain hardening exponent.Take the logarithm of both sides of the formula to get, and the strain hardening exponent of the material is obtained by tting the true stress-strain relationship curve of 5052 aluminum alloy. The mechanical properties of the Al5052 sheet are shown in Table 1. It can be seen that the stress-strain curves of the Al5052 sheet along the directions of 0°, 45°, and 90° are different. In order to reduce the error, we take the average value of the mechanical properties of the materials in each direction.  Fig. 2. The experimental device is mainly composed of a punch, a blank holder, a concave die, a back pressure unit and a magnetic eld control unit. The external magnetic eld is generated by a magnetic eld conrrol unit formed by a number of turns of a coil wound on the outside of the cavity mold. The power supply device, sliding rheostat and ammeter are connected in series, and the strength of the magnetic eld is controlled by the magnitude of the current.
This study will be divided into two groups, the diameters of the blanks selected for the experiment are 85mm and 90mm respectively. In each group of experiments, including conventional deep drawing forming, MR uid soft mold forming and MR uid inverse bulge deep drawing composite forming, and the height of inverse bulge pre-forming are 5mm, 7mm, 9mm, and 11mm respectively.
.  Figure 3 shows the process of using MR uid soft mold medium for inverse bulge deep drawing composite forming. This forming process is mainly completed in two stages, the inverse bulging preforming is carried out rstly, and then conducted the deep drawing nal forming. The whole forming process is conducted in a uniform magnetic eld with a magnetic eld strength of 0.1T. The MR uid will have a magnetorheological effect under the action of an external magnetic eld, and the magnetic particles are arranged in a chain structure along the direction of the magnetic eld. In the initial stage of forming, the back pressure unit moves upward to load, and the MR uid is regarded as a pressure transfer medium to transfer pressure under the action of back pressure to deform the sheet. When the height of the inverse bulge pre-forming reaches a predetermined height, the back pressure unit moves in the opposite direction to cooperate with the punch to load downwards. At this time, under the action of the bidirectional pressure of the punch and the magnetic medium, an aluminum alloy at-bottomed cylindrical part is nally formed after four stages of pressing down, attening, early drawing stage and nal drawing stage. During the forming process, the MR uid exible medium always acts on the surface of the sheet under the pressure of the back pressure unit, forcing the sheet to close to the punch for deformation, and the soft drawbead is formed at the gap between punch and blank holder in the process of sheet pressing.

Finite element simulation
As shown in Fig. 4, the nite element model of inverse bulge and deep drawing composite forming is established by using Dedorm-2D commercial software. Since the cylindrical part has axisymmetric geometric characteristics, and 1/2 axisymmetric part is selected for model establishment. The punch, blank holder, die and piston are set as rigid model, and the sheet and MR uid are rigid plastic model, and they are meshed. The sheet is divided into 750 elelments and the MR uid is divided into 5000 elements, and the boundary conditions are applied to the MR uid and the sheet along the X axis to limit the deformation. As shown in Fig. 1, the ow stress of the Al5052 sheet has been obtained in the tensile experiment. and the true stress-strain curve obtained from the experiment is applied to the establishment of the material model. The MR uid with a mass solid content of 56% was selected in the experiment, and the rheological stress parameters were set according to the constitutive model of the MR uid that has been studied in the literature [21]. The punch radius and the die radius is 5mm and 6mm respectivily, and the radius of the blank holder is 8mm. In order to improve the accuracy of the nite element simulation results about the in uence of the MR uid on the sheet deformation, the meshes of the MR uid plastic model was locally re ned. Table 2 shows the friction conditions between the sheet and the MR uid and the rigid mold. The loading speed of the back pressure unit along the Y-axis during the bulging process is 1mm/s, and the punch along the Y-axis downward loading speed is 0.5mm/s during the deep drawing process.

Wall thickness distribution
Under different forming conditions, the cylindrical parts with the drawing ratios are K 1 = 2.125 and K 2 = 2.25 respectively are shown in Fig. 5. After the experiment is completed, as shown in Fig. 6. measuring the wall thickness distribution of the two kinds of drawing ratios of cylindrical parts, and calculating the variation of the wall thickness. According to the distribution position of the measuring points, the cylindrical part can be divided into three deformation areas along the central axial section, are at the bottom deformation area I (points 1-4), the punch radius area II (points 5, 6) and the straight wall area (Points 7-13, 14) respectively. Figure 6a) b) show the wall thickness distribution of cylindrical parts with different drawing ratios under different forming conditions. We can nd that the wall thickness at the bottom of the cylinder and the measuring points near the punch corner area are thinned after deep drawing, where the wall thickness of the punch corner area thining seriously and the straight wall area (such as measuring points [10][11][12][13][14] thickening. As shown in Fig. 6, compared with the wall thickness distribution of conventional deep-drawn parts, the uniformity of the wall thickness distribution of the parts have improved after using the MR uid exible medium for forming, and the wall thickness thining trend near the bottom area and thickening trend near the punch corner area of the cylinder parts are both decreaseed. In the inverse bulge and deep drawing composite forming process, the MR uid acts as a force transmission medium to change the stress state of the sheet metal and suppress the occurrence of wrinkling defects effectively. With the increase of the inverse bulge height, the thinning of wall thickness decreases at the bottom and the punch corner area of the cylindrical parts. The thickening trend of the side wall of the cylindrical part is slowed down, and the distribution of the wall thickness is more uniform. However, when the pre-forming height is too high, the thickness of the bottom of the cylinder part becomes thinner because of the inverse bulge forming, where the material is enriched. The cylindrical wall was thicken and the wall thickness of the straight wall near the mouth of the cylindrical part is the most serious. Calculate the chang rate of wall thickness at each measuring point of the cylindrical part with different drawing ratios, as shown in Fig. 6c) d). It can be found that with the conventional drawing process conditions, the wall thickness of the punch llet area of the formed part is thinned seriously and the maximum thinning rate are 10.1% and 11.3% with the drawing ratio of K 1 = 2.125 and K 2 = 2.25 respectively, the wall thickness of the straight wall area is thicken robviously, and the maximum thickening rate are 24.1% and 21.2% respectively. Compared with conventional deep drawing conditions, the maximum wall thickness thining rate at the punch corner area of the cylindrical part formed with the MR uid soft medium has been reduced by 8.9% and 22.12% respectively, and the maximum wall thickness thickening rate of the cylinderical wall area is reduced by 11.6% and 12.7% respectively. The maximum wall thickness thining rate near the bottom center area (point 1) decreased by 36.4% and 27.7% respectively. The inverse bulge pre-forming process has a signi cant in uence on the wall thickness distribution of the formed part. With the increase of the inverse bulge height, the wall thickness increase rate and thinning rate at different measurement points are reduced, and the overall forming performance is improved. The inverse bulge pre-forming process has a signi cant in uence on the wall thickness distribution of the parts. With the increase of the inverse bulge height, the thickening and thinning rate of the wall thickness at different measurement points are reduced, and the overall forming performance of the cylinderical part has been improved. For cylindrical parts with drawing ratio K 1 = 2.125, when the inverse bulge height is 9mm, the maximum thining rate of the bottom wall thickness of the cylindrical part is 3.7%, and the maximum thining rate of the wall thickness at the punch corner area is 5.2%, and the maximum thickening rate at the straight wall area is 6.1%. For cylindrical parts with drawing ratio K 2 = 2.25, when the inverse bulge height is 5mm, the maximum wall thickness thining rate at the bottom area and the punch corner area of the cylinderical part is 2.9% and 9.1% respectively, and the maximum thickening rate at the straight wall area is 6%. Reasonable height of inverse bulge can suppress the phenomenon of wall thickness thining and thickening of the cylindrical part effectively. When the inverse bulge height is 11mm, the wall thickness of the bottom area of the cylindrical part with different drawing ratios are thinned extremely, extreme point appears near the punch corner area (point 7), where the thinning rates are 13.1% and 14.4% respectively. When the height of the inverse bulge preforming is lower, which is bene cial to the forming of the drawn part and the better the performance of the formed part.

Wall thickness change rate
As shown in Fig. 7, Comparing and analyzing the maximum change rate of wall thickness and the variance of the wall thickness of cylindrical parts with different drawing ratios. Figure 7a) shows the maximum thinning rate and thickening rate of the wall thickness of cylindrical parts under different forming conditions. The comparison of the wall thickness change rates of cylindrical parts with drawing ratios of K 1 = 2.125 and K 2 = 2.25 respectively, When the MR uid assisted deep drawing, the maximum wall thickness thining rates are 9.2% and 10.6% respectively. Compared with the conventional drawing conditions, which are reduced by 8.9% and 6.19% respectively. The maximum wall thickness thining values appear at measurement points 5 and 7 respectively. The maximum wall thicknesst thickening rates are 21.3% and 18.5% respectively, which are reduced by 11.6% and 12.7%, and the maximum wall thickness thickening values appear at the measurement points 13 and 14 respectively.It can be found that a reasonable amount of inverse bulge pre-forming will increase the maximum wall thickness thining rate of the cylindrical parts, and with the increase of the inverse bulge height, the maximum wall thickness thining rate will decrease. However, when the inverse bulge height is 11mm, the maximum wall thickness thining rate increases obvisouly. When the drawing ratio K 1 = 2.125, the maximum wall thickness thickening rate decreases with the increase of the inverse bulge height, and it will decreases to 6.1% as the inverse bulge height is 9mm. The maximum wall thickness thickening rate is the smallest, which is reduced to 6%, when the inverse bulge height is 5mm for the drawing ratio of the parts is K 2 = 2.25, and as the inverse bulge height increases, the maximum wall thickness thickening rate increases. Figure 7b) shows the mean value and variance of the wall thickness of the cylindrical parts with different drawing ratios under different forming conditions. The MR uid medium is used for deep drawing. After the MR uid is used for assisting deep drawing, the wall thickness variance of the cylindrical parts is compared with the conventional deep drawing, which are reduced by 40.8% and 37.2% respectively, and the uniformity of the wall thickness is improved. When the drawing ratio is 2.125, the mean value and variance value are continuously reduced with the increase of the inverse bulge height. When the inverse bulge height is 9mm, the variance value decreases by 86.31%, reduced to 0.0023. When the drawing ratio is 2.25, the wall thickness distribution is more uniform under the smaller inverse bulge pre-forming height, and the variance value is about 0.0025 as the inverse bulge height is 5mm, which is reduced by 82.8%. With the height of inverse bulge pre-forming increaseing, the variance value keeps increasing. When the inverse bulge height increases by 11mm, the wall thickness variance of the two kinds of drawing ratios of the cylindrical parts increases sharply and the uniformity of the wall thickness distribution is lower, that is the excessive inverse bulge height is not favorable to the deep drawing. When the drawing ratio is 2.125, the best pre-forming height is about 9mm. The best pre-forming height is constantly decreasing as the drawing ratio increase, this is because the large-diameter blank has a larger contact area with the ange area, which will increase the frictional force. And the inverse bulge deformation will reduce the thickness of the blank, resulting in the material is more di cult to ow. For cylindrical parts with a drawing ratio of 2.25, the best inverse bulge height is about 5mm.

Equivalent stress distribution after inverse bulge pre-forming
Under different forming processes, the equivalent stress distribution of the cylindrical parts with two drawing ratios after inverse bulge pre-forming is shown in Fig. 8. It is de ned that the side of the sheet material close to the blank holder is the outside, and the side close to the die is the inside. During the inverse bulge pre-forming process, the outside of the blank at the llet of the blank holder is stretched, and the inner side of the bulging center area of the sheet is compressed, and the outer side is stretched. As shown in Fig. 8a) and Fig. 8b), when the inverse bulge height is 7mm, the material in the bulging deformation area becames yield almost at the same time. Under the combined action of the MR uid and the blank holder, plastic deformation has occurred around the llet area of the blank holder. The maximum equivalent stress value exists on the inside of the sheet, and the minimum value appears on the inside of the transition area between the llet area and the free bulging forming area. The equivalent stress has a stress gradient along the thickness direction in the deformation area. As the height of the inverse bulge increases, the plastic deformation area of the rounded corner area expands continuously and the stress gradient along the thickness direction increases, the deformation begins to move to the center of the bulging forming area. When the inverse bulge height is 11mm, the maximum equivalent stress exists on the outer surface of the highest point of the bulging area. The circumferential stress and radial stress of the bulging center area are basically equal, which is obvious two-way tensile stress state, and the wall thickness is severely thinned. As shown in Fig. 8c), the maximum equivalent stress of cylindrical parts with different drawing ratios in the pre-forming stage increases with the height of the inverse bulge increase, and the difference value of the maximum equivalent stress decreases rstly and then increases. When the height of the inverse bulge pre-forming is the same, the cylindrical parts with a drawing ratio of 2.125 enters the deformation state earlier than the drawing ratio of 2.25, the plasic deformation area is larger and the inverse bulge effect is more obvious.

Stress analysis of deep drawing
The cylindrical part during deep drawing forming is shown in Fig. 9. We divide the cylindrical part into ve parts: ange area, die corner area, straight wall area, bottom corner area and bottom area, and the side close to the punch is the inner side of the cylinderical wall, and the side close to the die is the outer side of the cylinderical wall. Under the action of an external magnetic eld, the aluminum alloy after inverse bulge pre-forming is deep-drawn forming with soft die using MR uid medium, and analyzed the stress and strain state of cylindrical parts under different forming processes.
Since the inverse bulge pre-forming process has a signi cant effect on the drawing performance and stress state of the cylindrical part, we take measuring points along the outer area of the wall in order to further study the in uence of the inverse bulge pre-forming effect on the deep drawing process. In the early stage of the deep drawing forming, the inverse bulge area appears obvious and the sheet at the corner of the die forms a soft drawbead. As the drawing displacement increases, the inverse bulge pre-forming area is reduced gradually. When the drawing displacement is about 12mm, the inverse bulge deformation area basically disappears. And the sheet is drawn into the die with the increase of the drawing displacement. Figure 10a) shows the maximum radial stress of the cylindrical parts under different forming conditions at the early stage of deep drawing (the displacement of the punch is 12mm). During the deep drawing process, the deformation of the plate at the ange llet is the most severe, and stress concentration occurs in the inner area of the sheet at the transition between the die corner and the ange area, where the maximum radial tensile stress occurs. Meanwhile, the wrinkling defect here is the most di cult to overcome, and the tendency of wrinkling at the llet can be suppressed by improving the uidity of the material in the ange area. In the case of using the MR uid as the soft mold medium for forming, the maximum tensile stress values of the cylindrical parts with drawing ratios of 2.125 and 2.25 are smaller than that under conventional drawing conditions. At the early stage of deep drawing forming, the radial tensile stress value of the sheet in the ange decreases and the absolute value of the radial compressive stress increases under the action of back pressure, which is bene cial for the material to ow into the cavity of the die. Therefore, the tendency of wrinkling defects and lug phenomenon is suppressed effectively, and the surface quality of the side wall is better. When the inverse bulge height is 5mm, the amount of material deformation in the llet area is small and the effect of the soft drawbead is weaker, the maximum radial tensile stress value decreases and the compressive stress value increases. The soft drawbead has a signi cant effect after pre-forming with the increase of the deformation height. and the friction drag and resistance to deformation increaseing accordingly after the material at the die corner area has strain strengthening after the bending and anti-bending deformation processes.
When the drawing displacement is the same, the pre-forming effect has a similar in uence on the material deformation of the ange area of the cylindrical part with different drawing ratios. Therefore, the stress state of the sheet material in the ange area of the cylindrical part with a drawing ratio of K 1 = 2.125 is analyzed. In the entire inverse bulge and deep drawing forming process, the deformation of the materials in each area of the cylindrical part affects each other. The uidity of the sheet matel in the ange area is very critical to the quality of the nal formed part. The ow resistance of the material can be adjusted to control its uniformity of deformation.
In the early stage of deep drawing process, the circumferential stress distribution of the sheet metal in the ange area under different forming conditions is shown in Fig. 10 (b). It can be seen that the material in the ange area is subjected to circumferential compressive stress, and the sheet material is easy to lose stability and wrinkle. In the initial stage of the conventional deep drawing forming, the circumferential compressive stress in the ange area is relatively large. With the assistance of the magnetic mediam, the back pressure can be transmitted through the magnetic particles, so that the sheet metal is close to the surface of the punch, and the friction resistance is increased. The circumferential compressive stress value near the corner of the die increases. At the same time, the MR uid has a lubricating effect, which reduces the friction between the sheet material and the surface of the die, increases the uidity of the sheet material, and effectively reduces the circumferential compressive stress in the ange area.
However, the circumferential stress distribution of the sheet metal in the ange area is extremely uneven, and wrinkling defects are obvious during these two forming processes. After inverse pre-forming, a soft drawing bead is formed near the corner of the die, which increases the ow resistance of the sheet in the ange area and the amount of circumferential deformation, and reduces the value of compressive stress.
And with the increase of the inverse bulge height, the surface area of the sheet material used for the bottom forming of the cylindrical member gradually expands, and the suspended area increases accordingly, as shown in Fig. 11. The area of the suspended area under different forming processes is A, B, C and D, that is, A < B < C < D, the area of the soft draw bead is enlarged during the deep drawing process, and the plastic deformation ability of the sheet metal is improved. When the inverse bulge height is 5mm, the radial tensile stress near the corner of the die increases, and the circumferential compressive stress decreases. As the height of inverse height increases, the value of the circumferential compressive stress at the corner of the die increases, the distribution of compressive stress in the ange area is gradually uniform. When the inverse bulge height is about 9mm, the distribution of the compressive stress in the ange area is the most uniform, and the formation of the soft draw bead increases the area of the sheet metal against the punch and improves the forming performance of the cylindrical part. When the inverse bulge height is 11mm, the circumferential compressive stress value is too larget to cause wrinkling.
In the early stage of deep drawing, there is bending of the sheet at the corners of the die-reverse bending is caused by the effect of pre-forming deformation, and the inner and outer sides of the sheet are plastically deformed, and the stress has a stress gradient along the thickness. Analyzing the cylindrical parts with a drawing ratio of K1 = 2.125, as shown in Fig. 12, study the radial stress and equivalent stress distribution along the thickness direction at the llet of the deep part die under different inverse bulge forming conditions. The inner side of the cylinder wall is the radial tensile stress and the outer side is the radial compressive stress, and there is a stress gradient along the thickness direction, the greater the radial tensile stress is, the more likely the fracture occurs. In the conventional deep drawing process, the maximum radial tensile stress at the llet is 188Mpa, the maximum compressive stress is 48.2Mpa, and the stress gradient is 236.2Mpa, where the equivalent stress gradient is large, and the plastic deformation at the llet is obvious. In the process of MR uid soft die forming, the deformation at the corner of the die is small under the back pressure of the magnetic medium. At this time, the radial tensile stress and compressive stress are smaller, the radial stress gradient and equivalent strain gradient decrease. After the inverse bulge and deep drawing composite forming, due to the effect of soft drawbead in the early stage of deep drawing, the outer tensile stress and inner compressive stress decrease and the radial stress gradient decreases when the reverse bulging height is small. As the amount of pre-deformation increases, the tensile stress value at the outside of the sheet increases, and the compressive stress value at the inside decreases. When the inverse bulge height is about 9mm, the outside tensile stress is 187Mpa, and the inside compressive stress is 1.6Mpa, the stress gradient is 188.6Mpa. The stress neutral layer has moved, the radial compressive stress on the inner side turns into tensile stress. The equivalent stress gradient is the smallest and the material is easy to ow under tensile stress. When the inverse bulge height is 11mm, the tensile stress decreases along the thickness direction continuously, and the inner side of the sheet changes from compressive stress to tensile stress, and the stress gradient decreases. However, the bottom of the cylinder becomes in a cone after deep drawing due to the excessive pre-deformation and insu cient back pressure, and the forming effect is not good.

Conclusion
1. This paper proposed a composite forming process of inverse bulge pre-forming and deep drawing of cylindrical parts. The smart material of MR uid is used to transfer pressure under the external magnetic eld. In the pre-forming stage, the MR uid is used as the punch to bulge, and in the nal forming stage, the MR uid is used as the back pressure unit to form the deep drawing parts. When the inverse bulge height is about 9mm and 5mm, the forming quality of the cylindrical parts with the two drawing ratios is the best, while the inverse bulge height is too high or too low, the wrinkle defect cannot be suppressed effectively.
2. For the two kinds of drawing ratios of cylindrical parts, we completed respectively the experiments under different forming conditions. The results of the research show that the variance of the wall thickness of the formed part is reduced by 40.8% and 37.2%, respectively as using MR uid soft mold media for deep drawing. Reasonable pre-bulging height is conducive to improving the uniformity of wall thickness distribution. When the inverse bulge height is 9mm and 5mm, the wall thickness variance of the two drawing ratios of cylindrical parts is the smallest, which is 0.0023 and 0.0025 respectively.

3.
A nite element analysis model was established to analyze the equivalent stress distribution in the pre-forming stage under different forming conditions. the sheet near the llet area of the blank holder occurs plastic deformation rstly, and the maximum equivalent stress increases with the increase of the inverse bulge height, and the plastic deformation area increases signi cantly in the meanwhile.
When the inverse bulge height is 11mm, the maximum equivalent stress is on the outer surface of the highest of the bulging area. When the pre-forming height is the same, the smaller of the drawing ratio is, the pre-forming effect is more obvious.
4. The pre-forming effect will affect the distribution of sheet stress signi cantly. Take a part with a drawing ratio of K 1 = 2.125 as an example, the maximum radial stress in the ange area increases with the increase of the pre-forming height under the action of back pressure and soft drawbeads at the initial stage of deep drawing, while the compressive stress is reduced. The radial stress gradient and the equivalent stress gradient at the corners of the die are reduced. With the increase of the preforming height, the distribution of the circumferential is uniform. When the inverse bulge height is about 9mm, the stress gradient is small, and the larger radial tensile stress and circumferential compressive stress can suppress the wrinkle.

Declarations
Ethical Approval The development of exible media forming technology can improve the forming precision and the surface quality of the parts and provide the possibility for the processing and forming of thin-walled and complex-shaped parts. The true stress-strain curves of materials with different rolling directions