Pre-bulging hydromechanical deep-drawing forming performance of a hydraulic punch for stepped parts

Pre-bulging hydromechanical deep-drawing forming performance of a hydraulic punch for stepped parts | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Pre-bulging hydromechanical deep-drawing forming performance of a hydraulic punch for stepped parts Chenchen Dong, Jianping Ma, Haimei Han, Wenze Zhang, Fei Liu, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5345272/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract With the development of lightweight materials in various fields, there is a need to research and improve the application of aluminum alloys in sheet metal forming, including body covering parts and complex curved aircraft skins. Specifically, the forming quality and formability of complex stepped parts, such as automobile motor shells and oil bottom boxes, should be improved. Therefore, this study is based on the principle of pre-bulging hydromechanical deep-drawing (PHDD), conducting a forming study of 1060-O aluminum plate with stepped parts. First, based on the analysis of stepped parts, a forming device consisting of a hydraulic punch and rigid die is designed, and a PHDD test platform is built to conduct experiments. Second, the effects of pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of stepped parts are analyzed. Finally, to obtain parts with good formability under an optimal parameter combination, a four-factor and four-level orthogonal test is designed, and simulation analysis is conducted using DYNAFORM software. The results show that the wall thickness distribution of the stepped parts is more uniform under the PHDD process, and the movable die designed by the forming device can effectively improve the forming height of stepped parts, reaching 28.9 mm. This study has engineering applications for improving the formability and forming quality of stepped parts. Stepped parts Hydromechanical deep-drawing Pre-bulging Wall thickness distribution Formability Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Introduction Pre-bulging hydromechanical deep-drawing (PHDD) combines hydromechanical deep-drawing (HDD) and plate pre-bulging. HDD is a novel sheet metal forming method that combines hydraulic forming technology and ordinary stamping forming. HDD uses a liquid medium rather than a rigid mold and relies on liquid pressure to make the parts required for sheet metal forming. Compared with traditional die drawing [ 1 , 2 ], HDD has the advantages of good forming quality, low manufacturing cost, and high dimensional accuracy [ 3 , 4 ]. However, for some large thin-walled complex parts, the use of HDD is prone to problems such as insufficient and uneven deformation of sheet metal parts. Therefore, aircraft echelon thin-wall parts, automotive motor shells, and oil pans in HDD are prone to problems such as uneven wall thickness distribution and insufficient deformation. New technologies have been developed in sheet metal hydroforming technology, such as PHDD (Forward-, inverse-, and local-bulging), hydrodynamic deep-drawing with independent radical hydraulic pressure, forward and reverse pressurized hydrodynamic deep-drawing, and twin-plate pair hydroforming [ 5 , 6 ]. PHDD is a novel process developed on the basis of hydraulic drawing of sheet metal. The forming principle of PHDD is firstly under the initial pressure of the liquid medium, before the sheet forms a transition shape under the constraints of the mold, and HDD is applied, as shown in Fig. 1 . Compared with HDD, in the PHDD process, the forming parts have better moldability, a more uniform wall thickness distribution, and higher precision and stiffness [ 7 – 9 ]. With the development of lightweight materials in various fields, such as automobiles and aerospace, sheet metal forming is also developing in the direction of large deep-cavity thin-wall parts, complex curved parts, and deformation resistant materials. The use of aluminum alloys to form complex parts has been favored in these fields [ 10 – 12 ] as they provide effective lightweight materials, especially for body covering parts and large and complex curved aircraft skins. Larsen [ 13 ] found that using HDD could improve the formability of a motor hood by implementing pre-bulging forming and then HDD. Chen et al. [ 14 ] produced a new high-capacity engine oil sump, shown in Fig. 2 (a), by developing a hybrid sheet hydroforming process using a two-stage HDD process to obtain a stepped shell assembly. Kim et al. [ 15 ] proposed a multi-stage hydroforming process, shown in Fig. 2 (b), finding that it improved the formability of components with similar oil pan shapes and could effectively manufacture sheet metal parts with multi-step components. Zhang et al. [ 16 ] selected 0.3 mm thick H68 material, designed each drawing process through theoretical analysis, used finite element software to carry out each drawing process, and finally obtained a stepped cylinder with good formability through test verification, as shown in Fig. 2 (c). Ren et al. [ 17 ] used PAMSTAMP finite element software to analyze and calculate the three-time deep-drawing forming process, determined the appropriate blank holder clearance, designed three pairs of deep-drawing dies, inverted forming on the hydraulic press, and finally obtained second-order cylindrical parts with good forming quality, as shown in Fig. 2 (d). Lang et al. [ 18 ] evaluated the influence of the pre-bulging height and pressure on the hydromechanical forming process, optimized the pressure loading path, and finally obtained flat-bottom irregular box parts with high forming quality. Wang [ 19 ] used finite element software to analyze the deformation law of stepped sidewall box forming, designed an orthogonal test, and concluded that h > H > B > b > r > R, as shown in Fig. 2 (e). The aim of this study is to improve the formation of stepped parts by reducing the cracks at the top and transition corner, as well as the wrinkles at the flange. Therefore, a hydraulic punch drawing and forming device is developed using a microcomputer-controlled universal tensile testing machine (WDW-100GD). The forming effect of the device is verified using the step pre-bulging forming method, and a hydraulic drawing test of stepped parts is conducted by adjusting the position of the movable die freely with different plate heights. Experimental research is conducted on the test platform to analyze the influence of the pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of the parts. Furthermore, the deformation and forming laws of the stepped parts during hydraulic punch deep-drawing forming are revealed. To obtain parts with good filling and moldability, an optimal parameter combination is obtained by orthogonal test simulation and analysis. The test results show that the forming height and quality of the parts can be improved effectively by combining the designed movable die with a guiding flange cylinder. The proposed step pre-bulging forming method increases the formability of stepped parts. Experimental and simulation conditions Part process analysis The hydraulic punch drawing technology principle was used to obtain stepped parts with a high forming quality and formability. The designed stepped parts forming device, shown in Fig. 3 , was adjusted arbitrarily for each step height. The specific height of each step in mm was determined from bottom to top. The distance between the bottom surface of the ladder and the upper surface of the first step was the height of the first step, the distance between the top surface of the first step and the top surface of the ladder was the height of the second step, and the total height of the ladder was the lower surface of the ladder and the top surface of the ladder. To obtain stepped parts with high formability, this study used a 1060-O aluminum plate with a 0.8 mm thickness to conduct the relevant tests. Compared with other grades of aluminum alloy, 1060-O aluminum has good plasticity and strong corrosion resistance [ 20 ]. To improve the plasticity of the plate, the annealing process involved the furnace being heated to 400 ℃ with a holding time of 1 hour before the furnace was cooled to 300 ℃, and then air-cooled. Real stress-strain curves of 1060-O aluminum were fitted using unidirectional tensile tests and the Hollomon parameter. Values of k and n were obtained, with a relation of Principle of part forming The forming principle of the device is shown in Fig. 4 , which includes three stages: before forming, pre-bulging forming, and hydro-drawing. The position of the movable die was adjusted using plates of different heights, and the ideal stepped part was obtained by the joint constraint of the guide blank holder and the movable die. This study used the soft punch bulging method, where liquid replaced the punch and sheet metal was formed under the action of liquid pressure and the constraint of the movable die. First, the pre-bulging fluid pressure was applied in the hydraulic cavity, the plate bulged and produced a pre-deformation, and the plate material was drawn into a transition shape. Second, the forming pressure fluid was increased, and the transition shape was formed into a stepped part by the joint constraints of the movable die and the guide blank holder. The sub-plate was divided into two heights: one plate controlled the pre-bulging (pre-bulging plate) as shown in Fig. 4 (b), and the other plate controlled the forming (forming plate) as shown in Fig. 4 (c). Test device and platform To achieve various characteristics of stepped parts, such as a large gap in each size, high precision requirements, and a small transition fillet, this study designed the principle of PHDD forming of stepped parts. A pair of PHDD forming devices was developed, and a test platform was constructed. The designed platform could not only adjust the height of pre-bulging but also realize the whole hydraulic loading curve in the process of pre-bulging and forming. Test device Based on the principle of PHDD and the process analysis of stepped parts, this study developed a stepped part hydraulic punch drawing forming device, as shown in Fig. 5 . Its structure was mainly composed of a liquid-filled base, guide blank holder, movable die, work jack, sub-plate, clamp plate, sealing element, and fixing element. The device had a clearance fit between the work jack and the movable die and between the movable die and the guide blank holder to meet the positioning and guiding requirements. The holding force of the guide blank holder was controlled by adjusting the torque force of the screw with a torsional torque wrench. For the geometrical dimensions of the working parts of the device, the radius of each corner of the movable die and the radius of the transition corner at the bottom of the inner wall of the guide blank holder were both 6 mm. The liquid-filled base was provided with a hydraulic chamber and a connected liquid inlet hole to better connect with the hydraulic oil pipe. The liquid inlet port was milled flat, and a sealing groove was opened on the upper surface of the liquid-filled base for placing a sealing ring, which prevented leakage of the liquid in the hydraulic chamber. The guide blank holder, movable die, work jack, and sub-plate were coaxial. The order of the parts from outside to inside was: guide blank holder, movable die, and work jack. The bottom of the guide blank holder was detachably mounted on the liquid-filled base, the tops of the movable die and the work jack were detachably mounted on the clamp plate, and the sub-plate was set between the top of the guide blank holder and clamp plate. The bottom of the movable die and the work jack were fitted with the guide blank holder to form a die cavity with the shape of the part to be formed. The plate was placed between the guide blank holder and the liquid-filled base [ 21 ]. Test platform Based on the developed test device, a plate hydraulic punch drawing forming test platform was constructed, as shown in Fig. 6 . The test platform was composed of a WDW-100GD machine, micro-hydraulic station, data acquisition system, and forming device. The axial travel of the device was controlled by the WDW-100GD machine during the test, and the axial displacement was collected. Through the relief valve connected to the micro-hydraulic station, the liquid pressure was controlled to realize a constant pressure. The data acquisition system intuitively observed the loading of the liquid pressure in the process of sheet metal forming and obtained the curve of the liquid pressure change. The test was conducted on a WDW-100GD machine, and the test process consisted of two parts: pre-forming and final forming. To overcome the difficulty in forming stepped parts, a hydraulic loading path of pre-bulging and then drawing was adopted, in which the loading curve of the liquid chamber pressure was applied to the pre-bulging pressure loading curve. The liquid pressure loading curve with time is shown in Fig. 6 and was divided into pre-forming and final forming. The loading process involved repeated cycles of pressurization and pressure maintenance. In Fig. 6 , P a represents the pre-bulging pressure and P b represents the liquid chamber pressure [ 22 ]. Simulation modeling To achieve various characteristics of stepped parts, including a large size difference, small transition fillet, and high dimensional accuracy, a PHDD forming scheme was designed. Considering the incomplete filling of the tops of the parts obtained from the tests, orthogonal experimental simulation analysis was used to obtain an optimal parameter combination and stepped parts with good filling and moldability. UG software was used to establish the model, which was saved as an .igs format file and then imported into the DYNAFORM finite element simulation software. To reduce the solution calculation time, only half of the finite element model was selected for simulation, as shown in Fig. 7 . Based on the design of the hydraulic punch drawing principle of stepped parts, a liquid medium was used rather than the punch. Furthermore, Die 1, Die 2, Binder 1, and Binder 2 comprised the rigid body. The No. 36 three-parameter Barlat plasticity elastic-plastic plate material model was selected, and the Belytschko-Tsay shell plate element was used, with a self-applicable mesh used to divide blanks. The gap between the binder and plate was 1.1 t, or 0.88 mm. To obtain more accurate simulation results, the mesh was divided into rounded corners with a fine mesh size of 0.5 × 0.5 mm, and the remainder of the mesh had a size of 1 × 1 mm. According to the designed forming device and principle, the drawing mode of the simulation model was an inverted die form, as single action reverse drawing. To observe and analyze the formability of the two processes more directly, the working mode was divided into two working steps in the finite element software, and each working step consisted of two working steps: closing and deep-drawing. During the entire forming process, the die was stationary, and the binder moved in the + Z (vertical) direction at a certain speed. When the gap between the die and binder was 0.88 mm, the closing process was complete. Next, according to the setting of the hydraulic loading curve and the pressure value exerted by the binder on the plate, the purpose of hydraulic deep-drawing was achieved. Finally, the pre-forming and final forming of the plate were controlled by the constraint of the die. Experimental details The pre-bulging pressure and height are the main influencing factors for the pre-forming of stepped parts during plate pre-bulging forming. Pre-bulging pressure was applied before HDD so that the plate had a pre-deformation effect, which reduced the anisotropy of the plate deformation at a later stage. This also effectively prevented the wrinkling of the plate, reduced the stress concentration generated at the rounded corners of the concave die, prevented cracking, and supported the formation of parts. By controlling the pre-bulging height of the sheet, it was formed into a reasonable transition shape, and the formability was improved. Reasonable control of the pre-bulging pressure and height of the plate effectively controlled the generation of the failure of the formed part and improved the formability of the plate. Control of pre-bulging height A pre-bulging height that is too high can lead to cracking at the top of the stepped part as well as cracking and creasing at the transition corner of the stepped part. A pre-bulging height that is too low can lead to poor pre-forming of the stepped part, resulting in poor moldability of the final parts. Reasonable control of the pre-bulging pressure can effectively control the generation of failure and improve the formability of the sheet. The hydraulic punch deep-drawing forming device for stepped parts controls the position of the movable die using a sub-plate of different heights, thus adjusting the pre-bulging height of the stepped parts to achieve pre-forming. A physical drawing of the movable die test device is shown in Fig. 8 . In Fig. 8 (a), firstly, the top work jack was connected to the movable die by a specification M6 screw. The movable die was not designed as a whole, but the internal clearance of the movable die was matched with the work jack so that the plate was formed during the forming process through the die constraint. At the end of the final forming, the plate was close to the die, and the parts could not be easily disassembled without wrinkling; therefore, the part was removed using the work jack. Finally, the movable die was connected using a clamp plate through three M6 socket head cap screws. In this way, the movable die, clamp plate, and work jack were assembled to achieve the integrated design, which was not only convenient for disassembly but also ensured pre-forming and final forming processes, thus achieving a good forming effect. The forming height of the stepped part was controlled and was low when hydraulic drawing was conducted in the initial state. Therefore, pre-forming of the part was controlled by combining the sub-plate with the movable die of different heights. As shown in Fig. 8 (b), the part was formed under the joint constraints of guide blank holder, work jack, and movable die to improve the height of each step of the part. Control of pre-bulging pressure The pre-bulging pressure refers to the force exerted on the sheet by the liquid in the sealed state before the force applied to the metal blank by the movable die. Before the hydromechanical deep-drawing action began, pressure was applied to the liquid sealed inside the hydraulic chamber so that the sheet material was pressed against the die under the pressure of the liquid. To ensure that the liquid pressure in the pre-bulging and forming processes was loaded and maintained, a test platform was constructed to control the pre-bulging pressure. The micro-hydraulic station and the WDW-100GD machine were combined to control the pre-bulging pressure. To control the pre-bulging pressure, the test device was sealed, and the liquid pressure was controlled through the relief valve in the micro-hydraulic station, as shown in Fig. 9 . The plate was placed on the upper surface of the liquid-filled base. To prevent liquid overflow, a sealing ring was arranged between the guide blank holder and the liquid-filled base. A fluorine rubber O-ring was used as the sealing ring, with a compression rate of 25%. Therefore, a sealing groove was designed on the upper surface of the liquid-filled base in the developed device, with a depth of < 1.5 mm of the diameter of the sealing ring to ensure that it was subjected to pre-pressure before the test. The filling hole of the liquid-filled base was provided with an O-ring seal. The process of pressing and holding pressure was realized through the micro-hydraulic station. Under the action of pre-bulging pressure, the plate material was formed into a transition shape, and the free hanging area between the part and the die was reduced, thus improving the forming quality of the part. Results and discussion Failure of stepped parts after PHDD The failure of the specimen before the hydraulic drawing process of stepped parts is the main issue preventing stepped parts from forming [ 23 ]. Therefore, it is of great significance to analyze the failures and causes during hydraulic deep-drawing to improve the formability of stepped parts. To improve the forming quality of the parts, the causes of failure were analyzed, and corresponding solutions are proposed [ 24 , 25 ]. The influences of pre-bulging parameters and the blank holder force on the failure forms of the parts were analyzed. It was found that when the pre-bulging pressure was 2 and 3 MPa, the top and rounded corners of the stepped parts experienced large cracks, as shown in Fig. 9 (f). When the pre-bulging pressure was 4 MPa, the top of the first step cracked, as shown in Fig. 9 (c). When the pre-bulging pressure was 3 MPa and the pre-bulging height was 6 and 8 mm, only small cracks appeared on the top of the part. When the pre-bulging height was 10 mm, there was a large crack at the top. When the blank holder force was 1 kN, the flange of the part was seriously wrinkled, and when the blank holder force was 3 kN, the top of the part cracked. Therefore, when the blank holder force was 2 kN, the flange of the part only wrinkled slightly at the screw connection, which provided a reference for subsequent tests. From Figs. 9 (d) and 9(e), the main failures of the parts were cracking and wrinkling, including cracking at the top of the part, the transition corner, and the top of the first step, and wrinkling at the flange and the top fold. Effects of pre-bulging parameters on the forming height of stepped parts The forming height is an important index to measure the formability of parts. The forming height of the parts can be effectively improved by using the hydraulic drawing principle. In the entire forming stage, pre-bulging forming is crucial, especially for complex and stepped parts, because pre-bulging ensures that the plate in the early hanging area does not cause defects due to instability. Therefore, to obtain the influence of the forming principle on the formability of the part, the influence of the pre-bulging parameters on the forming height of the part was analyzed. Through research tests, it was found that the bursting pressure of the parts was 5 MPa. Therefore, to reasonably match the pre-bulging height and pressure, three pre-bulging pressures of 2, 3, and 4 MPa were selected. Under the condition that other parameters were consistent, the influence of the pre-bulging pressure on the forming height of parts was analyzed by using different pre-bulging pressures. The test results show that when the pre-bulging height was constant, the forming height of the parts with a pre-bulging pressure of 3 MPa was greater than that at 2 MPa. However, when the pre-bulging pressure was 4 MPa, the forming height of the part was lower than that at 3 MPa. This occurred because when the pre-bulging pressure was too large, the top of the pre-forming process of the part experienced excessive thinning. Furthermore, in the final forming process, the part cracked in advance, reducing the forming height. For the designed movable die with an internal depth of 14.45 mm, three pre-bulging heights of 6, 8, and 10 mm were selected. Under the condition that other parameters were constant, the influence of the pre-bulging height on the forming height of the parts was analyzed using different pre-bulging heights. The test results show that when the pre-bulging pressure was constant, the forming height of the part was higher than that for pre-bulging heights of 8 and 6 mm but lower than that for a pre-bulging height of 10 mm. This was because when the pre-bulging height was too large, the hanging area of the pre-forming process of the parts was large, and the top experienced excessive thinning. Furthermore, in the final forming process, the part cracked in advance, reducing the forming height. Based on the above test analysis, it was found that under the parameter combination of a pre-bulging pressure of 3 MPa and a pre-bulging height of 6 mm, the forming height of the part with good formability and no defects reached 28.9 mm. Effects of pre-bulging parameters on wall thickness distribution of stepped parts The wall thickness distribution is an important indicator for measuring the formability of the part, where the larger the minimum wall thickness, the smaller the maximum thinning rate, and the better the uniformity of the wall thickness distribution, according to the trend of the wall thickness distribution and the specific value in the weak points of the part [ 26 – 29 ]. In the process of PHDD, the pre-bulging parameter is the main influencing factor in the forming process of the parts. Therefore, analyzing its influence law on the forming process of the parts has an important role in its improvement. Figure 10 shows the wall thickness distribution of parts under different pre-bulging pressures when the pre-bulging height was 6, 8, and 10 mm, respectively. Figure 11 illustrates the wall thickness distribution of parts at different pre-bulging heights when the pre-bulging pressure was 2, 3, and 4 MPa, respectively. The general trend of the wall thickness distribution of the parts experienced cycles of increasing- decreasing-increasing-decreasing. This indicates that excessive thinning occurred at the top of the part with consistent material mobility, both at different pre-bulging pressures for the same pre-bulging height and at different pre-bulging heights for the same pre-bulging pressure. For the wall thickness distribution of a part, its minimum wall thickness is also one of its main indicators. Figure 12 shows the minimum wall thickness of parts under different pre-bulging parameters. Figure 12 (a) shows the minimum wall thickness of parts under different pre-bulging pressures, and Fig. 12 (b) shows the minimum wall thickness of parts under different pre-bulging heights. From Fig. 12 (a), when the pre-bulging height was 6 mm, the pre-bulging pressure was 4 MPa and the minimum wall thickness value of the part reached a maximum of 0.6 mm. Therefore, the wall thickness distribution of the part was more uniform under this combination of process parameters. From Fig. 12 (b), during the forming process of the stepped parts, the minimum wall thickness of the parts was larger and the wall thickness distribution was more uniform when the pre-bulging height was 6 mm. The above results only considered the minimum wall thickness of the parts; however, it is also necessary to comprehensively consider the filling of the material during the forming process and select parts with good moldability. Hardness distribution law of stepped parts As stepped parts are prone to wrinkles and cracks in the process of PHDD, the Vickers hardness values of parts at different positions were measured by the pressing method, and the ability of parts to resist deformation at different positions during plastic deformation was analyzed. Based on the experimental research and analysis, the parts with good formability and moldability were selected as those obtained under the parameters of a pre-bulging height of 6 mm and a pre-bulging pressure of 3 MPa. The part hardness distribution under these parameters is shown in Fig. 13 . From Fig. 13 , the hardness value at the top transition corner and the first step corner was the largest, whereas that at the top and flange of the first step was the smallest. Due to the use of PHDD tests, the suspended part of the stepped part could not form beneficial friction; hence, the hardness value of the top of the first step was the smallest. Due to the influence of the pressure side force at the flange, the material flow was blocked, leading to a small hardness value. Furthermore, the rounded corner was excessively thin, and crack defects occurred easily, leading to a large hardness value. Optimization of process parameters To improve the formability of stepped parts, the pre-bulging height, pre-bulging pressure, chamber pressure, and blank holder force were selected as the main process parameters. According to the analysis of the simulation and test results, the selection range of each factor was determined. The specific values of each process parameter are shown in Table 1 . To obtain concise and clear orthogonal test factor levels, pre-bulging height A, pre-bulging pressure B, chamber pressure C, and blank holder force D were used as orthogonal test factors. As the minimum wall thickness was the optimization goal, four factors and levels L 16 (4 4 ) were designed for the orthogonal test. The factor levels of the orthogonal test are shown in Table 2 . Table 1 Main process parameters of hydraulic deep-drawing simulation for stepped parts Parameters Pre-bulging height h i /mm Pre-bulging pressure P a /MPa Chamber pressure P b /MPa Blank holder force Q i /kN Value 6,8,10,12 2,3,4,5 6,8,10,12 8,10,12,14 Table 2 Factors and levels of the orthogonal test. Level Factors A/(mm) B/(MPa) C/(MPa) D/(kN) 1 6 2 6 8 2 8 3 8 10 3 10 4 10 12 4 12 5 12 14 According to the factor levels of the orthogonal test shown in Table 2 , 16 groups of process parameter combinations were formed. To ensure that there were no defects, such as cracking and wrinkling, in the forming process of stepped parts, a larger minimum wall thickness value was selected. In summary, the orthogonal test scheme and the results of 16 groups of process parameter combinations are shown in Table 3 . Among all process parameter combination schemes, the minimum wall thickness of parts under the process parameter combination of test scheme 1 was the largest, the distribution of the wall thickness of parts was more uniform, and the minimum wall thickness was 0.570 mm. Table 3 Schemes and results of the orthogonal test Number Factors Process parameter combination Minimum wall thickness/mm A/(mm) B/(MPa) C/(MPa) D/(kN) 1 6 2 6 8 A1B1C1D1 0.570 2 6 3 8 10 A1B2C2D2 0.453 3 6 4 10 12 A1B3C3D3 0.337 4 6 5 12 14 A1B4C4D4 0.363 5 8 2 8 12 A2B1C2D3 0.366 6 8 3 6 14 A2B2C1D4 0.539 7 8 4 12 8 A2B3C4D1 0.355 8 8 5 10 10 A2B4C3D2 0.343 9 10 2 10 14 A3B1C3D4 0.285 10 10 3 12 12 A3B2C4D3 0.144 11 10 4 6 10 A3B3C1D2 0.542 12 10 5 8 8 A3B4C2D1 0.495 13 12 2 12 10 A4B1C4D2 0.202 14 12 3 10 8 A4B2C3D1 0.337 15 12 4 8 14 A4B3C2D4 0.429 16 12 5 6 12 A4B4C1D3 0.539 As shown in Table 4 , to obtain the trend of each influencing parameter on the minimum wall thickness of the stepped parts and the optimal parameter combination [ 30 ], a range analysis was conducted on the orthogonal test results from Table 3 . The greater the range of each factor, the greater the influence of the factor on the test results. By comparing the range values in Table 4 , the order of the influence degree of each influencing factor on the minimum wall thickness of the stepped parts was as follows: chamber pressure C > blank holder force D > pre-bulging pressure B > pre-bulging height A. The optimal process parameter combination was A1B4C1D1. Table 4 Range analysis results of minimum wall thickness (mm) Parameter A B C D Mean 1 0.412 0.356 0.548 0.439 Mean 2 0.401 0.368 0.417 0.367 Mean 3 0.367 0.416 0.326 0.347 Mean 4 0.377 0.435 0.266 0.404 Range R 0.045 0.079 0.282 0.092 Rank 1 2 3 4 Optimal program combination A1B4C1D1 To directly assess the influence of various influencing factors on the minimum wall thickness of the stepped parts, the range analysis results of the minimum wall thickness in Table 4 were plotted as an orthogonal test effect plot, as shown in Fig. 14 . From Fig. 14 , the influence of the pre-bulging height A on the minimum wall thickness of the stepped parts first decreased then increased. This is due to the interaction between factors, which did not conform to the general law. Simultaneously, the orthogonal experimental effect diagram of the blank holder force D was analyzed. It was found that the influence of the blank holder force D on the minimum wall thickness of the stepped parts first decreased then increased, which indicates that there was an interaction between the blank holder force D and other factors. According to the optimal parameter combination obtained in Table 4 , the process parameters were selected as a pre-bulging height of 6 mm, pre-bulging pressure of 5 MPa, chamber pressure of 6 MPa, and blank holder force of 8 kN. DYNAFORM finite element software was used to simulate and analyze the optimal parameter combination, and the cloud map of the wall thickness distribution of the stepped parts under the optimal parameters was obtained, as shown in Fig. 15 . From Fig. 15 (a), the values of the wall thickness at the straight wall of the second step and at the top were smaller. From Fig. 15 (b), the value of the second step wall thickness of the stepped part was smaller, and the wall thickness gradually increased from the top of the second step, but at the straight wall and rounded corner of the first step, the wall thickness decreased. This is because under the joint constraints of the guide blank holder and the bottom of the movable die, the sheet began to thin by the combined action of compressive and tensile stresses. Conclusions To improve the forming quality of stepped parts, this study developed a pair of forming devices based on the principle of the HDD process and built a test platform to conduct experimental research. The effects of the pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of parts were analyzed. To further improve the part filling, an orthogonal test of four levels and factors was conducted. Through simulation analysis, the optimal parameter combination was obtained, and a stepped part with high formability was obtained. The main conclusions are as follows: Based on the principle of PHDD, the pre-bulging pressure and pre-bulging height were taken as the main factors for the formability analysis of stepped parts, and the forming height of the parts was analyzed. It was found that when the pre-bulging height was 6 mm and the pre-bulging pressure was 3 MPa, the forming height of the parts with good formability and no defects reached 28.9 mm. This combination of process parameters resulted in an optimal part forming height. The wall thickness distribution of the stepped parts experienced cycles of increasing - decreasing - increasing - decreasing. Excessive thinning occurred at the top and transition corners, where the wall thickness value was the smallest, and thinning occured at the top of the first step. When the pre-bulging height was 6 mm and the pre-bulging pressure was 4 MPa, the minimum wall thickness of the parts was 0.6 mm and the wall thickness distribution was more uniform. After using the PHDD test, the top of the first step of the stepped part produced an overhanging part, which did not form a beneficial friction. The flange of the part was affected by the blank holder force, the material flow was hindered, and the hardness value at the top of the first step was minimized. The hardness value was greatest at the top transition fillet and the first step fillet of the stepped part, which had the greatest resistance to plastic deformation. The optimal parameter combination obtained by the simulation orthogonal test was as follows: a pre-bulging height of 6 mm, pre-bulging pressure of 5 MPa, liquid chamber pressure of 6 MPa, and a blank holder force of 8 kN. The optimal process parameters were used for simulation and verification, and it was found that the wall thickness of the stepped parts at the second step was relatively small, indicating that the compression side force at the bottom of the plate played a role in the process of PHDD. Furthermore, there was serious top thinning under the action of tensile stress in the process of the radial flow of the plate. The optimum process parameters were verified by experiments, and it was found that the wall thickness value of the second step of the stepped parts was small. From the top of the second step, the wall thickness value gradually increased, but the wall thickness value began to decrease at the straight wall and rounded corner of the first step. The moldability of the parts was improved under the optimal parameters. Declarations Acknowledgements This work was financially supported by the National Natural Science Foundation of China (No. 52065014), Natural Science Foundation of Guangxi Province (No. 2023GXNSFBA026121), Guangxi Key Laboratory of Manufacturing System & Advanced Manufacturing Technology (No. 22-35-4-S013), and Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi (No. 2023KY0220). Conflict of interests: The authors declared that they have no conflicts of interest. References Yuan SJ, Liu W, Xu YC (2015) New development on technology and equipment of sheet hydroforming. J Mech Eng 51(08):20–28 Jalil A, Hoseinpour Gollo M, Hossein Seyedkashi SM (2017) Process analysis of hydrodynamic deep drawing of cone cups assisted by radial pressure. 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Int J Eng Res Africa 59:1–18 Yusuf S, Yakup T (2023) Experimental and statistical investigation of mechanical properties and surface roughness in additive manufacturing with selective laser melting of AlSi10Mg alloy. J Braz Soc Mech Sci Eng 45(10):515 Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 11 Nov, 2024 Reviewers invited by journal 04 Nov, 2024 Editor assigned by journal 01 Nov, 2024 First submitted to journal 28 Oct, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5345272","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":373831653,"identity":"7720bafb-3247-4cce-bf01-79d605e68015","order_by":0,"name":"Chenchen Dong","email":"","orcid":"","institution":"Guilin University of Electronic Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Chenchen","middleName":"","lastName":"Dong","suffix":""},{"id":373831654,"identity":"d1d1bb64-d3a6-4d0e-96ee-680bfc333e64","order_by":1,"name":"Jianping Ma","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/0lEQVRIie2RvWrDMBSFJQzJIqPVpskjFJSlIRCaV7kQ6JS5ZLzGoE7ZnTEvUTpe4aGLidZAMjhLOhXssbSFiv6MVTwWqm84gzgfR0KMBQJ/EyAXgjGe1c1yKqTEzkqUj4rqZpAW1Hmtry9iXU4Vgr93eUdHenk4DMZyg0msrVCMeNMufleuKgCzqk5iUhxRJdu9GEcYpet7j0IA5O4j1M4gqNu9mCD1otin2BrM+7dC0NsK5dKv7ADKzxWbZUiauig1lEN9cis851jNRVqY3P8Wu5i3z/owU/bx6fVteT2TMjdN61HcJ4ILYiyBnxOOvr6jT1+KpDPFQCAQ+Ld8AN9VY8nPlTGQAAAAAElFTkSuQmCC","orcid":"","institution":"Guilin University of Electronic Technology","correspondingAuthor":true,"prefix":"","firstName":"Jianping","middleName":"","lastName":"Ma","suffix":""},{"id":373831655,"identity":"a47ce7ed-4d80-4ac1-91d4-300d1e40d429","order_by":2,"name":"Haimei Han","email":"","orcid":"","institution":"Guilin University of Electronic Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Haimei","middleName":"","lastName":"Han","suffix":""},{"id":373831656,"identity":"a1fe1535-29c1-4ddb-9f22-0682edd6757b","order_by":3,"name":"Wenze Zhang","email":"","orcid":"","institution":"Guilin University of Electronic Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Wenze","middleName":"","lastName":"Zhang","suffix":""},{"id":373831657,"identity":"de6c8d88-898e-4777-8ae4-dae096757c06","order_by":4,"name":"Fei Liu","email":"","orcid":"","institution":"Guilin University of Electronic Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Fei","middleName":"","lastName":"Liu","suffix":""},{"id":373831658,"identity":"19fb4891-6f9b-451b-b7fa-caf87d881101","order_by":5,"name":"Lianfa Yang","email":"","orcid":"","institution":"Guilin University of Electronic Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Lianfa","middleName":"","lastName":"Yang","suffix":""}],"badges":[],"createdAt":"2024-10-28 08:22:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5345272/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5345272/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69101726,"identity":"56bb183b-cc5f-47e2-9684-18ed6a83516d","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":95219,"visible":true,"origin":"","legend":"\u003cp\u003eSheet metal PHDD forming principle: (a) before forming, (b) pre-bulging forming, (c) hydraulic drawing\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/ea1dc4253850d7ae2e752188.png"},{"id":69102266,"identity":"da8f1b7c-ec14-49af-a1f8-96c3acccd452","added_by":"auto","created_at":"2024-11-15 16:12:05","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":217168,"visible":true,"origin":"","legend":"\u003cp\u003eApplication of different molding methods for stepped parts\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/a9f65a511c047d39bd0080d7.png"},{"id":69102268,"identity":"749e5ed9-ac50-4819-9cdb-e69e82751a0f","added_by":"auto","created_at":"2024-11-15 16:12:05","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":29664,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic diagrams of stepped parts: (a) 2D, (b) 3D\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/e48247394dac53bab3c55542.png"},{"id":69101728,"identity":"fdd422e0-779b-4974-80b1-3a43d8153bca","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":70344,"visible":true,"origin":"","legend":"\u003cp\u003ePrinciple of PHDD for stepped parts: (a) before forming, (b) pre-bulging forming, (c) hydro-drawing\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/45e050e4f4806b43248507e7.png"},{"id":69101741,"identity":"0c6d6007-bf0b-41db-9100-f3fd3150c70c","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":139009,"visible":true,"origin":"","legend":"\u003cp\u003eHydraulic punch deep-drawing forming device for stepped parts: (a) Schematic drawing, (b) Physical drawing\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/f5d5d0308a804f030ea01dc8.png"},{"id":69102271,"identity":"d045605b-a63c-4b8b-bf18-644f16d6a8cf","added_by":"auto","created_at":"2024-11-15 16:12:05","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":223894,"visible":true,"origin":"","legend":"\u003cp\u003ePlate hydraulic punch drawing forming test platform\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/38d576daad21d6f1d5b647cd.png"},{"id":69101730,"identity":"1d7d5867-653c-4cf0-ac0e-38387caf1757","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":54384,"visible":true,"origin":"","legend":"\u003cp\u003eFinite element modeling of stepped parts: (a) Pre-forming, (b) Final forming\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/4e35cd3d6fdb66172b25c4cc.png"},{"id":69102267,"identity":"89804e50-e8ea-405f-a9f5-9407fd5edcf0","added_by":"auto","created_at":"2024-11-15 16:12:05","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":107383,"visible":true,"origin":"","legend":"\u003cp\u003eMovable die physical drawing: (a) Clamp plate and movable die assembly physical drawing, (b) Bottom of the movable die\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/ee8d9952509fd137e2160c9c.png"},{"id":69101737,"identity":"f886d0aa-a54a-4d37-841d-ad737fa5a28a","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":217615,"visible":true,"origin":"","legend":"\u003cp\u003eFailures in hydraulic deep-drawing of stepped parts\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/11e36ade90fdf36f7bf93a19.png"},{"id":69101736,"identity":"8f05b16a-14e3-4799-a15a-56d2d1b3c88e","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":62663,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of pre-bulging pressure on wall thickness distribution of stepped parts: (a) 6 mm, (b) 8 mm, (c) 10 mm\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/f4ea1a6e0fea4a118936de15.png"},{"id":69101732,"identity":"ae30b593-df1e-4b7f-be8b-59551f8a8ade","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":70764,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of pre-bulging height on wall thickness distribution of stepped parts: (a) 2 MPa, (b) 3 MPa, (c) 4 MPa\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/1f6aa2975b4c65523b442058.png"},{"id":69102270,"identity":"2ce92407-0b8c-4e0d-873f-c20f56905135","added_by":"auto","created_at":"2024-11-15 16:12:05","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":33471,"visible":true,"origin":"","legend":"\u003cp\u003eMinimum wall thickness of parts with different pre-bulging parameters\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/d5f47720037bd7b633ebbaab.png"},{"id":69101739,"identity":"cfa5c313-6412-466c-b03e-95ebf4edd247","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":189275,"visible":true,"origin":"","legend":"\u003cp\u003eMeasurement of the hardness of stepped parts at different positions\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/441ae018ec05cfe1f99d33dc.png"},{"id":69101731,"identity":"b73a5450-f3ef-40ed-a6f7-8c5094b30d23","added_by":"auto","created_at":"2024-11-15 16:04:05","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":52345,"visible":true,"origin":"","legend":"\u003cp\u003eOrthogonal test effect plot for minimum wall thickness of stepped parts\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/e94e9aeaf018f2cd572db486.png"},{"id":69102384,"identity":"f686c45e-42ae-445b-a72b-66b03539ae28","added_by":"auto","created_at":"2024-11-15 16:20:20","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":70783,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of wall thickness distribution under optimal parameters: (a) Simulation, (b) Experiment\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/151dee8748d76535673c70ec.png"},{"id":69102387,"identity":"d6830331-a7d0-462a-a267-7e0058ff75bc","added_by":"auto","created_at":"2024-11-15 16:20:26","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2366421,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5345272/v1/a5fab380-ed2c-4f2f-ab46-039b5f98a63f.pdf"}],"financialInterests":"","formattedTitle":"Pre-bulging hydromechanical deep-drawing forming performance of a hydraulic punch for stepped parts","fulltext":[{"header":"Introduction","content":"\u003cp\u003ePre-bulging hydromechanical deep-drawing (PHDD) combines hydromechanical deep-drawing (HDD) and plate pre-bulging. HDD is a novel sheet metal forming method that combines hydraulic forming technology and ordinary stamping forming. HDD uses a liquid medium rather than a rigid mold and relies on liquid pressure to make the parts required for sheet metal forming. Compared with traditional die drawing [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], HDD has the advantages of good forming quality, low manufacturing cost, and high dimensional accuracy [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, for some large thin-walled complex parts, the use of HDD is prone to problems such as insufficient and uneven deformation of sheet metal parts. Therefore, aircraft echelon thin-wall parts, automotive motor shells, and oil pans in HDD are prone to problems such as uneven wall thickness distribution and insufficient deformation. New technologies have been developed in sheet metal hydroforming technology, such as PHDD (Forward-, inverse-, and local-bulging), hydrodynamic deep-drawing with independent radical hydraulic pressure, forward and reverse pressurized hydrodynamic deep-drawing, and twin-plate pair hydroforming [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. PHDD is a novel process developed on the basis of hydraulic drawing of sheet metal. The forming principle of PHDD is firstly under the initial pressure of the liquid medium, before the sheet forms a transition shape under the constraints of the mold, and HDD is applied, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Compared with HDD, in the PHDD process, the forming parts have better moldability, a more uniform wall thickness distribution, and higher precision and stiffness [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith the development of lightweight materials in various fields, such as automobiles and aerospace, sheet metal forming is also developing in the direction of large deep-cavity thin-wall parts, complex curved parts, and deformation resistant materials. The use of aluminum alloys to form complex parts has been favored in these fields [\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] as they provide effective lightweight materials, especially for body covering parts and large and complex curved aircraft skins.\u003c/p\u003e \u003cp\u003eLarsen [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] found that using HDD could improve the formability of a motor hood by implementing pre-bulging forming and then HDD. Chen et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] produced a new high-capacity engine oil sump, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(a), by developing a hybrid sheet hydroforming process using a two-stage HDD process to obtain a stepped shell assembly. Kim et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] proposed a multi-stage hydroforming process, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(b), finding that it improved the formability of components with similar oil pan shapes and could effectively manufacture sheet metal parts with multi-step components. Zhang et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] selected 0.3 mm thick H68 material, designed each drawing process through theoretical analysis, used finite element software to carry out each drawing process, and finally obtained a stepped cylinder with good formability through test verification, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(c). Ren et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] used PAMSTAMP finite element software to analyze and calculate the three-time deep-drawing forming process, determined the appropriate blank holder clearance, designed three pairs of deep-drawing dies, inverted forming on the hydraulic press, and finally obtained second-order cylindrical parts with good forming quality, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(d). Lang et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] evaluated the influence of the pre-bulging height and pressure on the hydromechanical forming process, optimized the pressure loading path, and finally obtained flat-bottom irregular box parts with high forming quality. Wang [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] used finite element software to analyze the deformation law of stepped sidewall box forming, designed an orthogonal test, and concluded that h\u0026thinsp;\u0026gt;\u0026thinsp;H\u0026thinsp;\u0026gt;\u0026thinsp;B\u0026thinsp;\u0026gt;\u0026thinsp;b\u0026thinsp;\u0026gt;\u0026thinsp;r\u0026thinsp;\u0026gt;\u0026thinsp;R, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e(e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe aim of this study is to improve the formation of stepped parts by reducing the cracks at the top and transition corner, as well as the wrinkles at the flange. Therefore, a hydraulic punch drawing and forming device is developed using a microcomputer-controlled universal tensile testing machine (WDW-100GD). The forming effect of the device is verified using the step pre-bulging forming method, and a hydraulic drawing test of stepped parts is conducted by adjusting the position of the movable die freely with different plate heights. Experimental research is conducted on the test platform to analyze the influence of the pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of the parts. Furthermore, the deformation and forming laws of the stepped parts during hydraulic punch deep-drawing forming are revealed. To obtain parts with good filling and moldability, an optimal parameter combination is obtained by orthogonal test simulation and analysis. The test results show that the forming height and quality of the parts can be improved effectively by combining the designed movable die with a guiding flange cylinder. The proposed step pre-bulging forming method increases the formability of stepped parts.\u003c/p\u003e"},{"header":"Experimental and simulation conditions","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003ePart process analysis\u003c/h2\u003e \u003cp\u003eThe hydraulic punch drawing technology principle was used to obtain stepped parts with a high forming quality and formability. The designed stepped parts forming device, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, was adjusted arbitrarily for each step height. The specific height of each step in mm was determined from bottom to top. The distance between the bottom surface of the ladder and the upper surface of the first step was the height of the first step, the distance between the top surface of the first step and the top surface of the ladder was the height of the second step, and the total height of the ladder was the lower surface of the ladder and the top surface of the ladder.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo obtain stepped parts with high formability, this study used a 1060-O aluminum plate with a 0.8 mm thickness to conduct the relevant tests. Compared with other grades of aluminum alloy, 1060-O aluminum has good plasticity and strong corrosion resistance [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. To improve the plasticity of the plate, the annealing process involved the furnace being heated to 400 ℃ with a holding time of 1 hour before the furnace was cooled to 300 ℃, and then air-cooled. Real stress-strain curves of 1060-O aluminum were fitted using unidirectional tensile tests and the Hollomon parameter. Values of k and n were obtained, with a relation of \u003cimg src=\"data:image/png;base64,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\" width=\"126\" height=\"34\"\u003e\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003ePrinciple of part forming\u003c/h3\u003e\n\u003cp\u003eThe forming principle of the device is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, which includes three stages: before forming, pre-bulging forming, and hydro-drawing. The position of the movable die was adjusted using plates of different heights, and the ideal stepped part was obtained by the joint constraint of the guide blank holder and the movable die. This study used the soft punch bulging method, where liquid replaced the punch and sheet metal was formed under the action of liquid pressure and the constraint of the movable die. First, the pre-bulging fluid pressure was applied in the hydraulic cavity, the plate bulged and produced a pre-deformation, and the plate material was drawn into a transition shape. Second, the forming pressure fluid was increased, and the transition shape was formed into a stepped part by the joint constraints of the movable die and the guide blank holder. The sub-plate was divided into two heights: one plate controlled the pre-bulging (pre-bulging plate) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(b), and the other plate controlled the forming (forming plate) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e(c).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eTest device and platform\u003c/h3\u003e\n\u003cp\u003eTo achieve various characteristics of stepped parts, such as a large gap in each size, high precision requirements, and a small transition fillet, this study designed the principle of PHDD forming of stepped parts. A pair of PHDD forming devices was developed, and a test platform was constructed. The designed platform could not only adjust the height of pre-bulging but also realize the whole hydraulic loading curve in the process of pre-bulging and forming.\u003c/p\u003e\n\u003ch3\u003eTest device\u003c/h3\u003e\n\u003cp\u003eBased on the principle of PHDD and the process analysis of stepped parts, this study developed a stepped part hydraulic punch drawing forming device, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Its structure was mainly composed of a liquid-filled base, guide blank holder, movable die, work jack, sub-plate, clamp plate, sealing element, and fixing element. The device had a clearance fit between the work jack and the movable die and between the movable die and the guide blank holder to meet the positioning and guiding requirements. The holding force of the guide blank holder was controlled by adjusting the torque force of the screw with a torsional torque wrench. For the geometrical dimensions of the working parts of the device, the radius of each corner of the movable die and the radius of the transition corner at the bottom of the inner wall of the guide blank holder were both 6 mm.\u003c/p\u003e \u003cp\u003eThe liquid-filled base was provided with a hydraulic chamber and a connected liquid inlet hole to better connect with the hydraulic oil pipe. The liquid inlet port was milled flat, and a sealing groove was opened on the upper surface of the liquid-filled base for placing a sealing ring, which prevented leakage of the liquid in the hydraulic chamber. The guide blank holder, movable die, work jack, and sub-plate were coaxial. The order of the parts from outside to inside was: guide blank holder, movable die, and work jack. The bottom of the guide blank holder was detachably mounted on the liquid-filled base, the tops of the movable die and the work jack were detachably mounted on the clamp plate, and the sub-plate was set between the top of the guide blank holder and clamp plate. The bottom of the movable die and the work jack were fitted with the guide blank holder to form a die cavity with the shape of the part to be formed. The plate was placed between the guide blank holder and the liquid-filled base [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eTest platform\u003c/h3\u003e\n\u003cp\u003eBased on the developed test device, a plate hydraulic punch drawing forming test platform was constructed, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The test platform was composed of a WDW-100GD machine, micro-hydraulic station, data acquisition system, and forming device. The axial travel of the device was controlled by the WDW-100GD machine during the test, and the axial displacement was collected. Through the relief valve connected to the micro-hydraulic station, the liquid pressure was controlled to realize a constant pressure. The data acquisition system intuitively observed the loading of the liquid pressure in the process of sheet metal forming and obtained the curve of the liquid pressure change.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe test was conducted on a WDW-100GD machine, and the test process consisted of two parts: pre-forming and final forming. To overcome the difficulty in forming stepped parts, a hydraulic loading path of pre-bulging and then drawing was adopted, in which the loading curve of the liquid chamber pressure was applied to the pre-bulging pressure loading curve. The liquid pressure loading curve with time is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e and was divided into pre-forming and final forming. The loading process involved repeated cycles of pressurization and pressure maintenance. In Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, \u003cem\u003eP\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e represents the pre-bulging pressure and \u003cem\u003eP\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e represents the liquid chamber pressure [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eSimulation modeling\u003c/h2\u003e \u003cp\u003eTo achieve various characteristics of stepped parts, including a large size difference, small transition fillet, and high dimensional accuracy, a PHDD forming scheme was designed. Considering the incomplete filling of the tops of the parts obtained from the tests, orthogonal experimental simulation analysis was used to obtain an optimal parameter combination and stepped parts with good filling and moldability. UG software was used to establish the model, which was saved as an .igs format file and then imported into the DYNAFORM finite element simulation software. To reduce the solution calculation time, only half of the finite element model was selected for simulation, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Based on the design of the hydraulic punch drawing principle of stepped parts, a liquid medium was used rather than the punch. Furthermore, Die 1, Die 2, Binder 1, and Binder 2 comprised the rigid body. The No. 36 three-parameter Barlat plasticity elastic-plastic plate material model was selected, and the Belytschko-Tsay shell plate element was used, with a self-applicable mesh used to divide blanks. The gap between the binder and plate was 1.1 t, or 0.88 mm. To obtain more accurate simulation results, the mesh was divided into rounded corners with a fine mesh size of 0.5 \u0026times; 0.5 mm, and the remainder of the mesh had a size of 1 \u0026times; 1 mm.\u003c/p\u003e \u003cp\u003eAccording to the designed forming device and principle, the drawing mode of the simulation model was an inverted die form, as single action reverse drawing. To observe and analyze the formability of the two processes more directly, the working mode was divided into two working steps in the finite element software, and each working step consisted of two working steps: closing and deep-drawing. During the entire forming process, the die was stationary, and the binder moved in the +\u0026thinsp;Z (vertical) direction at a certain speed. When the gap between the die and binder was 0.88 mm, the closing process was complete. Next, according to the setting of the hydraulic loading curve and the pressure value exerted by the binder on the plate, the purpose of hydraulic deep-drawing was achieved. Finally, the pre-forming and final forming of the plate were controlled by the constraint of the die.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eExperimental details\u003c/h3\u003e\n\u003cp\u003eThe pre-bulging pressure and height are the main influencing factors for the pre-forming of stepped parts during plate pre-bulging forming. Pre-bulging pressure was applied before HDD so that the plate had a pre-deformation effect, which reduced the anisotropy of the plate deformation at a later stage. This also effectively prevented the wrinkling of the plate, reduced the stress concentration generated at the rounded corners of the concave die, prevented cracking, and supported the formation of parts. By controlling the pre-bulging height of the sheet, it was formed into a reasonable transition shape, and the formability was improved. Reasonable control of the pre-bulging pressure and height of the plate effectively controlled the generation of the failure of the formed part and improved the formability of the plate.\u003c/p\u003e\n\u003ch3\u003eControl of pre-bulging height\u003c/h3\u003e\n\u003cp\u003eA pre-bulging height that is too high can lead to cracking at the top of the stepped part as well as cracking and creasing at the transition corner of the stepped part. A pre-bulging height that is too low can lead to poor pre-forming of the stepped part, resulting in poor moldability of the final parts. Reasonable control of the pre-bulging pressure can effectively control the generation of failure and improve the formability of the sheet. The hydraulic punch deep-drawing forming device for stepped parts controls the position of the movable die using a sub-plate of different heights, thus adjusting the pre-bulging height of the stepped parts to achieve pre-forming.\u003c/p\u003e \u003cp\u003eA physical drawing of the movable die test device is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a), firstly, the top work jack was connected to the movable die by a specification M6 screw. The movable die was not designed as a whole, but the internal clearance of the movable die was matched with the work jack so that the plate was formed during the forming process through the die constraint. At the end of the final forming, the plate was close to the die, and the parts could not be easily disassembled without wrinkling; therefore, the part was removed using the work jack. Finally, the movable die was connected using a clamp plate through three M6 socket head cap screws. In this way, the movable die, clamp plate, and work jack were assembled to achieve the integrated design, which was not only convenient for disassembly but also ensured pre-forming and final forming processes, thus achieving a good forming effect. The forming height of the stepped part was controlled and was low when hydraulic drawing was conducted in the initial state. Therefore, pre-forming of the part was controlled by combining the sub-plate with the movable die of different heights. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(b), the part was formed under the joint constraints of guide blank holder, work jack, and movable die to improve the height of each step of the part.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eControl of pre-bulging pressure\u003c/h2\u003e \u003cp\u003eThe pre-bulging pressure refers to the force exerted on the sheet by the liquid in the sealed state before the force applied to the metal blank by the movable die. Before the hydromechanical deep-drawing action began, pressure was applied to the liquid sealed inside the hydraulic chamber so that the sheet material was pressed against the die under the pressure of the liquid. To ensure that the liquid pressure in the pre-bulging and forming processes was loaded and maintained, a test platform was constructed to control the pre-bulging pressure. The micro-hydraulic station and the WDW-100GD machine were combined to control the pre-bulging pressure.\u003c/p\u003e \u003cp\u003eTo control the pre-bulging pressure, the test device was sealed, and the liquid pressure was controlled through the relief valve in the micro-hydraulic station, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The plate was placed on the upper surface of the liquid-filled base. To prevent liquid overflow, a sealing ring was arranged between the guide blank holder and the liquid-filled base. A fluorine rubber O-ring was used as the sealing ring, with a compression rate of 25%. Therefore, a sealing groove was designed on the upper surface of the liquid-filled base in the developed device, with a depth of \u0026lt;\u0026thinsp;1.5 mm of the diameter of the sealing ring to ensure that it was subjected to pre-pressure before the test. The filling hole of the liquid-filled base was provided with an O-ring seal. The process of pressing and holding pressure was realized through the micro-hydraulic station. Under the action of pre-bulging pressure, the plate material was formed into a transition shape, and the free hanging area between the part and the die was reduced, thus improving the forming quality of the part.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results and discussion","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eFailure of stepped parts after PHDD\u003c/h2\u003e \u003cp\u003eThe failure of the specimen before the hydraulic drawing process of stepped parts is the main issue preventing stepped parts from forming [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Therefore, it is of great significance to analyze the failures and causes during hydraulic deep-drawing to improve the formability of stepped parts. To improve the forming quality of the parts, the causes of failure were analyzed, and corresponding solutions are proposed [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe influences of pre-bulging parameters and the blank holder force on the failure forms of the parts were analyzed. It was found that when the pre-bulging pressure was 2 and 3 MPa, the top and rounded corners of the stepped parts experienced large cracks, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(f). When the pre-bulging pressure was 4 MPa, the top of the first step cracked, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(c). When the pre-bulging pressure was 3 MPa and the pre-bulging height was 6 and 8 mm, only small cracks appeared on the top of the part. When the pre-bulging height was 10 mm, there was a large crack at the top. When the blank holder force was 1 kN, the flange of the part was seriously wrinkled, and when the blank holder force was 3 kN, the top of the part cracked. Therefore, when the blank holder force was 2 kN, the flange of the part only wrinkled slightly at the screw connection, which provided a reference for subsequent tests. From Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e(d) and 9(e), the main failures of the parts were cracking and wrinkling, including cracking at the top of the part, the transition corner, and the top of the first step, and wrinkling at the flange and the top fold.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eEffects of pre-bulging parameters on the forming height of stepped parts\u003c/h2\u003e \u003cp\u003eThe forming height is an important index to measure the formability of parts. The forming height of the parts can be effectively improved by using the hydraulic drawing principle. In the entire forming stage, pre-bulging forming is crucial, especially for complex and stepped parts, because pre-bulging ensures that the plate in the early hanging area does not cause defects due to instability. Therefore, to obtain the influence of the forming principle on the formability of the part, the influence of the pre-bulging parameters on the forming height of the part was analyzed.\u003c/p\u003e \u003cp\u003eThrough research tests, it was found that the bursting pressure of the parts was 5 MPa. Therefore, to reasonably match the pre-bulging height and pressure, three pre-bulging pressures of 2, 3, and 4 MPa were selected. Under the condition that other parameters were consistent, the influence of the pre-bulging pressure on the forming height of parts was analyzed by using different pre-bulging pressures. The test results show that when the pre-bulging height was constant, the forming height of the parts with a pre-bulging pressure of 3 MPa was greater than that at 2 MPa. However, when the pre-bulging pressure was 4 MPa, the forming height of the part was lower than that at 3 MPa. This occurred because when the pre-bulging pressure was too large, the top of the pre-forming process of the part experienced excessive thinning. Furthermore, in the final forming process, the part cracked in advance, reducing the forming height.\u003c/p\u003e \u003cp\u003eFor the designed movable die with an internal depth of 14.45 mm, three pre-bulging heights of 6, 8, and 10 mm were selected. Under the condition that other parameters were constant, the influence of the pre-bulging height on the forming height of the parts was analyzed using different pre-bulging heights. The test results show that when the pre-bulging pressure was constant, the forming height of the part was higher than that for pre-bulging heights of 8 and 6 mm but lower than that for a pre-bulging height of 10 mm. This was because when the pre-bulging height was too large, the hanging area of the pre-forming process of the parts was large, and the top experienced excessive thinning. Furthermore, in the final forming process, the part cracked in advance, reducing the forming height. Based on the above test analysis, it was found that under the parameter combination of a pre-bulging pressure of 3 MPa and a pre-bulging height of 6 mm, the forming height of the part with good formability and no defects reached 28.9 mm.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eEffects of pre-bulging parameters on wall thickness distribution of stepped parts\u003c/h2\u003e \u003cp\u003eThe wall thickness distribution is an important indicator for measuring the formability of the part, where the larger the minimum wall thickness, the smaller the maximum thinning rate, and the better the uniformity of the wall thickness distribution, according to the trend of the wall thickness distribution and the specific value in the weak points of the part [\u003cspan additionalcitationids=\"CR27 CR28\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. In the process of PHDD, the pre-bulging parameter is the main influencing factor in the forming process of the parts. Therefore, analyzing its influence law on the forming process of the parts has an important role in its improvement.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the wall thickness distribution of parts under different pre-bulging pressures when the pre-bulging height was 6, 8, and 10 mm, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e illustrates the wall thickness distribution of parts at different pre-bulging heights when the pre-bulging pressure was 2, 3, and 4 MPa, respectively. The general trend of the wall thickness distribution of the parts experienced cycles of increasing- decreasing-increasing-decreasing. This indicates that excessive thinning occurred at the top of the part with consistent material mobility, both at different pre-bulging pressures for the same pre-bulging height and at different pre-bulging heights for the same pre-bulging pressure.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the wall thickness distribution of a part, its minimum wall thickness is also one of its main indicators. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the minimum wall thickness of parts under different pre-bulging parameters. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a) shows the minimum wall thickness of parts under different pre-bulging pressures, and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(b) shows the minimum wall thickness of parts under different pre-bulging heights. From Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(a), when the pre-bulging height was 6 mm, the pre-bulging pressure was 4 MPa and the minimum wall thickness value of the part reached a maximum of 0.6 mm. Therefore, the wall thickness distribution of the part was more uniform under this combination of process parameters. From Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e(b), during the forming process of the stepped parts, the minimum wall thickness of the parts was larger and the wall thickness distribution was more uniform when the pre-bulging height was 6 mm. The above results only considered the minimum wall thickness of the parts; however, it is also necessary to comprehensively consider the filling of the material during the forming process and select parts with good moldability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eHardness distribution law of stepped parts\u003c/h2\u003e \u003cp\u003eAs stepped parts are prone to wrinkles and cracks in the process of PHDD, the Vickers hardness values of parts at different positions were measured by the pressing method, and the ability of parts to resist deformation at different positions during plastic deformation was analyzed. Based on the experimental research and analysis, the parts with good formability and moldability were selected as those obtained under the parameters of a pre-bulging height of 6 mm and a pre-bulging pressure of 3 MPa. The part hardness distribution under these parameters is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e. From Fig.\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e, the hardness value at the top transition corner and the first step corner was the largest, whereas that at the top and flange of the first step was the smallest. Due to the use of PHDD tests, the suspended part of the stepped part could not form beneficial friction; hence, the hardness value of the top of the first step was the smallest. Due to the influence of the pressure side force at the flange, the material flow was blocked, leading to a small hardness value. Furthermore, the rounded corner was excessively thin, and crack defects occurred easily, leading to a large hardness value.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eOptimization of process parameters\u003c/h2\u003e \u003cp\u003eTo improve the formability of stepped parts, the pre-bulging height, pre-bulging pressure, chamber pressure, and blank holder force were selected as the main process parameters. According to the analysis of the simulation and test results, the selection range of each factor was determined. The specific values of each process parameter are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. To obtain concise and clear orthogonal test factor levels, pre-bulging height A, pre-bulging pressure B, chamber pressure C, and blank holder force D were used as orthogonal test factors. As the minimum wall thickness was the optimization goal, four factors and levels L\u003csub\u003e16\u003c/sub\u003e (4\u003csup\u003e4\u003c/sup\u003e) were designed for the orthogonal test. The factor levels of the orthogonal test are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMain process parameters of hydraulic deep-drawing simulation for stepped parts\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-bulging height \u003cem\u003eh\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e/mm\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePre-bulging pressure\u003c/p\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eChamber pressure\u003c/p\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e/MPa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBlank holder force \u003cem\u003eQ\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e/kN\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValue\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6,8,10,12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2,3,4,5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6,8,10,12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e8,10,12,14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactors and levels of the orthogonal test.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eLevel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eFactors\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA/(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB/(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC/(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD/(kN)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAccording to the factor levels of the orthogonal test shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, 16 groups of process parameter combinations were formed. To ensure that there were no defects, such as cracking and wrinkling, in the forming process of stepped parts, a larger minimum wall thickness value was selected. In summary, the orthogonal test scheme and the results of 16 groups of process parameter combinations are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Among all process parameter combination schemes, the minimum wall thickness of parts under the process parameter combination of test scheme 1 was the largest, the distribution of the wall thickness of parts was more uniform, and the minimum wall thickness was 0.570 mm.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSchemes and results of the orthogonal test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNumber\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eFactors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eProcess parameter combination\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMinimum wall thickness/mm\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA/(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB/(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC/(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD/(kN)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA1B1C1D1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.570\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA1B2C2D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.453\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA1B3C3D3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.337\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA1B4C4D4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.363\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA2B1C2D3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.366\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA2B2C1D4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.539\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA2B3C4D1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.355\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA2B4C3D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.343\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA3B1C3D4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.285\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA3B2C4D3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.144\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA3B3C1D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.542\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA3B4C2D1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.495\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA4B1C4D2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.202\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA4B2C3D1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.337\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA4B3C2D4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.429\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eA4B4C1D3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.539\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, to obtain the trend of each influencing parameter on the minimum wall thickness of the stepped parts and the optimal parameter combination [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e], a range analysis was conducted on the orthogonal test results from Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The greater the range of each factor, the greater the influence of the factor on the test results. By comparing the range values in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the order of the influence degree of each influencing factor on the minimum wall thickness of the stepped parts was as follows: chamber pressure C\u0026thinsp;\u0026gt;\u0026thinsp;blank holder force D\u0026thinsp;\u0026gt;\u0026thinsp;pre-bulging pressure B\u0026thinsp;\u0026gt;\u0026thinsp;pre-bulging height A. The optimal process parameter combination was A1B4C1D1.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRange analysis results of minimum wall thickness (mm)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eD\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.412\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.439\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.368\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.367\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.326\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.347\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMean 4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.377\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.435\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.266\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.404\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRange R\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.045\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.079\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRank\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOptimal program combination\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eA1B4C1D1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo directly assess the influence of various influencing factors on the minimum wall thickness of the stepped parts, the range analysis results of the minimum wall thickness in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e were plotted as an orthogonal test effect plot, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e. From Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e, the influence of the pre-bulging height A on the minimum wall thickness of the stepped parts first decreased then increased. This is due to the interaction between factors, which did not conform to the general law. Simultaneously, the orthogonal experimental effect diagram of the blank holder force D was analyzed. It was found that the influence of the blank holder force D on the minimum wall thickness of the stepped parts first decreased then increased, which indicates that there was an interaction between the blank holder force D and other factors.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAccording to the optimal parameter combination obtained in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the process parameters were selected as a pre-bulging height of 6 mm, pre-bulging pressure of 5 MPa, chamber pressure of 6 MPa, and blank holder force of 8 kN. DYNAFORM finite element software was used to simulate and analyze the optimal parameter combination, and the cloud map of the wall thickness distribution of the stepped parts under the optimal parameters was obtained, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e. From Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e(a), the values of the wall thickness at the straight wall of the second step and at the top were smaller. From Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e(b), the value of the second step wall thickness of the stepped part was smaller, and the wall thickness gradually increased from the top of the second step, but at the straight wall and rounded corner of the first step, the wall thickness decreased. This is because under the joint constraints of the guide blank holder and the bottom of the movable die, the sheet began to thin by the combined action of compressive and tensile stresses.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eTo improve the forming quality of stepped parts, this study developed a pair of forming devices based on the principle of the HDD process and built a test platform to conduct experimental research.\u0026nbsp;The effects of the pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of parts were analyzed. To further improve the part filling, an orthogonal test of four levels and factors was conducted. Through simulation analysis, the optimal parameter combination was obtained, and a stepped part with high formability was obtained. The main conclusions are as follows:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003eBased on the principle of PHDD, the pre-bulging pressure and pre-bulging height were taken as the main factors for the formability analysis of stepped parts, and the forming height of the parts was analyzed. It was found that when the pre-bulging height was 6 mm and the pre-bulging pressure was 3 MPa, the forming height of the parts with good formability and no defects reached 28.9 mm. This combination of process parameters resulted in an optimal part forming height.\u003c/li\u003e\n \u003cli\u003eThe wall thickness distribution of the stepped parts experienced cycles of increasing - decreasing - increasing - decreasing. Excessive thinning occurred at the top and transition corners, where the wall thickness value was the smallest, and thinning occured at the top of the first step. When the pre-bulging height was 6 mm and the pre-bulging pressure was 4 MPa, the minimum wall thickness of the parts was 0.6 mm and the wall thickness distribution was more uniform.\u003c/li\u003e\n \u003cli\u003eAfter using the\u0026nbsp;PHDD\u0026nbsp;test, the top of the first step of the stepped part produced an overhanging part, which did not form a beneficial friction. The flange of the part was affected by the blank holder force, the material flow was hindered, and the hardness value at the top of the first step was minimized.\u0026nbsp;The hardness value was greatest at the top transition fillet and the first step fillet of the stepped part, which had the greatest resistance to plastic deformation.\u003c/li\u003e\n \u003cli\u003eThe optimal parameter combination obtained by the simulation orthogonal test was as follows: a pre-bulging height of 6 mm, pre-bulging pressure of 5 MPa, liquid chamber pressure of 6 MPa, and a blank holder force of 8 kN. The optimal process parameters were used for simulation and verification, and it was found that the wall thickness of the stepped parts at the second step was relatively small, indicating that the compression side force at the bottom of the plate played a role in the process of PHDD. Furthermore, there was serious top thinning under the action of tensile stress in the process of the radial flow of the plate. The optimum process parameters were verified by experiments, and it was found that the wall thickness value of the second step of the stepped parts was small. From the top of the second step, the wall thickness value gradually increased, but the wall thickness value began to decrease at the straight wall and rounded corner of the first step. The moldability of the parts was improved under the optimal parameters.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was financially supported by the National Natural Science Foundation of China (No. 52065014), Natural Science Foundation of Guangxi Province (No. 2023GXNSFBA026121), Guangxi Key Laboratory of Manufacturing System \u0026amp; Advanced Manufacturing Technology (No. 22-35-4-S013), and Middle-aged and Young Teachers\u0026apos; Basic Ability Promotion Project of Guangxi (No. 2023KY0220).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interests:\u003c/strong\u003e The authors declared that they have no conflicts of interest.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eYuan SJ, Liu W, Xu YC (2015) New development on technology and equipment of sheet hydroforming. 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Int J Mater Form 16(5):46\u0026ndash;56\u003c/li\u003e\n\u003cli\u003eCoomar S, Kumar SP (2022) Punch-less and die-less sheet hydroforming process for manufacturing of serpentine-shaped micro-channels in ultra-thin sheets. Proc Inst Mech Eng, Part C: J Mech Eng Sci 236(17):9610\u0026ndash;9621\u003c/li\u003e\n\u003cli\u003eAlavi Hashemi SH, Seyedkashi SM (2022) Investigation on improvement of limit drawing ratio in two-stage hydrodynamic deep drawing of cylindrical cups. J Braz Soc Mech Sci Eng 44(10):456\u003c/li\u003e\n\u003cli\u003eLiu Y, Li F, Li C, Xu, J (2019) Effect of reverse pre-bulging on magnetic medium deep drawing formability of aluminum spherical bottom cylindrical parts. Int J Adv Manuf Technol 103(9\u0026ndash;12):4649\u0026ndash;4657\u003c/li\u003e\n\u003cli\u003eDal SR, Darendeliler H (2022) Analysis of side-wall wrinkling in deep drawing processes. Key Eng Mater 6392:732\u0026ndash;743\u003c/li\u003e\n\u003cli\u003eOu L, An Z, Gao Z, Zhou\u003csup\u003e \u003c/sup\u003eS, Men Z (2020) Effects of process parameters on the thickness uniformity in two-point incremental forming (TPIF) with a positive die for an irregular stepped part. Materials 13(11):2634\u0026ndash;2634\u003c/li\u003e\n\u003cli\u003eWang H, Shen X (2021) A novel hydrodynamic deep drawing utilizing a combined floating and static die cavity. Int J Adv Manuf Technol 114(3):1\u0026ndash;11\u003c/li\u003e\n\u003cli\u003eBallikaya H, Savas V, Ozay C (2020) The limit drawing ratio in die angled hydromechanical deep drawing method. Int J Adv Manuf Technol 106(1\u0026ndash;2):791\u0026ndash;801\u003c/li\u003e\n\u003cli\u003eLarsen B (1977) Hydromechanical forming of sheet metal. Sheet Metal Industries.\u003c/li\u003e\n\u003cli\u003eChen D, Xu Y, Zhang S, Zhao ZJ, El-Aty AA, Ma Y, Li JM (2018) Evaluation of numerical and experimental investigations on the hybrid sheet hydroforming process to produce a novel high-capacity engine oil pan. Int J Adv Manuf Technol 97(9\u0026ndash;12):3625\u0026ndash;3636\u003c/li\u003e\n\u003cli\u003eKim TJ, Yang DY, Han SS (2004) Numerical modeling of the multi-stage sheet pair hydroforming process. J Mater Process Tech 151(1\u0026ndash;3):48\u0026ndash;53\u003c/li\u003e\n\u003cli\u003eZhang JP, Chen WL, Zhou YC (2020) Design and simulation of forming process of multi-step deep cylindrical parts. J Netshape Form Eng 5(04):31\u0026ndash;34\u003c/li\u003e\n\u003cli\u003eRen GY, Wang XK, He WF (2021) Analysis and numerical simulation of multi-drawing forming process of second-order cylindrical parts. 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Int J Adv Manuf Technol 132(11\u0026ndash;12):5733\u0026ndash;5752\u003c/li\u003e\n\u003cli\u003eTang Y, Zhang J, Zhan M, Jiao H, Cheng P, Dai M (2023) Internal hydroforming of large stainless-steel eggshells from stepped preforms. Metals 13(8):1352\u003c/li\u003e\n\u003cli\u003eJing XL, He ZZ, Feng XM, Li C, Zhou YY (2022) Study on hydroforming of AA6061-T6 aluminum alloy sheet based on upper sheet. Int J Adv Manuf Technol 123(11\u0026ndash;12):4447\u0026ndash;4464\u003c/li\u003e\n\u003cli\u003eEladi A, Abouellata OB, Samuel M, Tawakol AE (2022) Effect of hydroforming drawing cups on thickness variation and surface roughness. Int J Eng Res Africa 59:1\u0026ndash;18\u003c/li\u003e\n\u003cli\u003eYusuf S, Yakup T (2023) Experimental and statistical investigation of mechanical properties and surface roughness in additive manufacturing with selective laser melting of AlSi10Mg alloy. J Braz Soc Mech Sci Eng 45(10):515\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Stepped parts, Hydromechanical deep-drawing, Pre-bulging, Wall thickness distribution, Formability","lastPublishedDoi":"10.21203/rs.3.rs-5345272/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5345272/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWith the development of lightweight materials in various fields, there is a need to research and improve the application of aluminum alloys in sheet metal forming, including body covering parts and complex curved aircraft skins. Specifically, the forming quality and formability of complex stepped parts, such as automobile motor shells and oil bottom boxes, should be improved. Therefore, this study is based on the principle of pre-bulging hydromechanical deep-drawing (PHDD), conducting a forming study of 1060-O aluminum plate with stepped parts. First, based on the analysis of stepped parts, a forming device consisting of a hydraulic punch and rigid die is designed, and a PHDD test platform is built to conduct experiments. Second, the effects of pre-bulging parameters on the forming height, wall thickness distribution, and hardness distribution of stepped parts are analyzed. Finally, to obtain parts with good formability under an optimal parameter combination, a four-factor and four-level orthogonal test is designed, and simulation analysis is conducted using DYNAFORM software. The results show that the wall thickness distribution of the stepped parts is more uniform under the PHDD process, and the movable die designed by the forming device can effectively improve the forming height of stepped parts, reaching 28.9 mm. This study has engineering applications for improving the formability and forming quality of stepped parts.\u003c/p\u003e","manuscriptTitle":"Pre-bulging hydromechanical deep-drawing forming performance of a hydraulic punch for stepped parts","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-11-15 16:04:00","doi":"10.21203/rs.3.rs-5345272/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2024-11-11T13:41:14+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-11-04T12:00:13+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-11-01T10:54:19+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","date":"2024-10-28T04:20:45+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c7155b39-76ab-489d-aa2a-2030953c2767","owner":[],"postedDate":"November 15th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-06-21T14:45:01+00:00","versionOfRecord":[],"versionCreatedAt":"2024-11-15 16:04:00","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5345272","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5345272","identity":"rs-5345272","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}