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Hydroforming of automotive structural components with rectangular-sections
ARTICLE IN PRESS
International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206 www.elsevier.com/locate/ijmactool
Hydroforming of automotive structural components with rectangular-sections S.J. Yuan, C. Han, X.S. Wang School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China Available online 15 May 2006
Abstract An experimental and numerical simulation was conducted to investigate hydroforming of automotive rectangular-section structural components and the results were used as guidelines for some prototypes. The effect of loading path on the failures and thickness distribution was discussed and the reasons were analyzed for the failures, such as bursting and folding. Hydroforming with axial feeding is strongly sensitive to the loading path. Bursting occurs in transition zone in the calibration when the internal pressure increases faster than the axial feeding. Otherwise, folding will take place due to too much axial feeding. There is the maximum thickness at central point of the side of cross-section and the minimum thickness at the transition area. If the n value of the tube material is bigger, the thickness of the final part will be more uniform. By using a petal-like perform section shape, the pressure for forming the transition radii was greatly reduced and components with small radii can be formed with relatively low pressure. r 2006 Elsevier Ltd. All rights reserved. Keywords: Hydroforming; Internal high pressure forming; Hollow component; Automotive part
1. Introduction Most of automotive hollow components such as chassis parts and space frames have various rectangular and/or similar shape sections adapting to different loading to reduce weight [1,2]. An extraordinary feature of tube hydroforming is that a hollow component with variable closed-sections can be integrally formed in one process step so that the number of parts and weight is reduced and stiffness of the part is improved [3,4]. With global R&D activities [5–7], tube hydroforming has also been recognized as an important technology for manufacturing lightweight structural parts in automotive industry. The applications of the hydroformed structural parts have grown to considerable scale in North American and Europe and there is a large potential market in Asia [8,9]. The pressure to form a transition radius of a rectangular section is inversely proportional to its radius value. If there is
a very small radius in the component, a very high pressure is necessary to obtain the designed component shape. As a result, a heavy hydraulic press for closing die and axial cylinders with large tonnages are needed and the die structure must be strengthened so that the investment for equipment is higher and the die life is shorter. Therefore, how to reduce the pressure to form small transition radii in a hollow component is very important in tube hydroforming [10,11]. In this paper, a comprehensive investigation has been conducted into hydroforming of stainless steel tube in the square section die. The effect of loading path on the failures and thickness distribution is discussed and the reasons are analyzed for bursting and folding. A method is proposed for forming small corner by lower pressure through a petal-like perform section shape. The results were used as guidelines for hydroforming some automotive part prototypes. 2. Hydroforming of square section hollow component
Corresponding author. Tel/fax: +86 451 86418776. Also corresponding author. Tel.: +86 451 86414761;
fax: +86 451 86414751 E-mail addresses: [email protected] (S.J. Yuan), [email protected] (C. Han). 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.01.038
2.1. Dimension of part Fig. 1 shows the shape and dimensions of a square section hollow component to be formed in the experiment.
ARTICLE IN PRESS S.J. Yuan et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206
1202
Internal pressure p (MPa)
250
Fig. 1. Shape and dimensions of part.
Path 1 Path 2 Path 3 Path 4
200
150 100
50
Table 1 Mechanical properties of stainless steel 1Cr18Ni9Ti
0 Young’s modulus E (Gpa)
Yielding stress ss (MPa)
Tensile strength sb (MPa)
Elongation d(%)
208
368
628
50
n-value
0
2
4
6
8
Axial displacement s (mm) 0.32
Fig. 2. Load paths.
The side length of the square section is 45 mm and the transition radius is 6 mm. 2.2. Tube A tube with 40 mm in diameter and 2 mm in thickness was used in this experiment. The expansion ratio from the tube circle section to the square section is 36%. The material of the tube is a stainless steel, 1Cr18Ni9Ti. Its mechanical properties are shown in Table 1.
Fig. 3. Bursting in hydroforming without axial feeding.
2.3. Loading paths Four loading paths, i.e. the relationship of internal pressure and axial displacement, used in this experiment are shown in Fig. 2, indicated as Path 1, Path 2, Path 3, and Path 4. These paths can be divided into two groups: one is hydroforming without axial feeding, as shown by Path 1. It means that the axial cylinders do not feed materials into the expansion zone, the axial forces are used only for sealing and the tube is formed by free bulging. The other, including Path 2, Path 3 and Path 4, is that the axial cylinders push additional material into the expansion zone. In this case, the tube is formed under the simultaneous action of the internal pressure and the axial feeding. 2.3.1. Hydroforming without axial feeding Fig. 3 shows the part obtained by hydroforming without axial feeding. When the internal pressure is 105 MPa, the transition radius is 13.5 mm, which is 7.5 mm larger than the design value. However, the bursting occurred at the transition zone due to excessive thinning. In this case, the axial cylinders do not feed any material into the expansion zone, and the expansion of tube is conducted at plane strain state. The forming limit is lower and plastic deformation focuses mainly on the transition zone. Therefore, more material should be pushed into the expansion zone to change the stain state and improve the forming limit.
Fig. 4. Folding in hydroforming with unsatisfactory loading path.
2.3.2. Hydroforming with axial feeding Fig. 4 shows the shape of the part obtained with Path 2, by which the total axial displacement is 8 mm and the maximum calibration pressure is 120 MPa. Due to the axial displacement increasing faster than the pressure going up, folding occurs in the workpiece at the right side. Although the subsequent calibration pressure is very high, folding cannot be removed. The reason for the folding is that the material fed by the axial compression cannot be converted into the circumferential expansion. This material, therefore, is accumulated along the axial direction so that the folding is formed. If the internal pressure increases faster than the axial feeding moves, such as Path 3, the axial feeding cannot supply enough material for the circumferential expansion. As a result, the thickness becomes thinner and thinner, the bursting also occurred in transition zone as the calibration pressure is very high. In order to form a sound part with relatively uniform thickness distribution, it is necessary to
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choose a reasonable loading path to avoid folding, wrinkling and bursting. Fig. 5 shows a sound part obtained with Path 4. When the axial feeding is 5.5 mm at each end of the tube, two barrels occurred along the axial direction. When the internal pressure is 240 MPa and the axial feeding reaches 16 mm, the sound part was formed, as shown in Fig. 5(b). 2.4. Dimension and thickness distribution The dimension and tolerances of the square section part are designed with 45 mm70.1 mm in each side length and the transition radius 670.2 mm. The measured side length is 44.94 mm and the transition radius 6.2 mm.The geometry dimensions of the finished part are satisfactory with the design requirement, especially the transition radius conform to the designed value 670.2 mm. Fig. 6 shows the thickness distribution along the circumferential direction at the symmetric plane of the finished part. It can be seen from this figure that the maximum thickness is at the central point of each side of the square section and the minimum thickness is at the transition zone. The maximum thickness is 1.728 mm and the minimum thinning rate is 13.6%. The minimum thickness is 1.468 mm and the maximum thinning rate is 26.6%.
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3. Forming small transition radii with relatively lower pressure 3.1. Motivation Fig. 7(a) is a schematic diagram about the forces around the transition corner. It can be seen that the calibration pressure to shape the transition corner radius must be enough to overcome the friction force Ff between the die surface and the tube, and produce the tensile force Fa to make plastic deformation occurring in the tube. The higher the pressure, the bigger the friction force in the last calibration stage because the friction force is directly proportional to the pressure. If a petal-like section shape can be preformed, as shown in Fig. 7(b), the central zones of the four sides of the preform section do not contact with the die sides before calibration, thus the tube metal is easy to flow into the transition corner area in calibration stage. Moreover, a positive force Fb along the sides, whose direction is opposite to that of the friction force, is produced by the internal pressure and is beneficial to overcome the friction force Ff and push the material into the corner. Therefore, the pressure for forming the transition corner can be greatly reduced and the components with small radii can be formed with relatively lower pressure. 3.2. Experiment 3.2.1. Tube Tubes with 51 mm in diameter and 1.5 mm in thickness were used in the experiment. The material of the tube is carbon steel with carbon content of 0.2% (w.t.). Its mechanical properties are as follows: yielding stress ss ¼ 310 Mpa, tensile strength sb ¼ 435 Mpa and elongation d ¼ 28%.
Fig. 5. The part formed by hydroforming with satisfactory loading path. (a) Middle shape. (b) Finished part.
3.2.2. Dimensions of part Fig. 8 shows the shape and dimensions of part. For simple, a square section with transition radii 5 mm is selected. Three different side length of the square section are used to compare effect of preform section shape and expansion ratio on the pressure to form the transition radii. Ff t
Fa
corner
Ff
Fb
Die Surface
r
p
ε=0% ε = −10% ε = −20% ε = −30%
r
p
the most thinning
(a) (a)
Die Surface
(b)
(b)
Fig. 6. Thickness distribution. (a) Thickness distribution. (b) The most thinning position.
Fig. 7. Principle of forming small transition radii with relatively lower pressure. (a) Forces around transition radii area. (b) A petal-like section shape.
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S.J. Yuan et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206
For expansion ratio of 0%, the side length of the square section is a ¼ 42.2 mm; for expansion ratio 3.5%, a ¼ 43.5 mm; for expansion ratio 10%, a ¼ 46 mm. 3.2.3. Experiment results Fig. 9(a) shows the section shape of preforms obtained from the die with a parting line along diagonal of the square section. When the expansion ratio is 3.5%, the shape of the preform section is satisfactory and sound parts can be successfully formed with relatively lower pressure. The part with the expansion ratio 3.5% shown in Fig. 9(b) was formed from the preform with section shape shown in Fig. 9(a) by using actual forming pressure 90 MPa. An estimated forming pressure is 126 MPa by a simple empirical equation p ¼ t=r ss , in which thickness t is 1.5 mm, radius r is 5 mm and yielding stress ss is 310 MPa. The actual forming pressure is reduced by 28.6% than the estimated pressure.
Fig. 10. Finite element model.
3.3. Finite element simulation and analysis 3.3.1. Finite element model process The numerical simulations are carried out with a dynamic explicit code LS-DYNA. Because of the symmetrical shape, a half of the tube blank is modeled, as shown in Fig. 10. The tube is modeled as an isotropic material obeying Mises criterion and is meshed by Belytschko-Tsay shell elements. Coulomb friction model is adopted in this simulation and the friction factor is assigned according to practical processes. The material mode of the tube blank is s ¼ 648e0.22.
Perform Shape
Fig. 8. Shape and dimensions of part.
Fig. 9. Hydroformed part with a satisfactory preform cross-section shape. (a) Satisfactory preform cross-section shape. (b) Finished part.
Fig. 11. Shape and thickness distribution of the preforming.
3.3.2. Finite element simulation During performing, the lower die keeps static and the upper die moves downward to press the tube, and then the tube blank is preformed into the shape as shown in Fig. 11. At that time, the radii of the designed cross-section have been got nearly even though the internal pressure is still not exerted. The expansion ratio of perimeter from the tube blank to the final component is 3.5%. After performing, the radii of the up and down corners are 6.43 mm, and the radii of the left and right corners are 5.55 mm. At the transition zone of the edges, the thickness is increased by 2%. 3.3.3. Thickness distribution after hydroforming After hydroforming, the part has been formed into the final shape with the expansion ratio of 3.5%. The thickness distribution is shown in Fig. 12. In the forming zone, the thickness at the middle point of the side plane is thicker than other position. The thinnest point is located in the transition zone between the corner and the side plan, not in the middle of the side. Moreover, the thickness decreases gradually from the plane middle to the transition zone and increases from the transition zone to the middle of the corner, which is corresponding to the experiment. 3.3.4. Effect of n-value on thickness distributions The effect of n-value of materials is simulated on thickness distributions of hydroforming parts with the expansion ratio of 3.5%. For n ¼ 0.23, the minimum thickness at the transition area is 1.233 mm (the thinning
ARTICLE IN PRESS S.J. Yuan et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206
rate ¼ 17.8%); for n ¼ 0.32, the minimum thickness at the transition area is 1.318 mm (the thinning rate ¼ 12.1%). 4. Application in automotive prototype parts
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perimeter of section A–A is 124.82 mm and that of section C–C is 218.27 mm, which is about 1.75 times of that of section A–A. It cannot be formed from a simple tube so that preform is necessary. The part is successfully formed by using the bottle-shaped part preform, as shown in Fig. 15.
4.1. Rear axle arm part Fig. 13 shows the shape and typical cross-sections of the rear axle arm part for a car. The measured data indicated that the dimensions of the hydroformed part are corresponding with the design requirements. Nine steps were needed to make this part by conventional stamping process. By hydroforming, only three steps are necessary, i.e. bending-hydroforming-end cutting. A tube with diameter of F70 mm and thickness in 4 mm were used to form this part.
4.3. Engine cradle Fig. 16 shows prototype of an engine cradle, which is a hollow component with 3D axis and 18 typical crosssections varying from rectangular, trapezoidal to irregular. The excessive thinning at the corners of the workpiece is reduced through a satisfactory bending process and then the fracture during hydroforming is avoided. Several reasonable preform section shapes have been designed for
4.2. Turning arm
C
Fig. 14 shows a turning arm part used for a car. The most difficult to form this part is that there is a larger perimeter difference between section A–A and section C–C. The
45
B
15.5
A
A
B
C 224.7
(a) C-C R8¡À1
34.2
R5¡À1
15.5
R5
45
B-B
A-A
51.2 35¡À1
3¡ã
71¡À1
(b)
Fig. 12. Thickness distribution of finished part at pressure of 90 Mpa.
Fig. 14. Shape and dimensions of turning arm part. (a) Dimensions of turning arm part. (b) Typical cross-sections.
Fig. 13. Hydroformed rear axle arm part. (a) Hydroformed rear axle arm. (b) Three typical cross-sections.
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(3) The thickness distribution along the cross-section is as follow: the maximum thickness is at central point of the side of cross-section and the minimum thickness is at the transition area. If the n value is bigger, the thickness of the final part is more uniform. (4) The friction force between the die surface and tube is a main reason why higher pressure is needed to form small radii. By a petal-like perform section shape, the pressure for forming the transition radii is greatly reduced and the components with small radii can be formed with relatively lower pressure. For the part conducted in the experimental, the forming pressure is reduced by 28.6% than the estimated forming pressure. Fig. 15. Hydroformed turning arm. (a) Preform. (b) Finished part.
Acknowledgment This paper was financially supported by National Natural Science Foundation of China (Project number: 59975021, 50525516). The authors would like to take this opportunity to express their sincere appreciation.
References
Fig. 16. Shape and dimensions of engine cradle. (a) Hydroformed engine cradle. (b) Typical cross-sections.
typical cross-sections, by which the thickness distribution was controlled and the flash generated from the die parting surface in the final forming was avoided. 5. Conclusions (1) The forming limit in hydroforming without axial feeding is lower and plastic deformation focuses mainly on the transition zone between the corner and side. As a result, bursting occurs at transition zone as excessively thinning. (2) Hydroforming with axial feeding is strongly sensitive to loading path, i.e. the relationship of the internal pressure and the axial feeding. If the internal pressure increases faster than the axial feeding moves, bursting occurs in transition zone in the calibration. Otherwise, folding takes place due to more axial feeding.
[1] F. Dohmann, Ch. Hartl, Tube hydroforming—research and practical application, Journal of Materials Processing Technology 71 (1997) 174–186. [2] M. Koc, T. Altan, An overall review of the tube hydroforming (THF) technology, Journal of Materials Processing Technology 108 (2001) 384–393. [3] G. Nefussi, A. Combescure, Coupled buckling and plastic instability for tube hydroforming, International Journal of Mechanical Science 44 (2002) 899–914. [4] S.J. Yuan, X.S. Wang, G. Liu, L.H. Lang, Z.R. Wang, Research on hydroforming of tubular components with changeable cross-sections, in: Proceeding of the seven ICTP, Yokohama, Japan, October 27–November 1, 2002, pp. 1495–1500. [5] H.Y. Li, S.J. Yuan, Z.R. Wang, Research on Square Lightweight Component by Hydroforming Process, Journal of Materials Science and Technology 17 (2001) 158. [6] K. Sergert, Research in Hydroforming at the Institute of Metal forming Technology of the University of Stuttgart, in: Proceedings of Internal Conference on Hydroforming, Sttugart, Germany, 2003, pp. 245–258. [7] S.J. Yuan, G. Liu, X.S. Wang, Z.R. Wang, Use of wrinkles in tube hydroforming—idea and examples, in: International Conference on Hydroforming, Sttugart, Germany, 2003, pp. 79–90. [8] H. Abe, The state of the art in tube hydroforming technology in Japan, in: Proceedings of the TUBEHYDRO2003, Aichi, Japan, 2003, pp. 42–43. [9] B.S. Kang, The state of the art in tube hydroforming technology— numerical analysis and design of hydroforming processes using FEM, in: Proceedings of the TUBEHYDRO2003, Aichi, Japan, 2003, pp. 71–80. [10] S.J. Yuan, G. Liu, Z.R. Wang, Hydroforming of rectangular-section structural components with relatively lower pressure, in: Proceedings of the TUBEHYDRO2003, Aichi, Japan, 2003, pp. 13–17B. [11] T. Schulze, Werle, pre-forming-key technology in the hydroforming process chain, in: Proceedings of Internal Conference on Hydroforming, Sttugart, Germany, 2003, pp. 315–352.
International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206 www.elsevier.com/locate/ijmactool
Hydroforming of automotive structural components with rectangular-sections S.J. Yuan, C. Han, X.S. Wang School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China Available online 15 May 2006
Abstract An experimental and numerical simulation was conducted to investigate hydroforming of automotive rectangular-section structural components and the results were used as guidelines for some prototypes. The effect of loading path on the failures and thickness distribution was discussed and the reasons were analyzed for the failures, such as bursting and folding. Hydroforming with axial feeding is strongly sensitive to the loading path. Bursting occurs in transition zone in the calibration when the internal pressure increases faster than the axial feeding. Otherwise, folding will take place due to too much axial feeding. There is the maximum thickness at central point of the side of cross-section and the minimum thickness at the transition area. If the n value of the tube material is bigger, the thickness of the final part will be more uniform. By using a petal-like perform section shape, the pressure for forming the transition radii was greatly reduced and components with small radii can be formed with relatively low pressure. r 2006 Elsevier Ltd. All rights reserved. Keywords: Hydroforming; Internal high pressure forming; Hollow component; Automotive part
1. Introduction Most of automotive hollow components such as chassis parts and space frames have various rectangular and/or similar shape sections adapting to different loading to reduce weight [1,2]. An extraordinary feature of tube hydroforming is that a hollow component with variable closed-sections can be integrally formed in one process step so that the number of parts and weight is reduced and stiffness of the part is improved [3,4]. With global R&D activities [5–7], tube hydroforming has also been recognized as an important technology for manufacturing lightweight structural parts in automotive industry. The applications of the hydroformed structural parts have grown to considerable scale in North American and Europe and there is a large potential market in Asia [8,9]. The pressure to form a transition radius of a rectangular section is inversely proportional to its radius value. If there is
a very small radius in the component, a very high pressure is necessary to obtain the designed component shape. As a result, a heavy hydraulic press for closing die and axial cylinders with large tonnages are needed and the die structure must be strengthened so that the investment for equipment is higher and the die life is shorter. Therefore, how to reduce the pressure to form small transition radii in a hollow component is very important in tube hydroforming [10,11]. In this paper, a comprehensive investigation has been conducted into hydroforming of stainless steel tube in the square section die. The effect of loading path on the failures and thickness distribution is discussed and the reasons are analyzed for bursting and folding. A method is proposed for forming small corner by lower pressure through a petal-like perform section shape. The results were used as guidelines for hydroforming some automotive part prototypes. 2. Hydroforming of square section hollow component
Corresponding author. Tel/fax: +86 451 86418776. Also corresponding author. Tel.: +86 451 86414761;
fax: +86 451 86414751 E-mail addresses: [email protected] (S.J. Yuan), [email protected] (C. Han). 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.01.038
2.1. Dimension of part Fig. 1 shows the shape and dimensions of a square section hollow component to be formed in the experiment.
ARTICLE IN PRESS S.J. Yuan et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206
1202
Internal pressure p (MPa)
250
Fig. 1. Shape and dimensions of part.
Path 1 Path 2 Path 3 Path 4
200
150 100
50
Table 1 Mechanical properties of stainless steel 1Cr18Ni9Ti
0 Young’s modulus E (Gpa)
Yielding stress ss (MPa)
Tensile strength sb (MPa)
Elongation d(%)
208
368
628
50
n-value
0
2
4
6
8
Axial displacement s (mm) 0.32
Fig. 2. Load paths.
The side length of the square section is 45 mm and the transition radius is 6 mm. 2.2. Tube A tube with 40 mm in diameter and 2 mm in thickness was used in this experiment. The expansion ratio from the tube circle section to the square section is 36%. The material of the tube is a stainless steel, 1Cr18Ni9Ti. Its mechanical properties are shown in Table 1.
Fig. 3. Bursting in hydroforming without axial feeding.
2.3. Loading paths Four loading paths, i.e. the relationship of internal pressure and axial displacement, used in this experiment are shown in Fig. 2, indicated as Path 1, Path 2, Path 3, and Path 4. These paths can be divided into two groups: one is hydroforming without axial feeding, as shown by Path 1. It means that the axial cylinders do not feed materials into the expansion zone, the axial forces are used only for sealing and the tube is formed by free bulging. The other, including Path 2, Path 3 and Path 4, is that the axial cylinders push additional material into the expansion zone. In this case, the tube is formed under the simultaneous action of the internal pressure and the axial feeding. 2.3.1. Hydroforming without axial feeding Fig. 3 shows the part obtained by hydroforming without axial feeding. When the internal pressure is 105 MPa, the transition radius is 13.5 mm, which is 7.5 mm larger than the design value. However, the bursting occurred at the transition zone due to excessive thinning. In this case, the axial cylinders do not feed any material into the expansion zone, and the expansion of tube is conducted at plane strain state. The forming limit is lower and plastic deformation focuses mainly on the transition zone. Therefore, more material should be pushed into the expansion zone to change the stain state and improve the forming limit.
Fig. 4. Folding in hydroforming with unsatisfactory loading path.
2.3.2. Hydroforming with axial feeding Fig. 4 shows the shape of the part obtained with Path 2, by which the total axial displacement is 8 mm and the maximum calibration pressure is 120 MPa. Due to the axial displacement increasing faster than the pressure going up, folding occurs in the workpiece at the right side. Although the subsequent calibration pressure is very high, folding cannot be removed. The reason for the folding is that the material fed by the axial compression cannot be converted into the circumferential expansion. This material, therefore, is accumulated along the axial direction so that the folding is formed. If the internal pressure increases faster than the axial feeding moves, such as Path 3, the axial feeding cannot supply enough material for the circumferential expansion. As a result, the thickness becomes thinner and thinner, the bursting also occurred in transition zone as the calibration pressure is very high. In order to form a sound part with relatively uniform thickness distribution, it is necessary to
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choose a reasonable loading path to avoid folding, wrinkling and bursting. Fig. 5 shows a sound part obtained with Path 4. When the axial feeding is 5.5 mm at each end of the tube, two barrels occurred along the axial direction. When the internal pressure is 240 MPa and the axial feeding reaches 16 mm, the sound part was formed, as shown in Fig. 5(b). 2.4. Dimension and thickness distribution The dimension and tolerances of the square section part are designed with 45 mm70.1 mm in each side length and the transition radius 670.2 mm. The measured side length is 44.94 mm and the transition radius 6.2 mm.The geometry dimensions of the finished part are satisfactory with the design requirement, especially the transition radius conform to the designed value 670.2 mm. Fig. 6 shows the thickness distribution along the circumferential direction at the symmetric plane of the finished part. It can be seen from this figure that the maximum thickness is at the central point of each side of the square section and the minimum thickness is at the transition zone. The maximum thickness is 1.728 mm and the minimum thinning rate is 13.6%. The minimum thickness is 1.468 mm and the maximum thinning rate is 26.6%.
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3. Forming small transition radii with relatively lower pressure 3.1. Motivation Fig. 7(a) is a schematic diagram about the forces around the transition corner. It can be seen that the calibration pressure to shape the transition corner radius must be enough to overcome the friction force Ff between the die surface and the tube, and produce the tensile force Fa to make plastic deformation occurring in the tube. The higher the pressure, the bigger the friction force in the last calibration stage because the friction force is directly proportional to the pressure. If a petal-like section shape can be preformed, as shown in Fig. 7(b), the central zones of the four sides of the preform section do not contact with the die sides before calibration, thus the tube metal is easy to flow into the transition corner area in calibration stage. Moreover, a positive force Fb along the sides, whose direction is opposite to that of the friction force, is produced by the internal pressure and is beneficial to overcome the friction force Ff and push the material into the corner. Therefore, the pressure for forming the transition corner can be greatly reduced and the components with small radii can be formed with relatively lower pressure. 3.2. Experiment 3.2.1. Tube Tubes with 51 mm in diameter and 1.5 mm in thickness were used in the experiment. The material of the tube is carbon steel with carbon content of 0.2% (w.t.). Its mechanical properties are as follows: yielding stress ss ¼ 310 Mpa, tensile strength sb ¼ 435 Mpa and elongation d ¼ 28%.
Fig. 5. The part formed by hydroforming with satisfactory loading path. (a) Middle shape. (b) Finished part.
3.2.2. Dimensions of part Fig. 8 shows the shape and dimensions of part. For simple, a square section with transition radii 5 mm is selected. Three different side length of the square section are used to compare effect of preform section shape and expansion ratio on the pressure to form the transition radii. Ff t
Fa
corner
Ff
Fb
Die Surface
r
p
ε=0% ε = −10% ε = −20% ε = −30%
r
p
the most thinning
(a) (a)
Die Surface
(b)
(b)
Fig. 6. Thickness distribution. (a) Thickness distribution. (b) The most thinning position.
Fig. 7. Principle of forming small transition radii with relatively lower pressure. (a) Forces around transition radii area. (b) A petal-like section shape.
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For expansion ratio of 0%, the side length of the square section is a ¼ 42.2 mm; for expansion ratio 3.5%, a ¼ 43.5 mm; for expansion ratio 10%, a ¼ 46 mm. 3.2.3. Experiment results Fig. 9(a) shows the section shape of preforms obtained from the die with a parting line along diagonal of the square section. When the expansion ratio is 3.5%, the shape of the preform section is satisfactory and sound parts can be successfully formed with relatively lower pressure. The part with the expansion ratio 3.5% shown in Fig. 9(b) was formed from the preform with section shape shown in Fig. 9(a) by using actual forming pressure 90 MPa. An estimated forming pressure is 126 MPa by a simple empirical equation p ¼ t=r ss , in which thickness t is 1.5 mm, radius r is 5 mm and yielding stress ss is 310 MPa. The actual forming pressure is reduced by 28.6% than the estimated pressure.
Fig. 10. Finite element model.
3.3. Finite element simulation and analysis 3.3.1. Finite element model process The numerical simulations are carried out with a dynamic explicit code LS-DYNA. Because of the symmetrical shape, a half of the tube blank is modeled, as shown in Fig. 10. The tube is modeled as an isotropic material obeying Mises criterion and is meshed by Belytschko-Tsay shell elements. Coulomb friction model is adopted in this simulation and the friction factor is assigned according to practical processes. The material mode of the tube blank is s ¼ 648e0.22.
Perform Shape
Fig. 8. Shape and dimensions of part.
Fig. 9. Hydroformed part with a satisfactory preform cross-section shape. (a) Satisfactory preform cross-section shape. (b) Finished part.
Fig. 11. Shape and thickness distribution of the preforming.
3.3.2. Finite element simulation During performing, the lower die keeps static and the upper die moves downward to press the tube, and then the tube blank is preformed into the shape as shown in Fig. 11. At that time, the radii of the designed cross-section have been got nearly even though the internal pressure is still not exerted. The expansion ratio of perimeter from the tube blank to the final component is 3.5%. After performing, the radii of the up and down corners are 6.43 mm, and the radii of the left and right corners are 5.55 mm. At the transition zone of the edges, the thickness is increased by 2%. 3.3.3. Thickness distribution after hydroforming After hydroforming, the part has been formed into the final shape with the expansion ratio of 3.5%. The thickness distribution is shown in Fig. 12. In the forming zone, the thickness at the middle point of the side plane is thicker than other position. The thinnest point is located in the transition zone between the corner and the side plan, not in the middle of the side. Moreover, the thickness decreases gradually from the plane middle to the transition zone and increases from the transition zone to the middle of the corner, which is corresponding to the experiment. 3.3.4. Effect of n-value on thickness distributions The effect of n-value of materials is simulated on thickness distributions of hydroforming parts with the expansion ratio of 3.5%. For n ¼ 0.23, the minimum thickness at the transition area is 1.233 mm (the thinning
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rate ¼ 17.8%); for n ¼ 0.32, the minimum thickness at the transition area is 1.318 mm (the thinning rate ¼ 12.1%). 4. Application in automotive prototype parts
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perimeter of section A–A is 124.82 mm and that of section C–C is 218.27 mm, which is about 1.75 times of that of section A–A. It cannot be formed from a simple tube so that preform is necessary. The part is successfully formed by using the bottle-shaped part preform, as shown in Fig. 15.
4.1. Rear axle arm part Fig. 13 shows the shape and typical cross-sections of the rear axle arm part for a car. The measured data indicated that the dimensions of the hydroformed part are corresponding with the design requirements. Nine steps were needed to make this part by conventional stamping process. By hydroforming, only three steps are necessary, i.e. bending-hydroforming-end cutting. A tube with diameter of F70 mm and thickness in 4 mm were used to form this part.
4.3. Engine cradle Fig. 16 shows prototype of an engine cradle, which is a hollow component with 3D axis and 18 typical crosssections varying from rectangular, trapezoidal to irregular. The excessive thinning at the corners of the workpiece is reduced through a satisfactory bending process and then the fracture during hydroforming is avoided. Several reasonable preform section shapes have been designed for
4.2. Turning arm
C
Fig. 14 shows a turning arm part used for a car. The most difficult to form this part is that there is a larger perimeter difference between section A–A and section C–C. The
45
B
15.5
A
A
B
C 224.7
(a) C-C R8¡À1
34.2
R5¡À1
15.5
R5
45
B-B
A-A
51.2 35¡À1
3¡ã
71¡À1
(b)
Fig. 12. Thickness distribution of finished part at pressure of 90 Mpa.
Fig. 14. Shape and dimensions of turning arm part. (a) Dimensions of turning arm part. (b) Typical cross-sections.
Fig. 13. Hydroformed rear axle arm part. (a) Hydroformed rear axle arm. (b) Three typical cross-sections.
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S.J. Yuan et al. / International Journal of Machine Tools & Manufacture 46 (2006) 1201–1206
(3) The thickness distribution along the cross-section is as follow: the maximum thickness is at central point of the side of cross-section and the minimum thickness is at the transition area. If the n value is bigger, the thickness of the final part is more uniform. (4) The friction force between the die surface and tube is a main reason why higher pressure is needed to form small radii. By a petal-like perform section shape, the pressure for forming the transition radii is greatly reduced and the components with small radii can be formed with relatively lower pressure. For the part conducted in the experimental, the forming pressure is reduced by 28.6% than the estimated forming pressure. Fig. 15. Hydroformed turning arm. (a) Preform. (b) Finished part.
Acknowledgment This paper was financially supported by National Natural Science Foundation of China (Project number: 59975021, 50525516). The authors would like to take this opportunity to express their sincere appreciation.
References
Fig. 16. Shape and dimensions of engine cradle. (a) Hydroformed engine cradle. (b) Typical cross-sections.
typical cross-sections, by which the thickness distribution was controlled and the flash generated from the die parting surface in the final forming was avoided. 5. Conclusions (1) The forming limit in hydroforming without axial feeding is lower and plastic deformation focuses mainly on the transition zone between the corner and side. As a result, bursting occurs at transition zone as excessively thinning. (2) Hydroforming with axial feeding is strongly sensitive to loading path, i.e. the relationship of the internal pressure and the axial feeding. If the internal pressure increases faster than the axial feeding moves, bursting occurs in transition zone in the calibration. Otherwise, folding takes place due to more axial feeding.
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