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Global optimisation of the production of complex aluminium tubes by the hydroforming process
CIRP Journal of Manufacturing Science and Technology 9 (2015) 1–11
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CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Global optimisation of the production of complex aluminium tubes by the hydroforming process R. Bihamta a,1,*, Q.-H. Bui b, M. Guillot b, G. D’Amours c, A. Rahem c, M. Fafard b a
Alcoa Innovation, East Cre´mazie Blvd., Montreal, Qc H2M 0A6, Canada Aluminium Research Centre, REGAL, Laval University, Que´bec, Qc G1V 0A6, Canada c National Research Council Canada, Aluminium Technology Centre, Saguenay, Qc G7H 8C3, Canada b
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 24 March 2015
With the recent development of analysis software products, designers and engineers are able to design more complex parts to obtain better performance in the final products. In this study, the tube hydroforming process, including preceding processes, i.e. variable thickness tube drawing and two-step bending, are globally optimised to obtain parts without any problems like bursting or un-filled zones at the end of the forming processes. Unlike most previous studies which searched for an optimum hydroforming process by changing two hydroforming parameters, i.e. axial load feeding and internal pressure, in this study, the distribution of initial tube wall thickness and the variation of thickness due to bending steps will be taken into account in a global optimisation algorithm. The developed algorithm is a general-purpose algorithm that can encompass different processes and change various parameters in each process to be able to reach the global objective. The case study used was a part that needs two-step variable thickness tube drawing, and two bending steps before hydroforming. To verify the numerical results in each forming stage and at the end of all forming processes, extensive experiments were performed, and acceptable agreements were observed. ß 2015 CIRP.
Keywords: Tube hydroforming Tube bending Variable thickness tube drawing AA6061 Aluminium
Introduction Aluminium tubes, mostly produced by the tube hydroforming (THF) process, play an important role in transportation industries such as automotive and bicycle production. As shown in Fig. 1, in fabricating almost all THF parts, it is necessary to use some other preliminary processes like tube drawing, annealing heat treatment, tube bending, and preforming before the final THF process. The wider application of aluminium tubes by industry is hindered because of the reduced ductility and more complex material behaviour of aluminium in comparison with steels [1]. Various aspects of the THF process have been studied. Xu et al. [2] presented a paper to find the optimum loading path for a trapezoidsectional die. Cheng et al. [3] studied distribution of thickness in a Yshape tube by the finite element (FE) and experimental methods. Xu et al. [4] mathematically studied thickness distribution along the
* Corresponding author. Tel.: +1 586 256 4037; fax: +1 586 492 7205. E-mail address: [email protected] (R. Bihamta). 1 Formerly from Aluminium Research Centre, REGAL, Laval University, QC, Canada. http://dx.doi.org/10.1016/j.cirpj.2015.02.001 1755-5817/ß 2015 CIRP.
cross-section of a square-sectional hydroformed part. Fiorentino et al. [5] proposed a new procedure for friction estimation in THF processes. Koc¸ et al. [26] presented experimental and analytical approaches to characterise materials for the THF process. Korkolis and Kyriakides [6] evaluated the effect of loading path on the failure of inflated aluminium tubes. Hashemi et al. [7] applied a stressbased forming limit diagram to obtain optimum loading paths in THF. Song et al. [8] evaluated the effect of flow stress characteristics of tubular material on forming limit in the THF process. Bortot et al. [9] determined a new test method to characterise the flow stress for the tubes in the hydroforming applications. Kang et al. [10] studied tube size effect on hydroforming formability. The publications above are examples of research performed in this field. However, on the subject of this paper, which is studying the THF process including the preceding processes, there is only little research. For instance, Koc¸ [11] evaluated effect of die crushing and pre-bending on the thickness distribution and formability of complex tubes. Trana [12] showed that the preforming process can be performed by the hydroforming die closing, saving considerable time and production cost. Hwang and Altan [13] studied the crushing processes in combination with performance in a rectangular die. None of the above mentioned studies, however, included the initial tube
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Fig. 1. Tubular automobile parts produced by the THF method. (A) Roof headers, (B) instrument panel support, (C) radiator supports, (D) engine cradles, (E) roof rails, and (F) frame rails [http://www.vari-form.com] [24].
thickness as an optimisation variable. There is also no specialised optimisation algorithm, nor an automatic method to manage the optimisation procedure. Abedrabboa et al. [14] presented an optimisation process linked with a FE model to optimise the high-strength steel tube hydroforming process. In that study, despite having an optimisation algorithm for modification of the hydroforming parameters, they only took into account the THF process without preceding processes. In this paper, in the first step, a code was developed to assign various thicknesses to the initial tube wall. This shell with various thicknesses is considered as the tube issued from one- or two-step variable wall thickness tube drawing. It is worth mentioning that because of the annealing heat treatment after tube drawing, it is assumed that all material properties return to the initial state and there are not any residual stresses induced by the drawing. After assignment of thickness to the shell tube, the FE model is transferred automatically to the bending steps, and afterward the bent tube is transferred to the hydroforming step. Depending on the defined objectives and constraints, the optimisation loop will return to the initial step to change tube thickness and/or some parameters in the hydroforming step to reach the objective. All of the changes in the parameters of the preceding processes and hydroforming step are performed automatically without any user interaction. In the next sections, the processes and their FE models that are involved in the production of the case study part are explained. The experimental section explains the geometric features of the part and the experimental rig. Cold forming processes prior to hydroforming In general, for most THF processes, some preform processes are necessary. Without them, the tube cannot be positioned in the THF die appropriately. Furthermore, the quality of the preceding operations has a direct effect on the quality of final workpiece. In the following sections, the important cold forming processes prior to THF are studied numerically and experimentally. Variable thickness tube drawing Production of variable thickness tubes The variable thickness tube drawing process is a new enhancement applied to the classic tube drawing method to produce tubes with variable thickness along the tube’s length and/ or in the radial direction. As explained in more detail in prior publications like Bihamta et al. [15,16], in this method, the desired variation of wall thickness can be induced through the application of axial displacement of the conic mandrel. However, in this
process some parameters like material heat treatment, its alloying elements, and tool geometry, limit the minimum attainable thickness in one step; if smaller than that is required, it should be performed in more than one step. On the other hand, if two or more tube drawing steps are necessary, the synchronisation between two passes is a crucial factor. If the location of thickness reduction in the second step is not in the appropriate zone, there is a possibility of tube fracture. There are two solutions to avoid this problem. The first solution consists of applying a very accurate nondestructive measurement mechanism, such as a laser, to accurately measure the thickness along the tube axis and implement very precise axial displacement to the tube in the next steps. The implementation of the first solution requires very precise and expensive equipment. Another alternative is the application of mild transition between zones with variable wall thicknesses. This mild transition can guarantee that if there is inaccuracy in the second pass, the tube will not experience any rupture. In the zones that are more prone to bursting in the hydroforming step, augmentation of thickness in the initial tube can eliminate the chance of bursting, and the final thickness in the tube can be controlled. On the other hand, if a zone in the part undergoes lower loads than other regions when in service, the thickness of this region can be reduced to diminish overall weight of part. Details of the numerical and experimental studies on this process are outside the scope of this paper; interested readers can see Bihamta et al. [15,16]. Tube thickness as an optimisation variable in the THF process In this study, it was possible to use solid elements or shell elements to include initial tube thickness in the global THF process optimisation. If solid 3D elements are to be used in the tube bending and THF steps, four-node 2D elements can be used in the tube-bending step. Due to the axi-symmetric geometry of the tube drawing process, the results can then be rotated and converted to complete a 3D tube. In comparison with shell elements, this kind of element has more precision in prediction of thickness variation in the THF process [17], but utilising them seems to be computationally very expensive. On the other hand, application of shell elements for the simulation of THF and tube bending processes seems to be more efficient computationally, and provides acceptable results. Since it is common to do annealing heat treatment after one- or two-step tube drawing, the material property in the drawn tube (after heat treatment) is considered to be the same as the initial material. Therefore, the inclusion of the tube drawing processes in the global optimisation loop seems to be unnecessary, and will increase the computation time. Consequently, the parameter that was included from the tube drawing process is variation of thickness in the tube. For implementation of thickness in the initial tube, a code was developed and included as a part of the preprocessor in the optimisation loop to update values of thickness in the optimisation loop based on the optimisation iterations. This code reads coordinates of various elements and applies the different thicknesses upon request of the optimisation engine. An example of output of this code is presented in Fig. 2. Heat treatment Because of cold deformation in the tube drawing process, the ductility of tubes is reduced, increasing the risk of fracture in the rest of the production cycle, i.e. tube bending and THF. Figs. 3 and 4 show that for tubes drawn in one and two steps the ductility of tubes is reduced considerably with increasing thickness reduction;
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Fig. 2. Application of various thicknesses to the initial tube by the developed preprocessor.
this dictates the necessity for an annealing heat treatment. The level of yield stress also increased considerably with increased deformation (Table 1). In Fig. 5, the annealing heat treatment cycle applied to the tubes after two-step drawing is presented. In zone A of Fig. 5, the temperature of the tubes increased from room temperature to 405 8C as fast as possible. After reaching the maximum temperature
(405 8C), the tubes are kept there during 2 h (zone B), followed by controlled cooling at the 28 8C/h rate down to 260 8C (zone C), and subsequently cooled at the ambient temperature (zone D). The material properties used in the FE analysis for the tubes after annealing heat treatment is presented in Fig. 6. Hollomon’s equation is used for extrapolation of stresses up to larger stresses. Tube bending Rotary-draw tube bending There are various types of bending processes that can be applied as a preceding process in the THF production cycle. In this project the rotary-draw bending method was selected. As shown in Fig. 7, the tube is located between clamp die and bend die, and by the rotation of the bend die, the tube takes the form of the bending die.
Table 1 Specifications of samples in Figs. 3 and 4.
Fig. 3. Stress–strain curves for AA6061 tubes in the original condition (O) and only one-step drawn to outer diameter of 57.15 mm and various thicknesses (details are presented in Table 1).
Fig. 4. Stress–strain curves for AA6061 tubes drawn two steps from 63.5 mm to 57.15 mm and from 57.15 mm to 50.8 mm with various thicknesses (details are presented in Table 1).
Sample #
Initial outer diameter (OD) (mm)
OD after drawing (mm)
Final thickness (mm)
Total number of drawing steps
1 2 3 4 5 6 7 8
63.5 63.5 63.5 63.5 57.15 57.15 57.15 57.15
57.15 57.15 57.15 57.15 50.8 50.8 50.8 50.8
2.59 2.33 2.00 1.91 2.66 2.21 1.58 1.47
1 1 1 1 2 2 2 2
Fig. 5. The applied annealing heat treatment cycle.
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200 180 160
Stress (MPa)
140 120 100 80 60 40 20 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pressure die, and clamp die were modelled using the shell elements (Fig. 8). For the case of this paper, it was necessary to do bending in two steps; therefore the results of the first tube bending stage were transferred to the second bending step. Like experiments in the laboratory, the same dies were used to bend the tube in the next step. Also, to locate the tube from the first bending step to the second step, it is necessary to do some rotations and translations of the mesh; these values are included in the finite element model of the second bending step to enable its automatic performance during the optimisation process. Interested readers are referred to details in Appendix E from Bihamta [19]. Fig. 9 presents the results of tube bending in the second bending step.
Strain (mm/mm)
Fig. 6. Applied material property to the tubes after extrapolation by Holloman’s power law (s ¼ ken , n = 0.263, k = 211.48).
There are some considerations, like the minimum clamping length, multi radii tubes, distance between bends, and minimum bend radius, that should be considered for tube bending specially for tubes to be used in the THF process. Tubes that were not bent precisely will experience pinching in the die closing step, and will burst during the hydroforming step. However as described in detail in Bihamta et al. [18], the special design of the THF die in this case permits small variations in the geometry of bent tubes. It is worth mentioning that if minor flattening and/or wrinkling occurs in the tube bending step, it can be corrected in the hydroforming step. However some wrinkles are difficult to correct, and there is a risk of bursting in the deep wrinkles during the THF process. Therefore, flattening and wrinkling should be avoided as much as possible in the bending step. Regardless of all the advantages with variable thickness tubes, this kind of tube cannot be bent by methods that use a mandrel inside the tube, because the variation of thickness inside the tube hinders entrance of the mandrel into the tubes.
Tube hydroforming (THF) process Tube hydroforming (THF) is one of the most important processes and in some cases the exclusive method for the production of complex shaped tubes. In this process, a tube is located in the die and sealed by one of the sealing methods that will be explained in ‘‘Experiments’’ section. Then by the application of an appropriate loading path, i.e. axial load feeding and hydroforming pressure, it will take the geometry of the die. The liquid in this process is always water with some anticorrosion additives; for some low deformable materials like special aluminium alloys, hot gas is used. After assignment of the thickness distribution to the tube prior to bending, and the bending stage in two steps, the geometry of the
Numerical modelling of rotary-draw bending As explained before, to evaluate and optimise the THF process, it is necessary to include preceding forming processes like tube bending in the optimisation loop; otherwise, the optimisation process will neglect some effects like thickness variation in the bending zone and/or flattening and/or wrinkling by the tube bending zone. In the numerical modelling of the bending process, the tube wall thickness, with variation of thickness along it, is transferred to the bending step. In the FE model, the geometry of the bend die,
Fig. 7. Schematics of rotary-draw bending [http://www.copper.org/applications/ cuni/app_syscomp.html] [25].
Fig. 8. Modelling of the first step, rotary-draw bending (a) before performance of bending, (b) after bending, and (c) distribution of tube thickness at the end of process.
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unsuccessful loading path for the THF process, especially in the regions that experienced thickness reduction. In this study, the geometry of die and tube were designed and meshed in Pro/Engineer and HyperMesh softwares respectively. Because of the complex geometry of the THF die, for better establishment of contact between die parts and tube, different mesh densities are applied to the various parts of the tube in such a way that in the region with more complex geometry and more tube deformation, finer mesh (1.5 mm 1.5 mm) is used, and in other regions coarser meshes, i.e. 3 mm 3 mm are assigned. The surface-to-surface contact formulation is used to define the contact between die parts and tube with a friction coefficient of 0.05 as confirmed in Williams et al. [20]. Fix die was constrained in all directions. For the rear die and upper die they were left constraint free in the moving direction and in other direction they were constrained completely too. To apply, axial feeding to the tube, two rows of nodes in the 35 mm distance from two ends of tube were selected and two different displacements were applied to represent the axial motion of right and left pushers. The distance 35 mm is the length of the guiding zone in the pushers and there is not any variation of thickness in this length. Global optimisation Optimisation procedure
Fig. 9. Modelling of the second step, rotary-draw bending (a) before performance of bending, (b) after bending, and (c) distribution of tube thickness at the end of process.
tube is transferred to the final forming step (THF). As shown in Fig. 10, the tube has a maximum thickness reduction of 5% and thickness increase of 7.9% after two bending steps. Neglecting these thickness variations from prior steps can lead to an
The main objective of this study is to present a methodology for optimising the THF process while taking into account the preceding process. The developed optimisation procedure is able to take into account the preceding process models and automatically copy the results to the next step and to continue to the next optimisation loop. However, depending on user preference, some processes can be excluded from the global optimisation to save computational time. In the global optimisation of this study, the implicit solver of LSDYNA software was used as a FE solver. The shell element with four nodes was used because of its capability to have various thicknesses in each node. LS-OPT software was used as the base optimisation engine, and the required preprocessing and postprocessing operations were performed automatically by the developed codes. Readers interested in more details on optimisation codes can refer to Appendices A–E in Bihamta [19]. Optimisation variables The optimisation procedure of non-linear processes like hydroforming or tube bending with a huge number of elements (2.2 million elements for tube and dies in the hydroforming step) is time consuming. In this study, for the bending (first and second) and hydroforming steps using four CPUs, it takes approximately 2, 6, and 11 h respectively. Therefore, appropriate selection of optimisation variables is an important decision and the variables that seem to have less effect should be excluded. In the case of global optimisation of the THF process, three variables, i.e. hydroforming pressure, axial feeding, and tube initial thickness, are the optimisation variables. In Table 2, domain of change of Table 2 Optimisation variables with their ranges and starts values.
Fig. 10. Initial state of tube with the three-part THF die.
Variable
Start value
Minimum
Maximum
d1 (mm) p1 (MPa) p2 (MPa) th0 (mm)
26 50 56 1.6
24 47.5 55 1.35
34 55 60 1.65
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these variables with starting variables is summarised. For axial feeding only one variable (d1), for hydroforming pressure two variables (p1 and p2), and for initial thickness one variable (th0) is defined.th0 is the thickness of the central region of the tube. Variation of thickness in this zone is less concerned by the THF parameters (pressure and axial feeding). Therefore, by the third variable (thickness variation), the final thickness in this part will be controlled. It is worth mentioning that in other studies it might be interesting to have the thickness of more zones or even location of thickness change as optimisation variables.
This method was used in previous studies like Bihamta et al. [16] and showed acceptable results. For the optimisation algorithm, the leapfrog method is selected. Interested readers can refer to Stander et al. [21] and Myers and Montgomery [22].
Objectives and constraints
Variable thickness tube drawing
For this optimisation process, three direct and one indirect objective were defined. The direct objectives were minimisation of thickness reduction in all regions of the part, complete die filling, and minimisation of thickness increase in two ends of tube. In the tube hydroforming (THF) process, the material flow should be from the zone closer to the pushers to the central zones and material should not be localised in the zones close to the pushers. The localisation of material in these zones was represented by the thickness increase in the optimisation process. The indirect objective was to have the final thickness in the central region of the part in the acceptable range (1.2–1.3 mm). This is called an indirect objective because it is applied as constraint in the optimisation procedure. The other constraint was p2 p1 > 0; guaranteeing that the pressure curve is always increasing. After assignment of the displacement (d1) by the optimisation engine, it will be used directly for the right-hand side in the preprocessing code, and for the left-hand side it will be summed with 6 (as the initial investigation proved that for the left-hand side larger feed is required). However, two separate displacements can be defined as optimisation variables too. For the thickness reduction, all elements were selected to verify their thickness reduction percentages at the end of hydroforming. For die filling verification the displacement of a critical node in the radial direction is maximised. Finally, for the thickness increase minimisation, only the elements in the ends of tubes were selected (Fig. 11). As the values for the thickness increase in FE solver, they are reported as negative values; the responses of this parameter before being used in the minimisation function are multiplied by 1 to be able to use only the minimisation function to three objectives.
As explained earlier, the initial tube for the part selected for this paper, and for a majority of complex THF parts, should have variation of thickness. The experiments for the production of the variable thickness tube were performed in the prototype machine that was fabricated at the Aluminium Research CentreREGAL at Laval University. Interested readers can refer to prior publications on this subject like Bihamta et al. [15] and Bihamta et al. [16] for more details.
Sampling methods In the optimisation process to reduce the number of simulation points, a polynomial metamodel with linear order is selected. Also, for the point selection method, the D-optimal method is selected.
Experiments For production of the selected part in this paper, four different processes are required. In this section the summary of the experiments are presented.
Annealing heat treatment The required heat treatment for the tubes in this paper was performed in a TPS-(Blue M series) oven in the NRC-Aluminium Technology Centre. One of the important features of this oven is its capability for controlled cooling, which made application of heat treatment cycles like Fig. 5 possible. Tube bending The bending operation in this paper was performed by Alutech Ttrg Co. A non-destructive test (NDT) method, i.e. ultrasonic method, is used for measurement of thickness variation after bending the tube. The advantage of this method with respect to the other measurement methods, like measurement by the micrometre, is that in this method it is not necessary to cut the tube to measure its thickness; however, its precision is less than the measurement by micrometre. Tube hydroforming The hydroforming experiments for this paper were performed in an Interlaken HF-1000 press at the NRC-Aluminium Technology Centre. The maximum applicable force by this press in the axial direction and in the feeding cylinder directions are 8.89 MN and 667 kN respectively. This press also has the capability of applying axial feeding by four different cylinders in which two of them are used to apply the axial feeding, and the third one for movement of the rear part of the die. Fig. 12 presents a photo of the THF die and required accessories. The liquid utilised for application of pressure inside the tube was water; to avoid corrosion in the press, NOVACOOL 9034/5 was added. To lubricate the tubes, Hydrodraw 625 was sprayed on the tube outer surface, and after some minutes it dried in the ambient temperature. It is worth pointing out that during hydroforming, the surface of the dies should be sprayed with water to activate the lubricant on the tube surface. Results and discussion Variable thickness tube drawing
Fig. 11. Application of optimisation objectives (a) all regions of part (thickness reduction objective), (b) critical node to guarantee die filling, and (c) two ends of tube to minimise the thickness increase.
In prior publications, Bihamta et al. [15] and Bihamta et al. [16], the majority of the results like state of residual stresses, validation
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Fig. 14. Modified thickness distribution in the tube for two-step drawing.
preferred to increase the minimum thickness to fairly larger values (1.60 mm) to avoid rupture in the tubes with eccentricity. In Fig. 13 the transitions between different thicknesses are fairly sharp, and if appropriate synchronisation is not performed in the second step, there is chance of tube rupture, therefore the transition profile was modified to avoid this problem. Fig. 14 presents the modified thickness distribution. Because of volume constancy, the tube’s total length decreased after the slight increase in middle region thickness. The thickness measurement of the tubes after the drawing process was performed using a micrometre in five different points within the tube diameter after cutting the tubes into two halves. Tube bending
of FE model, optimisation on the initial tube, and tool geometry were presented; in this paper only the experimental results that were not published anywhere else are going to be discussed. Fig. 13 presents the experimental result of the two-step tube drawing; the minimum thickness at the end of the second step is 1.48 mm. In other experiments, the smaller value, i.e. 1.43 mm, for the minimum thickness was also obtained. However, because of considerable eccentricity (0.1–0.15 mm) in the initial tubes, it was
Thickness variation, especially its reduction in the bent regions, is the most important effect of the tube bending process that can affect results in the tube hydroforming step. Fig. 15 presents the thickness reduction prediction by the FE method, after two-step tube bending. The thickness reduction and increase in the outer and inner surfaces of the tube are 4.3% and 5.3% respectively. For validation of numerical results, the thickness of tubes was measured by the ultrasonic method and the average decrease and increase were 3.4% and 7.6% respectively. It seems that the difference between experiments and numerical results has origins such as error in thickness measurement, matching the correspondent points in the zone where there is transition of thickness, and also weakness of the shell element in thickness variation prediction.
Fig. 13. Thickness distribution in the tube after two-step drawing.
Fig. 15. Thickness variation percentages in the tube after two-step bending.
Fig. 12. (a) Three-part THF die installed in HF-1000 hydroforming press and (b) closer view of die showing two parts of three parts die and cylinder for opening the rear part of die.
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The sealing method in this study consists of developing a customised sealing method. This method, by application of a modified pusher design, takes advantage of both local deformation and O-ring sealing methods. Two rows of slots are designed for the O-rings, and the end of the pusher will perform the local deformation (Fig. 18). Two rows of O-rings will seal the tube under lower pressures, and the pusher displacement while there is pressure inside the tube can indent inside the tube without deforming it as in Fig. 17. Interested readers for more information on detail of sealing methods, can see [19]. Experimental and numerical results Fig. 16. Design of pusher for the local deformation method sealing (A) guiding zone, (B) indentation zone, and (C) sealing surface.
Tube hydroforming (THF) Tube sealing One of the most important factors that can completely influence the success of the THF process is appropriate sealing of the tube before and during the process. Without appropriate sealing, application of higher pressures is not possible. The local deformation method, by appropriate pusher design, it indents in the thickness of the tube and locally deforms it and seals the tube during the THF process. As shown in Fig. 16, each pusher has three different zones: the first zone is to guide the pusher inside the tube, and is called the guiding zone (zone A); the second zone is to indent in the thickness of the tube (zone B); and the third zone (zone C) is the surface which performs sealing during the THF process. In this study, however, this method in its original state was not successful because while using the local deformation method the tube started to deform from the thinnest part of tube (zone with the minimum thickness of 1.60 mm in the middle). In other words, the force for local deformation of the tube ends was larger than the force for deformation of the zone in the middle of the tube, causing the tube to deform in the middle zone, making the hydroforming process impossible (Fig. 17a). As seen in Fig. 17b, numerical modelling with the application of the same axial displacement (4 mm) showed the same deformation in the tube middle. It is worth noting that in the initial numerical studies, it was found that only 2.5 mm axial displacement would be enough to have an appropriate seal for hydroforming (without any problem in the middle of tube), but in the experiments (because of inaccuracies in the tube ends due to imperfect cutting), this value increased to 4 mm and caused this problem.
Three-part die closing sequence. The first step in the successful hydroforming of the THF dies with three parts is finding the appropriate closing sequence. Depending on the geometry of the workpiece, it may be necessary to close the rear and top dies with different closing speeds with respect to each other to avoid possible tube pinching due to die closing. However, with the numerical iterations, it was found that, for this case study, closing two dies with the same speed is the best closing cycle. In Fig. 19c, the preformed tube due to die closing is shown. Validation of THF process FE model. One of the appropriate methods for validation of the THF process numerical model is comparison of reaction forces on the pushers from experiments and finite element results. In Fig. 20 the resultant force on the right and left pushers are presented. As is clear, the maximum forces on the right pusher in the experiments and FE model are 145.3 kN and 153.6 kN respectively, and for the left pusher theses values are 168.8 kN and 160.4 kN. Obviously there is a good agreement between maximum forces predicted from FE and experiments. However, there are clearly some valleys in the experiment forces, these reductions in forces are from the nature of application of the force by the hydraulic pusher system. When the hydraulic system wants to apply the force, there is a delay (some fractions of seconds) between hydraulic valve opening and application of pusher force. This delay causes a reduction in forces and consequently some valleys in the experimental forces. On the other hand, there is a lag between the start of the forces in the experiments and FE; this lag results from the extra time that is spent sealing the tubes in the experiments. The real experiments for this tube took 176 s. Global optimisation results. It seems that the easiest and most efficient method to verify the optimisation result is to plot all simulation results in 3D scatter plots. With this kind of plot, it is
Fig. 17. Deformation of tube because of local deformation sealing forces (a) experimentally and (b) numerically.
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Fig. 20. Total forces on the pushers during the experiments. Fig. 18. Sealing by both O-ring and local deformation methods.
possible to observe three responses at different simulation points in the same graph. Fig. 21 presents a scatter plot for three responses, i.e. thickness reduction%, thickness increase%, and final shell thickness. In this study, the optimisation reached convergence at the end of the second iteration with a total number of 16 simulation points. However, the convergence of an optimisation problem depends on the convergence criterion defined for it. In this study, if the variation of the design variable and responses between iterations is less that 1%, it is assumed that convergence is reached. In Fig. 21, the point that is distinguished by the circle is the optimum point. The design variables corresponding to this point are (d1 = 30.8 mm, p1 = 47.5 MPa, p2 = 56.8 MPa, and th0 = 1.35 mm); correspondingly the thickness reduction, thickness increase, and final shell thickness are 12.8%, 59.6%, and 1.29 mm respectively. To validate the result of the global optimisation, the hydroformed tube was cut from the different sections and thickness variation in various directions was measured; very good agreement between them was observed. The details of the measurements and thickness variation were presented in [16]. Fig. 22 presents the loading path from the result of the optimisation results that was applied in the experiments. As is clear in this figure, because of different deformation in the right and left-hand sides of the tube, the total amount of axial feeding for these two sides is not the same. After application of this loading path, the part was produced successfully without any problems like bursting or unfilling (Fig. 19d).
An important output of the global optimisation loop is a correlation matrix between design variables and responses. The correlation matrix gives an idea of the importance of the variables in changing responses. In Table 3 an example of the correlation matrix in one of the iterations is presented; for thickness reduction% response, the most important parameters are axial feeding and the second step pressure (p2) respectively. Likewise, for die filling, the most important parameter is axial feeding. On
Fig. 21. 3D scatter plot of three responses of optimisation (blue points are simulation points of the first iteration and the red points are the result of the second iteration). (For interpretation of the references to colour in this legend, the reader is referred to the web version of the article.)
Hydroforming Pressure (MPa)
60 50 40
RightPusher Left Pusher
30 20 10 0 0
Fig. 19. Hydroforming from preceding processes up to end (a) initial tube with variable thickness, (b) after two-step bending, (c) preformed tube by closing of die parts, and (d) hydroformed part.
5
10
15
20
25
30
35
Axial Feeding (mm)
Fig. 22. Hydroforming pressure vs. right and left pushers displacements.
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Table 3 An example of correlation matrix between optimisation variables and responses.
Axial displacement Pressure 1 Pressure 2 Initial thickness
Thickness reduction%
Critical filling point
Final shell thickness
Thickness increase%
0.92 0.05 0.16 0.2
0.99 0.02 0.01 0.05
0.04 0.1 0.02 1
1 0.05 0.09 0.04
the other hand, for final thickness the most important parameter is tube initial thickness. This confirms that if a special thickness in a particular region of the part is required, the hydroforming parameters cannot guarantee specific thickness without changing tube initial thickness. The numbers in Table 3 can vary from an iteration to another slightly. However the trend of correlations is always the same. An important factor that should be verified in each numerical study based on metamodel studies is accuracy of the predicted responses vs. computed responses. As presented in Figs. 23–26, there is acceptable error between computed and predicted responses. Three error indicators, i.e. RMS error, Sqrt PRESS, and R-sq are used. Readers interested in definitions of these indicators can see Appendix C of Bihamta et al. [15]. Figs. 23–26 are the accuracy curves for the last iteration; similar curves are available for the prior iterations. In Fig. 27, the state of the effective plastic strain at the end of hydroforming is presented. One can see that except for some regions with locally high strain, the rest of the part is experiencing strain around 0.3 or less. As the effects of prior preceding processes,
Fig. 25. Accuracy model for the die filling response (RMS err: 0.00189 (0.00616%), Sqrt PRESS: 0.00493 (0.016%), R-sq = 0.999).
Fig. 26. Accuracy model for the final shell thickness response (RMS err: 3E5 (0.00255%), Sqrt PRESS: 9E5 (0.0068%), R-sq = 1).
Fig. 23. Accuracy model for the thickness reduction% response (RMS err: 0.0295 (0.21%), Sqrt PRESS: 0.0793 (0.59%), R-sq = 0.99).
Fig. 27. Contours of effective plastic strain at the end of THF process.
like bending, were taken into account in this study, the values presented in this paper for the strains at the end of hydroforming are fairly higher than the strain presented in [18] for a similar part.
Conclusion In this study, some numerical and experimental studies were performed on the THF process taking into account the effects of preceding processes. The preceding processes that were studied besides THF were variable thickness tube drawing, annealing heat treatment, and bending. The important results of this paper can be summarised as follows:
Fig. 24. Accuracy model for the thickness increase% response (RMS err: 0.0917 (0.182%), Sqrt PRESS: 0.245 (0.486%), R-sq = 1).
(a) In variable thickness tube drawing, the synchronisation between two-step drawing is an important parameter and can lead to tube failure if it is not performed well.
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(b) In the case that precise synchronisation between two steps of variable thickness tube drawing is not possible, the best alternative is to replace sharp transition of thickness with mild ones to reduce the risk of rupture due to inaccurate synchronisation. (c) Rotary-draw tube bending can lead to considerable variation in the thickness of tubes; ignorance of this fact can lead to unsuccessful hydroforming. (d) Geometrically complex tubes have some bent regions. These zones cannot get enough material by the axial displacement of the pushers, therefore the third parameter, i.e. initial tube thickness, can play a role in successful hydroforming of these parts. (e) The customised sealing method that was presented for the first time in this paper takes advantages of both local deformation and O-ring methods for sealing of tubes. (f) In the dies with three parts, the cycle of approaching of dies is a very important factor in appropriate preforming of the tube. (g) The loading path from numerical optimisation showed excellent agreement with the experiments in the final hydroforming.
Acknowledgements The authors thank the Natural Sciences and Engineering Research Council of Canada, National Research Council CanadaAluminium Technology Centre, Alfiniti, Aluminerie Alouette, C.R.O.I and Cycles Devinci for their financial and technical support of this research. A part of the presented research in this paper was financed by the Fonds Que´be´cois de la Recherche sur la Nature et les Technologies (FQRNT) by the intermediary of the Aluminium Research Centre-REGAL.
References [1] Korkolis, I., 2009, Formability and Hydroforming of Anisotropic Aluminum Tubes, PhD dissertation The University of Texas at Austin. [2] Xu, X., Zhang, W., Li, S., Lin, Z., 2009, Study of tube hydroforming in a trapezoidsectional die, Thin-Walled Struct, 47:1397–1403. [3] Cheng, D.M., Teng, B.G., Guo, B., Yuan, S.J., 2009, Thickness distribution of a hydroformed Y-shape tube, Mater Sci Eng A, 499:36–39. [4] Xu, X., Li, S., Zhang, W., Lin, Z., 2009, Analysis of thickness distribution of square-sectional hydroformed parts, JMater Process Technol, 209:158–164.
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[5] Fiorentino, A., Ceretti, E., Giardini, C., 2013, Tube hydroforming compression test for friction estimation; numerical inverse method, application, and analysis, Int J Adv Manuf Technol, 64:695–705. [6] Korkolis, Y.P., Kyriakides, S., 2009, Path-dependent failure of inflated aluminium tubes, Int J Plast, 25:2059–2080. [7] Hashemi, R., Assempour, A., Masoumi, K.E., 2009, Implementation of the forming limit stress diagram to obtain suitable load path in tube hydroforming considering M-K model, 146?Mater Des, 30:3545–3553. [8] Song, W.-J., Heo, S.-C., Ku, T.-W., Kim, J., Kang, B.-S., 2010, Evaluation of effect of flow stress characteristics of tubular material on forming limit in tube hydroforming process, Int J Mach Tools Manuf, 50:753–764. [9] Bortot, P., Ceretti, E., Giardini, C., 2008, The determination of flow stress of tubolar material for hydroforming applications, J Mater Process Technol, 203:381–388. [10] Kang, S.J., Kim, H.K., Kang, B.S., 2005, Tube size effect on hydroforming formability, J Mater Process Technol, 160:24–33. [11] Koc¸, M., 2004, Advances in tube hydroforming – an enabling technology for low-mass vehicle manufacturing-material, lubrication, loading, simulation issues, and alternatives, Tsinghua SciTechnol, 9:527–545. [12] Trana, K., 2002, Finite element simulation of the tube hydroforming process – bending, preforming and hydroforming, J Mater Process Technol, 127:401– 408. [13] Hwang, Y.-M., Altan, T., 2003, Finite element analysis of tube hydroforming processes in a rectangular die, Finite Elem Anal Des, 39:1071–1082. [14] Abedrabboa, N., Worswicka, M., Mayer, R., Riemsdijk, I.V., 2009, Optimization methods for the tube hydroforming process applied to advanced highstrength steels with experimental verification, J Mater Process Technol, 209:110–123. [15] Bihamta, R., Bui, Q.H., Guillot, M., D’Amours, G., Rahem, A., Fafard, M., 2011, A new method for production of variable thickness aluminium tubes: numerical and experimental studies, J Mater Process Technol, 211:578–589. [16] Bihamta, R., Bui, Q.-H., Guillot, M., D’Amours, G., Rahem, A., Fafard, M., 2012, Application of a new procedure for the optimization of variable thickness drawing of aluminium tubes, JManuf Sci Technol, 5:142–150. [17] D’Amours, G., Rahem, A., Williams, D., Worswick, M., Mayer, R., 2007, Crashworthiness of aluminium tubes: Part 1. Hydroforming at different corner-fill radii and end feeding levels, Materials Processing and Design: Modeling, Simulation and Applications Conference NUMIFORM 2007, . [18] Bihamta, R., D’Amours, G., Bui, Q.-H., Rahem, A., Fafard, M., 2013, Numerical study on the new design concept of hydroforming dies for the complex tubes, J Mater Des, 47:766–778. [19] Bihamta, R., 2011, Optimization of Hydroforming Process of Geometrically Complex Aluminium Tubes Taking Account of Preceding Forming Processes, PhD dissertation Laval University, Quebec City, Canada. [20] Williams, B.W., Worswick, M.J., D’Amours, G., Rahem, A., Mayer, R., 2010, Influence of forming effects on the axial crush response of hydroformed aluminum alloy tubes, Int J Impact Eng, 37:1008–1020. [21] Stander, N., Roux, W., Goel, T., Eggleston, T., Craig, K., 2009, A design optimization and probabilistic analysis tool for the engineering analyst, LS-OPT1 User’s Manual, Livermore Software Technology Corporation. [22] Myers, R.H., Montgomery, D.C., 2002, Response Surface Methodology, 2nd ed. John Wiley & Sons, New York. [24] http://www.vari-form.com. [25] http://www.copper.org/applications/cuni/app_syscomp.html. [26] Koc¸, M., Aue-u-lan, Y., Altan, T., 2001, On the characteristics of tubular materials for hydroforming—experimentation and analysis, Int J Mach Tools Manuf, 41:761–772.
Contents lists available at ScienceDirect
CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj
Global optimisation of the production of complex aluminium tubes by the hydroforming process R. Bihamta a,1,*, Q.-H. Bui b, M. Guillot b, G. D’Amours c, A. Rahem c, M. Fafard b a
Alcoa Innovation, East Cre´mazie Blvd., Montreal, Qc H2M 0A6, Canada Aluminium Research Centre, REGAL, Laval University, Que´bec, Qc G1V 0A6, Canada c National Research Council Canada, Aluminium Technology Centre, Saguenay, Qc G7H 8C3, Canada b
A R T I C L E I N F O
A B S T R A C T
Article history: Available online 24 March 2015
With the recent development of analysis software products, designers and engineers are able to design more complex parts to obtain better performance in the final products. In this study, the tube hydroforming process, including preceding processes, i.e. variable thickness tube drawing and two-step bending, are globally optimised to obtain parts without any problems like bursting or un-filled zones at the end of the forming processes. Unlike most previous studies which searched for an optimum hydroforming process by changing two hydroforming parameters, i.e. axial load feeding and internal pressure, in this study, the distribution of initial tube wall thickness and the variation of thickness due to bending steps will be taken into account in a global optimisation algorithm. The developed algorithm is a general-purpose algorithm that can encompass different processes and change various parameters in each process to be able to reach the global objective. The case study used was a part that needs two-step variable thickness tube drawing, and two bending steps before hydroforming. To verify the numerical results in each forming stage and at the end of all forming processes, extensive experiments were performed, and acceptable agreements were observed. ß 2015 CIRP.
Keywords: Tube hydroforming Tube bending Variable thickness tube drawing AA6061 Aluminium
Introduction Aluminium tubes, mostly produced by the tube hydroforming (THF) process, play an important role in transportation industries such as automotive and bicycle production. As shown in Fig. 1, in fabricating almost all THF parts, it is necessary to use some other preliminary processes like tube drawing, annealing heat treatment, tube bending, and preforming before the final THF process. The wider application of aluminium tubes by industry is hindered because of the reduced ductility and more complex material behaviour of aluminium in comparison with steels [1]. Various aspects of the THF process have been studied. Xu et al. [2] presented a paper to find the optimum loading path for a trapezoidsectional die. Cheng et al. [3] studied distribution of thickness in a Yshape tube by the finite element (FE) and experimental methods. Xu et al. [4] mathematically studied thickness distribution along the
* Corresponding author. Tel.: +1 586 256 4037; fax: +1 586 492 7205. E-mail address: [email protected] (R. Bihamta). 1 Formerly from Aluminium Research Centre, REGAL, Laval University, QC, Canada. http://dx.doi.org/10.1016/j.cirpj.2015.02.001 1755-5817/ß 2015 CIRP.
cross-section of a square-sectional hydroformed part. Fiorentino et al. [5] proposed a new procedure for friction estimation in THF processes. Koc¸ et al. [26] presented experimental and analytical approaches to characterise materials for the THF process. Korkolis and Kyriakides [6] evaluated the effect of loading path on the failure of inflated aluminium tubes. Hashemi et al. [7] applied a stressbased forming limit diagram to obtain optimum loading paths in THF. Song et al. [8] evaluated the effect of flow stress characteristics of tubular material on forming limit in the THF process. Bortot et al. [9] determined a new test method to characterise the flow stress for the tubes in the hydroforming applications. Kang et al. [10] studied tube size effect on hydroforming formability. The publications above are examples of research performed in this field. However, on the subject of this paper, which is studying the THF process including the preceding processes, there is only little research. For instance, Koc¸ [11] evaluated effect of die crushing and pre-bending on the thickness distribution and formability of complex tubes. Trana [12] showed that the preforming process can be performed by the hydroforming die closing, saving considerable time and production cost. Hwang and Altan [13] studied the crushing processes in combination with performance in a rectangular die. None of the above mentioned studies, however, included the initial tube
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Fig. 1. Tubular automobile parts produced by the THF method. (A) Roof headers, (B) instrument panel support, (C) radiator supports, (D) engine cradles, (E) roof rails, and (F) frame rails [http://www.vari-form.com] [24].
thickness as an optimisation variable. There is also no specialised optimisation algorithm, nor an automatic method to manage the optimisation procedure. Abedrabboa et al. [14] presented an optimisation process linked with a FE model to optimise the high-strength steel tube hydroforming process. In that study, despite having an optimisation algorithm for modification of the hydroforming parameters, they only took into account the THF process without preceding processes. In this paper, in the first step, a code was developed to assign various thicknesses to the initial tube wall. This shell with various thicknesses is considered as the tube issued from one- or two-step variable wall thickness tube drawing. It is worth mentioning that because of the annealing heat treatment after tube drawing, it is assumed that all material properties return to the initial state and there are not any residual stresses induced by the drawing. After assignment of thickness to the shell tube, the FE model is transferred automatically to the bending steps, and afterward the bent tube is transferred to the hydroforming step. Depending on the defined objectives and constraints, the optimisation loop will return to the initial step to change tube thickness and/or some parameters in the hydroforming step to reach the objective. All of the changes in the parameters of the preceding processes and hydroforming step are performed automatically without any user interaction. In the next sections, the processes and their FE models that are involved in the production of the case study part are explained. The experimental section explains the geometric features of the part and the experimental rig. Cold forming processes prior to hydroforming In general, for most THF processes, some preform processes are necessary. Without them, the tube cannot be positioned in the THF die appropriately. Furthermore, the quality of the preceding operations has a direct effect on the quality of final workpiece. In the following sections, the important cold forming processes prior to THF are studied numerically and experimentally. Variable thickness tube drawing Production of variable thickness tubes The variable thickness tube drawing process is a new enhancement applied to the classic tube drawing method to produce tubes with variable thickness along the tube’s length and/ or in the radial direction. As explained in more detail in prior publications like Bihamta et al. [15,16], in this method, the desired variation of wall thickness can be induced through the application of axial displacement of the conic mandrel. However, in this
process some parameters like material heat treatment, its alloying elements, and tool geometry, limit the minimum attainable thickness in one step; if smaller than that is required, it should be performed in more than one step. On the other hand, if two or more tube drawing steps are necessary, the synchronisation between two passes is a crucial factor. If the location of thickness reduction in the second step is not in the appropriate zone, there is a possibility of tube fracture. There are two solutions to avoid this problem. The first solution consists of applying a very accurate nondestructive measurement mechanism, such as a laser, to accurately measure the thickness along the tube axis and implement very precise axial displacement to the tube in the next steps. The implementation of the first solution requires very precise and expensive equipment. Another alternative is the application of mild transition between zones with variable wall thicknesses. This mild transition can guarantee that if there is inaccuracy in the second pass, the tube will not experience any rupture. In the zones that are more prone to bursting in the hydroforming step, augmentation of thickness in the initial tube can eliminate the chance of bursting, and the final thickness in the tube can be controlled. On the other hand, if a zone in the part undergoes lower loads than other regions when in service, the thickness of this region can be reduced to diminish overall weight of part. Details of the numerical and experimental studies on this process are outside the scope of this paper; interested readers can see Bihamta et al. [15,16]. Tube thickness as an optimisation variable in the THF process In this study, it was possible to use solid elements or shell elements to include initial tube thickness in the global THF process optimisation. If solid 3D elements are to be used in the tube bending and THF steps, four-node 2D elements can be used in the tube-bending step. Due to the axi-symmetric geometry of the tube drawing process, the results can then be rotated and converted to complete a 3D tube. In comparison with shell elements, this kind of element has more precision in prediction of thickness variation in the THF process [17], but utilising them seems to be computationally very expensive. On the other hand, application of shell elements for the simulation of THF and tube bending processes seems to be more efficient computationally, and provides acceptable results. Since it is common to do annealing heat treatment after one- or two-step tube drawing, the material property in the drawn tube (after heat treatment) is considered to be the same as the initial material. Therefore, the inclusion of the tube drawing processes in the global optimisation loop seems to be unnecessary, and will increase the computation time. Consequently, the parameter that was included from the tube drawing process is variation of thickness in the tube. For implementation of thickness in the initial tube, a code was developed and included as a part of the preprocessor in the optimisation loop to update values of thickness in the optimisation loop based on the optimisation iterations. This code reads coordinates of various elements and applies the different thicknesses upon request of the optimisation engine. An example of output of this code is presented in Fig. 2. Heat treatment Because of cold deformation in the tube drawing process, the ductility of tubes is reduced, increasing the risk of fracture in the rest of the production cycle, i.e. tube bending and THF. Figs. 3 and 4 show that for tubes drawn in one and two steps the ductility of tubes is reduced considerably with increasing thickness reduction;
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Fig. 2. Application of various thicknesses to the initial tube by the developed preprocessor.
this dictates the necessity for an annealing heat treatment. The level of yield stress also increased considerably with increased deformation (Table 1). In Fig. 5, the annealing heat treatment cycle applied to the tubes after two-step drawing is presented. In zone A of Fig. 5, the temperature of the tubes increased from room temperature to 405 8C as fast as possible. After reaching the maximum temperature
(405 8C), the tubes are kept there during 2 h (zone B), followed by controlled cooling at the 28 8C/h rate down to 260 8C (zone C), and subsequently cooled at the ambient temperature (zone D). The material properties used in the FE analysis for the tubes after annealing heat treatment is presented in Fig. 6. Hollomon’s equation is used for extrapolation of stresses up to larger stresses. Tube bending Rotary-draw tube bending There are various types of bending processes that can be applied as a preceding process in the THF production cycle. In this project the rotary-draw bending method was selected. As shown in Fig. 7, the tube is located between clamp die and bend die, and by the rotation of the bend die, the tube takes the form of the bending die.
Table 1 Specifications of samples in Figs. 3 and 4.
Fig. 3. Stress–strain curves for AA6061 tubes in the original condition (O) and only one-step drawn to outer diameter of 57.15 mm and various thicknesses (details are presented in Table 1).
Fig. 4. Stress–strain curves for AA6061 tubes drawn two steps from 63.5 mm to 57.15 mm and from 57.15 mm to 50.8 mm with various thicknesses (details are presented in Table 1).
Sample #
Initial outer diameter (OD) (mm)
OD after drawing (mm)
Final thickness (mm)
Total number of drawing steps
1 2 3 4 5 6 7 8
63.5 63.5 63.5 63.5 57.15 57.15 57.15 57.15
57.15 57.15 57.15 57.15 50.8 50.8 50.8 50.8
2.59 2.33 2.00 1.91 2.66 2.21 1.58 1.47
1 1 1 1 2 2 2 2
Fig. 5. The applied annealing heat treatment cycle.
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200 180 160
Stress (MPa)
140 120 100 80 60 40 20 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
pressure die, and clamp die were modelled using the shell elements (Fig. 8). For the case of this paper, it was necessary to do bending in two steps; therefore the results of the first tube bending stage were transferred to the second bending step. Like experiments in the laboratory, the same dies were used to bend the tube in the next step. Also, to locate the tube from the first bending step to the second step, it is necessary to do some rotations and translations of the mesh; these values are included in the finite element model of the second bending step to enable its automatic performance during the optimisation process. Interested readers are referred to details in Appendix E from Bihamta [19]. Fig. 9 presents the results of tube bending in the second bending step.
Strain (mm/mm)
Fig. 6. Applied material property to the tubes after extrapolation by Holloman’s power law (s ¼ ken , n = 0.263, k = 211.48).
There are some considerations, like the minimum clamping length, multi radii tubes, distance between bends, and minimum bend radius, that should be considered for tube bending specially for tubes to be used in the THF process. Tubes that were not bent precisely will experience pinching in the die closing step, and will burst during the hydroforming step. However as described in detail in Bihamta et al. [18], the special design of the THF die in this case permits small variations in the geometry of bent tubes. It is worth mentioning that if minor flattening and/or wrinkling occurs in the tube bending step, it can be corrected in the hydroforming step. However some wrinkles are difficult to correct, and there is a risk of bursting in the deep wrinkles during the THF process. Therefore, flattening and wrinkling should be avoided as much as possible in the bending step. Regardless of all the advantages with variable thickness tubes, this kind of tube cannot be bent by methods that use a mandrel inside the tube, because the variation of thickness inside the tube hinders entrance of the mandrel into the tubes.
Tube hydroforming (THF) process Tube hydroforming (THF) is one of the most important processes and in some cases the exclusive method for the production of complex shaped tubes. In this process, a tube is located in the die and sealed by one of the sealing methods that will be explained in ‘‘Experiments’’ section. Then by the application of an appropriate loading path, i.e. axial load feeding and hydroforming pressure, it will take the geometry of the die. The liquid in this process is always water with some anticorrosion additives; for some low deformable materials like special aluminium alloys, hot gas is used. After assignment of the thickness distribution to the tube prior to bending, and the bending stage in two steps, the geometry of the
Numerical modelling of rotary-draw bending As explained before, to evaluate and optimise the THF process, it is necessary to include preceding forming processes like tube bending in the optimisation loop; otherwise, the optimisation process will neglect some effects like thickness variation in the bending zone and/or flattening and/or wrinkling by the tube bending zone. In the numerical modelling of the bending process, the tube wall thickness, with variation of thickness along it, is transferred to the bending step. In the FE model, the geometry of the bend die,
Fig. 7. Schematics of rotary-draw bending [http://www.copper.org/applications/ cuni/app_syscomp.html] [25].
Fig. 8. Modelling of the first step, rotary-draw bending (a) before performance of bending, (b) after bending, and (c) distribution of tube thickness at the end of process.
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unsuccessful loading path for the THF process, especially in the regions that experienced thickness reduction. In this study, the geometry of die and tube were designed and meshed in Pro/Engineer and HyperMesh softwares respectively. Because of the complex geometry of the THF die, for better establishment of contact between die parts and tube, different mesh densities are applied to the various parts of the tube in such a way that in the region with more complex geometry and more tube deformation, finer mesh (1.5 mm 1.5 mm) is used, and in other regions coarser meshes, i.e. 3 mm 3 mm are assigned. The surface-to-surface contact formulation is used to define the contact between die parts and tube with a friction coefficient of 0.05 as confirmed in Williams et al. [20]. Fix die was constrained in all directions. For the rear die and upper die they were left constraint free in the moving direction and in other direction they were constrained completely too. To apply, axial feeding to the tube, two rows of nodes in the 35 mm distance from two ends of tube were selected and two different displacements were applied to represent the axial motion of right and left pushers. The distance 35 mm is the length of the guiding zone in the pushers and there is not any variation of thickness in this length. Global optimisation Optimisation procedure
Fig. 9. Modelling of the second step, rotary-draw bending (a) before performance of bending, (b) after bending, and (c) distribution of tube thickness at the end of process.
tube is transferred to the final forming step (THF). As shown in Fig. 10, the tube has a maximum thickness reduction of 5% and thickness increase of 7.9% after two bending steps. Neglecting these thickness variations from prior steps can lead to an
The main objective of this study is to present a methodology for optimising the THF process while taking into account the preceding process. The developed optimisation procedure is able to take into account the preceding process models and automatically copy the results to the next step and to continue to the next optimisation loop. However, depending on user preference, some processes can be excluded from the global optimisation to save computational time. In the global optimisation of this study, the implicit solver of LSDYNA software was used as a FE solver. The shell element with four nodes was used because of its capability to have various thicknesses in each node. LS-OPT software was used as the base optimisation engine, and the required preprocessing and postprocessing operations were performed automatically by the developed codes. Readers interested in more details on optimisation codes can refer to Appendices A–E in Bihamta [19]. Optimisation variables The optimisation procedure of non-linear processes like hydroforming or tube bending with a huge number of elements (2.2 million elements for tube and dies in the hydroforming step) is time consuming. In this study, for the bending (first and second) and hydroforming steps using four CPUs, it takes approximately 2, 6, and 11 h respectively. Therefore, appropriate selection of optimisation variables is an important decision and the variables that seem to have less effect should be excluded. In the case of global optimisation of the THF process, three variables, i.e. hydroforming pressure, axial feeding, and tube initial thickness, are the optimisation variables. In Table 2, domain of change of Table 2 Optimisation variables with their ranges and starts values.
Fig. 10. Initial state of tube with the three-part THF die.
Variable
Start value
Minimum
Maximum
d1 (mm) p1 (MPa) p2 (MPa) th0 (mm)
26 50 56 1.6
24 47.5 55 1.35
34 55 60 1.65
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these variables with starting variables is summarised. For axial feeding only one variable (d1), for hydroforming pressure two variables (p1 and p2), and for initial thickness one variable (th0) is defined.th0 is the thickness of the central region of the tube. Variation of thickness in this zone is less concerned by the THF parameters (pressure and axial feeding). Therefore, by the third variable (thickness variation), the final thickness in this part will be controlled. It is worth mentioning that in other studies it might be interesting to have the thickness of more zones or even location of thickness change as optimisation variables.
This method was used in previous studies like Bihamta et al. [16] and showed acceptable results. For the optimisation algorithm, the leapfrog method is selected. Interested readers can refer to Stander et al. [21] and Myers and Montgomery [22].
Objectives and constraints
Variable thickness tube drawing
For this optimisation process, three direct and one indirect objective were defined. The direct objectives were minimisation of thickness reduction in all regions of the part, complete die filling, and minimisation of thickness increase in two ends of tube. In the tube hydroforming (THF) process, the material flow should be from the zone closer to the pushers to the central zones and material should not be localised in the zones close to the pushers. The localisation of material in these zones was represented by the thickness increase in the optimisation process. The indirect objective was to have the final thickness in the central region of the part in the acceptable range (1.2–1.3 mm). This is called an indirect objective because it is applied as constraint in the optimisation procedure. The other constraint was p2 p1 > 0; guaranteeing that the pressure curve is always increasing. After assignment of the displacement (d1) by the optimisation engine, it will be used directly for the right-hand side in the preprocessing code, and for the left-hand side it will be summed with 6 (as the initial investigation proved that for the left-hand side larger feed is required). However, two separate displacements can be defined as optimisation variables too. For the thickness reduction, all elements were selected to verify their thickness reduction percentages at the end of hydroforming. For die filling verification the displacement of a critical node in the radial direction is maximised. Finally, for the thickness increase minimisation, only the elements in the ends of tubes were selected (Fig. 11). As the values for the thickness increase in FE solver, they are reported as negative values; the responses of this parameter before being used in the minimisation function are multiplied by 1 to be able to use only the minimisation function to three objectives.
As explained earlier, the initial tube for the part selected for this paper, and for a majority of complex THF parts, should have variation of thickness. The experiments for the production of the variable thickness tube were performed in the prototype machine that was fabricated at the Aluminium Research CentreREGAL at Laval University. Interested readers can refer to prior publications on this subject like Bihamta et al. [15] and Bihamta et al. [16] for more details.
Sampling methods In the optimisation process to reduce the number of simulation points, a polynomial metamodel with linear order is selected. Also, for the point selection method, the D-optimal method is selected.
Experiments For production of the selected part in this paper, four different processes are required. In this section the summary of the experiments are presented.
Annealing heat treatment The required heat treatment for the tubes in this paper was performed in a TPS-(Blue M series) oven in the NRC-Aluminium Technology Centre. One of the important features of this oven is its capability for controlled cooling, which made application of heat treatment cycles like Fig. 5 possible. Tube bending The bending operation in this paper was performed by Alutech Ttrg Co. A non-destructive test (NDT) method, i.e. ultrasonic method, is used for measurement of thickness variation after bending the tube. The advantage of this method with respect to the other measurement methods, like measurement by the micrometre, is that in this method it is not necessary to cut the tube to measure its thickness; however, its precision is less than the measurement by micrometre. Tube hydroforming The hydroforming experiments for this paper were performed in an Interlaken HF-1000 press at the NRC-Aluminium Technology Centre. The maximum applicable force by this press in the axial direction and in the feeding cylinder directions are 8.89 MN and 667 kN respectively. This press also has the capability of applying axial feeding by four different cylinders in which two of them are used to apply the axial feeding, and the third one for movement of the rear part of the die. Fig. 12 presents a photo of the THF die and required accessories. The liquid utilised for application of pressure inside the tube was water; to avoid corrosion in the press, NOVACOOL 9034/5 was added. To lubricate the tubes, Hydrodraw 625 was sprayed on the tube outer surface, and after some minutes it dried in the ambient temperature. It is worth pointing out that during hydroforming, the surface of the dies should be sprayed with water to activate the lubricant on the tube surface. Results and discussion Variable thickness tube drawing
Fig. 11. Application of optimisation objectives (a) all regions of part (thickness reduction objective), (b) critical node to guarantee die filling, and (c) two ends of tube to minimise the thickness increase.
In prior publications, Bihamta et al. [15] and Bihamta et al. [16], the majority of the results like state of residual stresses, validation
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Fig. 14. Modified thickness distribution in the tube for two-step drawing.
preferred to increase the minimum thickness to fairly larger values (1.60 mm) to avoid rupture in the tubes with eccentricity. In Fig. 13 the transitions between different thicknesses are fairly sharp, and if appropriate synchronisation is not performed in the second step, there is chance of tube rupture, therefore the transition profile was modified to avoid this problem. Fig. 14 presents the modified thickness distribution. Because of volume constancy, the tube’s total length decreased after the slight increase in middle region thickness. The thickness measurement of the tubes after the drawing process was performed using a micrometre in five different points within the tube diameter after cutting the tubes into two halves. Tube bending
of FE model, optimisation on the initial tube, and tool geometry were presented; in this paper only the experimental results that were not published anywhere else are going to be discussed. Fig. 13 presents the experimental result of the two-step tube drawing; the minimum thickness at the end of the second step is 1.48 mm. In other experiments, the smaller value, i.e. 1.43 mm, for the minimum thickness was also obtained. However, because of considerable eccentricity (0.1–0.15 mm) in the initial tubes, it was
Thickness variation, especially its reduction in the bent regions, is the most important effect of the tube bending process that can affect results in the tube hydroforming step. Fig. 15 presents the thickness reduction prediction by the FE method, after two-step tube bending. The thickness reduction and increase in the outer and inner surfaces of the tube are 4.3% and 5.3% respectively. For validation of numerical results, the thickness of tubes was measured by the ultrasonic method and the average decrease and increase were 3.4% and 7.6% respectively. It seems that the difference between experiments and numerical results has origins such as error in thickness measurement, matching the correspondent points in the zone where there is transition of thickness, and also weakness of the shell element in thickness variation prediction.
Fig. 13. Thickness distribution in the tube after two-step drawing.
Fig. 15. Thickness variation percentages in the tube after two-step bending.
Fig. 12. (a) Three-part THF die installed in HF-1000 hydroforming press and (b) closer view of die showing two parts of three parts die and cylinder for opening the rear part of die.
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The sealing method in this study consists of developing a customised sealing method. This method, by application of a modified pusher design, takes advantage of both local deformation and O-ring sealing methods. Two rows of slots are designed for the O-rings, and the end of the pusher will perform the local deformation (Fig. 18). Two rows of O-rings will seal the tube under lower pressures, and the pusher displacement while there is pressure inside the tube can indent inside the tube without deforming it as in Fig. 17. Interested readers for more information on detail of sealing methods, can see [19]. Experimental and numerical results Fig. 16. Design of pusher for the local deformation method sealing (A) guiding zone, (B) indentation zone, and (C) sealing surface.
Tube hydroforming (THF) Tube sealing One of the most important factors that can completely influence the success of the THF process is appropriate sealing of the tube before and during the process. Without appropriate sealing, application of higher pressures is not possible. The local deformation method, by appropriate pusher design, it indents in the thickness of the tube and locally deforms it and seals the tube during the THF process. As shown in Fig. 16, each pusher has three different zones: the first zone is to guide the pusher inside the tube, and is called the guiding zone (zone A); the second zone is to indent in the thickness of the tube (zone B); and the third zone (zone C) is the surface which performs sealing during the THF process. In this study, however, this method in its original state was not successful because while using the local deformation method the tube started to deform from the thinnest part of tube (zone with the minimum thickness of 1.60 mm in the middle). In other words, the force for local deformation of the tube ends was larger than the force for deformation of the zone in the middle of the tube, causing the tube to deform in the middle zone, making the hydroforming process impossible (Fig. 17a). As seen in Fig. 17b, numerical modelling with the application of the same axial displacement (4 mm) showed the same deformation in the tube middle. It is worth noting that in the initial numerical studies, it was found that only 2.5 mm axial displacement would be enough to have an appropriate seal for hydroforming (without any problem in the middle of tube), but in the experiments (because of inaccuracies in the tube ends due to imperfect cutting), this value increased to 4 mm and caused this problem.
Three-part die closing sequence. The first step in the successful hydroforming of the THF dies with three parts is finding the appropriate closing sequence. Depending on the geometry of the workpiece, it may be necessary to close the rear and top dies with different closing speeds with respect to each other to avoid possible tube pinching due to die closing. However, with the numerical iterations, it was found that, for this case study, closing two dies with the same speed is the best closing cycle. In Fig. 19c, the preformed tube due to die closing is shown. Validation of THF process FE model. One of the appropriate methods for validation of the THF process numerical model is comparison of reaction forces on the pushers from experiments and finite element results. In Fig. 20 the resultant force on the right and left pushers are presented. As is clear, the maximum forces on the right pusher in the experiments and FE model are 145.3 kN and 153.6 kN respectively, and for the left pusher theses values are 168.8 kN and 160.4 kN. Obviously there is a good agreement between maximum forces predicted from FE and experiments. However, there are clearly some valleys in the experiment forces, these reductions in forces are from the nature of application of the force by the hydraulic pusher system. When the hydraulic system wants to apply the force, there is a delay (some fractions of seconds) between hydraulic valve opening and application of pusher force. This delay causes a reduction in forces and consequently some valleys in the experimental forces. On the other hand, there is a lag between the start of the forces in the experiments and FE; this lag results from the extra time that is spent sealing the tubes in the experiments. The real experiments for this tube took 176 s. Global optimisation results. It seems that the easiest and most efficient method to verify the optimisation result is to plot all simulation results in 3D scatter plots. With this kind of plot, it is
Fig. 17. Deformation of tube because of local deformation sealing forces (a) experimentally and (b) numerically.
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Fig. 20. Total forces on the pushers during the experiments. Fig. 18. Sealing by both O-ring and local deformation methods.
possible to observe three responses at different simulation points in the same graph. Fig. 21 presents a scatter plot for three responses, i.e. thickness reduction%, thickness increase%, and final shell thickness. In this study, the optimisation reached convergence at the end of the second iteration with a total number of 16 simulation points. However, the convergence of an optimisation problem depends on the convergence criterion defined for it. In this study, if the variation of the design variable and responses between iterations is less that 1%, it is assumed that convergence is reached. In Fig. 21, the point that is distinguished by the circle is the optimum point. The design variables corresponding to this point are (d1 = 30.8 mm, p1 = 47.5 MPa, p2 = 56.8 MPa, and th0 = 1.35 mm); correspondingly the thickness reduction, thickness increase, and final shell thickness are 12.8%, 59.6%, and 1.29 mm respectively. To validate the result of the global optimisation, the hydroformed tube was cut from the different sections and thickness variation in various directions was measured; very good agreement between them was observed. The details of the measurements and thickness variation were presented in [16]. Fig. 22 presents the loading path from the result of the optimisation results that was applied in the experiments. As is clear in this figure, because of different deformation in the right and left-hand sides of the tube, the total amount of axial feeding for these two sides is not the same. After application of this loading path, the part was produced successfully without any problems like bursting or unfilling (Fig. 19d).
An important output of the global optimisation loop is a correlation matrix between design variables and responses. The correlation matrix gives an idea of the importance of the variables in changing responses. In Table 3 an example of the correlation matrix in one of the iterations is presented; for thickness reduction% response, the most important parameters are axial feeding and the second step pressure (p2) respectively. Likewise, for die filling, the most important parameter is axial feeding. On
Fig. 21. 3D scatter plot of three responses of optimisation (blue points are simulation points of the first iteration and the red points are the result of the second iteration). (For interpretation of the references to colour in this legend, the reader is referred to the web version of the article.)
Hydroforming Pressure (MPa)
60 50 40
RightPusher Left Pusher
30 20 10 0 0
Fig. 19. Hydroforming from preceding processes up to end (a) initial tube with variable thickness, (b) after two-step bending, (c) preformed tube by closing of die parts, and (d) hydroformed part.
5
10
15
20
25
30
35
Axial Feeding (mm)
Fig. 22. Hydroforming pressure vs. right and left pushers displacements.
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Table 3 An example of correlation matrix between optimisation variables and responses.
Axial displacement Pressure 1 Pressure 2 Initial thickness
Thickness reduction%
Critical filling point
Final shell thickness
Thickness increase%
0.92 0.05 0.16 0.2
0.99 0.02 0.01 0.05
0.04 0.1 0.02 1
1 0.05 0.09 0.04
the other hand, for final thickness the most important parameter is tube initial thickness. This confirms that if a special thickness in a particular region of the part is required, the hydroforming parameters cannot guarantee specific thickness without changing tube initial thickness. The numbers in Table 3 can vary from an iteration to another slightly. However the trend of correlations is always the same. An important factor that should be verified in each numerical study based on metamodel studies is accuracy of the predicted responses vs. computed responses. As presented in Figs. 23–26, there is acceptable error between computed and predicted responses. Three error indicators, i.e. RMS error, Sqrt PRESS, and R-sq are used. Readers interested in definitions of these indicators can see Appendix C of Bihamta et al. [15]. Figs. 23–26 are the accuracy curves for the last iteration; similar curves are available for the prior iterations. In Fig. 27, the state of the effective plastic strain at the end of hydroforming is presented. One can see that except for some regions with locally high strain, the rest of the part is experiencing strain around 0.3 or less. As the effects of prior preceding processes,
Fig. 25. Accuracy model for the die filling response (RMS err: 0.00189 (0.00616%), Sqrt PRESS: 0.00493 (0.016%), R-sq = 0.999).
Fig. 26. Accuracy model for the final shell thickness response (RMS err: 3E5 (0.00255%), Sqrt PRESS: 9E5 (0.0068%), R-sq = 1).
Fig. 23. Accuracy model for the thickness reduction% response (RMS err: 0.0295 (0.21%), Sqrt PRESS: 0.0793 (0.59%), R-sq = 0.99).
Fig. 27. Contours of effective plastic strain at the end of THF process.
like bending, were taken into account in this study, the values presented in this paper for the strains at the end of hydroforming are fairly higher than the strain presented in [18] for a similar part.
Conclusion In this study, some numerical and experimental studies were performed on the THF process taking into account the effects of preceding processes. The preceding processes that were studied besides THF were variable thickness tube drawing, annealing heat treatment, and bending. The important results of this paper can be summarised as follows:
Fig. 24. Accuracy model for the thickness increase% response (RMS err: 0.0917 (0.182%), Sqrt PRESS: 0.245 (0.486%), R-sq = 1).
(a) In variable thickness tube drawing, the synchronisation between two-step drawing is an important parameter and can lead to tube failure if it is not performed well.
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(b) In the case that precise synchronisation between two steps of variable thickness tube drawing is not possible, the best alternative is to replace sharp transition of thickness with mild ones to reduce the risk of rupture due to inaccurate synchronisation. (c) Rotary-draw tube bending can lead to considerable variation in the thickness of tubes; ignorance of this fact can lead to unsuccessful hydroforming. (d) Geometrically complex tubes have some bent regions. These zones cannot get enough material by the axial displacement of the pushers, therefore the third parameter, i.e. initial tube thickness, can play a role in successful hydroforming of these parts. (e) The customised sealing method that was presented for the first time in this paper takes advantages of both local deformation and O-ring methods for sealing of tubes. (f) In the dies with three parts, the cycle of approaching of dies is a very important factor in appropriate preforming of the tube. (g) The loading path from numerical optimisation showed excellent agreement with the experiments in the final hydroforming.
Acknowledgements The authors thank the Natural Sciences and Engineering Research Council of Canada, National Research Council CanadaAluminium Technology Centre, Alfiniti, Aluminerie Alouette, C.R.O.I and Cycles Devinci for their financial and technical support of this research. A part of the presented research in this paper was financed by the Fonds Que´be´cois de la Recherche sur la Nature et les Technologies (FQRNT) by the intermediary of the Aluminium Research Centre-REGAL.
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