Ability of the flexible hydroforming using segmented tool

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Ability of the flexible hydroforming using segmented tool Article in International Journal of Advanced Manufacturing Technology · July 2016 DOI: 10.1007/s00170-016-9160-9

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University of Tunis El Manar

University of Monastir

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"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

Ability of the flexible hydroforming using segmented tool. Naceur Selmi1, Hedi BelHadjSalah1

Abstract The newly developed multipoint flexible hydroforming process is an adequate combination between hydroforming and multipoint forming processes to inherit flexibility and advantage synergies. The single reconfigurable tool allows better flexibility, faster and easier setting to produce varieties of doubly curved surface shells. After reviewing the recent flexible processes using reconfigurable tools, the new process using multifaceted-segmented tool and the theoretical basis was presented. Numerical model was developed and experimental setup was designed and realized, to evaluate the ability of the new process, especially for thin shell parts. The investigations conducted on aluminum alloy blank sheets are focused on the sheet thickness and forming pressure as prevailing parameters, controlling the quality of produced shell. The analysis indicates particular favorable behavior of pivoting facets allowing to obtain better curvatures control and to avoid dimpling and edge buckling more than basic multipoint reconfigurable tool particularly for thin metal sheet product. The results obtained prove that the hydroforming with segmented tool is a relevant method to extent the latitude of the hydroforming process in flexibility and its ability for accurate doubly curved shell surface product.

Keywords Sheet hydroforming. Multipoint tool. Flexibility. Segmented tool. Curvature.

__________________________________________________________________

Naceur Selmi1 [email protected], Hedi BelHadjSalah1 [email protected]. 1

Mechanical Engineering Laboratory (LGM),

National Engineering School of Monastir (ENIM), University of Monastir, Tunisia

1 Introduction Nowadays several segments of advanced industries request to design and produce a wide variety of threedimensional metal sheet components with improved structural strength and quality, especially in aerospace, shipbuilding, automotive, modern architecture and building. The large multiplicity of used materials and the diversity of design tendencies, induce a fast and frequent change in product models proposed and produced with medium or small lot-size. Consequently, more polyvalent and resourceful forming tools and processes have to be suggested to satisfy these requirements. In this context, several innovative and flexible processes was developed these last decades, to improve the flexibility and quality of forming processes and methods to produce doubly curved shell parts with different final shapes, for faster prototyping stage and quicker tooling setup. The hydroforming and the multipoint flexible forming are the processes that carry the most of interests and potentialities as issued solutions. The hydroforming process is an effective way compared to conventional solid die forming processes, the fluid pressure used to substitute one of two opposed forming tools, permits less tool friction effect and better surface quality. The flexibility aspect of hydroforming is not limited only to the suppress one tool (die or punch) furthermore the fluid media is able to achieve a wide range of blank thicknesses, only by adjusting the fluid pressure on the blank to conform it tightly against the unique rigid tool on the opposite side. Accordingly better conformity and surface finish quality can be reached. The flexforming [1] is a particular version of hydroforming in which the fluid pressure drives the blank progressively to take the tool shape, through a thick flexible diaphragm. In this process, the diaphragm

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ under fluid pressure, performs the function of flexible blank holder as well as the complementary fluid tool. Hydroforming with segmented blank holder[2, 3], permits local variations of the peripheral blank flow, by individual driving of the pressure applied at each segment of flexible blank holder, to increase the ability to obtain variable depth shell surface with better thickness distribution. The multi-point flexible forming process (MPF) is another recent flexible method for manufacturing threedimensional sheet metal parts. In this process, the sheet metal is formed between two opposed matrices of adjustable punch elements, instead of the conventional fixed shape die sets. The die and punch are partitioned in arrayed punch elements with are shaped by adjusting separately in their height. By this approach, production of many parts with different geometry will be possible, just by using the same tools. By this manner, the reconstruction of new dies, accumulating and storing heavy rigid tools for long period will be reduced. Consequently, an evident advantage in time setup saving and manufacturing cost is obtained, especially in the field of small batch production or prototype developments, where various elements of shell type structure, have to be realized in reduced number. In phase of initial development, various advances was elaborated particularly in the fields of aerospace and shipbuilding. Schwartz and coworkers [4], investigated the ability of multipoint reconfigurable discrete dies for forming aircraft fuselage body panels. Wei Liu and allied [5] examines by numerical way the final shell part accuracy of the multi-point stretch forming process and the reduction of inaccuracies and springback by iterative compensations. Wang and co-workers [6] investigate on punch element effect on the quality of product. [7] Chen and all. Investigate the capacity of large size metal sheet product by sectional forming multipoint technology. Ming-Zhe Li and allied [8, 9] carried out many investigations on the on the capability of the multipoint flexible processes for manufacturing method for a 3-d surface sheet. Works of Yan [10], concerned the flexible multipoint forming and its adequacy for a production of aeronautic panel production of lighter structures of complex forms. However in multipoint processes, Zhang and allied [11], concluded that the number of punch elements need to be excessively increased, to obtain an acceptable regularity and quality for relatively complicated final parts, the direct contact between the blank and rounded extremities of punch elements provokes a severe dimpling on the final part. Zhang and al. works [12], highlighted that the softening of contact between multipoint matrices and blank faces, by insertion of elastomeric sheets interpolators, has been an alternative solution to moderate dimpling singularity. Furthermore, in the same way, Zhong and allied G. Sun and coworkers [13], , verified the ability of multipoint flexible blank holder technology to reduce

significantly edge wrinkling and spring back reduction by rearrangement of multipoint punch elements. Cai and allied [14], validate the optimal load path method to obtain significant reduction of dimpling defects. Zhong and allied [15], carried out numerical investigations, in the way to reduce wrinkling, dimpling and springback. Recently, Liu and al. [16], review the production of panels for high speed trains and confirm the ability of multipoint flexible processes for effective implementation in advanced industries. The Multipoint flexible hydroforming, is a new forming process designed and developed by authors [17], to extend the latitude of application and the flexibility of the basic hydroforming process. The fluid tool is adopted on one side, on the other side the rigid tool is substituted advantageously by one reconfigurable tool. The concept inherits conjunction advantages of both hydroforming and multipoint flexible processes and allows significant extensions in process ability and flexibility. In this process, only one shape setting operation is needed on the unique reconfigurable tool. On the other side of blank, the fluid pressure is the unique parameter to adjust, the needed setting time of reconfigurable tool is reduced to half, compared to complicated setting of conventional multipoint forming process with two die. Furthermore the contact severities of punch elements are limited to one side of the formed blank. The main problem of multipoint flexible processes is dimpling and edge buckling sensitivity for relatively thinner formed blank. - Currently the methods commonly adopted in the literature for multipoint flexible sheet forming processes to reduce dimpling defects are focused on two ways: - The use of elastomeric interpolator sheet between multipoint tool and formed blank; the increase of interpolator thickness moderates the dimples [12], but compressive elastic strain of elastomeric increases the springback and final part shape error. - The increase of punch elements density [11] moderates the dimpling severity and improves the profile accuracy of final part, but also increases excessively the tool cost, the time and the complexity of tool shape setting and adjustment. In the preliminary investigations, carried out on governing process parameters, regular profile with insignificant dimpling defect was obtained by the process for 2mm blank thickness( fig.1), but relatively thinner blanks (0.5 mm) was subject of severe dimpling and edge buckling defects (fig.2). The uses of conventional elastomeric interpolator, reduces slightly these defects, but did not overcomes springback and edge buckling. (fig.2).This conclusion is also approved later by investigation of Paunoiu and allied [18].

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ The uses of a rigid metallic medium, as alternate interpolator [17], between formed blank and multipoint tool is more efficient and robust way than conventional elastomeric soft interpolator, to reduce buckling and dimpling sensitivity for thin sheet (fig.3.b). This method avoids also the expensive recourse to increased density of punch elements, however, the monolithic metal sheet insert is not completely reversible and requires more forming pressure. Recently, Wei Liu and coworkers [19] carried out experimental and numerical investigations on similar version of hydroforming with moving multipoint tool, and reconfirmed that increased thickness of metallic cover sheet, inserted under multipoint punch, reduces stress concentrations and dimpling severities. Taking into account the effectiveness of the rigid metallic medium as interpolator, presented here before, as an alternative method allowing the multipoint flexible hydroforming process to produce successful relatively thinner shell part without dimpling or edge buckling defects. The objective of the present work, consists to enhance the design of the multipoint tool and the rigid interpolator setup. The sought-after goal is to make the rigid interpolator more flexible and immediately reusable for different forms. As well as the transformation of the reconfigurable tool to be able to express the slopes and the curves of the desired final form with a better regularity. For relatively thinner sheets or wider pin steps, the lacking stiffness of elastomeric medium cannot precludes overflow of formed bank leading to dimpling and wrinkling edge defect (fig.3.a) [17]. The conventional multipoint tool uses only height of its discrete punch elements to express the final surface form regardless their intermediary fitting of slopes and curvatures of final surface, which remains unspecified and lead to overflow defects. The contact pressure is excessive near contacted round head of punch elements and undersupplied elsewhere intermediate gaps, the height setting of punch elements cannot ensures regular slopes and curvatures. The segmentation of the tool surface with little rigid facet elements moderates the contact pressure by widened contact surface. These facets can materialize the tangent planes as illustrated in figures 5 and 6, this method allows more regular contact pressure and better control of the slopes and curvatures of blank surface. 2 Presentation of the flexible hydroforming with segmented die. The hydroforming with flexible segmented die proposed in this paper, is a new improved process design to extend the ability of reconfigurable tool for better control of local curvatures by inserting a collection of little rigid facets, to materialize local

tangent planes, between formed blank and discrete punch elements (Fig. 4, 5). The rigid metallic medium will then undergo a bidirectional segmentation to obtain a flexible collection of rigid facets, able to line up easily the local tangent planes of surface, which increase its capacity for a better interpolation of local curvatures. The flexible segmented assembly is more able to immediate reprocess for other final shapes with less forming pressure. In this work, numerical investigations was carried out, to evaluate the relevance of the new process, the experimental setup was built to validate the awaited improvement in quality and defect reduction by producing doubly curved thin shell. 2.1 The experimental setup The process prototype assembly, was designed and realized by authors (fig.4), to evaluate the ability of the proposed process to produce better shell product quality. The assembly includes three basic units. The upper unit constitutes the essential of the hydroforming unit, the fluid under pressure, provided by an external generator, feeds the module to fill a die cavity, which includes in its lower part, a flexible membrane separator to transmit the pressure to the higher face of sheets stack, maintained in the central unit. The central unit includes the blank maintained between, holding system and intermediate interpolating mechanism. The fluid pressure deforms this stack, in order to conform it to the shape expressed by the flexible tooling of the lower unit. The upper side of the blank is retained, for this prototype, simply by one floating flexible blank holder at the outer region of formed blank to limit the experimental setup complexity(fig.4), this holding method did not need supplementary holding transition surface, and will be then compatible to multipoint sectional forming methods. The lower module contains mainly the reconfigurable matrix, composed of a finite number of mobile punch elements. The individual regulation in height position allows expressing discretely the shape of the final part. The reconfigurable tool is composed of 121 punch elements arranged in a matrix of 11x11elements. These elements was positioned with a regular step of 10 mm in two orthogonal directions in horizontal reference plane, the segmented medium contains 11x11 flexibly linked rigid facets, stepped as the multipoint punches, Each rigid facet allows better isolation from stress concentration, which are localized at zone of contact with punch element. At the other side, rigid facet ensures more uniform contact pressure with contacted blank surface. The punch elements are with spherical heads of 4 mm radius, the height are individually settled and locked in position by a screw and nut mechanism.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

Fig.1: Ssuccessful thick shell (2mm)

Fig.2 dimpling and edge buckling for thin shell product (0.5 mm)

Figure 3: Overflow defect (a), rigid interpolating medium (b).

Figure 4: Experimental setup design.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

variations and allows a local representation (figure 6-b) around any settled point (M(ij)), as follow:

2.2 The multi-facets segmentation principle The new method consists to segment the rigid interpolator in two orthogonal directions, to obtain a flexible tablet of rigid square facets. By this way, each facet will be free to rotate around punch elements extremities, and will be smoothly auto-adapted to different local slopes of doubly curved die shape (fig.5). In other means, this concept consists to express locally the die shape by its tangent plane around each punch elements position. In geometrical topology, it is well known, that surface curvatures are directly related to the directional variations of normal and tangent vectors which are directly linked to tangent plane (fig 6.a). For any regular surface settled by multipoint die and represented by equation (1) in Cartesian coordinate system. 𝑧 = 𝑓(𝑥, 𝑦) = z(xi, yj)

(1).

The second fundamental form of surface, represented by the curvature tensor, illustrates slope and curvature

⃗⃗⃗⃗⃗⃗⃗⃗⃗ Mij M(X1 , X2 ) = X1 . ⃗⃗⃗ e1 + X2 . ⃗⃗⃗ e2 +X3 (X1 , X2 ).n ⃗ (2) (Mij , ⃗⃗⃗ e1 , ⃗⃗⃗ e2 , n ⃗ ) is the local coordinate system, ⃗⃗⃗ e1 , ⃗⃗⃗ e2 are eigenvectors of curvature tensor, situated in local tangent plane and n ⃗ the local normal vector[20]. In this coordinate system, the normal component X3 is expressed as symmetrical quadratic form of the tangent components [21] (See also Porteous (1994) for more details.): X3 (X1 , X2 ) = Where: 𝐾1 =

1 2

.(𝐾1 .X 1 ²+𝐾2 .X2 2 )

1 R1

, 𝐾2 =

1 R2

(3)

.

The factor parameters 𝐾1 , 𝐾2 are the principal eigenvalues of curvature tensor. These parameters are simply the inverse of the minimum and the maximum of normal curvature radii of the surface at the discrete point Mij (fig.6.b).

Fig. 5: Segmented interpolating by rigid facets (a), Design examples for facet and punch element (b).

Fig. 6: Surface representation: Cartesian representation (a), Local curvature eigenvectors representation (b).

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ 2.3 Finite Element Analysis The process version, illustrated in figure 7, was modelled under Abaqus/CAE 6.14 software, the multipoint elements was configured to set the desired final shape. For this work, the investigations was performed for a parabolic final shape (equation 4) as follows: Z= f(x, y) = (x² + y²)/500.

(4)

The analytical field option was used to assign directly the height position setting (z) of multipoint tool constituted of 121 punch elements (11x11) in a square matrix of size 110 mm x 110 mm. The Multi-facets segmented medium is a flexible tablet of 11x11 rigid thick facets. The floating flexible blank holder is inserted between blank and upper elastomeric membrane separator. Shell deformable parts of model are meshed using S4R elements. Rigid punch elements

are modeled as discrete rigid parts and meshed in R3D4 elements. The shape function (equation 4), can be settled before forming step, (fixed multipoint method) or progressively modified throughout the forming step (progressive method). Fluid pressure is applied on the upper side of the membrane sheet in a smooth load path. The elasto-plastic material model was used for aluminium alloy material sheets (E = 73 000 Mpa,  =0.3) with strain-stress curve presented in figure 8a.The Mooney–Rivlin hyperelastic material model was used for elastomeric interpolators, this model was built from the uniaxial test data presented in figure 8.b. The Coulomb law was used with friction coefficient of 0.1 for general contact interaction between constituents of the model. Dynamic/explicit method was used for the simulation.

Fig 7: Simulation model of Multi-facets flexible hydroforming.

a b Fig. 8: Stress–strain curve for Aluminium alloy (a). Uniaxial data for hyperelastic material (b).

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

2.4 Experimental investigations For this paper, the main aim is to quantify the quality and to highlight the relevance of the new version of the flexible hydroforming process including the multifaceted interpolation mechanism. The process parameters include the hydroforming pressure as main control parameter, depth or drawing ratio, as well as the parameters of reconfigurable tool such as density of multipoint punch elements. The sheet parameters affecting the final product quality are taken in account such as the material proprieties, the curvatures of final part shape and the initial blank thickness. The final product quality of processes using conventional reconfigurable tools are very sensitive to the blank thickness, dimpling and edge buckling defects for thinner formed blank are attached to punch elements with rounded tips. The forming pressure and the blank thickness are the most influent parameters affecting the final product quality of flexible processes. Consequently, the main purpose of this work consist to the highlights the effectiveness of new designed segmented tool, particularly for thinner blanks.

blank and all punch elements of the reconfigurable die. The pressure is related to thickness, yield stress and minimal curvature radius, according to the equation (5) to reach a plastic strains, the stress must significantly exceed the material yield stress to reduce the spring back level. The needed forming pressure must be able to produces yield stress for all curvatures, in final configuration with complete contact between formed shell and the surface expressed by reconfigurable tool. 𝑝 ≥ 𝜎𝑦

𝑡 𝑅

(5)

Where 𝜎𝑦 is the material yield stress, t is the Blank thickness, R is the lowest radius of curvature corresponding to the highest eigenvalues of the final surface curvature tensor. To evaluate the quality of part profile, measurement was done in 21 equidistant locations (fig.9), along outer edge and diagonal path on convex side by reversing the produced part on the reference plane of measuring setup. These measurements allows evaluating the conformity and the regularity of the profile as well as the amplitude of the spring back, by comparison with the exact wanted profiles.

To limit the complexity, the prevalent parameters selected for this investigation, are limited to blank thickness and hydroforming pressure. At the end of the loading step, the final hydroforming pressure must be able establish the contact between the

Fig. 9: device Profile paths and measurement setup.

3 Results and discussion 3.1 Process behavior During loading step, the blank will be enclosed firstly between outer facets, and flexible blank holder, the fluid pressure deforms progressively the

blank and its flexible holder (fig 10: a, b, c), more facets are involved in the contact, and the retention effect are then increased progressively. The touched facets are auto oriented to create progressively smoother and relatively wider zone of contact (fig 10: d, e, f), no happens of overflow

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ beyond the limit of multifaceted tablet medium, which prevents occurrence of dimples and buckling. Each facet of flexible tablet rotates automatically and faces the local tangent plane of final surface around the local multipoint punch element; this adaptive alignment goes only by progressive encloses of facets between surface of blank and consecutive punch elements without need of additional mechanism to set the local tangents. If the pressure is sufficiently high to establish completely the contact throughout the forming step, more blank surface will be affected favorably, that’s allow better profile calibration and springback reduction of final part shape. Under forming pressure, edges of the blank are tightly confined between flexible blank holder and outer facets of flexible pivoting tablet (fig10 a to f), consequently edges are better maintained and constrained, that’s introduces favorable stretching affect to reduce edge buckling, and precludes dimpling and buckling overflow. 3.2 Effect of blank thickness The ability of the multifaceted flexible hydroforming, to produce doubly curved shell is tested both by numerical and experimental ways. For initial blank of 0.5 mm, better regular profiles are obtained for both outer edges and diagonal paths (fig.11.c,12, 13), without dimpling or edge buckling, and the spring back was significantly reduced, and can be easy eliminated by height compensation of settled target surface expressed by reconfigurable matrix. Thicker blanks 2mm are clearly with better profiles and more robust toward dimpling and edge buckling, with significantly reduced spring back level (fig.14, 15). 3.3 Effect of pressure The profiles obtained for the edge and diagonal path are with improved regularity and very near from exact profile settled by multipoint tool. The experimental profiles are in good concordance with those obtained by finite elements simulations. The experimental and numerical investigations highlighted the relatively upgraded profile quality; there is no dimpling undulations or edge wrinkling. The increases of final pressure reduces the spring back level but increases slightly the thickness strain variation in the middle region, (fig.16 a).

Relatively increased final pressure allows establishing earlier the complete contact with multifaceted tool, after that the supplement of forming pressure continue to stretch slightly the formed blank. The relatively wider contact zone with auto oriented flat facets, gives more uniform contact pressure and prevents occurrence of dimpling and edge wrinkling by the improved interpolating, contrarily to basic multipoint tool with rounded punch elements, the increases of pressure accentuates buckling and dimpling imprints. Increases of pressure reduces also the spring back level, but increases the curvature contrasts effect produced by change of curvatures in the middle regions between consecutive facets, this contrast is apparent for thin shell (0.5 mm) (fig.16 a, fig.17 b). There is no need to increase excessively the forming pressure; the spring back can be efficiently reduced by readjusting of multipoint tool. The comparison of the new process using segmented multifaceted die with basics multipoint die methods illustrated in fig (18) highlights the relevance of the new concept. The new process design provides important reduction of contact pressure and better contact conditions. The agreement between numerical and experimental results is illustrated in graphs of figures 12 to 17, for edge and diagonal profiles, obtained by finite elements simulations and measurement on produced parts, these results validate the effect of predominant parameter, the comparison with conventional flexible methods in figure 18, proves the ability of the new process to produce thin shells with improved robustness of profile quality and accuracy. The flexible hydroforming using segmented tool, with its innovative reconfigurable tool, is able to produce thick or thin doubly curved shell product, with upgraded surface quality and regularity. This process provides a flexible and low cost method for sheet forming production, potential industrial application can been envisaged for prototyping, small or medium lot size production of variety of structural shell product in automotive aerospace or shipbuilding.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

Fig 10: Adaptive alignment of facets: Slope follow-up progression (a, b, c). Contact surface progression (d, e, f).

(a) (b) (c) Fig. 11: Multifaceted tablet (a), flexible blank holder (b), successful 0.5 mm shell part produced(c).

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ Profile of 0,5mm blank : Pressure : 0,4 MPa Exp/FEM Exact profile (Path2)

Path2 FEM

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Path position Figure 12: Experimental and Numerical profiles for 0.5mm and pressure of 0.4 MPa.

Profile of 0,5mm blank : Pressure : 1,6 MPa EXP/FEM. Exact profile (Path2) Exact profile (Path 1)

Path2 FEM Path 1 FEM

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Path position Figure 13: Experimental and Numerical profiles for 0.5mm and pressure of 1.6 MPa.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

Profile of 2mm blank : Pressure : 1,6 MPa EXP/FEM Exact profile(Path2)

Path2 FEM

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Figure 14: Experimental and Numerical profiles for 2mm and pressure of 1.6 MPa.

Profile of 2mm blank : Pressure : 6,4 MPa EXP/FEM. Exact profile(Path2)

Path2 FEM

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Figure 15: Experimental and Numerical profiles for 2mm and pressure of 6.4 MPa.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

(a)

(b)

Figure 16: Effect of pressure on strain thickness: (a: 0.5 mm), (b: 2mm).

a

b

c

d

Figure 17: Shell products (0.5mm, 0.4MPa): (a), (0.5mm, 1.6MPa): (b), (2mm, 1.6MPa): (c), (2mm, 6.4MPa): (d).

a

d

b

c

e

f

Figure 18: Profile quality comparison of for formed shell of 0.5 mm and of 1.6 Mpa: forming pressure hydroforming with basic multipoint tool without interpolator (a, d), 2mm elastomeric interpolator (b, e), segmented die with facets elements(c, f).

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ 4 Conclusions The flexible hydroforming with segmented tool proposed in this work, is a new way of sheet hydroforming process using multipoint tool together with a segmented rigid medium, to enhance the quality of manufactured doubly curved shells. In this paper, both numerical simulation and experimental investigations were performed to validate the ability of the process for avoidance of dimpling and edge buckling. The basic result deductions can be recapitulated as follows: 1. During forming of relatively thin blank, the excessive contact pressure is near contacted punch elements and undersupplied elsewhere, the only height setting of punch elements cannot control efficiently the unrestrained blank flow beyond the settled surface limits. The segmentation of tool surface with little rigid facet elements moderates the contact pressure by wider contact surface. 2. Theoretical formulation based on the second fundamental form of surface enlightens better on local slopes and curvature variations of shell surface; Accordingly segmented reconfigurable tool including pivoting rigid facets elements to materializes tangent planes, permits better interpolating and accurate description of the local slopes and curvatures variations compared to conventional multipoint tool with punch elements. 3. The investigations focused on the forming pressure and the blank thickness as prevailing parameters; validate the efficiency of the new designed process. The concentrated contact pressure was relocated at the side of punch element and rigid facet interface. The widened contact surface of rigid facet provides lower and more uniform contact pressure and better isolation of the formed shell from contact severities witch increases the robustness to dimpling and edge buckling and reduces significantly springback. 4. The enhanced quality of doubly curved shell obtained by the flexible hydroforming with segmented tool confirms the extended potentialities of this process in flexibility and accuracy for thin or thick shells. This process with low cost and reduced number of constituents can been effectively implemented for prototyping and small or medium lot size production.

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"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________ 14.

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Viorel Paunoiu, Virgil Teodor, Nicuşor Baroiu, the hydro-multipoint forming process of sheet metal parts, Journal of Machine Engineering, Vol. 15, No. 3, 2015. Wei Liu, Yi-Zhe Chen, Yong-Chao Xu, ShiJian Yuan, Evaluation on dimpling and geometrical profile of curved surface shell by hydroforming with reconfigurable multipoint tool, Int J Adv Manuf Technol,DOI: 10.1007/s00170-015-8264-y. Xiao Peng Zhang, WuJun Che, Jean-Claud Paul, Computing lines of curvature for implicit surfaces, Computer Aided Geometric Design,26(2009)923–940, Doi:10.1016/j.cagd.2009. .07.004. Hemant Tyagi, Elıf Vural, Pascal Frossard, Tangent space estimation for smooth embeddings of Riemannian manifolds, Information and Inference (2013) 2 (1): 69114 doi:10.1093/imaiai/iat003.

"The final publication is available at Springer via http://dx.doi.org/ [10.1007/s00170-016-9160-9]". Article title: Ability of the flexible hydroforming using segmented tool, DOI: 10.1007/s00170-016-9160-9 _______________________________________________________________________________________

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