Three-Dimensional Experimental and Numerical Simulation of Sheet Metal Forming Process Based on Flexible Multipoint Die

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1 Three-Dimensional Experimental and Numerical Simulation of Sheet Metal Forming Process Based on Flexible Multipoint Die Abdulkareem Jalil Kadhim, and Mostafa Imad Abbas Abstract--- In this paper, an experimental and numerical simulations for the multipoint sheet metal forming process using pins with a spherical shaped ends. Bezier technique was used to represent the surface in (3D) model. MATLAB software was also used to represent the curves and surfaces then to determine the coordinate of all points located on the surface. A commercially available finite element program code ANSYS 11 was applied to model and analyze the contact problems at the multi-point die sheet metal interface during the forming process. The numerical and experimental results were focused on forming load estimation, thickness variation and stress distribution in the blank. Keywords-- Bezier surfaces, multipoint die, FEM, S I. INTRODUCTION HEET metal forming is an effecting means for producing sheet metal parts of complex three dimensional shapes. This conventional process involves a matched solid die set that forms a cavity into which the sheet is displaced. In this process, different shaped parts will require different dies. Sometimes, to form a sheet metal parts several sets may be needed. The design and manufacturing of dies is a costly work and must rely on the experience of designers and workers. The idea of die forming of variable shape has always been attractive as a means of reducing die design costs, since it permit design iterations to be rapid and nearly cost free The proposed reconfigurable tool consists of one or more matrices of discrete pins in which top surfaces of pins approximate the actual die profile. Different tool configurations can be achieved by changing the pin locations relative to each other, which eliminates the need for multiple tools. Such a tool would help reducing the cost and time required for designing and fabricating dies for various products. Several researchers have studied re-configurable tooling systems in metal forming. Walczyk and Hardt [1, 2] developed discrete reconfigurable dies for forming sheet metal. The system consists of small, individually positioned pins, mounted in two rectangular matrices. The die in this system is an opposed die, which is formed by the pins on each of the matrices. Abdulkareem Jalil Kadhim, Assistant Professor, University of Babylon, Iraq These discrete pins are positioned to approximate the continuous surface of the matched dies with the help of numerical control. Papazian [3,4] used the same principle of reconfigurable dies to build a system for sheet stretch forming. It differs from the system in Hardt in that it uses stretch forming rather than opposed die forming. J.J.Chen [5] studied the basic principles and deformation characteristics of SMPF. Three typical forming methods (Overlap region method, Assortative region method and Multi pass forming method) are summarized. Ovidiu Viorel [6] presented an algorithm for spring back compensation in deformation with multipoint reconfigurable die and the results of the virtual compensation of this phenomenon using the finite element method. C. Maier [7] determined the rules type for pins position-material response (spring back) in order to assure dimensional precision of the deep-drawn complex parts. P. Cekan [8] focused on studying finite element simulation of the sheet metal forming to investigate the influence of the pins network type on the deformation process in reconfigurable multipoint forming with fixed configuration. Zhong-Yi.C. [9] studied the numerical simulations of the processes for forming spherical and saddle-shaped parts by finite element analysis. The contacting process between sheet metal and punch elements was investigated, and the variations of forming force with respect to the tool travel were analyzed. Virgil Teodor et al [10] presented a method for multipoint forming primary configuration considering that the part surface is defined as a points matrix and the problem solution is obtained using MatLab program. Then using the finite element method to analyze the deformation in sheet metal. N. Baroiu [11] focused in a qualitative study of the tool geometry in the reconfigurable multipoint forming considering the influence of the contact points in deformation process and the presence and the absence of the interpolators in deformation system. Eugen Găvan [12] concerned with the development of a method for die punch geometry configuration using Matlab program. On this basis, the theoretical analysis is particularly applied to the simulation of a curved thin steel plate deformation using finite element method. 16

2 II. SIMULATION AND EXPERIMENTAL WORK A. Numerical Simulation The following steps highlight the general procedure to simulate the problem in ANSYS11 software package: B. Element Type Selection The finite element model is composed of seven parts: upper die, lower die, plate, upper and lower elastic cushion layer (continuous and non- continuous), blank holder. The plate material is modeled with (Visco106 element). It is assumed that the pins, the blank holder are rigid and are represented by (Solid element 42). The rubber (elastic cushion) material is modeled with (Hyperelastic element 182).The contact interface between the die and the deformed material is represented by (contact element 172 and target 169). C. Material properties Two types of material have been proposed for the analysis, aluminum and steel, to investigate the effect of strain hardening. The properties of both the materials are shown below. TABLE I MECHANICAL PROPERTIES OF THE SHEET MATERIAL Aluminum Steel Modulus of elasticity(e) 68 Gpa 210 Gpa Tangent modulus(e T ) 0.1 Gpa 100 Gpa Yield stress (σ y ) 68 Mpa 312 Mpa Density (ρ) Kg/m Poissonʼs ratio(υ) Surface(2) consists of four Bezier surfaces (each surface of the Bezier type with 4*4 control points). (C 0 ) continuity is used as a property to connect the surfaces with each other. Control points of the surface (2) b 11 (0,0,20) b 12 (30,0, 20) b 13 (60,0, 0) b 14 (90,0,0) b 21 (0,30,20) b 22 (30,30, 20) b 23 (60,30, 0) b 24 (90,30,0) b 31 (0,60, 0) b 32 (30,60, 0) b 33 (60,60,20) b 34 (90,60,20) b 41 (0,90,0) b 42 (30,90,0) b 43 (60,90,20) b 44 (90,90,20) Bezier surfaces with 4*4 control points for the two surfaces can be shown in Fig (1). To describe the behavior of the elastic cushion, Mooney- Rivlin (2 parameters) hyperelastic material model were used. In the following analyses, the friction coefficient is assumed to be (0.1). TABLE II MECHANICAL PROPERTIES OF THE ELASTIC CUSHION Modulus of elasticity(e) 2.87 Mpa Poissonʼs ratio(υ) Mooney-Rivlin Constant C Mpa C Mpa Fig. 1 Representation of the used two surfaces with (4*4) control points surface D. Axisymmetric (3D) Model in the Simulation To reduce CPU time and considering the symmetry characteristic, only one quarter of (3D) model have been established with spherical pin type, the working array consist of (10*10) pins with the dimension of blank (plate) (180 x 180 x 1 mm) to represent the doubly curved Bezier Surface. The center distance of each two pins equal to 20 mm and the radius of each pin is equal to 8.5mm. Bezier surface technique is used to represent two types of surfaces in which each surface have 4*4 control points Control points of the surface (1) b 11 (0,0,20) b 12 (60,0, 0) b 13 (120,0, 0) b 14 (180,0,20) b 21 (0,60,30) b 22 (60,60, 15) b 23 (120,60, 15) b 24 (180,60,30) b 31 (0,120,20) b 32 (60,120, 0) b 33 (120,120, 0) b 34 (180,120,30) b 41 (0,180,20) b 42 (60,180, 0) b 43 (120,180, 0) b 44 (180,180,20) 17

3 Fig. 2 Three dimensional FEM modeling of the forming to deform the two surfaces Fig. 4 Assembly of the multi-point die autocad designed die experimental tool Two pieces of elastic cushion (8 mm) are used in experimental work as an interpolator between die and the sheet metal Fig. 3 Axisymmetric model show the position of non- continuous elastic cushion (thickness 6 mm) IV. RESULTS AND DISCUSSION Fig.(5) represents the load forming displacement relationship for experimental test when using die with spherical pin in two cases (when using elastic cushion and without using elastic cushion),. It has been shown that the two curves starts from value of (16 KN) of forming load. This is the value of the load required to maintain the contact between the upper and the lower die since the four springs at each side of the die lift the upper die at a distance required to insert the sheet metal with two rubber sheets. III. DESIGN AND FABRICATIN OF MULTIPOINT DIE Design of the experimental (die-punch) tool composed of two working arrays with (320) pins for each array, (16) rows on x- direction and (20) columns on y- direction. The pins are arranged face to face, both on x and y- directions. The distance between the centers of the pins is equal to (20 mm). Spherical pins were used in the experimental work. The pins locked into position by locking nuts to withstand the forming load and give the die more rigidity. Fig (4) shows the AutoCAD designed die and the experimental setup.. Fig. 5The forming Load and displacement relationship 18

4 Fig. 6 Thickness Variation along the sheet metal for curve 1 when use (Solid die, spherical pin, with using elastic cushion and with using non-continuous elastic cushion Fig.(6) Shows the thickness variation along the sheet metal, this figure also show the effect of applying elastic cushion (continuous and non-continuous ) on spherical pin compared with the solid die. It has been shown that the elastic cushion has a great effect on the sheet metal thickness variation, since spherical pin alone create a local dimpling due to high stresses concentration produced by the head of the pin. Fig.(7) and (8) show the isometric view of contour map for Von-Mises stress distribution through the sheet metal for surface( 1) and surface (2) respectively, it can been shown that the maximum Von-Mises stress value was found at the curved edge region because this region is suffered from various complex contact stresses which is occurred between parts of the forming die due to the blank holder load and most of the metal deformation occurred at this region. It can be shown that the dimpling phenomenon is very clear on the sheet metal in the (3D) model. One of the methods utilized for increasing the reconfigurable multi-point formed parts quality is by using elastic cushion (interpolator) which is inserted between the pins and the blank The interpolator changes the behavior of all the system of deformation, resulting both advantages and disadvantages in this type of process. The advantages of using the elastic interpolator are: good surface quality of the part as a result of dimpling phenomenon elimination; a uniform pressure distribution upon the blank which assures a uniform material deformation.there are also some disadvantages regarding the properties and thickness of the elastic cushion used in the system. First disadvantage of using soft materials is that the pins can push through the pad and dimple the sheet metal. Also, this thing happens when the interpolator is too thin. Second is that when the interpolator is hard, it will not conform to the blank geometry. Fig. 7 Views of contour map for Von-Mises stress distribution for surface 1 A-Top view B - Isometric 19

5 elastic cushions. A series of experimental and numerical results are obtained, these results reveal the effects of the shape of the pin on the sheet metal deformation and the role played by the elastic cushion. (1) The numerical and experiments results show the effect of localized deformation. The localized deformation reduced the surface quality of the part due to the presence of dimpling. (2) To suppress dimple effectively, a thick elastic cushion should be employed. But a thicker elastic cushion may make more discrepancy between the formed part and that of designed part. (3) The use of elastic cushion normalized the stress variation in the shaped product Fig. 8 Views of contour map for Von-Mises stress distribution for surface 1 A-Top view B Isometric Fig. 9 Von-Mises Stress distribution along the sheet metal when using spherical pin with the elastic cushion for curve 1 REFERENCES [1] Walczyk DF, Hardt DE. A comparison of rapid fabrication methods for sheet metal forming dies. ASME J Manuf Sci Engng 1999;121(1): [2] Walczyk DF, Hardt DE. Design and analysis of reconfigurable discrete dies for sheet metal forming. J Manuf Syst 1998;17(6): [3] Nardiello J, Christ R, Papazian JM. Block Set Form Die Assembly,USA Patent 6,053,026; April [4] Papazian JM, Anagnostou EL, Christ RJ, Hoitsma D, Orivile P,Schwarz RC, Spitzer K, Barkley C. Tooling for Rapid Sheet metal parts production. Sixth Joint FAA/DoD/NASA Conference on Aging Aircraft; September [5] J.J. Chen, M. Z. Li, W. Liu and C. T.Wang "Sectional multipoint forming technology for large-size sheet metal" Int J Adv Manuf Technol Vol. 25, pp , (2005). [6] Paunoiu, V., Maier, C., Epureanu, A., Banu, M., and Nicoara, D., "Virtual Compensation of Springback in Sheet Metal Deformation Using Reconfigurable Multipoint Die" The Annals Dunarea de Jos University of Galati, Fascicle V, pp ,(2007). [7] C. Maier, M. Banu, Paunoiu V. and Epureanu A.," Steet metal forming analysis with multipoint reconfigurable die using data mining technique", The Annals Dunarea de Jos University of Galati, Fascicle V, pp , (2007). [8] P. Cekan, V. Paunoiu, E. Gavan Numerical Simulations in Reconfigurable Multipoint Forming ", Proceedings of the 11 th ESAFORM Conference on Material Forming, Lyon (France), pp April (2008). [9] Zhong-Yi C, Shao-Hui W and Ming-Zhe L "Numerical Investigation of Multi-Point Forming Process for Sheet Metal: Wrinkling, Dimpling and Springback", Int J Adv Manuf Technol Vol. 37, pp ,(2008). [10] Teodor, V., Gavan, E., Nicoara, D., " Algorithm for The Geometric Configuration of The Reconfigurable Multipoint Forming Dies", The Annals Dunarea de Jos University of Galati, Fascicle V, pp , (2009). [11] N. Baroiu,V. Paunoiu, V. Teodor, C. Maier and G. Bercu "Study of The Tool Geometry in Reconfigurable Multi-Point Forming", The Annals Dunarea de Jos University of Galati, Fascicle V, pp , (2011). [12] Eugen Găvan, Viorel Păunoiu, Catalina Maier and Virgil Teodor "Numerical Analysis of Multi-point Forming Process" International Journal of Modern Manufacturing Technologies Vol. 3, No. 2, pp (2011). Fig. 10 Von-Mises Stress distribution along the sheet metal when using spherical pin with use the non-continuous elastic cushion for curve 1 V. CONCLUSIONS Extensive experimental and numerical simulations of multipoint forming processes have been performed by finite element methods to investigate the multi-point forming processes for the parts of different shapes using different 20