Accurate Welding Line Prediction.pdf

Key Engineering Materials Vol. 424 (2010) pp 87-95 Online available since 2009/Dec/03 at www.scientific.net © (2010) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.424.87

Accurate Welding Line Prediction in Extrusion Processes T. Kloppenborg1, a, N. Ben Khalifa1, b, A. E. Tekkaya1,c 1

Institute of Forming Technology and Lightweight Construction, Technische Universität Dortmund, Germany

a

[email protected], [email protected] c [email protected]

Keywords: Extrusion, Welding Line, Seam Weld, Finite Element Method

Abstract. In contrast to conventional extrusion processes, where a lot of research is done on in the welding quality, in composite extrusion, research is investigated into the welding line positioning. As a result of the process principle, the reinforcing elements are embedded into the longitudinal welding line. Hence, an undefined material flow inside the welding chamber induces reinforcement deflection, which can lead to reduced mechanical properties, as momentum of inertia. Therefore and to reduce costly experimental investigations, a new method of an automated numerical welding line prediction was developed. The results form HyperXtrude finite element calculations are used for special particle tracing simulations to predict the welding line in the profile cross section accurately. The procedures of segmentation and characteristic extraction are presented to approximate the welding line by cubic spline functions. The method was fully programmed in the Java program language, and works well for all HyperXtrude process models consisting of tetrahedral elements. Introduction Porthole die extrusion leads to longitudinal seam welds in the manufactured profiles. Die bridges divide the billet material into different feeders before the metal streams are rejoined around the mandrel and in the welding chamber. The welding line extends over the whole profile length. In general, these types of dies are used for the manufacturing of hollow profiles (Fig. 1i). Advanced and innovative extrusion processes have been developed to extend the requirements of the bridges. In composite extrusion, the bridges are not only utilized to fix the mandrel in the material flow, but also to feed high strength wires in-between the material streams to embed them in the welding chamber at the moment of material rejoining. The supply of the endless wires in the same profile makes additional bridges necessary, which lead to a more complex material flow and to additional seam welds (Fig. 1ii).

Fig. 1: Comparison of: i) Conventional bridge die ii) Composite bridge die

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In extrusion industry the interest is focused on the welding line position and on the seam weld quality. The seam weld position is only taken into consideration when an aesthetical aspect for the application of the profiles becomes necessary. In this case, the die is generally designed to weld the material streams in the profile curvatures to achieve an accurate profile surface. More important for the extrusion industry is the seam weld quality. Bad welding between the two metal streams can result in profile defects, as cracks, and complete failure of the structure under load. Hence, much research has been investigated in recent decades to understand the welding [1-6]. For the composite extrusion process the welding line position is as well important as the welding quality. The material flow in the welding chamber is not usually accurate enough for a well positioning of the reinforcing elements in the final extrusion product. However, with the insertion of reinforcement, a problem can occur which is negligible in the conventional extrusion process. Namely, depending on the material flow conditions in the die, reinforcing elements are deflected horizontally and vertically in relation to the supply position, which yields a change in the mechanical properties like moment of inertia (Fig. 2).

Fig. 2:

Reinforcement deflection in composite extrusion

In [7] Schomäcker analyzed the main effects of the positioning failures. He examined the process experimentally and found out that the position of the elements is mainly influenced by the press on, the temperature distribution, the forming velocity, the die design and the position of the supply channels. It is obvious that the degree of difficulty to predict the material flow rises with the complexity of the die. Hence, for high-quality die designing, technical know-how is necessary, which has to be acquired over a long time. But the process comprehension is limited so that cost intensive trial-and-error experiments are often essential. For composite extrusion, Schomäcker established that an experimental analysis of all influencing parameters on reinforcement positioning exceeds the economic efficiency of the die development process. For this reason, the use of numerical simulations becomes more interesting [8]. Especially the process conditions in the inaccessible die, such as distribution of the material flow, temperature, and pressure, can be visualized [9]. In [10] Schikorra presented two methods to predict the longitudinal seam weld. It could be shown that the effective strain rate or the equivalent strain and the particle tracings are the criteria for the welding line position (Fig. 3) and concluded that these criteria can be helpful to improve reinforcement positioning. However, the determination of the seam weld position was mainly performed optically and thus implies a more qualitative character. In order to substantiate these criteria, it is necessary to predict the longitudinal seam weld more accurately and in an automated way. Especially in case of an automated process optimization, it can be helpful to approximate the weld line, for example, by polynomials. The polynomials can then be useful as an optimization criterion.

Fig. 3: Criteria to predict the weld line formation in composite extrusion [3]

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In the present paper, an automated detection of the welding line position using particle tracings is presented. The method was programmed in java code and is applicable on any extrusion models calculated with HyperXtrude Software. The program works only on unstructured tetrahedral grids in Euclidean 3D- Space. The method is illustrated on a double-T shaped profile and validated on experimental investigations. Particle tracing In many scientific areas as well as in technical applications, finite element simulation is of central importance. The results of numerical calculations are data sets which usually describe the flow behavior in a 3D-environment. To understand the flow characteristics of the simulated process, a meaningful visualization of the data is necessary. The raw data are defined on a discrete structure, a finite element mesh. In the nodes of the mesh the velocity and other results, e.g. temperature, stresses and strains, are stored. In particle tracing individual material particle traces are generated based on the velocity vector field. For the calculation of the flow lines numerical integration of an ordinary differential equation (ODE) is essential [11]. r dp( t ) r r = v( p( t )) dt

(1)

r r where p( t ) represents the position of the particle at time t , starting at time t0 at position p0 . r For the initial vector p0 is essential that: r r p( t0 ) = p0

(2)

For fixed time steps {t0 ,t1 ,...,tn } , the positions { p0 , p1 ,..., pn } can be calculated, which are a set of particle positions to generate the flow line. In Computational Fluid Dynamics (CFD) time dependent and time independent velocity fields are differentiated. Latter, the velocity field is also time dependent. For the simulation of the extrusion process using the Euler-Flow-Formulation, the velocity vectors are time independent, which is why following the explanations are focused only on this problem. Nevertheless, many aspects described later are valid as well for time dependent velocity fields. Darmofal et al. [12] gives a detailed overview of both types of flow fields. Particle tracing is valid for two-dimensional as well as three-dimensional problems. The technique described in the following is referred to 3D finite element models but for a better understanding two dimensional examples are shown. Numerical integration is a standard procedure for solving Eq. 1. For the implementation of particle tracing, additional procedures are necessary. These are element localization, velocity interpolation and integration. For each procedure, many methods are known, while in the following only the implemented ones are given. The basic algorithm for particle tracing is shown in Fig. 4 as pseudo code.

while

Define an element which contains the starting point {element localization} particle in the element do calculate the velocity at the actual position {velocity interpolation} calculate the new position {integration} calculate the element at the new position {element localization }

end while Fig. 4: Particle tracing in pseudo code [13]

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Element localization. Firstly, the element in which the particle point is provided has to be identified before an interpolation of the velocity vectors of the element nodes can be realized. This operation has to be evaluated at the beginning of the particle tracing simulation as well as in every flow line generation loop. The finite element mesh for extrusion simulation is mostly unstructured as a result of different element shapes, element dimensions and element types. For this case, Ren et al. [14] presented an efficient element identification. Here, the characteristic of shared element planes is utilized. This is feasible for all elements except the elements on the model surface. It is helpful to consider that for small time steps, the new position of the particles is in one of the direct finite element neighbors. Based hereon, a heuristic search method can be useful to detect the element of the new particle position. Ren et al. restricted the method to tetrahedral elements and recommended that other element types should be deconstructed into tetrahedral elements. The deconstruction can result in highly distorted tetrahedral elements, in which the interpolation error increases. Hence, hexahedral elements should be prevented. To check if the particles are inside the element, the normal vectors of the element faces can be r used. This method is usable for every element type. For every element face s the normal vector ni is calculated. The orientation of the vector is directed normal to the element. Every element face is considered as plane which divides the space into two parts. The part which is positive concerning the normal vector includes no particles that are inside the element. In converse argumentation, the particles inside the elements are on the negative side of all element planes. Hence, it is sufficient to check if the normal vector for every element plane has a positive portion. This can be calculated r with the vector product. ps stands for any particle point on the element face s . The method is useable for tetrahedral and convex hexahedral elements r r r ( p − ps ) ⋅ ns > 0

(3)

For the determination of the initial position the described heuristical method is inefficient. Alternatively, at the beginning of the particle tracing every element is checked systematically to find the elements in which the particle is placed. The complete search is only executed once, so that the computational time is acceptable. For the subsequent element detections the more time efficient heuristical method is used. This search algorithm also uses the point test. Is a particle at time t r located at the position p( t ) in element E is firstly tested if the particle is also in element E at r position p( t + 1 ) . In case of a failure of the point test at element plane s, the point test is recursively conducted for the neighbor element on face s . This procedure is continued until the element is r found in which p( t + 1 ) is allocated or no further neighbor element is found. Finally, the particle leaves the finite element model. Fig. 5 demonstrates the procedure for the two-dimensional case.

Fig. 5: Principle of neighbor element search: r r (i) Point p is located in element A , no normal vector is directed in direction p ; r r (ii) Normal vector n2 is directed in p , the search is accomplished in element C ; r r (iii) Normal vector n3 is directed in p , the search is accomplished in element D ; r r r (iv) Normal vector n1 and n2 are directed in p , the search is accomplished in B or C

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Interpolation. The velocity vectors are only known at the nodes of the finite elements. At every other point in the mesh a velocity vector has to be interpolated. Within the element identification it is known in which element the particle point is positioned and which nodes are to be used for the interpolation. Dependent on the element types, Sardajoen et al. described different methods [13]. The interpolation is not only used for the velocity vectors but also for values of temperature and stress along the flow lines. In the following, the interpolation of tetrahedron elements which were implemented is shown. For the interpolation in a tetrahedron, the volume weighting is used which is based on volume r r r r r weights. Let p be a point in a tetrahedron consisting of nodes x0 ,x1 ,x2 ,x3 . Then the tetrahedron can r be subdivided into four sub-tetrahedrons, in all of which p is a corner node. The weight for each node of the main tetrahedron is the ratio of the volume of the sub-tetrahedron to the volume of the main tetrahedron (Eq.4) [13]. The interpolated velocity is than calculated as a sum of the weight multiplicated with the corresponding velocity vector (Eq.5). In Fig. 6i the principle is presented for a 2-dimensional triangle element. w0 =

v123 p

w1 =

v023 p

w2 =

v0123 v0123 r r r r r v p = w0 v0 + w1v1 + w2 v2 + w3v3

v013 p v0123

w3 =

v012 p v0123

(4) (5)

Integration. The solution of the basic equation of the particle tracing (Eq. 1) is conventionally solved by numerical methods. Many integration methods are known in the literature, ranging from the simple first-order Euler scheme to the fourth-order Runge-Kutta scheme or even higher-order methods, applied with fixed or variable time steps. An extensive analysis of different integration algorithms and the applicability in particle tracing is proposed in [12]. In the following, the implemented second order Runge-Kutta scheme is shortly presented. The integration method was chosen in order to gain a good agreement between accuracy and calculation time. The second-order r Runge-Kutta scheme is also known as Heun’s scheme. Starting from position pi at time t = ti , the r position pi +1 at time t = ti +1 is calculated in two steps. r r r r p*i+1 = pi + v( pi ) ⋅ t (6) r r 1 r r r r* pi +1 = pi + ( v( pi ) + ⋅v( p i +1 )) ⋅ t (7) 2 The integration principle is shown in Fig. 6ii. There are further numerical methods with higher accuracy in literature. In [11] such a method is presented for tetrahedron element meshes.

Fig. 6: i) Area weighting [13]; ii) Second order Runge-Kutta schema

Additional features. The results from the finite element calculations with commercial code HyperXtrude are not error free. The errors are affecting on the particle tracing results. In dead zones for example as well on the contact area no material flow is present. In the ideal case, here the

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velocity field is zero, but the experience has shown that velocity remains due to numerical errors. The velocity vectors are small but arbitrarily directed, for example contrary to the extrusion direction. Within the dead zones, for example, circulation of the particle traces can occur. Here, the flow lines run on cyclic tracks and can not leave the area. In such a case, it is convenient to restrict the length of the flow line.

Method for numerical weld line prediction In the following, the method is presented which can be used to predict the longitudinal seam weld position in the final profile cross section more accurately and in an automated way. In Fig. 7 a simplified 2-dimensional extrusion model is shown. Based on the velocity vectors particle traces have been calculated starting from different die feeder positions, running through the welding chamber into the extruded profile. It is obvious that the material which forms the longitudinal seam weld position is diagrammed by tracings which have started next to the mandrel.

Fig. 7: Schematic illustration of the seam weld formation A 3-dimensional extrusion process model was set-up for weld line prediction. It is based on experimental investigations on a 2.5 MN press. The model was implemented in the commercial implicit finite element code HyperXtrude from Altair to calculate the velocity vectors for particle tracing. The container, the die and the leaking profile are illustrated together with the profile cross section and the used parameters in Fig. 8. A full model was considered in spite of the symmetrical character.

Fig. 8: i) Initial extrusion process model ii) Cross-section of the profile and simulation parameters The billet, made of AA-6060, is preheated to 480°C and then extruded with a punch velocity of 1 mm/s. A Coulomb friction coefficient of 0.577 was utilized on the die and the container wall. Here, the friction shear stress is limited by the shear yield point so that the static friction implements von Mises shear friction with a friction value of 1. The model consists of 809.926 four-node

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tetrahedral elements with linear shape functions. In order to reduce the calculation time, the analysis type was set to steady-state extrusion. The calculated velocities on the nodes of each element were used to simulate particle tracing lines through the numerical model. In Fig. 9 the basic procedure is demonstrated. The particle start position and the resulting position of the particles in the final cross-section are demonstrated. The traces follow the material flow, starting in the feeders at the die entrance. Then they cross the bearing area and terminate on a predefined cross section. For seam weld detection, only the particle tracings around the feeders have been calculated.

Fig. 9: Method for welding line prediction Due to the friction on the die wall, particles have started with a small border distance. An undersized border distance indicates that particles leave the model. Thus, the number of dots in the final cross section decreases and the detection of the seam weld position becomes difficult. Contrary to this, an oversized border distance will increase the distance between the flow lines in the final cross section. Therefore, the border distance was sequentially increased until the longitudinal seam weld was well visualized. Neglecting the particle dots on the profile surface, it can easily be seen that the method indicates an accurate reference value for the detection of longitudinal seam weld formation. Segmentation. The emphasized contour of the seam weld can be used to extract a continuous seam weld characteristic with the help of a pattern matching method. Therefore particles which do not belong to the seam weld have to be deleted. These are positioned on the profile surface or somewhere in the profile cross section due to modelling defects. However, all particles that fall below a predefined distance value to the profile surface are not further considered. Thus, exclusive particles remain that illustrate the seam weld and result from modelling defects. For extrusion process models with multiple feeders, a welding of the material out of two different feeders results in one segment of the weld line. For the identification of every segment, particles out of the same feeder are assigned with the same index. In the profile cross-section every particle point neighbors are checked to characterize the different weld line segments. If there is no neighbor the particle contains out of modeling defects and is deleted. In Fig.10 the particle points before (i) and after (ii) the segmentation procedure are opposed. The five weld line segments are uniformly displayed in terms of color. Characteristic extraction. A continuous weld line can be derived based on segmented particle points. The aim of the procedure is to describe the welding line by a curve for quantitative estimation. Through the segmentation procedure the particle points are already the part segments of the welding line assigned. The approximation is conducted for every weld line segment and than combined to an continuous weld line. The flexible curve character is approximated by cubic spline functions. In contrast to a characteristic polynomial, any curves can be approximated in this way. Fig. 10 iii) shows the results of the characteristic extraction.

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Fig. 10:

i) Simulated particle points; ii) Particle points after segmentation; iii) Approximated weld line

Experimental verification In Fig. 11 the numerical results are compared to experimental investigations. It can be shown that there is a sufficient correlation between the experimentally determined welding line position and the simulated one. The differences are based on the numerical errors and/or modeling errors from the finite element calculation.

Fig. 11:

Comparison of simulated welding line and experimental results

Conclusion and Outlook In this paper a method for an automated welding line prediction is presented. The results from HyperXtrude calculations are used for the simulation of particle tracing that form the weld line in the profile cross-section. The procedures of segmentation and characteristic extraction are presented to approximate the weld line with cubic spline function. The method was fully programmed in the Java program language and works well for all HyperXtrude process models consisting of tetrahedral elements. In case of composite extrusion, the method can be a helpful tool to optimize the reinforcement position numerically. In further investigations the method will by implemented in a closed loop algorithm to optimize the welding line regarding a predefined optimal weld line.

Acknowledgment This paper is based on investigations within the scope of the Transregional Collaborative Research Center/ TR10 and is kindly supported by the German Research Foundation (DFG).

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[10] M. Schikorra, M. Kleiner: Simulation-Based Analysis of Composite Extrusion Processes, CIRP Annals, Vol.56/1, 2007, General Assembly, Dresden, Germany [11] P. Kipfer, F. Reck and G. Greiner: Local Exact Particle Tracing on Unstructured Grids. Computer Graphics Forum, 22(2):133–142, 2003. [12] D. L. Darmofal and R. Haimes: An analysis of 3D particle path integration algorithms. J. Comput. Phys., 123(1):182–195, 1996. [13] I. Ari Sadarjoen, Theo van Walsum, Andrea J. S. Him and Frits H. Post: Practicle Tracing Algorithms for 3D Curvilinear Grids. In: Scientific Visualization, Overviews, Methodologies, and Techniques, Seiten 311–335, Washington, DC, USA, 1994. IEEE Computer Society. [14] Ren, Jicheng, Guangzhou Zeng and Shenquan Liu: Interactive Particle TracingAlgorithm for Unstructured Grids. In: ICSC ’95: Proceedings of the Third International Computer Science Conference on Image Analysis Applications and Computer Graphics, pp. 59–65, London, UK, 1995. Springer-Verlag.

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Accurate Welding Line Prediction in Extrusion Processes 10.4028/www.scientific.net/KEM.424.87 DOI References [3] L. Donati, L. Tomesani, G. Minak, Characterization of seam weld quality in AA6082 extruded profiles Journal of Materials Processing Technology 191 (2007) pp. 127–131 doi:10.1016/j.jmatprotec.2007.03.073 [9] G. Liu, J. Zhou, J. Duszczyk: FE Analysis of metal flow and weld seam formation in a porthole die during the extension of a magnesium alloy into a square tube and the effect of ram speed on weld strength, JMPT 200, 2008, p.185-198 doi:10.1016/j.jmatprotec.2007.09.032 [11] P. Kipfer, F. Reck and G. Greiner: Local Exact Particle Tracing on Unstructured Grids. Computer Graphics Forum, 22(2):133–142, 2003. doi:10.1111/1467-8659.00655 [12] D. L. Darmofal and R. Haimes: An analysis of 3D particle path integration algorithms. J. Comput. Phys., 123(1):182–195, 1996. doi:10.1006/jcph.1996.0015