Considerations on the Incremental Forming of Deep Geometries

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1 Considerations on the Incremental Forming of Deep Geometries G. Ambrogio, L. Filice, G.L. Manco 1 University of Calabria Rende (CS), Italy URL: g.ambrogio@unical.it; l.filice@unical.it; leonardo.manco@unical.it ABSTRACT: New research trends on Incremental Forming processes are strongly based on the development of more efficient control tools or design procedures, able to reduce the time associated to the preliminary setup phase. The latter, in fact, still penalises the industrial application of the above process. If adequate knowledge has been reached nowadays, thanks to the activity of several researchers all over the World, the process feasibility of complex or irregular geometries is still related to the execution of some preliminary trial & errors experimental tests. It seems quite obvious that more efforts have to be spent to increase the process control capability by means of innovative and generalised solutions, such as artificial intelligence techniques, neural networks, numerical simulations and so on. With this perspective, the present paper aims to improve the IF control capability for complex shapes by means of an optimised FE model. Keywords: Incremental Forming, Material Behaviour, Numerical Simulations. 1 INTRODUCTION Although Incremental Sheet Forming of industrial parts is not very common, a number of studies were carried out in order to overcame some specific problems [1]. At the same time, the capability to obtain a very high material thinning as compared to any traditional sheet metal forming process and the possibility to use a very cheap equipment suggest to improve the knowledge and the development of Incremental Forming technique. One of the most investigated aspects concerns the material formability and, in particular, the maximum slope angle allowable by the forming material and the process parameters. However, a simple approach based on the sin law, according to spinning, is not completely convincing since material thinning follows a more complex behaviour. In this context the importance of a prediction model or a numerical simulation, to evaluate the thickness distribution is of course a key-factor. Moreover, in the last years, the finite element analysis showed its potentiality as predicting tool in manufacturing processes. In particular the introduction of the explicit approach represented an important innovation to investigate the sheet metal forming processes. Many works were carried out to show the robustness and the reliability of the numerical results, but nowadays this has to be assessed for the Incremental Forming Processes, specially when complex shapes are investigated. The last ones, in fact, are characterised by a different mechanical behaviour, then the absence of a very robust law, able to define the deformation behaviour, increases the difficulties in the process design. For these reasons the application of a FE model could represent a strategic tool for the process development. Up to now, several study were focused on the FEM analysis, taking into account simple shapes [2, 3]. In the present paper the robustness of the numerical results was tested simulating the IF operation for more complex geometries, characterised by a variable wall inclination angle, and contemporary compared with experimental ones. An experimental campaign was firstly executed to validate the FEM capability in thinning prediction for complex shapes. A good overlapping between experimental and numerical data was found out. All the details will be explained in the paper. 2 FORMABILITY ANALYSIS The material formability and the full understanding of the process mechanics are still an open point in the ISF research. Many improvements have been already introduced in the process knowledge, from

2 both a fundamental research point of view and the implementation of simple laws suitable for industrial users. From the literature review [4, 5], initially, the process formability was simply classified by means of two parameters: the FLD 0 point, which corresponds to the intersection between the major strain axis and the FLC; the α max, which represent the maximum slope angle of the wall, that can be safely manufactured. Unfortunately, due to the process complexity, some drawbacks can be recognized with this indexes: first of all, both the FLD 0 and the α max values directly depend on the adopted process parameters, so that they can not synthetically describe the whole process; secondly, although the α max is easier to be used from an industrial point of view, at the same time it supplies only a partial knowledge on the process feasibility. Some applications, in fact, showed that slope angles, higher than the critical one, can be safely obtained specially when complex geometry, characterized by a variable slope wall, has to be manufactured [6]. The latter, for instance, are usually characterized by different slopes, sometimes higher than the critical one, with a depth associated to each slope usually low. According to that, it was shown [7] that a correlation between the critical slope angle (α max ) and the workpiece depth (H f ) exists for given material and process parameters. In other words, when the critical angle is adopted, it is reasonable to think that material damage occurs only after a given depth. In this direction, an analytical law was statistically derived by the authors, aimed to predict the maximum allowed depth for fixed process parameters and wall inclination angle. Even if the model suitability was firstly statistical evaluated by using performance indexes and, then, experimentally validated with respect to new geometrical configurations, it was based on a single slope geometry. On the contrary, its extension to more general multi-slope shapes would require the execution of a exponential number of tests. Starting by these results a new investigation was firstly executed and then numerically evaluated. 3 EXPERIMENTAL CAMPAIGN With the aim to well asses how formability limit changes increasing the product complexity, a more general experimental campaign was designed. It is quite obvious that introducing new degrees of freedom in the geometry the problem complexity proportionally increases. Actually, the analysis complexity increases since the maximum reachable height is not only influenced by the process parameters or the material properties. On the contrary, the transverse section changes and the partial slopes of the wall angle play a relevant role on the final results. With this perspective, the prediction of the maximum formability for a multislope geometry could become NP-hard problem, since higher number of factors increase the problem dimension, thus increasing the solution times. Here, for sake of simplicity, some factors were fixed or neglected. To do that, firstly, it was decided to keep constant the process parameters during the whole experimental campaign; more in detail: Punch diameter (D p ) was fixed equal to 12 mm; Tool depth step (p) was fixed equal to 1 mm; Sheet thickness (s) equal to1 mm was utilised. Contemporary, an aluminium alloy AA 1050-O was used for the experimental campaign, in order to manufacture a frustum of cone, characterised by a double curvature along the transverse section. According to the major base diameter (D 0 ), the maximum design height to reach (H f ) was fixed equal to 70 mm, defining a sort of cubic working space. Vice versa, two different slopes were imposed, respectively the former H 1 =20 mm and the latter H 2 =50 mm (Figure 1). Fig. 1. Sketch of the manufactured geometry. In order to explore the critical region of the research space, both safe and unsafe wall inclination angle were taken into account for α 1 and α 2 values, as shown in the next table 1. Of course the cases in which α 1 and α 2 coincide the geometry results in a simple conical shape.

3 Table1. Investigated wall inclination angles Input parameters α 1 [ ] α 2 [ ] An orthogonal experimental plane was executed, with three repetitions for each angles combination. A circular baking plate was used to sustain the blank during the punch movement, and five millimetres of gap were always left between the first loop of the trajectory and the baking plate. In figures 2 and 3, two experimental results are proposed to represent both process success and failure. corresponds to sound condition, actually failed after 26mm. It seems obvious that a more efficient control procedure needs to be based on the punctual measure of sheet thickness during the process development. In fact, it is very common to associate to the maximum thinning the maximum material formability in this process. Since this dimension can not be easily measured during the process and it is characterised by a polynomial trend, neither the Sine Law can robustly describe the material behaviour, an alternative solution can derive performing an optimised FE model. 4 NUMERICAL ANALYSIS 4.1 Model design Fig. 2. Sound component obtained with α 1 = 65 and α 2 =70. Despite it is a common opinion among the researchers that experimental approach usually supplies more robust data as compared to numerical simulation, nowadays remarkable improvements were introduced in the FE analysis thus dramatically enhancing its suitability. In the research here addressed, the code Dynaform was used as simulation tool. It implements the dynamic equilibrium equations and results very efficient, also for the use of a smart remeshing criterion, based on the strain controlled shell element subdividing. The simulation is conditionally stable because the imposed high speed of the punch may induce dumping phenomena. For this reason a check on the total kinetic energy was done, verifying that the imposed quota is less than the 10% of the total plastic energy, so that the dynamic effect in the simulation is negligible. The material behaviour has been supplied by a proper power law while the tool has been modelled as rigid surface. Fig. 3. Broken component obtained α 1 =65 and α 2 = 75. Beside ISF is strongly characterised by a localised process mechanics, so that the general idea is that only the portion of material in contact with the punch undergoes to plastic deformation, the experimental results suggested that it is not completely true for complex and varying geometry. In fact, the experimental results highlighted how formability is influenced by the history of material deformation or by the thinning in the first part. For this reason, a geometrical condition α 1 =75 - H 1 =20mm and α 2 =70 -H 2 =70mm, which should Fig. 4. Thickness distribution with α 1 = 65 and α 2 =70.

4 4.2 Thinning analysis At the end of the numerical simulations, each test was compared with the experimental one. The comparisons of both numerical and experimental measures are shown respectively for α 1 = [ ] in the next figures 5, 6 and 7. As it can be observed, a good overlapping was determined for the whole campaign; from a quantitative point of view, in fact, the maximum error is of the tenth of millimetres. Fig. 5. Experimental-Numerical comparisons for α 1 =65. These results confirm the suitability of the FE simulation to predict material thinning even in IF processes. In this case, for instance, this constitute an interesting result since, how it can be observed in the previous figures, breaking occurs when thickness reaches more or less the value of 0.20 mm. 5 CONCLUSIONS An effective design tool in ISF of multi-slopes shapes was set-up permitting to assess some interesting conclusions: despite the process mechanics in ISF is strongly localised, the product feasibility is not simply related to the process conditions and material properties but the sheet behaviour is directly influenced by the 3D profile; a suitable numerical model represents a good trade-off between CPU times and results reliability. Starting from these assumptions, even if the model was validated on double-slope specimens, the approach can be easily extended to monitoring and control multi-slopes shapes. REFERENCES Fig. 6. Experimental-Numerical comparisons for α 1 =70. Fig. 7. Experimental-Numerical comparison for α 1 = Jesweit J., Micari F., Hirt G., Bramley A., Douflou J., Allwood J. Asymmetric Single Point Incremental Forming of Sheet, Annals of the CIRP, 54/2, (2005) Bambach M., Hirt G., Ames J., Quantitative validation of FEM Simulation for Incremental Sheet Forming using Optical Deformation Measurement, Advanced Materials Research, vol.6-8, (2005), Henrard C., Habraken A.M., Szekeres A., Duflou J., He S., Van Bael A., Van Houtte P., Comparison of FEM Simulations for the Incremental Forming Process, Advanced Materials Research, vol.6-8, (2005), Iseki H., An experimental and theoretical study on a forming limit curve in incremental forming of sheet metal using spherical roller, In: Proc. Metal Forming, (2000), Filice L., Fratini L., Micari F., Analysis of material formability in Incremental Forming, Annals of the CIRP, 51/1, (2002) Ambrogio g., De Napoli L., Filice L., Gagliardi F., Muzzupappa M., Application of Incremental Forming Process for high customised medical product manufacturing, Journal of Materials Proc. Tech., vol , (2005), Ambrogio G., Filice L., Manco L., Micari F., A depth dependent analytical approach to determine material breaking in SPIF, In: Proc. of Esaform 2007, (2007), Vol. 907,

5 Identification of material parameters to predict Single Point Incremental Forming forces C. Bouffioux 1,3, P. Eyckens 2, C. Henrard 3, R. Aerens 4, A. Van Bael 2, H. Sol 5, J. R. Duflou 6, A.M. Habraken 3 1 Department MEMC, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium, currently in 3 2 Department MTM, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, B-3001 Heverlee, Belgium philip.eyckens@mtm.kuleuven.be; Albert.VanBael@mtm.kuleuven.be 3 Department ArGEnCo, Université de Liège, Chemin des Chevreuils 1, B-4000 Liège, Belgium. Anne.Habraken; Christophe.Henrard; Chantal.Bouffioux@ulg.ac.be 4 SIRRIS, Celestijnenlaan 300C, B-3001 Heverlee, Belgium. Richard.Aerens@sirris.be 5 Department MEMC, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussels, Belgium. hugos@vub.ac.be 6 Department PMA, Katholieke Universiteit Leuven, Celestijnenlaan 300B, B-3001 Heverlee, Belgium joost.duflou@mech.kuleuven.ac.be ABSTRACT: The purpose of this article is to develop an inverse method for adjusting the material parameters for single point incremental forming (SPIF). The main idea consists in FEM simulations of simple tests involving the SPIF specificities (the line test ) performed on the machine used for the process itself. This approach decreases the equipment cost. It has the advantage that the material parameters are fitted for heterogeneous stress and strain fields close to the ones occurring during the actual process. A first set of material parameters, adjusted for the aluminum alloy AA3103 with classical tests (tensile and cyclic shear tests), is compared with parameters adjusted by the line test. It is shown that the chosen tests and the strain state level have an important impact on the adjusted material data and on the accuracy of the tool force prediction reached during the SPIF process. Key words: Sheet metal forming, Inverse method, FEM simulations, Aluminum alloy AA3103, SPIF process 1 INTRODUCTION Single Point Incremental Forming (SPIF) is a new sheet metal forming process adapted to both rapid prototyping and small batch production at low cost. A clamped sheet is deformed by a spherical tool following a specific tool path defining the final required shape without costly dies. A wide variety of shapes can be made [1]. Accuracy of the FEM simulations of this process depends both on the constitutive law and the identification of the material parameters. A simple isotropic hardening model is not sufficient to provide an accurate force prediction [2]. A specific inverse method has been studied to provide the materials parameters using the results of experiments performed directly on a SPIF machine. The material is an annealed aluminium alloy AA3103-O. A first set of material parameters, adjusted by the inverse method using classical tests (tensile and cyclic shear tests) is compared with a new set of data adjusted by both a tensile test and an indent test performed with the actual SPIF equipment. To validate the material data set, the evolution of the predicted tool force during a line test is compared with the experimental results.

6 2 MATERIAL LAW 2.1 Description of the constitutive law The elastic range is described by Hooke s law where the Young s modulus E= MPa and the Poisson s ratio ν= 0.36 were identified using an acoustic method. The plastic part is described by Hill 48 law: F ( σ ) = [(H + G) σ11 + (H + F) σ 22 2Hσ11σ Nσ12 ] σ F 0 2 HILL = (1) where the parameters F, G, H, N and the yield stress σ F are identified using a tensile test in the rolling direction. The hardening equation is described by the Swift law (2): σ (2) p n F = K( ε 0 + ε ) where ε p is the plastic strain and K, ε 0 and n are the material parameters. If kinematic hardening is used, the stress tensor in (1) is replaced by σ X where X is the backstress. The material is assumed to have the same behaviour in tension and in compression at the beginning of the process, so no initial back-stress is defined. The kinematic hardening can be described by two formulations: the Amstrong-Frederick: X& p p = C X (X SAT. ε& ε&.x) (3) with C X the saturation rate, X SAT the saturation value of kinematic hardening and ε& p the anisotropic equivalent plastic strain rate; or the Ziegler hardening equations: X& 1 p p = CA ( σ X) ε& G A X ε& σf (4) with C A the initial kinematic hardening modulus and G A the rate at which the kinematic hardening modulus decreases with increasing plastic deformation. 3 DATA ADJUSTED BY CLASSICAL TESTS 3.1 Parameters identification The first identification method consists in performing tensile tests, monotonic shear tests and Bauschinger tests at two different levels of pre-strain (10 and 30%). The material parameters, adjusted by the inverse method, give a good correlation between the experiments and simulation results. The isotropic Swift law (2) is fitted with the parameters defined in table 1 but such tests do not indicate clearly whether there is or not a kinematic hardening. Table 1. Data adjusted by classical tests (Units: N, mm) Yield surface coefficients Swift parameters Back-stress data HILL classic F= G= H= N= L= M= 4.06 K= 183 ε 0 = n= C x = 0 X sat = Parameters validation by the line test A line test performed with the SPIF machine is used to verify the accuracy of the fitted data: a square plate with a thickness of 1.5 mm is clamped along its edges (Figure 1). The spherical tool radius is 5 mm. The tests are performed three times and the bolts of the frame are tightened using the same torque to ensure the reproducibility of the results. 182 mm Tool force (N) tool step 1 Y 182 mm Fig. 1. Description of the line test step 2 X step 3 step 4 step Time (sec) experim. test Bricks Shells Shells improved & sliding Fig. 2. Evolution of tool force during the line test (Lagamine) The displacement of the tool is composed of five steps with an initial position tangent to the surface of the plate: a first indent of 5 mm (step 1), a line movement at the same depth along the X axis (step 2), then a second indent up to the depth of 10 mm (step 3) followed by a line at the same depth along the X axis (step 4) and the unloading (step5). tool 1 Z mm 100 mm 42 mm 3 Y X

7 In the FEM simulations, the nodes along the edges are fixed. The tool force is computed by the static implicit strategy. The Coulomb s friction coefficient of 0.05 is applied between the tool and the sheet. The mesh is adjusted to limit the number of elements while keeping accuracy. Two element types are tested: brick with three layers along the thickness and shell elements. Figure 2 shows that the numerical force evolution of the tool is higher than the experimental one. 3.3 Discussion The oscillations in the numerical model are due to the contact elements. The sensitivity analysis shows that, unlike the bricks, the shell elements predict the same tool force for both a coarse and a very fine mesh. Those elements are also suitable for the inverse method since the computation time is lower than when using the brick elements. The effects of the geometry inaccuracy of the plate (dimension, thickness, flatness) and the tool (initial position, diameter), of the machine elasticity, of the force measurement, of the FEM parameters (elements stiffness, number of layers for the bricks), of the material data values and of the friction coefficient have been examined. Alone or combined, none of these parameters can explain such a gap between predicted and experimental forces. 3.4 Sliding sensitivity Previous experimental tests performed on a plate with a thickness of 1.2 mm showed that such a test is highly sensitive to sliding at the edges. The force was up to 35% lower when the bolts were tightened without a sufficient torque. A numerical sensitivity analysis showed that a small sliding of about 0.08 mm of the edges could decrease the tool force of 16%. Then, for the experiments in figure 2, the careful clamping of the frame provides an average sliding of only mm. A new model with springs regularly distributed along the edges allowing translation of the boundaries is combined with all of the imperfections inducing a tool force reduction. The spring stiffness is fitted to reproduce the same sliding as in the real process. The tool force of this model, called: Shell improved & sliding in figure 2, shows a small force reduction. In conclusion, the simulation inaccuracy cannot be explained by these performed investigations. 4 DATA ADJUSTED BY INDENT TEST 4.1 Parameters identification The new identification method consists in fitting material data using both a classical tensile test and an indent test corresponding to the first step of the line test described in section 3.2. The latter test contains heterogeneous stress and strain fields with tension, compression and shear stresses. The obtained material parameters are expected to be more accurate, since the deformation fields are much closer to those occurring in the SPIF process [3]. Stress (MPa) Tensile test Strain Tool force (N) ( ) Line test (step 1) Time (sec) Exp. Hill - AF (kine) V.M.-Ziegler (kine) Fig. 3. Tensile test and the step 1 of the line test for the different material models and the experiment Table 2. Data adjusted (Units: N, mm) Yield surface Swift coefficients parameters HILL - AF (kine) Von Mises - Ziegler (kine) F= G= H= N= L= M= 4.06 F= G= H= 1 N= L= M= 3 K= ε 0 = n= K= ε 0 = n= Back stress data C x = 29.7 X sat = 26 C A = 800 G A = 45.9 Figure 3 shows a poor fitting in tension but a good force prediction in the indent test. Table 2 defines the parameter values fitted for both hardening model described in section 2. The Ziegler hardening is coupled with Von Mises yield locus to allow comparison with Abaqus. Unlike the first investigation, a kinematic hardening is predicted in this case. 4.2 Parameters verification on experiments The two material models are used to simulate the

8 line test with brick elements (the kinematic hardening is currently not available with shells). Figure 4 shows a quite good correlation between the levels of predicted and measured tool force, especially for the first two steps of the line test. Tool force (N) step 1 step 2 step 3 step 4 step Time (sec) experim. test Hill - AF kiné VM - Ziegler (kine) Fig. 4. Evolution of tool force during the line test (Lagamine) The comparison between Lagamine (home-made code by the MS²F ARGENCO department) and implicit Abaqus FEM codes shows that the parameters identification depends on the stiffness of the brick elements. The tool force with Abaqus with reduced-integration elements and an artificial Hourglass stiffness of 1.33MPa gives the same level of force prediction than Lagamine for both tensile and line tests. performed to check it [4] but not fully analysed yet. The coupling of an initial back-stress and a kinematic hardening adapted to shell elements could be the best way to fit the right initial yield locus and its evolution. The shell elements having accurate results and a short computation time should be more suitable to the inverse method. As a next step, the indentation depth can be increased or the whole line test can be used to a better data fitting. 5 CONCLUSIONS The identification method of material data is far from being trivial. The strain state reached during the chosen tests have an important impact on the adjusted material data and on the accuracy of the tool force prediction during the process. The classical method used to identify material data by a combination of tensile and cyclic shear tests seems not adapted to the SPIF process on the aluminium alloy AA3103. Our new approach based on tests inducing stress and strain fields, similar to those present in the real process, predicts a better tool force σ 2 ACKNOWLEDGEMENTS HILL classic (iso) HILL - AF (kine) V.M.- Ziegler (kine) Fig. 5. Yield loci in principal stress direction at the end of the step 1 of the line test for the different material models Figure 5 shows the yield locus shapes at the end of the indent test in an element below the tool, for the three different material models (see tables 1 and 2). 4.1 Discussion Figure 5 shows that data fitted by the indent test induce a kinematic hardening and a modification of the yield locus in compression but almost no adjustment in tension. Our model did not introduce an initial back-stress as the annealed material is supposed to have the same initial behaviour in tension and compression. This assumption could be wrong but should require a physical explanation. A simple bending test has been σ 1 The authors of this article would like to thank the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) and the Belgian Federal Science Policy Office (Contract P6-24) for their financial support. As Research Director, A.M. Habraken would like to thank the Fund for Scientific Research (FNRS, Belgium) for its support. REFERENCES 1. J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. R. Duflou, J. Allwood, Asymmetric Single Point Incremental Forming of Sheet Metal, CIRP Annals 2005, Vol. 54/2, Technische Rundschau, Switzerland, pp P. Flores, L. Duchêne, C. Bouffioux, T.Lelotte, C. Henrard, N. Pernin, A. Van Bael, S. He, J. Duflou, A.M.Habraken, Model Identification and FE Simulations: Effect of Different Yield Loci and Hardening Laws in Sheet Forming, Int Journal of Plasticity, 23/3, 2007, pp J.R. Duflou, J. Verbert, B. Belkassem, J. Gu, H. Sol, C. Henrard, A.M. Habraken, Process Window Enhancement for Single Point Incremental Forming through Multi-Step Toolpaths, to appear. 4. R. Aerens, S. Masselis, Le pliage en l'air, Sirris report, MC 110, march 2000.

9 Behaviour modelling of aluminium alloy sheet for Single Point Incremental Forming N. Decultot 1, V. Velay 1, L. Robert 1, G. Bernhart 1, E. Massoni 2, 1 Research Centre on Tools Materials and Processes (CROMeP) Ecole Mines Albi ALBI Cedex 9, France URL: {nicolas.decultot,vincent.velay,laurent.robert,gerard.bernhart}@enstimac.fr 2 Centre for Material Forming (CEMEF) Ecole des Mines de Paris - BP Sophia-Antipolis, Cedex URL: Elisabeth.massoni@ensmp.fr; ABSTRACT: The aim of this work is to identify behaviour models of an aluminium alloy sheet formed by incremental stamping process by using both numerical simulations (FEM) and experimental procedures. The procedure developed will be used in Single Point Incremental Forming (SPIF) in using several original experimental tests allowing to reproduce loading paths close to those induced in the industrial operations and full-field measurements by 3D-Digital Image Correlation (DIC). Key words: Incremental Forming, Numerical Simulations, 3D-Digital Image Correlation, Behaviour Models 1 INTRODUCTION This paper refers to the new forming procedures used in sheet metal forming processes, commonly named Single Point Incremental Forming (SPIF) process. It is characterised by a high flexibility which allows an interesting technology improvement to manufacture sheet metal parts in controlling only a simple tool. Different steps of this process are shown in figure 1 [1]. Incremental displacements of the punch in various directions allow to form the sheet in order to provide the required shape. moulds and allows reducing costs when prototypes or batches have to be manufactured. However, Finite Element simulations are time-consuming because of the incremental characteristics of this process [2]. In this paper, we focus on the behaviour of an aluminium alloy 2024-T3 sheet that is forming with a incremental stamping test, process less complex than SPIF. Behaviour model parameters have been identified by tensile tests in 3 directions. 2 EXPERIMENTAL TESTS 2.1 Tensile tests Simple tensile tests in 3 directions, 0 (x axis), 45 and 90 have been performed and shown a weak anisotropy as shown in figure 2. Fig. 1. Different steps of the Single Point Incremental Forming Due to specific strain paths induced by the process and the fact that the plastic zone is strictly limited to the contact region between the tool and the workpiece, forming-limit curves and forming strategies are different from the classical deep drawing or stamping processes. Moreover this technology, in comparison with stamping process avoids using Fig. 2. Tensile tests in 3 directions and simulated tensile test identified by the x-axis direction results (rational curve)

10 The x-axis simulated curve is used to identify the model behaviour parameters (see section 3.2) 2.2 Incremental stamping test The incremental stamping test is carried out on a servo-electric tensile testing machine. The experimental set up is slightly modified in order to clamp the sheet and to consider the punch displacement to stamp it. The tool is 30 mm in diameter and presents a spherical active part like shown in figure 3. In this case, punch displacement and global force induced are measured. 2 cameras Punch Blank holder Fig. 3. Incremental stamping test This device is also instrumented by a cameras stereo-rig in order to perform displacement/strain fields measurements by 3D-Digital Image Correlation (3D-DIC) [3] (Vic-3D system). 3 NUMERICAL SIMULATIONS 3.1 Meshing and boundary conditions Shell elements are used to model the sheet. Dimensions are 130 mm in diameter (internal diameter of the blank holder) and 1 mm in thickness. Finite Element (FE) calculation considers 9 integration points in the thickness and are performed with ABAQUS/explicit. The meshing is shown in figure 4. Fig. 4. ABAQUS meshing The boundary conditions include a punch displacement, which are considered as a rigid body, and a clamping of all the external nodes. The value of the coefficient of friction is chosen equal to 0,2 according to stamping value found in the literature. 3.2 Behaviour model In a first approach, elasto-plastic model is used. It includes a Von Mises yield criterion and an isotropic hardening law as presented in equations (1) and (2). f = σ R (1) eq R 0 -bλ R = Q(1- e ) (2) with: R : Isotropic hardening law R : Yield strength σ 0 eq : Von Mises equivalent stress Q et b : Materials parameters The plastic multiplier, λ is calculated from the consistency condition, f = f = 0. Thus, it is f f deduced from the relation : σ + R = 0. σ R 1 f λ = H ( f ) : σ where h=b(q-r). h σ Parameters of the elasto-plastic model have been identified with x-axis direction tensile test. The following values have been found: R 0 =300 MPa; Q=250 MPa; b=10; E= MPa (Young Modulus). 4 RESULTS First, some displacement/strain fields measurements obtained by 3D-DIC are shown in figure 5: (a) outof-plane displacement field, (b) longitudinal and (c) shear strain fields, for an imposed tool displacement of 4 mm corresponding to a 900N force. The Area Of Interest (AOI) presented in figure 5 corresponds to almost the cameras field of view. On this area an experimental mesh (3D points cloud) is built. Results provided by 3D-DIC are the shape (3D points cloud) and the displacement vector at each point.

11 (a) - Z displacement field (punch axis) In the model, the sheet dimensions was reduced to the dimensions of the AOI. The experimental mesh provided by the 3D-DIC computation was projected on the FE mesh as shown in figure 7. For each FE mesh node of the external AOI, the measured displacement vectors of the corresponding experimental node are extracted as shown in figure 8. Thus, the displacement vectors of the AOI external nodes are imposed boundary conditions and the sheet is not more clamped. (b) - ε xx strain field Fig. 7. FE mesh in blue circle and experimental mesh in red cross (c) - ε xy strain field Fig. 5. Displacement/strain fields are obtained by 3D-DIC technique Figure 6 presents the evolution of the global force versus punch displacement. FE response over assess the experimental curve for a punch displacement up to 4 mm. Crack initiation of the sheet was observed for a punch displacement up to 15 mm. Fig. 8. Experimental nodes corresponding to FE mesh nodes Figure 9 presents the evolution of the global force versus punch displacement for both the experimental measurement and this new simulation which takes care to the measured boundary conditions (simulation 2). Fig. 6. Comparison between the experimental and simulated global force in function of the punch displacement To explain these differences, several hypothesis are proposed. First of them concerns the study of clamping boundary condition influence. Fig. 9. Comparison between the experimental and the new simulated global force in function of the punch displacement Taking into account true (measured) boundary conditions improves greatly the simulation results.

12 However, the sheet tensioning in the incremental stamping test beginning can explain that FE response over assess the experimental curve for the lower punch displacement. Figure 10 shows the 3D-DIC measured and the FE obtained sheet z-displacement fields. - The behaviour model does not consider damage and sheet anisotropy. Procedure used in incremental stamping (3D-DIC measures, imposed boundary conditions, model developed) will be used and improved for SPIF. In order to reproduce the strain paths observed in the industrial SPIF process, a SPIF test prototype is actually developed in the laboratory (see figure 11). This prototype is multi-instrumented (3D force sensor, 3D-DIC or multi-vision based DIC) and allows to generate complex shape pieces. The 3D force sensor of this prototype will allow to measure friction between punch and sheet. Fig D-DIC measured (bottom) and the FE results (top) sheet displacement fields for a 15 mm imposed punch displacement For an imposed punch displacement of 15 mm, the maximum sheet displacement measured by 3D-DIC is mm, about 2.33% error. The sheet thickness diminution (1 mm to 0,8 mm), not considered by shell elements, can explain this difference. 5 CONCLUSIONS AND DISCUSSIONS The comparison between experimental and FE displacements fields and evolution of the global force versus punch displacement give very similar results. At this stage, strain fields values are quite different and work is going on about that point. Nevertheless, one can explain these differences: - Vic-3D software and Abaqus do not use the same method to calculate strains. - The boundary conditions in displacement for the external nodes add actually strains on the sheet border that are not observed in the experimental strain field. Fig. 11. SPIF test prototype Tensile load-unload tests are carried out to quantify the sheet damage. Tensile tests using 3D-DIC are carrying out in order to identify more precisely anisotropic yield criterion. Finally, in the incremental forming process, the horizontal punch displacements on the sheet induce tensile and compressive stresses which will require an improvement of the behaviour model formulation REFERENCES 1. T.J. Kim and D.Y. Yang, Improvement of formability for the incremental sheet metal forming process, International Journal of Mechanical Sciences, 42, (2000), pp S. He, A. Van Bael, P. Van Houtte, Y. Tunckol, J. Duflou, C. Henrard, C. Bouffioux, A.M. Habraken, Effect of FEM choices in the modelling of incremental forming of aluminium sheets, Proc. 8 th ESAFORM conf., (2005), Cluj-Napoca, Romania 3. L. Robert, F. Nazaret, J-J. Orteu, T. Cutard, Use of 3-D Digital Image Correlation to characterize the mechanical behavior of a Fiber Reinforced Refractory Castable, Experimental Mechanics, 9(11) (2007), pp

13 Tensile tests with bending: a mechanism for incremental forming. W.C. Emmens 1, A.H. van den Boogaard 2 1 Corus RD&T, P.O. Box , 1970 CA IJmuiden, the Netherlands w.c.emmens@utwente.nl 2 University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands a.h.vandenboogaard@utwente.nl ABSTRACT: In incremental sheet forming (ISF) large uniform strains can be obtained well above the common forming limit. Bending-under-tension has been proposed as a possible mechanism. This paper describes tension tests with repetitive bending to simulate this effect. Indeed very large levels of uniform elongation have been obtained, up to 300 %. The maximum strain increases with decreasing bending radius, and is reached at a certain optimum pulling speed. The material hardening seems little affected by the cyclic bending operations, and a hardening curve for large strains could be constructed. Key words: Incremental forming, Tensile testing, Bending-under-tension 1 INTRODUCTION AND BACKGROUND In incremental sheet forming (ISF) large uniform strains can be obtained well above the common forming limit curve making it an attractive forming process. Little effort has been done so far to discover the underlying mechanism. Common ISF comprises the forming of the sheet over a hemispherical punch. This requires repetitive bending and unbending. It has been proposed that bending-under-tension might be acting as a mechanism allowing large uniform straining, based on observed relations in incremental forming [1,2]. Bending-under-tension can be investigated in several ways. Well known is the pulling of a strip over a single 90 o radius with back tension. This paper describes tests with repetitive bending. In such a test a long tensile test specimen is tested, but at the same time a set of three rollers as in a three point bending test is continuously moving up and down, as presented in figure 2. In a situation of combined bending and stretching the net pulling force is governed by both the bending strain and the stretching strain. In case of a perfectly plastic, non-hardening material, and ignoring second order effects, the net tension force per unit width T is given by: T = σ t ( e / eb ) = σ e 2R T = σ t e < eb e > eb (1) where σ is the material flow stress, t is the sheet thickness, e is the strain (elongation) at the strip centre, R is the bending radius of the strip centre, and e b = t/2r is the bending strain of the outer fibre. σ.t T e e b Fig 1. Left: Graphic presentation of equation (1) for a situation of constant bending radius R; e b =t/2r. Right: stress distribution for the case e=e b /2. For a situation of constant bending radius, as often encountered in practice, the relation between tension force T and net strain e is graphically presented in figure 1. This illustrates an important phenomenon: a strip being bent can be stretched with (much) lower force than the same strip not being bent. This implies that in our tests only material actually being bent at any time will elongate as that requires the lowest tension force: a true incremental mechanism.

14 Consequently material not visited by the rolls will not elongate, and the effective length of the specimen is equal to the stroke of the up-down movement. The figure illustrates also a second important effect: initially the force increases with strain, a situation of stable deformation! The condition of non-hardening material may look severe, however a detailed analysis shows that in a situation of pre-stressed material the actual situation is not that much different. In our tests this is the case after a certain amount of stretching, say 50%. Based on the assumption that only material being bent will elongate we can derive a simple relation between strain increment and speed: v ε cb incr = (2) vud where ε incr is the strain increment at each passage of the roll set, v cb is the cross-bar speed, and v ud is the up-down speed of the roll set. Note that the roll set has three rolls, so that each passage shows several bending and unbending operations; in the ideal case we have e = ε incr /6. 2 EXPERIMENTAL PROCEDURES D P L D was 15 mm, distance L was 35 mm. The speed of the up-down movement was held constant at 66 mm/s, the stroke was held constant at 140 mm. The testing speed (cross-bar speed) was varied during the tests. Testing material was common DC04 steel of 0.8 mm thickness and 20 mm width. 3 RESULTS In the following reference is made to common tensile tests occasionally. These are tests carried out with the same equipment and specimens, but without any rolls, so only tension and no bending. 3.1 Strain A charactersitic of this test is that the strain is not uniform over the length of the specimen. However there is always a zone of uniform elongation and fixed length, being the zone 'visited' by the rolls. The width strain and thickness strain of that zone has been measured, and the length strain was calculated from that. Figure 3 presents the relation between the true length strain in that zone and the total elongation (cross-bar displacement). The relation is proportional, this contrary to ordinary tensile tests were the engineering strain increases proportionally to the elongation. This is a direct consequence of the specific nature of the test and confirms that indeed only material being bent at any time does elongate and that we are dealing with a proper incremental mechanism. 1.5 strip threeroll set true length strain Fig. 2. Left: schematic representation of the test; right: picture of the roll set. A simple three-roll device was constructed that was installed in a standard MTS testing machine, see figure 2. The device allowed provisional change of the centre roll depth setting P. This setting determines the angle of bending, but indirectly also the actual bending radius of the strip (deeper setting = smaller actual radius). Note that a value of 0 still implies some bending of the material. Roll diameter 0.0 common tensile test elongation (mm) Fig. 3. Relation between measured uniform strain (true strain) and total elongation of the specimen. The dashed line shows the expected relation: the true strain becomes 1 when the elongation is equal to the up-down stroke (= 140 mm). Note that the highest recorded length strain is 1.37 ( 300%).

15 The ratio between length strain and thickness strain is plotted in figure 4 as a function of depth setting. This ratio can be regarded as an apparent r-value, the actual r-value of the material was 2.5. The results show that a deeper setting (read: smaller actual bending radius) shifts the strain state towards planestrain. apparent r-value depth setting (mm) Fig. 4. Ratio between width strain and thickness strain plotted as a function of depth setting. 3.2 Force For all tests a force-displacement curve was recorded just as in a common tensile test. The maximum recorded force for each test is presented in figure 5. The force shows a strong influence of the pulling speed. This is not surprising, a higher pulling speed means a larger strain increment (equation 2), and hence a higher pulling force (equation 1). max. puling force (kn) level for common tensile test 0.4 mm 0.9 mm 1.5 mm 2.3 mm pulling speed (mm/s) Fig. 5. Maximum pulling force plotted as a function of pulling speed with the depth setting as parameter. The influence of depth setting can be understood by realizing that the actual bending radius was actually much larger than the roll radius due to the bending stiffness of the strip, and that a deeper setting reduces the actual bending radius, and hence the pulling force. Similar is a second effect of the speed: a higher pulling force also means that the strip is tightened more, also resulting in a lower force. Basically this graph shows the combined influence of strain increment e (read: pulling speed), and bending radius R. The solid lines are predictions by a simple model that calculates the actual bending radius by a balance of forces according to equations (1) and (2); the agreement with the measured data indicates that indeed this actual bending radius is controlling the pulling force. 3.3 Formability The maximum obtained elongation is plotted in figure 6; the relation between elongation and true length strain can be derived from figure 3. This figure is rather complex but it can be noticed that - with an exception for the lowest depth setting of 0.4 mm - the largest level of elongation is obtained at a certain optimum speed, and this optimum speed increases with increasing depth setting. Furthermore the largest level of elongation increases with increasing depth setting, or better: decreasing actual bending radius. elongation at fracture (mm) mm 1.5 mm 0.9 mm 0.4 mm pulling speed (mm/s) level for common tensile test Fig. 6. Elongation at fracture plotted as a function of pulling speed with the depth setting as parameter. The points in figure 6 denoted by an open symbol require further discussion. These are points taken from experiments where the maximum pulling force as shown in figure 5 exceeds 4 kn. Investigation showed that in those cases the elongation is no longer restricted to the zone visited by the roll set, but that other areas deform plastically as well. This means that the proposed incremental mechanism cannot operate fully, and a consequence is that the elongation at fracture drops rapidly. A further effect is that the relation between elongation and true

16 length strain deviates from that shown in figure 2 (the corresponding points have been omitted in that figure for reasons of clarity). 3.4 Hardening As mentioned before, all specimens showed after testing a zone of uniform elongation. That zone was often large enough to measure the level of hardening of the material by performing a second, conventional tensile test. The results allowed the construction of a true hardening curve, see figure 7. Al results form a single curve within an acceptable level of scatter. This is surprising as the specimens have been subjected to bending and unbending operations. Some data are taken from specimens tested at high speed with only a few bending cycles, others from specimens tested at low speed subjected to a large number of bending cycles. Yet this does not show any effect. It suggests that the bendingunbending operations do not affect the hardening of the material, the latter only being determined by the level of length strain, and fitting perfectly to the Ludwuk-Nadai curve constructed from C and n values measured at undeformed material. true stress (MPa) Ludwik-Nadai curve true strain Fig. 7. Hardening curve constructed from the tested specimens. 4 DISCUSSION The aim of this research was to see if indeed bending-under-tension can create large uniform strains. The answer is simply yes, and apparently a low amount of bending is sufficient (a few degrees). The influence of experimental conditions is considerable, a fact sometimes overlooked in other publications [3]. The simple formulae presented at the introduction predict two major parameters: the pulling speed governing the strain increment at each passage of the roll set, and the actual bending radius R. Both are observed clearly, although the actual bending radius could only be affected indirectly. The speed also presents a limitation: a too high speed results in a pulling force so high that the incremental mechanism fails, rapidly lowering the maximum elongation. However, as the pulling force decreases with increasing depth setting, or better: decreasing actual bending radius, this limit is less severe in cases of a small bending radius. Analysis shows that the actual radius is still much larger than the roll radius, so much larger strains can still be expected if the actual bending radius is reduced further. This will also bring the situation more closely to situations occurring in actual incremental sheet forming operations. This will be the subject of future investigation. 5 CONCLUSIONS 1. Stretching with simultaneous bending does allow large uniform straining even in cases where the angle of bending is low. 2. The underlying mechanism is that at any moment only material actually being bent is deforming. This mechanism fails if the pulling force (or indirectly: pulling speed) becomes too high. 3. The actual bending radius of the material seems to be much larger than the roll radius introducing an influence of bending angle (penetration depth). 4. The maximum obtainable level of uniform strain increases with increasing bending angle and is obtained at an optimum pulling speed. 5. The level of hardening of the material seems only little affected by the cyclic bending/unbending operations. REFERENCES 1. T. Sawada, G. Fukuhara, M. Sakamoto; Deformation Mechanism of Sheet Metal in Stretch Forming with Computer Numerical Control Machine Tools; J. JSTP, vol 42, no. 489 ( ), pp W.C. Emmens; Water Jet Forming of Steel Beverage Cans; Proceedings 1st ICNFT, Harbin, China, Sept. 6-9, 2004, pp ; also: Int. J. of Machine Tools & Manufacture, vol (2006), pp J.C. Benedyk, D. Stawarz, N.M. Parikh; A Method for Increasing Elongation Values for Ferrous and Nonferrous Sheet Metals; J. of Materials, Vol. 6 (1971), nr 1, pp 16-29

17 Small-scale Finite Element Modelling of the Plastic Deformation Zone in the Incremental Forming Process P. Eyckens 1, A. Van Bael 1,2, R. Aerens 3, J. Duflou 3, P. Van Houtte DWKROLHNH8QLYHUVLWHLW/HXYHQ±.DVWHHOSDUN$UHQEHUJ%+HYHUOHH%HOJLXP HPDLOV 3KLOLS(\FNHQV#PWPNXOHXYHQEH$OEHUW9DQ%DHO#PWPNXOHXYHQEH3DXO9DQ+RXWWH#PWPNXOHXYHQEH,:7.+/LP/LPEXUJ&DWKROLF8QLYHUVLW\&ROOHJH&DPSXV'LHSHQEHHN$JRUDODDQJHERXZ%EXV %'LHSHQEHHN%HOJLXP 30$.DWKROLHNH8QLYHUVLWHLW/HXYHQ±&HOHVWLMQHQODDQ%%+HYHUOHH%HOJLXP HPDLOV5LFKDUG$HUHQV#VLUULVEH-RRVW'XIORX#PHFKNXOHXYHQEH ABSTRACT: In this paper, the Finite Element submodelling technique is applied to model the small plastic zone in the Incremental Forming process with an adequately fine (sub-millimetre) mesh at a computationally acceptable cost. The focus lies on the distribution of the contact pressure between sheet and forming tool. Different forming conditions of truncated cones are considered. Results show that the contact consists of two distinguishable parts. The obtained insights can be applied in the physical modelling of forming forces, which allows improving part accuracy through compensation for the mechanical stiffness of the forming machine. Key words: Incremental forming, Contact pressure distribution, Finite Elements, Submodelling technique. 1 INTRODUCTION The Implicit Finite Element (FE) simulations of the Single Point Incremental Forming (SPIF) process have been shown to be very computationally intensive. This is, amongst other reasons, due to the constantly changing contact between the tool and the metal sheet. In the past, partial FE models with nonphysical boundary conditions (BC s), such as symmetry BC s, and relatively coarse meshes have been used to model the process within reasonable calculation times [1]. In this paper, a new strategy is presented to model the small plastic zone under the SPIF forming tool in a more accurate manner. Only a small piece of the unclamped sheet is considered in the FE model, which allows for a much finer mesh with respect to the forming tool radius, while retaining reasonable calculation times. The FE submodelling technique [2] allows the BC s on the edges of this model to be physically meaningful. The same approach has been used to study out-of-plane shear in SPIF [3]. This paper describes FE models on different scales for the SPIF fabrication of truncated cones of AA3003-O aluminium alloy sheet under different process conditions. The forming force components are compared to experimental measurements, and the distribution of the contact pressure under the forming tool is investigated for different process conditions. The resulting insights are useful for the physical modelling of the forming force, which can be used to compensate for the machine stiffness and consequently to increase the accuracy of SPIF parts. 2 FINITE ELEMENT MODEL DESCRIPTION 7KH63,)FDVHVWXGLHV In the present study, four different Incremental Forming processes of truncated cones are modelled with FE simulations. An overview of the main experimental parameters is given in table 1. Table1. Parameters of the SPIF processes Name: FG FG FG FG Wall angle Tool diameter (mm) FDOORSKHLJKW P Step size (mm) Number of contours In all cases, a succession of circular tool contours (with diminishing radius) was used to form the cones. The main differences lie in the wall angle

18 (20 or 60 ) and the diameter of the forming tool (10 or 25mm). The scallop height, i.e. the resulting roughness height on the cone inner wall due to the tool contact, is PDQG PIRUWKHFRQHVZLWK a 20 and 60 wall angle, respectively. The (vertical) step size of the tool in-between contours is deduced from the previous parameters. For all cones, the radius of the first tool path contour was 75mm, and a backing plate with circumferential orifice with a radius of 91mm was used. The material is the aluminium alloy AA3003-O (annealed state) with a sheet thickness of 1.2mm. 7KH)(JOREDOPRGHODQGVXEPRGHOV Each of the 4 SPIF processes is simulated with 3 implicit FE models at different scales. In all cases the sheet is modelled as several layers of linear brick elements, while the forming tool is modelled as an analytical rigid sphere. Isotropic hardening (Swifttype) of the sheet is assumed, in combination with the isotropic Von Mises yield criterion. Coulomb friction with a friction coefficient of 0.05 is used. First, a 40 pie model (global model: * ) with a relative coarse mesh, containing 3 layers of elements and (non-physical) symmetry boundary conditions was used, as shown in figure Pie model = Global model * Large submodel 6 Small submodel 6 Fig. 1. The mesh of the FE models. Next, a small piece of the sheet was modelled, i.e. the large submodel 6. The BC s on the edges of this model were obtained as a linear interpolation of the nodal solution of the global model, shown schematically in figure 1 with an arrow. The imposed tool path remains unchanged. This procedure is repeated to model the process at an even smaller scale, resulting in the small submodel 6, in which 5 layers of elements are used. Table 2 shows the model and element dimensions at the 3 different scales. The centre of both submodels 6 and 6 was chosen depending on the cone wall angle, as to obtain a steady state in forming forces. The calculation times for any of these models was about 1 to 2 days on a 16GB-RAM 2.4GHz CPU. Table2. FE model parameters of the SPIF processes * 91.0mm * 40.0 * 1.2mm Model mm * 10.5 * 1.2mm dimensions 6 7.0mm * 3.3 * 1.2mm Approx. element * 1.2 * 1.4 * 0.4 dimensions * 0.4 * 0.4 (mm) * 0.14 * 0.24 * 4300 Approx. number of elements Distance from cone FG[[ 55.0mm centre to submodel centre (6 & 6) FG[[ 65.0mm 3 RESULTS )RUPLQJIRUFHFRPSRQHQWV Experimental and modelled forming force components are shown in table 3 for the contour during which the tool path moves closest to the centre of both submodels 6 and 6. Table3. Average force components (unit: N) )] )U )W FG cont. 29 FG cont. 18 FG cont. 24 FG cont. 16 H[S 283,9-37,3 58,2 * 303,1-16,7 37, ,2-18,8 46, ,3-16,9 52,2 H[S 329,6 6,6 54,6 * 380,5 8,6 37, ,7 2,2 39, ,1-0,6 37,9 H[S 509,4 176,5 106,3 * 691,1 248,0 141, ,5 209,5 158, ,2 180,4 164,6 H[S 754,1 339,0 119,2 * 979,5 422,0 212, ,0 377,3 207,2 6 The component )] lies along the direction perpendicular to the initial sheet surface, while )U and )W are the components along the local radial and

19 tool movement direction, respectively. During a contour, the predicted force components oscillate due to the meshing of the sheet. The amplitude of these oscillations is in general smaller in the centre of the submodels compared to the global model, thanks to the finer mesh [3]. The averages in table 3 are calculated in the central part (1/3 rd ) of each model, to exclude spurious force oscillations at the model edges. Results of the 6-model of FG are shown in italic in table 3, since the contact zone appeared to be too large to be fully covered by this model. The components )] and )U are usually overpredicted by the FE models. However, there is a trend of better predictions when a smaller submodel (with finer mesh) is used. This is most evident in the )]- component of the cones with the higher wall angle of 60, e.g. the relative overprediction for the cone FG drops from 135% for the *-model to 119% for the 6-model. Also, the experimental and simulated )U-components of FG are found to be negative. It means that the tool is pushed outwards rather than in the direction of the cone centre. The relative error of the )W-component prediction is generally the largest, and in all cases except FG, there is no significant improvement when a smaller FE model is used. This can be attributed to the simple contact model used, as this component is mainly due to frictional contact shear forces. &RQWDFW 3UHVVXUH 500 MPa 250 MPa 100 MPa 0 Pa 7RROPRYHPHQW GLUHFWLRQ 7RRO UDGLXV 7RRO FHQWHU &RQH ZDOO UHJLRQ &RQH ERWWRP UHJLRQ 7KHGLVWULEXWLRQRIWRROFRQWDFWSUHVVXUH The simulated contact area between the tool and the sheet oscillates for the same reason as the force components. Table 4 gives the averaged contact area $ obtained by the same averaging procedure as used for the forces. It also gives the variation in contact area $, i.e. the maximal minus minimal value of contact area for the given contour. FG6±FRQW FG6±FRQW Table4. Average contact area and variation (unit: mm²) $ $ * 2,4 1,7 FG cont 29 FG cont 18 FG cont 24 FG cont ,7 0,3 6 1,1 0,3 * 6,2 3,5 6 1,4 0,3 6 1,4 0,3 * 15,3 8,2 6 2,1 0,8 6 2,1 0,6 * 36,6 17,8 6 7,9 1,2 6 FG6±FRQW FG6±FRQW Fig. 2. The distribution of contact pressure under the tool. The view is perpendicular to the initial sheet surface.

20 It can be seen that for both submodels practically identical results are found, while the *-model yields much higher values of $ and $. It can thus be argued that the coarse mesh of this model results in an overprediction of the contact area. Figure 2 shows the distribution of the contact pressure for all four cases. The position, size and movement direction of the tool with respect to the cone wall and bottom region are clarified in the upper part of figure 2. The contact in the cone wall region appears approximately to be a line contact for the cones with a wall angle of 60. There is also a non-negligible sickle-shaped contact in the cone bottom region. For the cones with the low wall angle of 20, the contact in the cone bottom region is the dominant feature, while the contact in the cone wall region is much less pronounced. Note that the point on the tool surface directly below the tool centre is not or barely in contact with the sheet. &RQHLQQHUVXUIDFHJHRPHWU\ Figure 3 illustrates the geometry of the inner surface of the cone FG in the tool contact zone and compares it to the distribution of contact pressure. direction of the cone centre, resulting in contact in the cone bottom region. CONCLUSIONS The FE submodelling technique has been used to improve the modelling of the plastic deformation zone in the SPIF process. Although the constitutive model of the sheet was too simple to accurately predict the forming force components, the quality of the forming force predictions was improved through the use of finer, sub-millimetre meshes. The comparison of the distribution of the contact pressure under different working conditions reveals that the contact can generally be split up into two parts. Firstly, the contact with the cone wall or ZDOO FRQWDFW, is well approximated as a line contact at larger wall angles, while it diminishes at small wall angles. Secondly, the contact on the cone bottom or JURRYH FRQWDFW, appears to be sickle-shaped. It can be attributed to the presence of a contact groove in the sheet material, formed during the previous contour of the tool. It makes an important contribution to the overall contact, even when the wall angle is as large as 60. At very low wall angles, like 20 in the present study, it is responsible for the radial component of the forming force to become nearly zero or even negative, which means that the tool is pushed outwards instead of in the direction of the cone centre. *URRYHRI SUHYLRXVFRQWRXU *URRYHRI FXUUHQWFRQWRXU ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support from the Institute for the Promotion of Innovation by Science and Technology in Flanders (IWT) and from the Interuniversity Attraction Poles Program from the Belgian State through the Belgian Science Policy agency, contract IAP6/24. FG6±FRQW Fig. 3. (left) Contours of equal height (i.e. along the z- direction) of the inner cone surface, with intervals of 0.05mm, and (right) the contact pressure. The view and the colour code for the contact pressure are the same as in figure 2. It can be seen that a groove in the inner sheet surface is formed as the tool moves. The groove that was formed by the tool during its previous contour can also be seen. This groove is situated more near the cone wall, since the radius of the previous circular contour was larger. During the tool movement, the groove of the previous contour is displaced in the REFERENCES 1. S. He, A. Van Bael, P. Van Houtte, A. Szekerez, J. Duflou, C. Henrard, A.M. Habraken, Finite Element Modeling of Incremental Forming of Aluminum Sheets, $GYDQFHG0DWHULDOV5HVHDUFK 6-8 (2005), ABAQUS User s manual, version 6.6, P. Eyckens, S. He, A. Van Bael, J. Duflou and P. Van Houtte, Finite Element Based Formability Prediction of Sheets Subjected to the Incremental Forming Process, In: &RPSXWDWLRQDO 3ODVWLFLW\,; )XQGDPHQWDOV DQG $SSOLFDWLRQV, eds, E. Oñate, R. Owen, B. Suárez, Barcelona (2007)

21 Dyna-Die: Towards Full Kinematic Incremental Forming V. Franzen, L. Kwiatkowski, G. Sebastiani, R. Shankar, A. E. Tekkaya, M. Kleiner Institute of Forming Technology and Lightweight Construction (IUL), Technical University of Dortmund - Baroper Str. 301, Dortmund, Germany URL: Volker.Franzen@iul.uni-dortmund.de; Lukas.Kwiatkowski@iul.uni-dortmund.de; Gerd.Sebastiani@iul.uni-dortmund.de ABSTRACT: This article focuses on the realization of a simple and kinematic tool setup for incremental sheet metal forming. It allows achieving a similar geometrical accuracy like a full specific support, but minimizes the tool setup and increases the process flexibility at the same time. In incremental sheet metal forming different process variants are in use. The simplest one is the single point incremental forming process which works with a single forming tool and does not require any support. The partially supported incremental forming process uses a simple tool setup for a static support of the sheet when forming only in local areas. In the fully supported incremental forming process a specific die is used which includes the geometry of the part to be manufactured. Here, a good geometrical accuracy can be achieved, but expensive and specific tools are needed for the support. In the full kinematic incremental forming process both the forming tool and the supporting tool move synchronously in three axes. This process is very flexible regarding the part geometry and promises a good accuracy. However, the mechanical setup is very complex and requests a specialized machine. The setup described in this article includes a kinematic support which can be mounted on a conventional milling machine. The presented dynamic support consists of an exchangeable support tool, which is fixed on a rotating plate. During the incremental forming process the dynamic support moves synchronously with the forming tool. This way, a flexible forming with simple tools and low costs is realized. The parts manufactured by the Dyna-Die have been compared to parts which were produced using a full and a partial static support as well as without any support. The discussion of the results completes this contribution. Key words: incremental forming, sheet metal forming, kinematic, dynamic die 1 INTRODUCTION In recent years the interest in small batch production processes has increased significantly. In this context a special focus should be placed on incremental sheet metal forming (ISF). This forming process can be conducted in a conventional milling machine by mounting the forming tool in the spindle while the sheet metal is fixed with a clamp. Since the spindle can be moved in three ore more independent axes complex part geometries can be realized. Within this process sheet metals are formed stepwise with only a localized plastification. Consequently, universal tools can be used to achieve different geometrical shapes. For conventional forming techniques like deep drawing or stamping tools are predefined by the shape of the desired part and can only be used for this special purpose. Compared to them, the main economic advantage of ISF arises: a low-priced and flexible production of sheet metals for small series and prototypes. Although the first attempts for producing parts with sheet metal forming are mentioned in the patent of Leszack [1] in 1967, the initial process development started since the late 1990s [2]. Up to now, several variants of ISF have been investigated to proof their feasibility for producing parts with a wide range of materials [3]. Single point incremental forming (SPIF) can be performed easily without any die so that no additional tooling costs arise. However, without any supporting die it is not able to produce parts with sharp edges and the resulting deviations

22 between the produced and the desired geometry are quite high. To reduce the deviations, two different types of static dies are commonly in use. While partial dies support only a local region of the sheet metal, specific dies have to contain the final shape of the desired part geometry. Partially supported dies consist of a simple and cheap construction, but comparing both types, the specific dies allow a production of parts with higher precision. On the other hand, full specific dies can only be used for one production task. With the motivation of improving the process flexibility and the geometrical accuracy at the same time the use of a second moving tool seems to be promising. Fig. 1: Theoretical setup for kinematic ISF Meier et al. [4] presented one possibility to realize this full kinematic variation of incremental sheet metal forming (KISF) by the use of two robots. Another possibility is shown by Maidagan et al. [5] where a tricept robot as a master tool is combined with a moving XYZ-table for the supporting slave tool. In this article, the authors present a simple method to upgrade a conventional milling machine with a dynamic die (Dyna-Die). Taking into account that the forming mechanisms for ISF are not completely clarified at present the construction of a specialized machine is quite complex. The setup showed in the following article does not require high investment costs and allows the production of simple parts in order to investigate and design the KISF process. To show the capability of the presented solution, experiments are conducted by using different types of supports. This is followed by an analysis of the geometrical accuracy for each part. 2 EXPERIMENTAL SETUP 2.1 Setup requirements With the aim of approaching the described KISF process a second moving tool has to be implemented into the previously used experimental setup. In addition, the second tool has to move mechanically independent from the first one to have the possibility of synchronization. Taking into account that the whole available space in the milling machine in Z- direction is needed to perform the ISF with static supports, the movement of the second tool should be reduced to the XY-plane. Furthermore, inexpensive parts have to be used for this setup to guarantee a low cost upgrade. 2.2 Realized setup The realized dynamic die is shown in detail in Fig. 2. The additional tool movement is achieved by a rotating table. As a matter of course, only rotational symmetric parts can be produced. In the presented case the second tool is realized as a cone which is mounted on the rotating plate. The produced conical parts have a diameter of 168 mm at the top and a height of 40 mm, the flange angel is 60. During forming the contact zone between both tools moves from the cone`s top down to the plate. The cone tool can be mounted at four different radii, so different part diameter can be achieved. Since, the second tool is exchangeable other part geometries can be produced. The shown setup includes an additional unspecific support in the center of the plate which can also be removed. In further investigations it will be possible to investigate if this feature is necessary for the evolution and the design of KISF for nonsymmetric parts. Cone Main tool Fig. 2: Experimental setup Dyna-Die 3 EXPERIMENTAL PROCEDURE Partial support Workpiece (Fixed) Rotating table The focus of this analysis is on the achievable accuracy of the Dyna-Die, which represents a very simple and cheap method of a two point, full kinematic ISF process variant. The parts manufactured by the Dyna-Die are therefore compared to three other common ISF process variants, which are:

23 - SPIF, which works without a supporting tool - ISF with partial support - ISF with full specific support part, has to increase due to its conical shape. After becoming familiar with the setup, sufficient synchronicity could be achieved. 3.3 Accuracy measurements The accuracy of the manufactured parts has been measured with the help of an optical measurement system (ATOS) by GOM. This way, STL files of the manufactured parts have been created, which could be imported into the CAD system in order to compare them with the reference model. For the deviation analysis again CATIA V5 R17 has been used. The measured STL model has been orientated close to the reference CAD model by a best-fit procedure, which is included in CATIA. Fig. 3: ISF process variants All experiments presented in this text use Al 99.5 (semi-rigid). This material allows a high strain and can be formed with comparably low forming forces. A pin-shaped tool with a diameter of 10 mm has been used due to the smallest radius in the part of 6 mm. 3.1 Preparation The experiments have been carried out on a conventional 3-axes CNC milling machine. In this case, the NC machining suite, which is included in CATIA V5 R17, has been used to generate the unidirectional tool path. The authors preferred a unidirectional tool path without any correction methods. This way, the deviation of the different processes is not influenced by optimized tool paths. 3.2 Procedure During forming the sheet has been fixed on a frame which moves downwards by gravity and the tool motion respectively. The sheet is coated with oil as lubrication on both sides. The velocity of both tools is approximately 2200 mm/min. The speed of the upper tool, which is moved by the milling machine, has been adjusted manually during the process in order to achieve a synchronous motion of both tools. While the rotational speed of the table with the support tool keeps constant, the speed of the forming tool, which moves along the circumference of the 4 RESULTS AND DISCUSSION 4.1 Accuracy The accuracy achieved with the Dyna-Die is similar to ISF using a full specific support. The deviation is in the range of aproximately 1.2 mm (in total). The process variants with partial support and no support showed less accurate results. No correction strategies have been considered in the tool paths. Fig. 4 shows a comparison between the results of the parts manufactured by the described process variants. The deviation depicted in the figure is scaled by factor ten. Graph a) in the figure represents the deviation of the part manufactured by the Dyna-Die. Compared to graph b), which shows the part manufactured with a full specific support, the deviation is in a similar range, but in the opposite direction at the flange area. The full specific support does not allow a negative deviation and the manufacturing of parts which are smaller than the used die. In contrast, the Dyna-Die provides the possibility to change the relative position between both tools. In b), an increased deviation in the part s center is observed. This could be caused by the influence of the bending at the edge of the part. A similar bending effect could not be recognized by the use of the Dyna-Die. A partial support like used in c) leads to an increased deviation. Here, an even stronger bending effect has been observed which is caused by less support of the sheet during the forming process. In d), no support has been used during the

24 incremental forming process. This causes strong evasive movements of the sheet and leads to high geometrical deviations of the manufactured part. The authors are aware of the fact that correction methods in the tool path generation will improve the part accuracy. Therefore, further experiments are necessary. It was found out that the Dyna-Die in the current state is not as reliable as a full specific support setup because some of the parts showed cracks. This is probably caused by the lack of synchrony in the motion of the upper and lower tool as the speed of the forming tool has been adjusted manually. 5 CONCLUSIONS The Dyna-Die presented in this paper, involves a simple tool setup, which can be used as an upgrade for a conventional milling machine. It allows the production of rotationally symmetric parts in a full kinematical way as both the forming tool and the support are moving during the forming process. The experiments have shown that the described kinematic ISF process is capable of producing parts in an equal quality and accuracy as the ISF with a full static support. With some small modifications concerning the synchronous motion of both tools this simple and cheap setup allows fundamental research in full kinematic ISF before focusing on the manufacturing of more complex parts. The authors assume that tool path correction methods, like e.g. surface reconstruction, and optimized process strategies, will improve the accuracy of the manufactured parts. ACKNOWLEDGEMENTS The authors would like to thank the NRW Graduate School of Production Engineering for their kind assistance. The work was carried out as part of the research project Modellierung inkrementeller Blechumformprozesse mit kinematischer Gestalterzeugung and is part of the Priority Programme SPP 1146 Modellierung Inkrementeller Umformverfahren. The authors wish to thank the German Research Foundation (DFG) for its kind support. REFERENCES Fig. 4: Comparison of accuracy for different ISF process variants The results of a fully supported manufacturing process were only slightly better than the parts produced by the Dyna-Die. The partially supported process delivered worse results. In order to have similar manufacturing conditions, no correction method has been used in the tool path. 4.2 Surface quality The rotating tool of the Dyna-Die has left marks (scratches) on the surface of the sheet although lubrication has been used. Compared to the other ISF process variants used in the experiments, the surface quality on the lower side of the sheet has been clearly worse. 1. Leszak E., Apparatus and process for incremental dieless forming, Patent US A (1967). 2. K. Kitazawa, A. Nakajima, Cylindrical Incremental Drawing of Sheet Metals by CNC Forming Process, Advanced Technology of Plasticity Vol.2 (1999) 3. J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric single point incremental forming of sheet metal, Annals of CIRP, 54, , (2005). 4. H. Meier, V. Smukala, O. Dewald, J Zhang, Two Point Incremental Forming with Two Moving Forming Tools, Key Engineering Materials, Vol. 344, pp (2007) 5. E. Maidagan, J. Zettler, M. Bambach, P.P. Rodríguez, G. Hirt, A New Incremental Sheet Forming Process Based on a Flexible Supporting Die System, Key Engineering Materials, Vol. 344, pp (2007)

25 Time reduction in implicit single point incremental sheet forming simulation by refinement - derefinement A. Hadoush 1, A.H. van den Boogaard 2 1 Netherlands Institute for Metals Research, Mekelweg 2, P.O. Box 5008, 2600 GA Delft, The Netherlands URL: a.hadoush@nimr.nl 2 Faculty of Engineering Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands URL: a.h.vandenboogaard@ctw.utwente.nl ABSTRACT: This paper presents the implementation of a refinement - derefinement (RD) approach to reduce the computing time in single point incremental sheet forming (SPIF) simulation. The results of this approach are compared to a reference model that has a fine enough mesh to satisfy the process requirements. The fine mesh is created by refining an intermediate coarse mesh entirely. The RD approach performs one level of refinement derefinement on the same intermediate coarse mesh based on a geometrical error indicator. The integration point data is mapped by a least squares method. The simulation of forming a 45 degree pyramid is considered as reference test. The refinement derefinement approach reduces the computing time for the reference model by 50%. The achieved equivalent plastic strain by this approach shows a good agreement with the reference model. Key words: Incremental Forming, Refinement - Derefinement. 1 INTRODUCTION Nowadays, FE simulation of metal forming has been used by industry to better predict the geometry of their products and their structural behaviour. Because single point incremental forming (SPIF) is a dieless process, it is perfectly suited for prototyping and small volume production. SPIF is a displacement controlled process performed on a CNC machine. A clamped blank is deformed by the movement of the tool that follows a certain tool path, a sketch for SPIF is shown in Figure 1. blank dieless forming tool blank holder Fig. 1. SPIF process [1] The SPIF numerical simulation faces several challenges e.g. the simulation computing time, the material model as well as the large deformation achieved by the process. The implicit simulation of SPIF provides a very good agreement with experimental data [1]. This paper presents a refinement derefinement (RD) strategy to get over the necessity of having an initially fine mesh, would result in an enormous computing time. A fine mesh in the vicinity of the forming tool is required since there is a small contact area between the forming tool and the blank compared to the blank area. This fact hints that part of the blank needs to have a fine mesh while the rest of the blank can have a coarse mesh. During the process, the mesh connectivity is continuously changing, because of the moving tool. The main goal of the approach is to keep the number of elements as low as possible during the entire simulation. 2 REFINEMENT DEREFINEMENT h adaptivity is used to perform refinement and derefinement [2]. The strategy consists of adapting the number of grid points and changing the connectivity. Grid points are added to areas where

26 more accuracy is demanded and can be deleted in areas where the solution is accurate enough. In this paper, the nominated elements for refinement and its neighbours are refined once and will be called mother elements. Considering linear triangular elements, each mother element is divided into 4 elements, the new elements will be called refined elements. To preserve mesh compatibility, the neighbour elements of the mother elements are split into 2 elements. Any 2 split elements born out of the same mother element can be united and refined into refined elements [3]. Meanwhile, the derefinement performs only on the refined and split elements. It degenerates the previous connectivity in a reverse order. An example for element generation and degeneration is shown in figure 2. a. b. Fig. 2. Mesh generation a) refinement takes place at the lower left part, b) the lower left part is derefined and the upper right is refined 2.1 Remeshing criterion An error indicator is used instead of an error estimator since it is computationally cheaper. Particularly, the geometrical error indicator is used. It measures the variation of the geometry within the blank [4]. Briefly, a set of tangent axes is determined for each element. The variation of these sets of tangents from one element to its neighbouring elements indicates the variation of the geometry. A nodal averaging technique is used to quantify this variation. If the variation within a group of elements exceeds a certain user input value, that group of elements is refined. Opposite wise, if the variation within a group of refined elements is less than the user input value, the derefinement takes place on that group. 2.2 Data mapping When a new grid connectivity is created, the state variables have to transfer from the old mesh to the new mesh. There are several approaches. One approach is using the old nodal value to evaluate the new nodal value, then determine the state variables at the integration points [3]. Another approach is to use a patch recovery, that depends on selecting specific locations within a group of elements, creating a smoothed field out of it and evaluate the new data [5]. The chosen approach is the least squares method. The method fits a linear field based on all available integration points. The location of the integration points and its values are used to create the linear field, then the location of the new integration point is used to determine its value. Regardless the approach, data transfer predicts the exact value for the state variables when it maps mother element into split element or refined element. However it either over estimates or under estimates the new value for the following derefined cases: split into refined, refined into split, refined into mother and split into mother. The error is introduced because of fitting piecewise linear fields into one linear field. The least squares method is the optimum approach. It minimizes the error during data transfer and it is not computationally expensive compared to the other approaches. 2.3 RD implementation test The RD approach is coded in the in-house implicit FE package DiekA. The correctness of the implementation has to be checked before going for SPIF simulation. For that purpose, an initial linear field for the equivalent plastic strain is prescribed for a FE strip model. The strip experiences 648 RD combination. Theoretically and numerically within the machine accuracy, the linear field must remain the same. This is achieved in the RD implementation test as shown in figure 3. Fig. 3. The initial linear field of the equivalent plastic strain (left) and the final field (right). 3 CASE STUDY To verify whether the RD approach leads to CPU time reduction, a 45 o pyramidal shape simulation is chosen as case study. An analytical spherical tool of 10 mm radius is used. The tool follows a counter clockwise tool path for 34 loops, it moves 0.5 mm vertically downward for each loop. The pyramidal shape is made out of a 100 * 100 * 1.2 mm initially

27 flat blank. The blank is fully clamped at the edges. 3.1 Discretization An intermediate coarse mesh is created, that consists of 800 linear triangular elements. The mesh is entirely refined producing 3200 elements. The latest mesh will be called the reference mesh. The reference mesh is used to perform the reference simulation. The intermediate coarse mesh is used in the RD approach and will be called the RD mesh. The RD approach controls the generation or the degeneration of elements from the RD mesh to reference mesh. Two element types are used: discrete Kirchhoff triangle DKT and discrete shear triangle DST [6,7]. Both elements have 6 degrees of freedom per node. The elements contain both bending and membrane stiffness. It has 3 integration points in plane and 5 in thickness. DST is implicitly coupled by transverse shear stiffness of the material, while DKT is explicitly coupled by enforcing zero transverse shear strain at selected locations [5]. 3.2 Material model In order to focus on the numerical technique, the material model is kept as simple as possible. The isotropic yield behaviour of the material is modelled by the von Mises criterion. The elastoplastic nonlinear hardening is governed by the Nadai relation as follows in Equation 1 σ = C ( ε + ε ε + (1) n ) = 500( ) Where and are the flow stress and the plastic strain respectively. The material has Young s modulus of 200 GPa and Poisson s ratio of 0.3. For realistic calculation, the authors acknowledge that a better material model is required, that includes the anisotropic behaviour of the sheets and the cyclic mode of deformation. is 0.438; the RD simulation over estimates it by 6%. A comparable strain distribution is achieved, but less smooth. As expected, a similar situation is observed for the plastic strain component xx as plotted in figure 5. Fig. 4. DKT element, the equivalent plastic strain at the mid plane for the reference (top) and the RD (bottom) 4 RESULTS AND DISCUSSION At first, there is no significant difference in the achieved equivalent plastic strain by DKT or DST elements. DKT requires 40% less computing time than DST for the same simulation. The equivalent plastic strain for the middle integration point in thickness direction is plotted in figure 4. The achieved maximum strain in the reference simulation Fig. 5. DKT element, the plastic strain component xx at the mid plane for the reference (top) and the RD (bottom) However, at the outer integration points, the RD approach yields less accurate results. The maximum equivalent plastic strain is in the reference simulation, the RD simulation over estimates it by 21% as plotted in figure 6. The reason for that is the

28 equivalent plastic strain and the flow stress are mapped independently and regardless the nonlinearity that relate the stress to the strain. The frequent smoothing of the flow stress results in over estimation of the plastic strain for the following steps in an incremental way. Computing time 32.3 hr 15.8 hr Number of nodes DKT, DST, The Ref DKT, The RD DST, The RD Simulation increments Fig. 7. The history of mesh growth during the implementation simulation for both elements. 5 CONCLUSIONS Fig. 6. DST element, the equivalent plastic strain at the highest integration point for the reference (top) and the RD (bottom) The performance of the simulations is listed in table 1 and 2 for DKT and DST respectively. The RD performs well. It achieves almost 50% reduction in computing time compared to the reference simulation for both elements. As plotted in figure 7, the reduction in computing time is achieved by keeping the number of nodes and consequently the number of elements as low as possible. The RD mesh is fine enough for the first couple of loops. Then, the geometrical variation within the blank triggers overall mesh growth, in order to capture the present curvature of the blank in the region of the tool path. Table 1. Simulation performance for DKT element. Reference RD No. of steps No. of elements No. of nodes Computing time 19.9 hr 9.93 hr Table 2. Simulation performance for DST element. Reference RD No. of steps No. of elements No. of nodes The overall performance of the RD approach is good. It achieves 50% reduction of the computing time. A better mapping that includes the nonlinearity is required to reduce the over estimation of the equivalent plastic strain. The RD approach can adapt the mesh connectivity considering the tool path and the size of the blank. REFERENCES 1. M. Bambach, G. Hirt, J. Ames, Modelling of optimization strategies in the incremental sheet metal forming process, In: Proc. NUMIFORM, Columbus, Ohio (2004). 2. A. Huerta, P. Diez and A. Rodriguez-Ferran, Adaptivity and error estimation, In: Proc. The 6 th International Conference on Numerical methods in Industrial Forming processes, Rotterdam (1998) T. Meinders, Developments in numerical simulations of real-life deep drawing process, PhD thesis, University of Twente, Enschede (2000). 4. J. Bonet, Error estimators and enrichment procedures for the finite element analysis of thin sheet metal forming processes, International Journal for Numerical Methods in Engineering, 34, (1994) R.D. Cook, D.S. Malkus, M.E. Plesha and R.J. Witt, Concepts and application of finite element analysis, 4 th edition, John Wiley & Sons. Inc. (2002) 6. J.-L. Batoz, K.-J. Bathe and L.W. Ho, A study of threenode triangular plate bending elements, International Journal for Numerical Methods in Engineering, 18.7, (1980) J. L Batoz and P. Lardeur, A discrete shear triangular nine D.O.F. element for the analysis of thick to vary thin plates, International Journal for Numerical Methods in Engineering, 28.3, (1989)

29 Dimensional Accuracy of Single Point Incremental Forming M. Ham 1, J. Jeswiet 2 1 Factuly of Engineering and Applied Sciences, University of Ontario Institute of Technology Oshawa, ON, L1H 7K4, Canada URL: marnie.ham@uoit.ca 2 Mechanical and Materials Engineering, Queen s University Kingston, ON, K7L 3N, Canada URL: jeswiet@me.queensu.ca Dimensional Accuracy of Single Point Incremental Forming (SPIF) is studied with the use of a Box-Behnken design analysis. The dimensional accuracy of this process is determined by comparing parts manufactured using SPIF with the part drawings used to create the manufacturing toolpaths. Five factors are varied in the manufacturing of the SPIF process, and they are: material type, material thickness, formed shape, tool size, and incremental step size. The Box-Behnken design analysis allows for determination of how these factors affect the dimensional accuracy. Key words: forming, sheet metal, incremental forming 1 INTRODUCTION This paper presents a new study of dimensional accuracy in Single Point Incremental Forming (SPIF). SPIF is an inexpensive modern sheet metal forming process capable of making complicated shapes described in the CIRP keynote by Jeswiet et al [1]. Although SPIF is a viable process many challenges still need addressing. The new information is in the form of comparisons between part drawings and parts formed with SPIF. This work is complementary to work reported previously [1, 2, 3, 4]. Dimensional accuracy is of vital importance in any manufacturing process. All manufacturing processes have different allowable dimensional tolerances. SPIF can not be marketed as a viable forming method unless information like dimensional accuracy has been determined. The dimensional accuracy study is important for determining how accurate SPIF is; this could lead to understanding of possible applications for SPIF. 2 EXPERIMENTAL METHOFOLOGY Various parameters affect the formability of SPIF; a keynote by Jeswiet et al. [1] discusses many of them and an experimental design (DOE) was utilized to determine the most critical forming parameters [2]. The five main forming parameters (factors) under consideration in SPIF: material type, material thickness, forming tool size, shape of part, and incremental step size; the response to the factors is maximum forming angle [2, 3, 4]. The objective of this study is to determine the effect of the five forming parameters on the dimensional accuracy of parts manufactured using SPIF. The dimensional accuracy results are presented graphically, in 3D, a pictorial comparison between the CAD drawings and the actual parts. A Box- Behnken response surface experimental design methodology is used.

30 2.1 Experiment Set-up for Manufacturing Samples A Box-Behnken experimental design is executed using the five forming factors listed above. The five factors are varied at three levels; the factors and levels are given in Table 9.1. Details on the Box- Behnken design can be found in [3, 5]. The Box- Behnken design can analyze five factors in three levels in forty six experimental runs including centre point replication to improve the variance in the design [5]. Fig. 1. Scanning of Part# using ShapeGrabber Table1. Box-Behnken Design Coding of Experimental Factors Coding Material Thickness Tool Size Step Size Shape Type [mm] [mm] [mm] thin dome medium cone thick pyramid thin medium thick Experimental Methodology for Laser Scanning Utilizing the parts created using the Box-Behnken design DOE for the maximum forming angle. The parts are scanned using a ShapeGrabber laser scanning system. Due to the highly reflective nature of aluminum, the parts needed to be coated to ensure scanning without errors. After experimenting with various coatings; carbon black, candle soot, spray starch and spray deodorant, spray deodorant is found to give the most even and thin coat. Using both the ShapeGrabber and the IMAlign software, the scanned image of the parts can be manipulated or added to. In the case of these parts scans are need to capture the full shape and depth of each part. Figure 1 shows the ShapeGrabber being used to scan a part. Figure 2 shows the image of a part after compiling the multiple scans. Fig. 2. IMAlign screen capture of Part # After compiling the scans of the part, they can be compared to the drawings used to produce the toolpaths for manufacturing the parts. This is done through the use of IMInspect. IMInspect allows the user to define the scales of the CAD and scanned part file; in this case all measurements are made in mm. IMInspect also allows for setting the greatest deviations. The default is 4 mm; this is the setting used for analysis. The scale can be adjusted after to get the best view of the comparison. To do the comparison in IMInspect, data and a reference is needed; in this case, the data is the scanned part and the reference is the CAD drawing. Figure 3 shows the IMInspect comparison of a dome using the default scale of ± 4 mm and figure 4 shows the comparison of the same part using a magnified scale of 0 to 1 mm error. The comparisons from IMInspect determine the deviations between the CAD (reference) and the actual part (data). The 3D colour pictures show the scanned image with a colour coding to represent the deviations between the reference (CAD) and the data (scanned image). The scale for each image is shown on the right of each figure. Figure 3 has a scale ranging from -4 mm to +4 mm in 0.5mm increments. The purple on the bottom of the scale is the to

31 -4.00 mm range and the red is the 3.50 to 4.00 mm range. In this picture the majority of the deviations range from -1.5 to 1.5 mm. Fig. 3. IMInspect Comparison (Scale ±4mm) In Figure 4, the scale is zoomed in to 0 to 1 mm with increments of 0.05 mm. The purple (Zone F) range is now representing the 0 to 0.05 mm deviations from the reference. The red (Zone A) range is 0.95 to 1 mm. The white areas are out of the 0 to 1 mm range. In this picture it is much clearer that the bottom of the form is closer to the CAD reference than the areas which are formed first and near the backing plate. 3.1 IMInspect Comparison for Dimensional Accuracy Using the experimental methodology explained in Section 2.2, each part is laser scanned to determine the deviations from the reference. Figures 5 to 8, show different shaped parts made using 0.9 mm AA6451 material. The tool size and step size as well as shape are different in different figures. Figure 5 and 6 below show 48 cones. The scale shown is 0 to 1 mm, with the white areas at the point of the cone and base, being out of the 0-1 mm error range. These cones are formed using all of the same forming parameters and should produce the same cones. As can be seen from the figures, these cones come out to be very similar. Figure 7 shows a 56 dome; here a large deviation is noted at the tip, just as is seen in the cones. In the dome, the deviation at the tip (last area formed) is still within 1 mm error of the reference. The rest of the dome has errors much less than that of the cone, ranging from mm to mm. Figure 8 shows a 39 pyramid, with a large range of colours shown. The tip of the pyramid also shows the largest deviation from the reference. In the pyramid two sides have similar deviations and the other two sides also are similar. In the case of the pyramid, the errors are similar to those found in the cones. Fig. 4. IMInspect Comparison (Scale 0 to 1mm) 3 RESULTS FROM INSPECTION ANALYSIS Fig Cone (Scale 0 to 1mm) IMInspect produces not only the graphical comparison shown in figures 3 and 4, but will also give numerical data on the fit of the data to the reference.

32 In total forty-six parts were made, compared, and analyzed. The analysis includes: mean and standard deviations error from reference, as well as the maximum and minimum errors and the probability of points within one and three standard deviations. 15% of the parts have maximum errors less than ±1 mm, 48% of the parts are within 2 mm, 76% are within 3 mm and all parts are within ±4 mm. The overall average mean is 0.13 mm and all parts have a mean error of less than 1 mm. 4 CONCLUSIONS Fig Cone (Scale 0 to 1mm) The comparisons show most of the deviations between are within 0 and 1 mm. The overall mean deviation is 0.13 mm. More analysis is need for more complex parts. The results of this study have increased the understanding how accurately SPIF parts are to the drawings. These studies can lead to the manipulation of toolpaths to account for the expected deviations and an ultimate increase in forming accuracy. ACKNOWLEDGEMENTS Fig Dome (Scale 0 to 1mm) The authors thank Queen s University Department of Mechanical and Materials Engineering, the Natural Science and Engineering Research Council of Canada, Novelis Global Technology Centre and Human Mobility Research Centre (HMRC) for their support in this research. The authors would also like to thank Mr. A. Eggleton for performing the laser scanning. REFERENCES Fig. 8. Pyramid Part #39 (Scale 0 to 1mm) 1. J. Jeswiet, F. Micari, G. Hirt, J. Duflou, J. Allwood, A. Bramley, Asymmetric Single Point Incremental Forming of Sheet Metal. Annals of CIRP (2005) 54/2/ M. Ham, and J. Jeswiet, Single Point Incremental Forming and the Forming Criteria for AA3003. Annals of CIRP (2006) 55/2/ M. Ham, and J. Jeswiet, Single Point Incremental Forming Limits Using A Box-Behnken Design of Experiment. Key Eng. Mtls (2007) M. Ham, and J. Jeswiet, Forming Limit Curves in Single Point Incremental Forming. Annals of CIRP (2007) 56/2/ G. Box and D. Behnken, Some New Three Level Designs for the Study of Quantitative Variables. Technometrics (1960), 2, 4,

33 Incremental forming of colour-coated sheets T. Katajarinne 1, L. Vihtonen 2, S. Kivivuori 1 1 Helsinki University of Technology, Laboratory of Processing and Heat Treatment of Materials, P.O.Box 6200, FI TKK, Helsinki, Finland URL: Tuomas.Katajarinne@tkk.fi; Seppo.Kivivuori@tkk.fi 2 Helsinki University of Technology, BIT Research Centre, Po BOX 5500, FI TKK, Finland URL: lotta.vihtonen@tkk.fi ABSTRACT: Incremental sheet forming (ISF) is a highly flexible manufacturing process suitable for low volume and rapid prototype production of sheet metal parts. This paper focuses on the usability of colourcoated (pre-painted) sheets in ISF. Forming limits for steel, zinc and paint need to be considered. Based on tests with stretch forming and ISF the behaviour of colour-coated sheets is studied. Key words: Incremental forming, colour-coated sheets, surface failure 1 INTRODUCTION Pre-painted materials combine the strength and formability of steel with high corrosion resistance. The result is a material ready for production without the need of post-processing. ISF is a highly flexible manufacturing process suitable for low volume and rapid prototype production of sheet metal parts [1,2]. By utilizing colour-coated sheets in ISF the flexibility can be increased further. However demands on the actual process conditions differ between forming un-coated and coated sheets. Much attention has been given to the strains that can be attained in ISF for different materials. Forming limits for ISF have commonly been found to be considerably higher than those achieved by the Nakazima test. It is generally concluded that conventional forming limit curves (FLD s) cannot be used for ISF [3,4,5]. With colour-coated sheets the problem is further complicated. Not only the forming limit for steel but also the forming limits for zinc and paint need to be considered. One practical approach for the forming limits is the observation of the forming angle. Due to the local plastic deformation under the tool a forming angle too steep results in the rupture of the sheet. This paper focuses on the usability of colour-coated sheets in ISF. Robot assisted incremental forming by pressing (RAIFP) is used for two point incremental forming (TPIF) [6]. Incremental sheet forming is also compared against stretch forming of colourcoated sheets by studying the forming limits and coating durability. Differences in formability and material behaviour are observed when comparing formability results of the two methods. 2 FORMING OF COLOUR-COATED SHEETS 2.1 The colour-coated sheets In colour-coated sheets the steel is covered by a zinc layer which is followed by a layer of pre-treatment before the primer and top coat. The material used in the testing was DX53D, a hot dip galvanized deep drawing steel. The sheet is covered on both sides with a polyurethane based colour-coating. Table 1 lists the thickness of the sheet and coating. Table 1. Thickness of layers Layer Thickness (µm) Steel sheet 570 Coating 50

34 2.2 ISF of colour-coated sheets Incremental sheet forming of the coated sheets was preformed by the Helsinki University of Technology (TKK) set up of RAIFP [6]. The forming is based on a strong industrial robot that performs ISF, TPIF was used but single point incremental forming (SPIF) is also possible with the apparatus. The material is deformed by pressing and sliding a forming tool on the surface of the blank. As the parts are formed on the convex surface a support tool is necessary. The forming equipment is shown in figure 1. Fig. 2. The test geometry 2.3 Stretch forming tests The stretch forming test were preformed with a 300/200 ton hydraulic press using a hemispheric forming tool with a diameter of 100 mm. The punch travel was controlled and stopped right after sheet rupture. No lubrication was used during the forming tests. Figure 3 shows an example of a stretch formed sheet. Fig. 1. The RAIFP set up The tool paths of the test geometries were made with CAD and CAM software and translated with an interpreter software to the robot. A hemispherical tool with a diameter of 10 mm was used for the actual forming. The test geometry was a square cone with an upper side length of 36 mm. The test geometry in shown in figure 2. Fig. 3. A stretch formed colour-coated sheet 3 RESULTS AND DISCUSSION For the ISF tests forming angles from 30 to 70 with 5 intervals were used for the square cone. A low viscosity oil with PTFE addition was used as lubrication. The formed cones were

35 stereomicroscopically examined for surface defects. Sheets with silk screen printed grids were used to measure the actual strains in forming. The reached forming angles were considerably large before the occurrence of failure in the paint surface. Table 2 lists the results of the ocular surface examination by stereomicroscopy preformed on both sides of the sheet. Table 2. Surface condition after ISF Forming angle ( ) Ocular examination 30 Intact 35 Intact 40 Intact 45 Intact 50 Intact 55 Sound with traces of rupture 60 Rupture in top coat, primer sound 65 Rupture in top coat, rupture in primer 70 Sheet failure By forming from the opposite side of the silk printed grid the grid could be used for strain measurement. The initial grid size was 2x2 mm. For the 30, 45 and 60 cones tensile test specimens were prepared. Tensile test were preformed using a 100 kn MTS tensile testing machine. The specimens were cut horizontally from the cones. The forming tool travel and original rolling direction is longitudinal on the specimens, the principal strain is in the transverse direction. Figure 4 shows a combination of the actual strain measurements and the tensile test results. The tensile test results contain curves for both deformed and un deformed colourcoated sheet. Stress (MPa) ISF angle ,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Effective strain Forming angle ( ) pre strain as an output level the tensile test results were added to the plots in figure 4. Silk printed sheets were also utilized in the stretch forming tests to determine the strains. Table 3 lists the strains measured from the ruptured colour-coated sheets in stretch forming. The strains were measured from the intact squares nearest to the rupture at three locations. Table 3. Measured strains in stretch forming Direction Logarithmic strain ε major 0,102 ε minor 0,065 As observed in table 3 the achieved strains before rupture are considerably smaller than in incremental forming. The surface of the colour coating remained intact until sheet rupture in stretch forming. The results of the tests are plotted in figure 5. Again the reverse forming angle is used in the plotting. Effective strain 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 Point of sheet failure in stretch forming Surface condition vs forming angle Intact Surface Failure of sheet Failure of paint surface Critical area for paint Forming angle ( ) Fig. 5. Surface condition vs. forming angle in ISF As can be observed from figure 5 the strains with ISF are larger than for stretch forming. No visible surface defects can be observed when approaching the critical area. Once the critical area is reached an increase of the forming angle leads to the failure of the coating followed rapidly by the failure of the primer and finally by the sheet rupture. Figures 6 and 7 show ruptured and intact coatings at different forming angles. The magnification is identical in both pictures. Fig. 4. The measured effective strain vs. forming angle and stress-strain curve of deformed cones. The measured elongation from the grids was converted to effective strain. Using the value of the

36 The strains differ in the two forming methods. With the square cone geometry the minor strain was between zero and 2 % of the major strain. In stretch forming the strain was clearly biaxial, the minor strain reaching approximately 60% of the major strain. A clear difference can be observed when comparing the forming methods. With traditional forming methods rupture of the sheet limits the forming and formability. In incremental forming the colour coating limits the formability. ACKNOWLEDGEMENTS Fig. 6. Ruptured coating at 25 forming angle This research was supported by the Finnish Funding Agency for Technology and Innovation. REFERENCES Fig. 7. Intact coating at 45 forming angle 5. CONCLUSIONS 6. The effect of ISF deformation on painted sheet surface has been analysed. Colour-coated (polyurethane based) sheets are suitable for incremental forming. Ocular examination of both sides of the sheet did not reveal any detrimental effect from the forming tool. T. Nakagawa, Advances in Prototype and Low Volume Sheet Forming and Tooling, Journal of Materials Processing Technology 98 (2000), P. Groche, R. Schneider: Umformtechnik für die Produkte von morgen, Mat. wiss. U. Werkstofftech. 31 (2000) Nr. 11, L. Filice, L. Fratini and F. Micari, Analysis of Material Formability in Incremental Forming, CIRP Annals Manufacturing Technology, Volume 51, Issue 1, 2002, G. Hirt, S. Junk, M. Bambach, I. Chouvalova, Process limits and material behaviour in incremental sheet forming with CNC-tools, Materials Science Forum. Vol , Part , J. Jeswiet, D. Young, Forming limit diagrams for singlepoint incremental forming of aluminium sheet, Journal of Engineering Manufacture. Vol. 219, no. B4, L. Lamminen, T. Tuominen, S. Kivivuori, Incremental Sheet Forming with an Industrial Robot, Proceedings of 3rd International Conference on Advanced Materials Processing (ICAMP-3), pp. 331.

37 Preliminary Studies on Single Point Incremental Forming for Thermoplastic Materials V. S. Le 1, A. Ghiotti 1, G. Lucchetta 1 1 DIMEG University of Padova - Via Venezia, 1, Padova, Italy URL: vansy.le@unipd.it 1 DIMEG University of Padova - Via Venezia, 1, Padova, Italy URL: andrea.ghiotti@unipd.it 1 DIMEG University of Padova - Via Venezia, 1, Padova, Italy URL: giovanni.lucchetta@ unipd.it ABSTRACT: This paper presents some preliminary investigations on applicability of Single Point Incremental Forming techniques (SPIF) to thermoplastic materials. A fractional factorial design of experiments with three replications was performed to investigate the effects of forming parameters on material formability. To study the formability of the thermoplastic sheets, a cone-shaped part with circular generatrix with varying wall angles with respect to depth was considered. The formability of SPIF to the thermoplastic sheets can be defined in terms of the maximum wall angle reached without tearing and/or failure. This angle was measured at position where the mechanical failure of the deformed sheet occurred such as wrinkling, crushing and tearing. It is concluded that the existing knowledge and know-how of sheet metal on SPIF process can be applied to thermoplastic sheets that has potential and preeminent benefits. Key words: Incremental forming, Single Point Incremental Forming (SPIF), Polymer, Thermoplastic Sheet 1 INTRODUCTION In recent years, sheet thermoplastic materials have gained increasing interest for applications in many civil and industrial sectors, due to their preeminent characteristics differing from metal sheets. In fact, the structural and thermal properties (i.e. resistance to impact and to temperature, bearing capabilities, etc.) make them particularly suitable to all the applications in which a high strength/mass ratio and a good formability is required such as in medical, aerospace and automotive sectors. Injection moulding technology has traditionally received extensive attention for the production of polymers parts [7,8]. Although the high flexibility in the design of components shapes, the economical competitiveness of the process requires large production batches to amortize the costs of dies and tooling. Otherwise, flat components can be obtained by deforming sheet polymers in thermoforming processes as combination of drawing and stretching mechanisms [3]. However, these processes present strong limitations, particularly with respect to the forming of small to medium batch production. Thermoforming requires expensive and dedicated plants equipped with complex dies. In case of shapes, in which the stretching mechanism prevails, a review of the literature points out a lack in controlling the uniformity of large deformations before necking and/or rupture [3]. Additionally, the material squeezing realized by the simultaneous contact of the two dies causes relatively large localized tensile loads, which tends to tear the polymer sheet. Therefore, the improvement of the material forming limits and the manufacturing processes, especially for the small to medium production of complex shape components, is required. Single Point Incremental Forming (SPIF) technology has been introduced in the recent past to manufacture sheet metal products by using Computer Numerical Control machines (CNC). The major advantage of incremental forming is represented by the possibility to manufacture sheet metal parts difficult to form with traditional processes in a rapid and economic way without expensive dies and long set-up times. In SPIF the tooling is usually a simple frame for the sheet metal clamping, while the deformation is realized by using a tool that is moved along a predefined path by a robot or a CNC machine. Although the process can be rather slow compared to the traditional stamping or drawing processes, single point incremental forming process of metal sheets represents the best way to manufacture prototypes and complex

38 components produced in small batches for aeronautical, automotive and medical applications. At the present time, researchers have obtained feasible results and potential applications on sheet metal products [1, 2, 5]. With the target of realizing advantages similar to SPIF of sheet metals, this paper presents some preliminary investigations on applicability of SPIF techniques to thermoplastic materials. The maximum wall angle is also considered as index of maximum formability of thermoplastic sheet. To reduce the amount of tests and, consequently, the duration of experimental campaign, Design Of Experiment techniques (DOE) were applied to the design of the experimental plan. In order to evaluate the formability, the variation of the wall angle with respect to the depth of the formed part was considered. A cone-shape part with a circular arc as generatrix was selected. In order to obtain accurate results, a factorial plan of experiments with three replications was designed. vertical coordinate given by: x = d (2) z M1 The value of d is the maximum height of the cone and z M1 the vertical coordinate of the tool when the failure appears. This value is recorded by the CNCcontroller interface and verified by using a Coordinate Measuring Machine (CMM). 2.2 Experimental equipments In the experiments, square polypropylene sheets (400x400x3 mm) were used. They were clamped on the frame and put on the machine table (see Fig. 2). The forming zone was a circle of 300 mm diameter. The tools were manufactured in stainless steel with ball-shaped top. The whole experimental campaign was carried out on a Cielle 30x35-β CNC. The part model was modelled in Pro Engineer Wildfire 2.0. This model was used to generate tool-path and to output numerical control codes. 2 EXPERIMENTS 2.1 Design model for experiment A cone-shaped part with a circular arc as generatrix was selected to test the formability in the experiments. The part geometry was designed in order to enable investigating all of the wall angles from 0 to 90 degrees. Since the thickness of the part changes according to the cosine s law and the slope of part increases with its depth, the analyzed region is limited to an angle minor than 90 degrees (see Fig. 1). Fig. 1. Geometric illustration of part profile Fig. 1 shows the generatrix of a part studied during in the experiments. The analyzed area is outlined by the arc of MN. The wall angle φ of a generic point on the generatrix, defined by the tangent to the profile, can be calculated as follows: x φ = arccos (1) R where R is the radius of the circular arc and x the z M1 d Fig. 2. Setting of experimental equipment Due to the friction between the surface of thermoplastic sheet and the tool, local heating can exceed the softening temperature of the thermoplastic polymer. In this case, the material formability increases but the deformation is not stable during the process. In order to avoid this effect, water-miscible metalworking fluid was used in the percentage of 25% (Blasocut 2000). 2.3 Testing procedure Fig. 3. Mechanical failures on formed part The square thermoplastic sheet was clamped on the support frame. A constant lubrication is granted by a

39 hydraulic system during the experiments (see Fig. 2). The sheets were deformed until either wrinkling or tearing occurred. If the tool is not stopped after the wrinkling appears, the material deforms in a nonuniform way and the wrinkling shown in Fig. 3 appears. The wall angle at which either wrinkling or tearing occurred was considered as the index of the maximum material formability. It was calculated by formula (1). Each experiment was performed three times to verify the repeatability. 3 DESIGN OF EXPERIMENTS As introduced above, this work is a preliminary investigation of SPIF applied to thermoplastic materials. Thus, it is necessary to comprehend preliminarily effects of forming parameters on these materials. The objective of this experiment is to determine which forming parameters influence the formability of thermoplastic sheet and to understand the interacting effects. Table 1. The levels of factors for experiments Source Low level High level Step size (mm) Tool size (mm) 6 12 Feed rate (mm/min) Spindle speed (rpm) Table 2. Design of Experiments Run Oder Step size Tool size Feed rate S. speed On the basis of the main parameters affecting the SPIF of sheet metals analyzed in the literature [5], four forming parameters (factors) were considered in the single point incremental forming experiments on thermoplastic sheets: (i) step size, (ii) tool size, (iii) feed rate and (iv) spindle speed. Low level and high level of factors are shown on Table 1 and were chosen on the basis of a preliminary sensitivity analysis. The wall angle is the response of experiments. The maximum wall angle is defined as maximum index of formability achieved before failure. A factorial design of experiment was prepared in twenty-four runs, with three replications for each experiment (see Table 2). The 2-level fractional factorial design presents clear advantages in terms of reduction of costs, time, and resources needed to make the runs. The proposed plan did not consider effects of other parameters such as: type of material, thickness of polymer sheets, shape and local heating. 4 RESULS OF EXPERIMENT Table 3. The Analysis of Variance Source Seq SS Adj SS Adj MS F P Main Effects 67, , , ,66 0,00 2-Way Intera. 12, ,2474 4, ,58 0,00 R. Error 1,5340 1,5240 0,0959 Pure Error 1,5340 1,5340 0,0959 Total 81,1494 S = 0, R 2 = 98,11% R 2 adj = 97,28% The Analysis of Variance (ANOVA) is summarized in Table 3. It describes the effects of the input parameters and of their interactions on the output variable. It is shown that all the analyzed parameters and their 2-way interactions are relevant to the process (very low P-values) and this model has a fairly good fit. Therefore, all the factors (forming parameters) have to be taken into account and used to model the response surface. Table 3 also indicates that the correlation coefficient R 2 and adjusted R 2 adg values (R 2 = 98,11% and R 2 adj = 97,28%) for accuracy of this model are very satisfactory. Fig. 4. Main effects for maximum wall angle

40 Main effects of forming parameters for maximum wall angle and their interactions are described on Fig. 4 and Fig. 5. The increase in step size and feed rate contributes to decrease φ max, that means a decrease in formability. In particular, the step size is particularly significant for the formability when its value is larger. These results are in accordance with previous researches carried out on SPIF of metal sheets [5]. Due to the excessive vertical movement of the tool and the high friction between the polymer sheet and the tool, the deformed part is wrinkled and torn easily at larger step. The combination of smaller tool and larger step size contributes to significant decrease of formability as illustrated on Fig. 5. to increase the formability of thermoplastic sheets only with either large tool size, small step size or large feed rate. The local heating originated by higher speed is reduced by the use of coolant to proper temperature for plastic deformation. The combination between higher feed rate and higher spindle speed also improved the formability. The interaction between tool size (or step size) and spindle speed is relative significant for larger tool size (for smaller step size). Thus, the improvement of formability in thermoplastic sheets depends on the variation of four forming parameters. Shapes used to demonstrate the abilities of forming thermoplastic sheets are shown on Fig CONCLUSIONS Fig. 5. Interaction among forming parameters for φ max When using a small radius, the tool penetrated easily into the sheet and some pieces of chip are spited out. Thus, the formability decreases significantly if the radius of the forming tool is small. The interaction plot shows that smaller radius tool and larger step size (or feed rate) contribute to decrease significantly the formability. Results obtained in similar experiments carried out on metal sheets show a different behaviour of polymers compared to metals. Fig. 6. Some shapes were formed in thermoplastic sheet Also the increase of spindle speed affects formability. In SPIF of metal sheet, previous researches indicated that decreasing in the spindle speed can result into a better formability. A reduction of the spindle speed can eliminate sliding friction and can retain only rolling friction. In this experiment, the increase in spindle speed contributed Design of Experiments is developed to comprehend preliminarily the Single Point Incremental Forming of thermoplastic sheets. All effects of forming parameters and their interactions are illustrated graphically as prediction of effects of parameters on formability. These experiments show that tool size has a significant effect on formability of thermoplastic sheets. Interactions between step size and tool size or tool size and feed rate have significant effects in the polymer formability. Additionally, an increase in spindle speed also contributes significantly to increase formability. REFERENCES 1. J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric single point incremental forming of sheet metal, CIRP Annals, 54, (2005), F. Capece Minutolo, M. Durante, A. Formisano and A. Langella, Evaluation of the maximum slope angle of simple geometries carried out by incremental forming process, Journal of Materials Processing Technology, 194, (2007), Louis P. Inzinna, Herman F. Nied, Apparatus for die forming thermoplastic sheet material, US Patent References, (1991), J.R. Duflou, B. Callebaut, J. Verbert and H. De Baerdemaeker, Improved SPIF performance through dynamic local heating, Int. Journal of Machine Tools and Manufacture, 48, (2008), M. Ham and J. Jeswiet, Forming limit curves in single point incremental forming, CIRP Annals - Manufacturing Technology, 56, (2007), Rohrbacher, F., Spain, P.L. and Fahlsing, R.A., Process for forming a composite structure of thermoplastic polymer and sheet moulding compound, Composites, 23, (1992), J. C. Gerdeen, H. W. Lord, R. A. L. Rorrer, Engineering design with polymers and composites, Taylor & Francis, CRC Press (2006). 8. M. J. Gordon, Industrial design of plastics products, Wiley-Interscience Publication (2003).

41 Advanced process limits by rolling of helical gears R. Neugebauer 1, U. Hellfritzsch 1, M.Lahl 1 1 Fraunhofer Institute for Machine Tools and Forming Technology IWU, Chemnitz, Germany URL: reimund.neugebauer@iwu.fraunhofer.de udo.hellfritzsch@iwu.fraunhofer.de mike.lahl@iwu.fraunhofer.de ABSTRACT: A new developed method describes the gear-rolling-process and an alternative pitch design of forming tools. A model was created to analyze rolling processes which determined that in contrast to flat rolling tools, round tools for helical gears need additional kinematic compensation during diameter-related variable pitch forming processes. The new method shows up to a 50% improvement in pitch accuracy and the ability to roll high teeth gears (up to 10 mm in height and a tooth-height-coefficient larger than 2,7). The Fraunhofer Institute IWU has carried out research for many years to provide insight in generating high gearing typical of transmissions with rolling techniques and surpassing the limits of forming feasibility. Key words: Forming, Rolling, Gears, Rolling tools, Pitch accuracy 1 INTRODUCTION Rolling of helical gears is a competitive alternative to metal-cutting production processes due to the benefits derived from forming manufacturing processes such: - no loss of material and no need to dispose of chips, - very short processing times, - over 60% boost in strength in the flank zone, - highest surface quality (R a = 0.2 µm; R z = 1.4 µm), - improved load capacity caused by contour-related fiber orientation. The basic prerequisite for applying rolling processes to manufacturing higher tooth profiles is enhancing the potential gear qualities in terms of flank shape, accuracy of pitch concerning the assessment criteria formulated in the DIN 3960 through 3962 quality standards [1] and economical tool life qualities. 2 ROLLING OF HELICAL GEARS Rolling has found the widest range of application among the forming techniques for teeth shaping. There is a distinction made between forming techniques and generating techniques [2], [3]. The foremost generating techniques are rolling with flat tools and rolling with round tools. 2.1 Flat Rolling Technique Cold rolling with flat tools consists of two rolling rods moving in opposite directions that mesh with the rolling blank symmetric to rotation. It is centered between tips on both ends and can rotate freely. The upper and lower rolling rods have translatory and synchronous motion in relation to one another, they encounter the rolling blank simultaneously and they set it into rotation by means of friction and form closure. 2.2 Round Rolling Technique The round rolling technique clamps the original form that is symmetric to rotation between the tips in the axial direction. Depending upon the technique, two or three round tools with the same direction of rotation and a constant speed form the toothed geometry into the blank (Figure 1).

42 round Rundwerkzeug rolling tool Walzteil rolling component round Rundwerkzeug rolling tool Figure 1: Round rolling technique with two rolling tools 1. Initial rolling phase d v penetration path per workpiece targeted tooth height penetration path critical forming range 2. Calibrating rolling phase d Wk machine capacity 26,4% maximum rolling force 105,6kN contortion number of workpiece variable pitches arises from the fact that the rolling process is dependent upon the diameter over its entire length. That means, the tool initially rolls to the preliminary dimension of the original shape that is symmetric to rotation both with round tools and flat tools. The longer the process of the tool teeth penetrating into the rolling blank, the more the penetrating diameters change with one another [4]. Figure 3 shows 6 workpiece seamings for rolling a targeted z=12 teeth as an example of the penetration process dependant upon diameter. The diameter before lathing (d v ) determines the beginning of rolling into the rolling blank based on the pitch (p A ) while the rolling or reference circle diameter d Wk or d 0 determines the end of rolling (p K ) when the toothed wheeled works are fully formed. A rolling circle diameter of the tool and workpiece gear cutting develops at every point in time of the rolling process that is dependent upon penetration. This gradual change in the corresponding rolling circles has to be accommodated not only in the design of the rolling tools but also in the design of the process routine. This is the reason why a differentiated procedure is called for with the rolling techniques being investigated. start of rolling process Initial rolling phase beginning of penetration process Figure 2: Penetration path into the workpiece The penetration into the workpiece (Figure 2) is done by reducing the axle base of the round tools in the radial direction. And since the workpiece can be seamed several times, the round rolling technique can be deemed as forming at an infinite tool length. This is an advantage it has in relation to rolling with flat tools that are limited in their length and it explains the challenge presented by rolling with round rolling tools. In other words, the design of the round rolling technique does not make it possible to give tools variable pitches (i.e., with variable spaces from one tooth to another) to ensure a pitch-precision process of penetration of tool teeth into the rolling blank which is dependent upon the diameter. 2.3 Pitch-variable Rolling Process State-of-the-art are engineering flat tools with a constant tooth pitch over the entire length while rounded tools also roll at a constant tooth pitch since the tools and rolling component seam several times. The idea of designing rolling techniques with end Walzende of rolling start of Anwalzbeginn rolling process end Walzende of rolling d V d initial pitch p A after start diameter d v 0 / Wk calibration-pitch p K after reference circle diameter d 0 or rolling circle diameter d Wk p U pa = z U d0 / wk π pk = = z z A blank p dv π = z K blank d V Calibration phase end of rolling process pitch-variable rolling process rolled gear Figure 3: Pitch-specific penetration process into a rolling blank depending upon diameter Correcting the pitch with the flat-rolling technique is a linearization of adjusting the toothed pitches from the first tooth of the tool run-in p A to the tooth pitch p K when the calibrating zone has been reached. Pitch correction in the rolling process with round tools uses a Speed-Controlled Forced Synchronization. Speed-Controlled Forced Synchronization The rolling component is clamped firmly in the speed-controlled synchronous run-in and force d Wk

43 driven by a separate drive train for a technique with variable pitches over the penetration process of the rolling tool dependant upon diameter. The calculation rules shown in Figure 4 are used to calculate the workpiece speed at a constant specified tool speed and then it is implemented in the control system as a setpoint curve. The rolling process is broken down into three phases for precision definition of terms. n n n 1,Ws 2,Ws 3,Ws n = n = n = 1,Wz d 2,Wz d 3,Wz d D v,ws D Wk,i D Wk a,wz Wk,i Wk Initial rolling phase Penetration phase Calibrating phase Figure 4: Diameter-dependant speed adjustment in the round rolling process At the beginning of the initial rolling phase, the tip circle diameter D a,wz of the rolling tools and the diameter before lathing d v of the rolling blank generate with one another. The tip circle pitch of the tool forms the initial rolling number z A on the circumference of the blank. The same procedure can be determined with mathematical precision for phase 3 of the rolling process, i.e. the calibrating process as well as the ratios of speeds to diameter can also be precisely defined in the zone of full formation. The rolling circle diameter of the tool (D Wk ) and the workpiece (d Wk ) generate with one another in the calibrating zone of forming. The speed of the rolling tools n Wz is specified as a constant target speed over the entire process while the rolling circle diameter of the tool (D Wk,i ) and the workpiece (d Wk,i ), each generated in forming phase i, roll in the zone of the penetration phase [6]. 3 TESTS Various helical gears were formed with round and flat tools to verify the tool and process designs described here. The selected gears were rolled both with round and flat tools to compare rolling techniques. Hardened steel 16MnCr5 was used as the reference material because MnCr-alloyed hardened steels are suited for high-stress wear-resistant components in automobile manufacture and mechanical engineering, especially for gear cutting. These experimental tests on the pitch-dynamic rolling process with the flat-tool technique were carried out on a flat-profile-rolling machine and the rolling tests with the round rolling technique were realized on the PWZ Spezial Two-Roller Machine at the Fraunhofer Institute for Machine Tools and Forming Technology IWU in Chemnitz. Test Findings The gear-geometry measurements of ten pitchconstant (state-of-the-art) and pitch-variable rolling workpieces were broken down into the geometrically relevant gear variations as per DIN 3962, flank shape, flank line, true running and pitch accuracy. Pitch accuracy was accorded a higher priority since these findings are directly impacted by the pitchvariable modification in techniques while flank formation and true running accuracy are only impacted indirectly. Figure 5 shows a compressed summary and comparison of findings from pitchconstant and pitch-variable tool design when rolling a high gear module m n =1.6 tooth number z=10 with flat tools. F p, f p [µm] total cumulative pitch error F p F p = 51µm F p = 26µm f p = 26µm f p = 14µm adjacent pitch error f p part number state of the art rolling (quality 10) pitch-variable rolling (quality 8) state of the art rolling (qual. 9) pitch-variable rolling (quality 7) Figure 5: Pitch accuracy with state-of-the-art rolling and pitchvariable rolling (high gear m n =1.6 z=10 - flat tools) Concerning flat tool rolling, the resulting pitchprecision penetration process alone was able to drive down the pitch variations, reducing quality nearly 50% (f p -improvement from 26µm to 14µm) and improving gear quality by 2 quality classes (9 to 7). The geometric variation as per DIN 3962 was also

44 scaled back by approximately 50% (F p -improvement from 51µm to 26 µm). Figure 6 shows a summary and comparison of findings of pitch-constant and pitch-variable process design when rolling the high gearing module m n =1.6 mm, tooth number z=10 with round tools. The pitchprecision penetration process of the tool teeth into the rolling component reduced pitch variations by approximately 30% (f p decrease from 26µm to 18 µm) and gear quality improved by one quality class (9 to 8). The geometric variation was driven down by approximately 40% with the described total cumulative pitch error F p from 44µm to 27µm. That means that the qualitative improvement potential increases (due to diameter-dependent and a pitchprecision process) with the resulting increasing discrepancies between initial rolling and calibration pitch when rolling into the full material. A pitch-adapted forming process based on diameter can make a contribution to rolling high gears since the mathematical discrepancy between the initial rolling and calibrating pitch increases the greater the module and tooth height. Special segments for future manufacture of high gears with rolling processes could be reverse gears (since quality requirements are low), sun wheels and planetary gears (Figure 7). Volkswagen AG has even been successful at proving that extremly high gearing can be rolled with the high gear for the reverse gear where module 3.75 was rolled into the full material (16MnCr5) at an extreme tooth height of 10.3 mm and a tooth height coefficient of y=2.7 (refer to Figure 8). 60 F p, f p [µm] F p = 44µm F p = 27µm f p = 26µm m f p = 18µm total cumulative pitch error F p adjacent pitch error f p part number state of the art rolling (quality 9) pitch-variable rolling (quality 7) state of the art rolling (qual. 9) pitch-variable rolling (quality 8) Figure 6: Pitch accuracy with state-of-the-art rolling and pitchvariable rolling (high gear m n =1.6 z=10 - round tools) 4 OUTLOOK Conclusions can be drawn on large-module gears from the qualitative findings of rolling processes for their pitch-variable process design using measurements to assess them. high gearing normal gearing stub-tooth gearing tooth-height coefficient y high gears, planet gears, sun wheels, camshaft gears attached gears, pinions not critical transmission gearing, reverse gear shafts future targets state-of-the-art (gear quality 7 8) critical (gear quality8) first results of research at IWU Chemnitz (gear quality 9 10) state-of-the-art (gear quality 7 8) impact of gear parameters: m n, z, h z, b, α, β, x Figure 7: State-of-the-art with gear rolling rollability This is promising since the state-of-the-art practical limit for cross rolling of spur-toothed gear into the full material is approx. module 1.6 (normal gears). Figure 8: Transmission helical gear rolling into the full material for the first time at IWU (reverse gear at VW AG) In conclusion, gear quality 10 as per DIN 3962 were achieved and greater potential was found for enhancing this process in geometrically exact rolling tools in a process design specifically adapted by varying machine setting parameters. Next steps will be proving that gear geometries provide better component properties due to its process-oriented property advantages (adapted fiber orientation and increased hardness in the load-bearing flanks and tooth base zone) in comparison to conventional cutting processes. REFERENCES [1] Grzeskowiak, J.: Possibility on cold and warm Forging of Gears; Int. Conf. On Rotary Metal-working Processes, London, [2] Lange, K.: Umformtechnik, Band 2 - Massivumformung; Springer Verlag Berlin (1988). [3] Linke, H.: Stirnradverzahnungen; Carl Hanser Verlag, München, [4] Neugebauer, R.; Hellfritzsch, U.: Optimierte Auslegung von Walzwerkzeugen zur umformenden Herstellung von Stirnradverzahn.; UTF Science II/2003. [5] Hellfritzsch, U.; Lorenz, B.; Quaas, J.: Werkzeug und Verfahren zum Querwalzen von Verzahnungen sowie Verfahren zur Herstellung eines solchen Werkzeuges, Deutsches Patent C2, [6] Hellfritzsch, U.: Optimierung von Verzahnungsqualitäten beim Walzen von Stirnradverzahn.; Diss., Verlag Wissenschaftliche Scripten, Band 32, 2006.

45 Comparison between the numerical simulations of incremental sheet forming and conventional stretch forming process V. Oleksik 1, O. Bologa 1, R. Breaz 1, G. Racz 1 1 Lucian Blaga University of Sibiu, Engineering Faculty, 4 Emil Cioran Street, , Sibiu, Romania URL: valentin.oleksik@ulbsibiu.ro; octavian.bologa@ulbsibiu.ro; radu.breaz@ulbsibiu.ro; gabriel.racz@ulbsibiu.ro. ABSTRACT: The paper presents a comparison study based on the simulation by the finite element method of incremental sheet metal forming and classical stretch forming process. Four separate different analysis were performed, one for stretch forming and three different process versions for incremental forming. The thinning of the sheet, the variation in time of Von Mises stresses in four nodes, the section profile of the obtained parts and the forces developed in the processes being studied. Key words: Incremental forming, Stretch forming, Numerical simulation 1 INTRODUCTION The current paper refers to one of the new nonconventional forming process for sheets metal, namely incremental forming. The incremental sheet metal forming represents a complex metal forming process, at which, as compared to classical stretch forming process, the kinematics comprises beneath a movement on vertical direction also a movement in the blank's plane [1, 2]. Problems occur during calculation of stress, strain, thinning and the forces in the process of incremental sheet metal forming and in the conventional stretch forming have been analysed in this paper. 2 THE FINITE ELEMENT MODEL To tackle the non-linear analysis, a parameterised model, used in the analysis through the finite elements method, has been built, described through the Dynaform software. The forming system that is being used as base for the numerical simulations consists of a die, blankholder and hemispherical punch for incremental forming, respectively rectangular punch for stretch forming. In the case of incremental forming the punch is placed unsymmetrical. It is sought to realise a frustumshaped part with a height of 8 mm and a side length at the small base of 100 mm. The trajectories followed by the punch for the numerical simulation of the incremental forming process are presented in figure 1. In case 1 (fig. 1, a), in the first stage, the punch has a vertical movement. In the second stage the punch follows a rectangular trajectory around the die borders. In the case 2 (fig. 1, b), the punch has a stepped (8 steps) movement on the vertical direction. After each vertical step the punch follows a rectangular trajectory like in case 1. In case 3, the punch has, in the first stage, a vertical movement. In the second stage, the punch follows a trajectory which tries to cover the all formed surface. The punch moves on Ox direction along the die border, has a stepped movement on Oy direction and back on the Ox direction. In the case of stretch forming (case 4) the punch has only a vertical movement at the sheet level. In all cases, there are no imposed boundary conditions on the nodes placed on the circumference, because the blankholder eliminates this necessity. A thin circular sheet blank (D = 240 mm), placed on an active die with rectangular working zone is considered. The punch diameter is D p = 12 mm, the die radius R die = 6 mm, the clearance between punch and die border c = 6 mm and the initial thickness t = 1 mm.

46 (a) (b) (c) Fig. 1. The three different trajectories for the incremental forming simulations The finite element network associated with the part s geometry is built so that it allows an unfolding of the analysis in good conditions, without necessitating a re-mesh because of its exaggerated distortions. The Thin-Shell-163-type element was used. A shear factor of 5/6 and a total of 7 integration points through the thickness were used in order to catch the variation of the stresses and strains through the thickness. The material associated with the part s elements corresponds to a deep-drawing sheet DDQ. The Dynaform material model 36 (Barlat s 3- parameter plasticity) was chosen. This model combines isotropic elastic behaviour with anisotropic plastic potential developed by Barlat and Lian [3, 4]. The considered elasticity modulus is E = 0.7e+5 MPa, the transversal contraction coefficient is ν = 0.28, while the yield stress is σ Y = 290 MPa, the strength coefficient K = 524 MPa and hardening coefficient n = The anisotropic characteristic s width to thickness strain ratio values R 00 = 1.89; R 45 = 1.61; R 90 = THE RESULTS OF NUMERICAL SIMULATIONS The numerical results of the simulations were centred on the determination of the thinning (fig. 2), variation in time of equivalent Von Misses stress in four nodes (fig. 3), the precision of the parts obtained by these different processes (fig. 4) and the forces on the process (fig. 5). (a) (b) (c) Fig. 2. The thinning variation in the four studied cases (d)

47 (a) (b) (c) Fig. 3. The in-time variation of equivalent Von Mises stress for four nodes in the four studied cases As can be seen from figure 2 (a, b, c), the value of maximal thinning for incremental forming (regardless of the chosen technological variant) is around 27-28% and is located along the part's edges. The maximal thinning occurs for case 3 (figure 2, c), namely for the incremental forming in several vertical steps. In the case of conventional stretch forming, the maximal thinning has a value of 6% and is located in the tops of the formed part. In all four cases, the thinning from the part's central area has values of up to 5 times less than that from the areas located along the part's edges. We study the in-time variation for four nodes located in the tops of the formed part. Node 7361 is the node located in the very spot where the punch enters the material at the first step during incremental forming. From figure 3, a, b, c it can be seen how in case 1 the stress in the nodes reaches successive maximal values when the punch passes them. In case 2, the stress value in the nodes increases progressively as the part's height increases, but still decalated, and in case 3 the stress increases abruptly in the nodes located (d) at the beginning of the trajectory and then remains almost constant, while in the nodes located at the trajectory's end, the stress increases slowly until the end. For the conventional stretch forming (figure 3, d), in the four nodes the stress increases abruptly in the four nodes and remains relatively constant, its value being equal for all four nodes. Another problem is the precision of the part formed through the four procedures. For this, the part was cut with the plane xoz. For the case of incremental forming (especially for cases 1 and 2, figure 4 a, b) there can be noticed a rather significant convexity on the part's bottom. From this point of view, the most unfavorable case is the one of the forming in a sing vertical step, where this convexity can reach values of up to 1.7 mm. For the conventional stretch forming, the part's bottom is plane (case 4, figure 4, d). A shape close to the one obtained with conventional stretch forming is achieved in case 3 (figure 4, c), where even a small concavity of the part's bottom can be noticed. This technological variant is unfortunately also the most time-consuming one, the punch going along a complex trajectory. (a) (b) (c) (d) Fig. 4. The section profile for the four studied cases

48 Figure 5, (a, b, c, d) presents the variation graphs of the forces present in the four studied cases. From the start, it can be noticed that the force obtained in the case of conventional stretch forming is almost 7 times bigger than that needed in any of the cases studied through incremental forming. From figure 5, it can be seen that the maximal force the component of the force on vertical direction (F z ) presents a maximum at the punch's penetration in the material and then local maxima at the final of each line on the horizontal direction of the punch. In figure 5, b it can be seen that the maximal force increases progressively with the increase of the punch's penetration depth. (a) (b) (c) Fig. 5. The time variation of the forces in the four studied cases (d) In case 3 (figure 5, c) the maximal force also has a maximum at the moment of the punch's penetration in the material, followed by local maxima with close values at the end of each horizontal line. In all 3 cases of incremental forming, the value of forces in the plane xoy is of approximately 5 times less than the force on vertical direction. Of course, the value of these forces on horizontal direction is zero for the case of conventional stretch forming (figure 5, d). 4 CONCLUSIONS Following the study by numerical simulation of the four technological forming variants it can be concluded that the best variant from the point of view of material behaviour and achieved precision is the variant of conventional stretch forming. Nevertheless, this technology employs complex tools and is thus automatically more expensive and requires also large forming forces. A satisfying variant is case 3, where the results from a qualitative point of view are close to the ones from the conventional stretch forming and the forces are much smaller. A solution can also be to form the part in a first step with a punch whose shape is close to the desired one, followed by the shape's correction through incremental forming. REFERENCES 1. H. Iseki, An approximate deformation analysis and FEM analysis for the incremental bulging of sheet metal using a spherical roller, In: Journal of Materials Processing Technology, No. 111, (2001) G. Hirt, S. Junk, N. Witulski, Incremental Sheet Forming: Quality Evaluation and Process Simulation, In: Proceedings of the 7 th International Conference on Technology of Plasticity, Yokohama, Japan, (2002) p I. Cerro, E. Maidagan, J. Arana, A. Rivero, P.P. Rodriguez, Theoretical and experimental analysis of the dieless incremental sheet forming process In: Journal of Materials Processing Technology, Vol. 177, (2006) M. Yamashita, M. Gotoh, S-Y. Atsumi, Numerical simulation of incremental forming of sheet metal, In: Journal of Materials Processing Technology, Vol. 199, (2008)

49 A new approach for toolpath programming in Incremental Sheet Forming M. Rauch 1, J.Y. Hascoet 1, J.C. Hamann 2, Y. Plennel 2 1 Institut de Recherche en Communications et Cybernetique de Nantes (IRCCyN) UMR CNRS 6597, 1 rue de la Noe, BP92101, Nantes Cedex 03, France. URL: matthieu.rauch@irccyn.ec-nantes.fr jean-yves.hascoet@irccyn.ec-nantes.fr 2 Airbus, France URL: jean-christophe.hamann@airbus.com yannick.plennel@airbus.com ABSTRACT: Because of involved means and process implementation, toolpath generation is a key topic linked to incremental sheet forming. Process characteristics ask for specifically dedicated toolpaths. This paper firstly evaluates the impact of toolpath type and of other programming parameters on process implementation through an experimental campaign performed on a parallel kinematics machine tool. Then, a new approach to perform Intelligent CAM programmed toolpaths is proposed. This innovative toolpath programming concept is based on toolpath optimization thanks to real time tool force evaluation made into CNC controller. A feasibility study is finally achieved in a conclusive way. Key words: Toolpath optimization, Incremental Sheet forming, Intelligent CAM programming, Forming force Control, CNC data 1 INTRODUCTION Incremental sheet forming is a recently emerging process to manufacture sheet metal parts that is well suited for small batch production or prototyping [1, 2]. As the process implementation consists in making the tool performing computer generated toolpaths on z-levels that decrease under a determinate step, toolpath generation becomes a key topic linked to incremental sheet forming, regarding both on productivity and conformity. Until recently, most of the research was focused on sheet metal formability using this process [3-6] and most authors employ standard CAM generated milling toolpaths. However, Kopac et al. considered in [7] the working direction effects in single point forming. Attanasio proved in [8] that it is better to program constant scallop height toolpaths than constant axial increment toolpaths. To optimize parts accuracy, Ambrogio et al. propose to program vitiated trajectories, which are deliberately wrong but lead to acceptable parts once the forming constraints are relaxed [9, 10]. Another solution is proposed by Hirt in [11] where the toolpaths are adapted after having measured the first produced part. It could be beneficial to study works about toolpath optimization for milling applications, which have already been widely studied, to propose new optimization ways for incremental sheet forming [12-14]. Hence, the first objective of this paper is to evaluate the effects of incremental sheet forming toolpaths on the implementation of incremental sheet forming process, especially regarding to productivity and conformity. The study focuses not only on trajectory parameters but also on the toolpath shape itself. Related works highlighted the fact that the choice of forming trajectory has an effect on the process performances, for example [2]. Then, the second aim of this work is to propose a new approach to generate intelligent forming toolpath. This approach is called ICAM (Intelligent Computer Aided Manufacturing) programming. It is based on real time tool force evaluation performed without any additional equipment. According to the estimated force, forming toolpaths are compensated on-line to reduce loads and maintain sheet metal integrity.

50 2 TOOLPATHS EFFECTS ON PROCESS IMPLEMENTATION: FIRST RESULTS 2.1 Experimental setup An experimental study of single point incremental forming was performed to evaluate the effects of the process parameters when producing an entire shape (Fig. 1). Fig. 1. Test Part Three parameters were studied: feedrate, axial increment and forming strategy (1-2-3). Strategies 1 and 2 are contour parallel and Strategy 3 is a spiral toolpath. Strategy 1 consists in z-level contouring; after each level the axial increment is taken plainly along z-axis. In Strategy 2, the axial increment is obtained gradually along one side of the square shape. In Strategy 3, a quarter of the axial increment is taken along each side of the square. The objective of this work is not to propose new forming strategies but to underscore the effects of toolpaths shape on the process implementation, in particular on productivity, conformity and cost issues. Other parameters were the same for all experiments. Sheets were made of aluminum alloy (5086) and had a 0.6 mm thickness. Forming tool radius was 10 mm Results According to the experimental results given in Table 1, feedrate has no influence on forming force. Forming times are linked to feedrate and axial increment combination. Forming strategy has an effect on forces and on final part accuracy. Among the tested toolpaths, Strategy 1 offers here the best compromise. Nevertheless, coupled effects are also observed, so that process implementation depends on a proper combination of all toolpaths parameters. As a consequence, CAM software generated toolpaths cannot be directly used for incremental sheet forming applications because their parameters are optimized for another manufacturing process. It is a fact that most authors are using such strategies and obtain interesting results. But any productivity or quality improvement will need to optimize these CAM milling orientated toolpaths according to the stakes conveyed by the forming process. Table 1. Experimental Results Axial Forming Forming Depth Feedrate Strategy Inc. Force Time Error (m/min) (mm) (N) (min) (mm) INTELLIGENT CAM PROGRAMMING TOOLPATH GENERATION Because of the elastic springback, it difficult to predict sheet metal position after tool release. Forming toolpaths programming is consequently quite complicated. Moreover, in two points incremental forming, if toolpaths are not well adapted, sheet metal can be gripped between die and tool, what can affect the part and damage the forming device. As a result, CAM milling toolpaths are not suitable anymore. It is also necessary to control and adjust toolpaths according to what is really going on the machine tool. Forming loads stand besides for a performing parameter for controlling process implementation, as shown by Duflou in [15]. On this point, Filice et al. proposed in [16] an interesting method to control online the implementation of single point incremental sheet forming. However, this approach is based on 3d dynamometer acquisition prediction models, what penalize its efficiency in a flexible production environment. In a previous work, a new method to optimize NC machining processes by controlling the force between tool and manufactured part has been proposed by the authors [17]. Its major objective is to integrate process constraints in toolpaths programming and control. In practice, this approach, called ICAM (Intelligent Computer Aided Programming), consists in decoupling toolpath generation between the CAM software and the CNC.

51 Basic toolpaths are generated by CAM software and sent to CNC. Then, during the running of the program, these toolpaths are optimized by the NC controller according to real time process data. No additional equipment is necessary neither to acquire tool force data nor to perform adaptative force control. Therefore, high flexibility and high efficiency are insured. In this paper, ICAM approach is implemented for incremental sheet forming applications. The developed method divides into two levels. The first one consists in collecting tool forces directly from CNC data. In the second level, machine tool is driven not only by the CAM software generated G- code file, but also by the force estimation obtained in real-time in the first level. subroutine that clears the tool (Fig. 2). For the first one, tool jog parameter is modified real-time into the CNC. A difficulty conveyed by this optimization lies into its duration. Final part accuracy can be affected by the jog variations. This way of adapting toolpaths is rather dedicated to positive forming applications where a too high forming force is often due to an wrong position of forming die. 3.1 Tool force collection The objective is not to perform process monitoring operations, but to dispose of an assistance tool dedicated to toolpath optimisation during process implementation. Proposed approach consists in acquiring forming loads directly from CNC data, without any additional equipment. On a practical point of view, forming load estimation divides into three steps. Step 1 lies in catching servomotor torques generated by machine tool dynamics during the axis displacement, without any process effort. For that, torques values are acquired while the NC program is executed without the sheet metal. Indeed, recent CNC controllers let the user access axis torques while running a NC program. Step 2 is performed in forming conditions. Torques values are acquired during the manufacturing of the part. Measured values contain both forming and dynamics contributions. During Step 3, forming loads are calculated from estimated forming torques and from the geometrical transformation model of the machine tool. As a result, it is possible to estimate instantaneous forming loads from CNC data. 3.2 Toolpath adaptation Second level of the method consists in adapting toolpaths according to the results of forming force estimations. The major objective is to prevent any sheet metal damage caused by a too high forming force. Two approaches were identified to implement it: to modify the forming tool jog or to call a Fig. 2 Toolpath adaptations Another way to prevent the sheet metal from damaging is to call a tool clearance routine (Fig. 2). This routine generates a retract movement along tool axis, so that it is possible to limit the tool load even in five-axis trajectories. On a practical point of view, as soon as tool force overtakes a preset value, forming NC program calls the clearance subroutine. Retraction value is defined by user before running the NC program. As toolpath modification is only local, this approach is efficient for local tool overloads. This solution suits also to single incremental forming applications. 3.3 Feasibility study A feasibility study was performed to validate first level of the method. Machine tool used was the five axis parallel kinematics parallel machine of the laboratory. Servomotor torques where acquired by CNC controller (Siemens 840D). The interest of using a parallel kinematics machine tool is to prove the efficiency of ICAM approach with unusual machine architectures. The experiment was performed in single point forming and consisted in carrying out a 100 mm diameter toolpath with a 2 mm z-increment on a 0.6 mm sheet metal. Forming forces were calculated from servomotor acquisitions according to ICAM approach. Results are on Fig. 3 and showed a good concordance between Kistler dynamometer data and the ones from CNC.

52 Fig. 3. Results of a validation test This validation test consequently highlighted the efficiency of ICAM approach. Indeed, its objective is not to perform process monitoring but to get forming force evaluations with the view to adapt toolpath if necessary. 4 CONCLUSION Toolpath generation is one key topic linked to incremental sheet forming. It is also necessary to develop specific toolpath generation to improve its efficiency. In this paper, an experimental study highlighted the effect of the forming strategy and other programming parameters on the efficiency of the process. Its results show that rough milling CAM software toolpaths are not sufficient anymore to properly implement incremental sheet forming. Hence, the implementation of Intelligent CAM programmed toolpaths for incremental sheet forming is presented. This new approach enables to adapt manufacturing toolpaths during the machining of a part regarding to process data. Toolpath optimization is carried out into the CNC controller. No additional equipment is necessary to collect data or drive the machine tool, what insures its flexibility and its efficiency. A feasibility study was finally achieved in a conclusive way. ACKNOWLEDGEMENT This work was carried out within the context of the working group Manufacturing 21 which gathers 15 French research laboratories. The topics approached are: the modelling of the manufacturing process, the virtual machining, and the emerging of new manufacturing methods. REFERENCES 1. E. Hagan and J. Jeswiet, A review of conventional and modern single-point sheet metal forming methods, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 217 (2), (2003), J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou and J. Allwood, Asymmetric single point incremental forming of sheet metal, CIRP Annals - Manufacturing Technology, 54 (2), (2005), M.-S. Shim and J.-J. Park, The formability of aluminum sheet in incremental forming, Journal of Materials Processing Technology, 113 (1-3), (2001), Y. H. Kim and J. J. Park, Effect of process parameters on formability in incremental forming of sheet metal, Journal of Materials Processing Technology, , (2002), J.-J. Park and Y.-H. Kim, Fundamental studies on the incremental sheet metal forming technique, Journal of Materials Processing Technology, 140 (1-3), (2003), E. Ceretti, C. Giardini and A. Attanasio, Experimental and simulative results in sheet incremental forming on CNC machines, Journal of Materials Processing Technology, 152 (2), (2004), J. Kopac and Z. Kampus, Incremental sheet metal forming on CNC milling machine-tool, Journal of Materials Processing Technology, , (2005), A. Attanasio, E. Ceretti and C. Giardini, Optimization of tool path in two points incremental forming, Journal of Materials Processing Technology, 177 (1-3), (2006), G. Ambrogio, I. Costantino, L. De Napoli, L. Filice, L. Fratini and M. Muzzupappa, Influence of some relevant process parameters on the dimensional accuracy in incremental forming: a numerical and experimental investigation, Journal of Materials Processing Technology, , (2004), G. Ambrogio, L. De Napoli, L. Filice, F. Gagliardi and M. Muzzupappa, Application of Incremental Forming process for high customised medical product manufacturing, Journal of Materials Processing Technology, , (2005), G. Hirt, J. Ames, M. Bambach and R. Kopp, Forming strategies and process modelling for CNC incremental sheet forming, CIRP Annals - Manufacturing Technology, 53 (1), (2004), A. Dugas, J. J. Lee and J. Y. Hascoet, Feed Rate and Tracking Errors Simulation in High Speed Milling, In: 4th International ESAFORM Conference on Material Forming, Liege (Belgium), (2001), V. Pateloup, E. Duc and P. Ray, Corner optimization for pocket machining, International Journal of Machine Tools and Manufacture, 44 (12-13), (2004), Y. Tang, Optimization strategy in end milling process for high speed machining of hardened die/mold steel, Journal of University of Science and Technology Beijing, Mineral, Metallurgy, Material, 13 (3), (2006), J. Duflou, Y. Tunckol, A. Szekeres and P. Vanherck, Experimental study on force measurements for single point incremental forming, Journal of Materials Processing Technology, 189 (1-3), (2007), L. Filice, G. Ambrogio and F. Micari, On-Line Control of Single Point Incremental Forming Operations through Punch Force Monitoring, Annals of CIRP, 55 (1), (2006), J. Y. Hascoet and M. Rauch, A new approach of the tool path generation in manufacturing operations using CNC data, In: International Conference on High Speed milling, Suzhou (China), (2006),

53 On some computational aspects for incremental sheet metal forming simulations C. Robert 1,2, P. Dal Santo 1, A. Delamézière 2, A. Potiron 1, J.-L. Batoz 3 1 ENSAM - LPMI 2 bd du Ronceray, BP Angers Cedex, France camille.robert@angers.ensam.fr 2 GIP-InSIC 27 rue d Hellieule, Saint-Dié-des-Vosges, France 3 UTC - GSU, Centre Pierre Guillaumat 2, BP 60319, rue du Docteur Schweitzer, Compiègne Cedex, France ABSTRACT: The paper deals with some numerical aspects to simulate efficiently the incremental sheet forming process. Firstly, in order to consider the production of real industrial parts, complex tool paths are needed and a Computed Aided Manufacturing software is used to provide them. Second the finite element simulation is highly CPU time consuming and in an attempt to decrease that time, a simplified elasto-plastic scheme based on the incremental deformation theory of plasticity has been introduced in ABAQUS. Taking into account the equivalent plastic strain, the stress flow and the actual thickness of the sheet, a reduction of CPU time and a good prediction are observed (considering the flow rate elasto-plastic scheme as reference). Key words: Incremental sheet forming, FEM, plasticity, ABAQUS, CAM 1 INTRODUCTION The incremental sheet forming process (ISF) has been developed in the context of sheet metal forming to increase the flexibility of that important industrial process [1]. ISF is mainly used to produce small batch size or as a rapid prototyping process in different industries, from transportation to medical field [2, 3]. ISF allows a significant reduction of the tooling cost for small production of sheet parts since traditional, expensive and complex tools are replaced by a simple hemispherical punch moving on a controlled tool path. To increase the quality of the final geometry, it is still possible to use a die. But that die can be manufactured in a cheap material because the applied forces are low [4]. Another advantage of this process is the high limit of formability, compared to classical limit forming observed in stamping [5,6]. In the industrial context, the numerical simulation must efficiently predict the geometry of the part, the thickness, the strains and the stresses in the sheet throughout the forming process. In ISF the contact zone between the tool and the sheet is limited and is always changing with the movement of the tool along its path. Each material point of the sheet is then subjected to elasto-plastic loading and unloading depending if the tool is far or not from that point. In an attempt to reduce the CPU time we studied the computational aspects involved to represent the elasto-plastic material behaviour. The classical elasto-plastic integration scheme based on the flow rule requires several iterations. The incremental deformation theory of plasticity is considered as an alternative to reduce the CPU time. The first part of this paper deals with these two aspects of the plasticity (i.e. flow rule and incremental deformation theory). After that, the implementation of CAM tool path into ABAQUS is explained. Finally, results obtained for a benchmark are presented and discussed. 2 MODELLING OF BEHAVIOUR LAW 2.1 Flow rule method The flow rule theory of plasticity is dominantly used in the context of computational plasticity for metals. With this method, the direction of the plastic flow is the same as the direction of the outward normal to the yield surface. To determine the state variables, a

54 plastic corrector, also called Lagrange multiplier, is necessary. The stress tensor σ is related to the elastic strain tensor ε el by: iterations in order to stay on the yield surface (points C and D). The normality of the computed yield function is used at each iteration. σ : el el = C ε (1) where C el denotes the elastic stiffness tensor. The evolution of the isotropic hardening is modelling by the Swift law: pl ( ε + ε ) n R = K 0 (2) pl where ε is the equivalent plastic strain. K, ε 0 and n are three experimental parameters. The yield surface f can be defined by the Von Mises criterion, with the deviatoric stress tensor S: 3 f = S : S R 2 (3) The normality flow rule determines the increment of plastic strain tensor and the increment of equivalent plastic strain: pl = & f ε& λ σ & pl ε = & λ where λ & denotes the plastic corrector. The consistency condition is: (4) f f df = σ& + R& σ : R (5) In the case of a plastic flow rule, equation (5) should be zero. We can determine the plastic corrector: f el : C : ε& &λ = σ (6) f el f : C : + HR σ σ where HR denote the tangent stiffness plastic modulus: R HR = ε pl = n. K pl n ( ε + ε ) 1 0 (7) On the figure 1, the Von Mises criterion is plotted (bold ellipse) in the principal stresses (with the hypothesis of plane stresses) at the end of increment. Numerically, the first step is to take into account an elastic prediction (i.e. ε el = ε) and the yield function f is computed. Then, if f is greater than zero (point B on the figure 1), the stresses are updated Fig. 1. Flow rule method 2.2 Incremental strain method The incremental deformation theory is based on a simplification of the elasto-plastic scheme. Contrary to the flow rule method, it does not take into account the normal to the yield surface but only the strain tensor to obtain the stress state [7]. The advantage of this method is that no iteration is necessary and the CPU time should be reduced. At a given time, stress and strain are defined by the point Q on the figure 2. To get the stress at the next increment of time (point R), we use an elasto-plastic modulus E ep. The incremental strain ( ε) is composed additively by elastic ( ε el ) and plastic ( ε pl ) components as: el pl ε = ε + ε (8) Let C pl the plastic stiffness tensor and 0 ε el the total elastic strain at the initial state of the current incremental step, we defined ε * as: ε * el el pl = 0 ε + ε = ε + ε (9) The elasto-plastic stiffness tensor C ep is: ep ( ) 1 el ( ) 1 + pl C = C ( C ) 1 (10) A relation between the stress tensor σ and the strain ε * is then obtained: σ ep * = C :ε (11)

55 4 RESULTS In this study, we analyse the forming of a cup with a diameter of 85mm and a depth of 25mm as show on the figure 3. The initial flange dimensions are: 140mm*140mm*1.5mm. The material parameters for the aluminium sheet are: E = 69 GPa, ν = 0.3, K = 150 MPa, ε 0 = 0.013, n = and ρ = 2700 Kg/m 3. We used a hemispherical tool having a diameter of 30mm. 3 TOOL PATH Fig. 2. Incremental deformation method The efficiency of Single Point Incremental Forming is strongly dependent of the tool paths strategy. These may be very complex in the case of industrial parts [8]. Our idea is to use a Computer Aided Manufacturing (CAM) software to determine the tool path. The generated paths are used as data entry to a finite element simulation package. The CAD/CAM software CATIA is chosen. The tool paths are saved in a universal APT file format. Commonly, this universal format can be post-treated to generate control files for numerical machines. In this case The APT file is automatically generated by a Visual Basic script. Python scripts are used within ABAQUS to translate the data of the APT file in order to describe the time tool positions components in ABAQUS explicit. The maximum velocity is an input parameter. We use smooth amplitude curves (already implemented into ABAQUS) A and B to get, between two points, a continuum acceleration which is described by: P = P B A + t t ξ = t t 3 2 ( P P ) ξ ( 10 15ξ + 6ξ ) A A B A (12) P is the location at the time t, P A and P B are the locations of point A and B respectively. The acceleration is then controlled to avoid high inertia effects in the dynamic explicit scheme. Fig. 3. Final geometry of the cup The finite elements used are shells with 4 nodes and reduced integration (S4R) and with 9 Simpson points in the thickness direction. The global size of elements is 2*2mm and the model has degrees of freedom. The tool is modelled by an analytic rigid surface. The ABAQUS explicit solver is used without mass scaling and the maximum velocity of the tool is 25m/s. This high velocity is not representative of the real process, but is here a numerical parameter considering that a quasi-static problem is solved thanks an explicit dynamic method. A high velocity can be used if the ratio of kinetic energy on the deformation energy is small during the simulation (i.e. small inertia effects). The tool path is defined by a five circle pocket generated by CATIA (figure 4) and integrated into ABAQUS. Fig. 4. CATIA tool path In order to have an estimation of the reduction of CPU time, the two elasto-plastic schemes are coded into an ABAQUS user subroutine VUMAT. Let t is and t fr the CPU time with incremental deformation theory and flow rule theory respectively. The time benefit t benef is given by:

56 t benef t fr tis = 100 (13) t fr In this case, the time benefit is 4.2%. Let σ 0 is and σ 0 fr the stress flow with incremental deformation theory and flow rule theory respectively, ε pl is and ε pl fr the equivalent plastic strain and th is and th fr the thickness of the sheet. An estimation of the quality of the results given by the incremental strain theory is given by: 0 σ is σ ERRσ = σ ε ERRε = 100 pl is ε fr ε pl fr fr 0 fr pl fr this th ERRth = 100 th fr (14) Where ERRσ is the stress flow error, ERRε is the equivalent plastic train error and ERRth the thickness error. These errors are showed on figure 5, figure 6 and figure 7 respectively at the end of forming process. Fig. 5. Stress flow error (%) Fig. 6. Equivalent plastic train error (%) 5 CONCLUSIONS In this paper, the incremental deformation theory of plasticity has been implemented in ABAQUS using a behaviour law implemented in a specific user function (VUMAT). The model has been tested on a cup forming process. The results are compared with those obtained with the classical flow rule theory. We found that the numerical errors are acceptable while a reduction of CPU time was observed. An integration of the tool path definition created by CATIA in ABAQUS has also been developed using Visual Basic and Python scripts and the maximal velocity of the tool is then controlled. REFERENCES 1. M. Yamashita, M. Gotoh and S.-Y. Atsumi, Numerical simulation of incremental forming of sheet metal, Journal of Material Processing Technology, 199, (2008) F. Micary, G Ambrogio and L.Filice, Shape and dimensional accuracy in Single Point Incremental Forming: State of the art and future trends, Journal of Material Processing Technology, 191, (2007) J. Kopac and Z. Kampus, Incremental sheet metal forming on CNC milling machine-tool, Journal of Material Processing Technology, , (2005) E. Ceretti, C. Giardini and A. Attanasio, Experimental and simulative results in sheet incremental forming on CNC machines, Journal of Material Processing Technology, 150, (2004) G. Hussain and L. Gao, A novel method to test the thinning limits of sheet metals in negative incremental forming, International Journal of Machine Tools & Manufacture, 47, (2007) Y.H. Kim and J.J. Park, Effect of process parameters on formability in incremental forming of sheet metal, Journal of Material Processing Technology, (2002) N. Ramakrishnan, K.M. Singh, R.K.V. Suresh and N. Srinivasan, An algorithm based on total-elasticincremental-plastic strain for large deformation plasticity Journal of Material Processing Technology, 86, (1999) M. Bambach, M. Cannamela, M. Azaouzi, G. Hirt, J.-L. Batoz, Computer-aided tool path optimization for single point incremental sheet forming, Advanced Methods in Material Forming, Springer, 2007, pp Fig. 7. Thickness error (%)

57 Multi Stage Strategies for Single Point Incremental Forming of a Cup M. Skjoedt 1, N. Bay 1, B. Endelt 2, G. Ingarao 3 1 Department of Mechanical Engineering, Technical University of Denmark, DTU - Building 425, DK-2800, Kgs. Lyngby, Denmark URL: msk@ipl.dtu.dk; nbay@ipl.dtu.dk 2 Department of Production, Aalborg University, Fibigerstræde 16, DK-9220, Aalborg Ø, Denmark URL: endelt@production.aau.dk 3 Department of Manufacturing and Management Engineering, University of Palermo, Viale delle Scienze, Palermo, Italy URL: p.ingarao@dtpm.unipa.it ABSTRACT: A five stage forming strategy for Single Point Incremental Forming of a circular cylindrical cup with a height/radius ratio of one is presented. Geometrical relations are discussed and theoretical strains are calculated. The influence of forming direction (upwards or downwards) is investigated for the second stage comparing explicit FE analysis with experiments. Good agreement is found between calculated and measured thickness distribution, overall geometry and strains. Using the proposed multi stage strategy it is shown possible to produce a cup with a height close to the radius and sides parallel to the symmetry axis in about half of the depth. Key words: Incremental forming, multi stage, FEM 1 INTRODUCTION Single Point Incremental Forming (SPIF) is a relative new sheet forming process which offers the possibility of forming complex parts without dedicated dies using only a single point tool and a standard 3-axis CNC machine. The process enables strains much higher than traditional sheet forming processes, but is limited by the type of deformation which is close to plane strain for geometries formed in one stage. A consequence of this is the sine-law, t = t 0 sin(90 -α), which relates the drawing angle α with the thickness after forming. This law has proven to give a good description of the thickness distribution and as a result it is not possible to form parts with drawing angles higher than about in one stage. For a 90 drawing angle the sine-law predicts a thickness equal to zero and strains going towards infinity. One way to get around the limitations prescribed by the sine-law is to use a multi stage strategy, and this is the subject of the present paper. 2 MULTI STAGE STRATEGIES Using a multi stage forming strategy is not a new idea in SPIF. Kitazawa et al. [1] used different two stage strategies to produce hemi ellipsoidal shapes and investigated the limits before fracture varying the radius and the height of the geometry. Jeswiet et al. [2] used a three stage strategy to form an automotive headlight reflector. As far as the authors know, no work has yet been presented in literature, where a multi stage strategy allows forming of a part with a 90 drawing angle in SPIF. In two point incremental forming (TPIF) a 90 drawing angle has been achieved, [3,4]. 3 MULTI STAGE STRATEGY 3.1 Forming of cups A fundamental difference between deep drawing and SPIF is the plate area included in the deformation. In deep drawing it is the drawn-in flange, which is deformed, whereas limited deformation is introduced in the bottom of the cup. For deep

58 drawing steel forming of cups with a height/radius ratio h/r 2 is possible. SPIF of a cup with a ratio h/r = 1 is considered almost impossible. The plate area included in the deformation in SPIF is the area surrounded by the first round of the tool path or the hole in the backing plate, i.e. forming may be characterized as stretching. Fig. 1 shows the thickness strain for a round and a square cup assuming that thickness is evenly distributed. In SPIF the distribution of thickness is normally far from this. ε t h/r r round square Fig. 1. Thickness strain for different h/r ratios stage strategy The idea in the present work is to extend deformation to all the material available which is indicated by the horizontal, dotted line in Fig. 2. The first stage stretches this into a 45 cone. The following stages will gradually move the middle of this section towards the corner. All stages except the first can be performed going either downwards or upwards. This gives a total of 16 different strategies. r h = r a 5 4 b c Fig. 2. Five stage strategy for forming a cup with h/r = 1. In the present paper only the first four stages are considered and in those, two different strategies are investigated, i.e. down-up-down-down (DUDD) and down-down-down-up (DDDU). Influence from direction of forming is investigated in detail for the second stage. Theoretical principal strains can be calculated assuming the deformation to be pure stretching and the meridional strain to be evenly distributed. The circumferential strain is zero at points a and c and maximum in b in Fig. 2. The maximum thickness strain is higher than in Fig. 1 for h/r = 1. This is because the circumferential strain is not evenly distributed. 2r ε φ = ln = ln( 2) r ( 1 ) 2πr ε θ, max = ln = ln( 2) πr ( 2 ) ε = ln 4 1. ( 3 ) ( ) 4 t, max 4 SIMULTION AND EXPERIMENTAL SETUP 4.1 Setup of FE model LS-DYNA version ls971s is adopted to simulate the process using explicit time integration. The forming tool and the backing plate are considered rigid. Time scaling is used simulating the process to be 1500 times faster than the actual experiments. The influence from time scaling and the use of rigid tools are investigated by Qin et al. [5] and the applied settings are considered reasonable. Maximum time step is based on a characteristic length equal to shell area divided by the longest diagonal. As a precaution DYNA uses 0.9 times this value. Fully integrated shells (type 16 in DYNA) are used with five integration points in thickness. Adaptive remeshing is adopted. The movement of the tool in the simulation is identical to that in the experiments including the rotation. The sheet material used is AA1050 H111/O and considered isotropic with a flow stress as stated in equation 4. The values for C and n are average of what is used by Hirt et al. [6] and Filice et al. [7]. Coulomb friction is assumed with μ = 0.1. C n 0.14 σ = ε = 111 ε MPa ( 4 ) y 4.2 Experimental setup Experiments are conducted on a 3-axis milling machine. All sheets are 1 mm thick and the forming speed is 1000 mm/min. The tool, which has a radius of 6 mm and a semi-spherical tip, is rotated at 27 rpm. The rotational speed ensures a surface speed at the maximum radius equal to the forming speed. Diluted cutting fluid is used as lubrication, and the part is cleaned between each stage to remove loose wear particles. Tool paths are programmed using Pro/ENGINEER. First stage has a fixed vertical step size of 0.5 mm and following stages have a distance

59 between tool paths below 1 mm. The geometries used for the different stages are as shown in Fig. 2 with h = 70 mm and r = 80.5 mm. A small undeformed section remains in the middle (r = 0-10 mm) since the tool cannot form a cone with a sharp pointed end. 5 RESULTS 5.1 First two stages Experiments are compared with simulations for the first two stages only, i.e. down-down (DD) and down-up (DU). A comparison of the achieved geometries can be seen in Fig. 3. There is almost perfect agreement for the DD strategy. Regarding the DU strategy the simulated geometry is more pointed in the center region and about 10 mm too deep. The DD strategy causes a distribution similar to a normal, one stage SPIF, where increasing angle causes decreasing thickness. Using the DU strategy this is not the case, and most of the reduction in thickness occurs in the center part where the drawing angle is low. This is necessary if vertical sides are to be achieved in the subsequent stages. Thickness [mm] DD Exp. DU Exp. 0.2 DD Num. DU Num Depth [mm] Fig. 4 Comparison of thickness from experiments and simulations as function of depth. 5.1.a Two stages: down-down (DD) Adopting the strategy DD not all of the geometry is formed during the second stage, leaving a residual cone in the center. This is because the depth of the part is increased in the second stage, whereas the tool path only goes 70 mm down as in the first stage. As the tool moves down during the second stage a small plateau is formed beneath it. This plateau is observed experimentally as well as in the simulation, Fig. 5. Kitazawa et al. [1] obtained similar experimental results. 5.1.b Two stages: down-up (DU) Adopting the strategy DU no residual cone is observed after the second stage, but material build up in front of the tool is noticed, which changes the point contact to a line contact, Fig. 5. Again this phenomenon is observed in both experiments and simulations. A similar observation is found in experiments by Kitazawa et al. [8]. The line contact causes process forces in the XY plane to increase and care should be taken not to exceed the force limits of the machine when forming harder materials. Fig. 3 Comparison of geometry achieved by simulation and by experiment for DD strategy (top) and DU strategy (bottom). Legend displays thickness in mm. Fig. 4 compares the measured thickness distribution with the calculated one. For both geometries very good agreement is obtained until a depth of 60 mm. Fig. 5 Left: formation of plateau (DD strategy), right: formation of line contact (DU strategy).

60 5.2 Strategy DUDD and DDDU The DDDU strategy can be performed without fracture, whereas the DUDD strategy results in fracture in stage 4 just after finishing the vertical section of the part, Fig. 6. The fracture appears in a zone with heavy thickness strain, see Fig. 7. Thickness measurements below this point are for the first three stages only since the fourth stage could not be completed. Both strategies give minimum thickness in the bending section between the vertical and the horizontal work piece parts. This corresponds well with the theoretical strains which indicate a maximum thickness strain in the corner of the cup. Using the suggested strategy it seems that the critical area is not the vertical sides themselves but the transition zone between vertical and horizontal. The reason is that this zone experiences a deformation close to equal bi-axial stretching. 6 CONCLUSION The multi stage strategy presented is able to produce a cup with a 90 drawing angle which has not been possible before. It demonstrates that strains far from plane strain can be achieved in SPIF and that strain paths may be far from linear. The distribution of strains is not only depending on the geometry of the tool path but also on the direction (downwards or upwards). The proposed strategy needs to be refined by further research but presents a promising concept for forming parts with vertical sides in SPIF. ACKNOWLEDGEMENTS The authors would like to thank Professor Joachim Danckert and Mr. Mikkel Steffensen from Department of Production, Aalborg University for their help with LS-DYNA. Furthermore Professor Fabrizio Micari from Department of Manufacturing and Management Engineering, University of Palermo is acknowledged for providing a LS-DYNA model facilitating the start of simulating SPIF in this work. REFERENCES Thickness [mm] Fig. 6 Geometry after 4 stages of forming (left DDDU and right DUDD) DDDU 0.60 DUD(D) 0.40 fracture 0.20 vertical bend horizontal Distance along surface [mm] Fig. 7 Measured thickness as function of the distance along the surface for the two strategies DDDU and DUDD. Both strategies increase the maximum drawing angle since they allow forming of the third stage. Experiments show, that the geometry obtained after this stage cannot be formed in single stage SPIF. The DDDU strategy also allows forming of the fourth stage which has vertical sides to a depth equal to 35 mm and a total depth approximately equal to the radius. 1. Kitazawa, K., and Nakane, M., Hemi-ellipsoidal stretch-expanding of aluminum sheet by CNC incremental forming process with two path method, Keikinzoku/Journal of Japan Institute of Light Metals, 47, (1997), , (in Japanese). 2. Jeswiet, J. and Hagan, E., Rapid proto-typing of a headlight with sheet metal, Technical Paper - Society of Manufacturing Engineers, (2002), Hirt, G., Ames, J., and Bambach, M., A new forming strategy to realise parts designed for deep-drawing by incremental CNC sheet forming, Steel Research International, 76, (2005), Kitazawa, K., and Nakajima, A., Method for producing aluminum cylindrical shell having uniform wall-thickness by CNC incremental forming process, Keikinzoku/Journal of Japan Institute of Light Metals, 47, (1997), , (in Japanese). 5. Qin Q., Masuku E.S., Bramley A., Mileham A.R., and Owen G.W., Incremental sheet forming simulation and accuracy, Proceedings of 8th ICTP, (2005). 6. Hirt, G. and Bambach, M., Modelling incremental sheet forming using a meshless surface representation based on radial basis functions, Proceedings of 8th ICTP, (2005). 7. Filice, L., Fratini, L., and Micari, F., Analysis of material formability in incremental forming, CIRP Annals - Manufacturing Technology, 51, (2002), Kitazawa, K., Wakabayashi, A., Murata, K., and Yaejima, K., Metal-flow phenomena in computerized numerically controlled incremental stretch-expanding of aluminum sheets, Keikinzoku/Journal of Japan Institute of Light Metals, 46, (1996), 65-70, (in Japanese).

61 Multi-Step toolpath approach to overcome forming limitations in single point incremental forming J. Verbert 1, B. Belkassem 2, C. Henrard 3, A.M. Habraken 3, J. Gu 2, H. Sol 2, B. Lauwers 1, J.R.Duflou 1 1 Katholieke Universiteit Leuven Department of Mechanical Engineering - Leuven URL: Johan.Verbert@mech.kuleuven.be; 2 Vrije Universiteit Brussel - Vakgroep Mechanica van Materialen en Constructies Brussels URL: Bachir.Belkassem@vub.ac.be; 3 Université de Liège - Département M&S Mécanique des matériaux et Structures - Liège URL: Christophe.Henrard@ulg.ac.be; ABSTRACT: Although Incremental Forming offers distinct advantages over traditional forming processes, such as short lead times and low setup costs, the process still has some drawbacks. Besides the obtainable accuracy, one of the main challenges of the process are the process limits. Many workpiece geometries cannot be manufactured due to the fact that the maximum wall angle that can be formed is limited for a certain sheet material and thickness to a given angle. Different solutions to this approach have been proposed and this paper further investigates one of those solutions, the multi step approach for single point incremental forming. Experiments were performed and compared with simulations to better understand the phenomena underlying the improved process performance. Key words: SPIF, Incremental forming, Process limits. 1 INTRODUCTION Single Point Incremental Forming (SPIF) is a sheet metal part production technique by which a sheet metal part is formed in a stepwise fashion by a CNC controlled spherical tool without the need for any supporting die. This technique allows a fast and cheap production of customized or small series of sheet metal parts [1]. Besides the obtainable accuracy [2], one of the main challenges of the process are the process limits. Many workpiece geometries cannot be manufactured due to the fact that the maximum wall angle that can be formed is limited for a certain sheet material and thickness to a given angle α (see Figure 1) [3]. If a sufficiently large portion of a workpiece has a wall angle that exceeds this angle, the part will fail during manufacturing. A Fig. 1: Sectional view of a cone α C B 2 THEORETICAL BACKGROUND AND OBJECTIVE The process limits of SPIF can be intuitively explained intuitively by the sine law. The zone of material AB in the original flat sheet (see Figure 1) will be stretched into the zone CB of the final part during the forming process. T CB = T AB sin( 90 α) Formula 1: Sine law Assuming that only in-plane strains occur, the sine law can be used to estimate the final thickness of the part at zone CB (T CB ) from the original thickness of the zone AB (T AB ) and the wall angle of the part (α). It has experimentally been verified that the process more or less follows this law [4] with a tendency to overform slightly [5]. In Table 1 a set of maximum wall angles for commonly used materials is given as a function of the thickness of the sheet and the diameter of the tool used during forming. As can be seen from the table, parts with (semi-) vertical walls are impossible to form using standard milling toolpaths as generated by most CAD/CAM packages.

62 Material Thickness (mm) Tool Ø (mm) Max. wall angle Al 3003-O Al 3003-O AA AA Ti Grade DC AISI Table 1: Common materials with their failure angles From the sine law formula it follows that the steeper the wall angle, the greater the thinning of the zone CB. In order to increase the maximum wall angle, one could increase the starting thickness (T AB ) of the sheet, as can be seen in the experiments reported in Table 1. This strategy has its limitations due to maximum machine load and overall part thickness specifications. Finally, the only way to obtain large wall angles is to aim for material redistribution by shifting material from other zones in the part to the inclined wall areas. Several authors have already reported on multi-pass forming. Consecutive toolpaths, corresponding to virtual parts with increasing wall angles, are being executed in a multi-step procedure. [5][6][7]. The aim of this paper is to further investigate the mechanics behind the multi-step forming approach to contribute to a better understanding of the material relocation mechanism underlying the enlarged process window. 3 EXPERIMENTAL EXPLORATION 3.1 Experimental Setup The experiments were performed on a three-axis milling machine with a horizontal spindle. This allowed in-process observation of the part being formed by means of a stereo camera setup and Digital Image Correlation (DIC). For each of the tests, a spherical tool with a diameter of 10mm was chosen with the feedrate set to 2m/min and the spindle speed fixed at 100 rotations/min. Oil was used as lubricant. The setup allowed to remove the part within its clamping rig from the machine without unclamping the part itself, allowing the part to remain clamped during consecutive manufacturing and measuring steps. 3.2 Comparison of the thickness distribution for single and multi-step formed parts For the first set of experiments, two cones with a 70 degree wall angle were manufactured. Both cones have an upper inner diameter of 178mm and a internal depth of 30mm. The diameter of the backing plate was 182mm. A single-step reference part was compared with a part formed with two intermediate steps at 50 and 60. The sheet material was Al3003-O with a thickness of 1.2mm. In Figure 2 the thickness profiles of both cones are plotted in function of the radius. As can be seen, the wall thickness of the multi-step cone is significantly larger than the thickness obtained with the singlestep toolpath. However, the thickness of the bottom of the multi-step part is lower than the thickness of the bottom of the single-step part. Using the multistep approach has clearly led to a shift of material from the bottom, which would otherwise have remained unprocessed, to the wall of the part. 3.3 Forming of a cylindrical part in 5 steps Fig. 2: Geometry and thickness in function of radius 3.3.a Test setup Aim of this experiment was to quantify the material flow during consecutive steps of forming. A cone was manufactured in 5 passes with a 10 increase in the wall angle between each step, starting from 50. The sheet material used for these tests was AA3103 with a thickness of 1.5mm. The workpiece had an upper diameter of 128mm and a programmed depth of 30mm. The diameter of the backing plate was 131mm, close to the part to eliminate most of the bending that is induced by multi-step forming. A 10mm diameter tool and a contouring toolpath were used with a stepdown of 1mm per contour.

63 Fig. 3: Thickness in function of radial dimension 3.3.b Experimental results In Figure 3 the measured thickness profiles of the cones in the different steps and the theoretical sine law thickness are plotted against the radial dimension. As can be seen, the thickness profile of the first step (50 ) determines the thickness profiles of the following steps. The part was close to failure near the bottom since the thickness of the 90 part is, at its thinnest point, lower than the failure thickness as predicted by the sine law for c Digital Image Correlation results To be able to track the material flow during the process, the outer surface of the cone was measured during forming with a Limess stereo camera setup. After processing this data with a Digital Image Correlation system (DIC), 36 points from the outer surface of the cone, defining a planar section of the outer surface, were selected and tracked during the forming process (see Figure 4). The thick curves represent the shape of the part at the end of each of the five consecutive forming steps. The thin curves visualise the trajectories of each of the observed points on the outer surface based on 2030 intermediate observations. As can be seen in Figure 4, the sine law is an acceptable approximation for the first step of the multi step approach: when forming the first, 50 cone, the points are translated quasi downwards. This corresponds to a very limited tangential strain. For the next steps, however, the sine law is no longer valid. Instead of a downward translation, the points are quasi rotated about the backing plate edge. The closer to the bottom of the part, the larger the horizontal distance between two consecutive step sections becomes and the more the rotational motion transforms into a downward translation. In contrast with single-step forming, where maximum thinning and failure typically occur 10 to 15mm below the backing plate level, the edge of the cone bottom is also the location where failure can be expected to occur first in a multi-step strategy. Fig. 4: DIC results Fig. 5: Simulated and measured profiles 3.3.d FE Simulation The same experiments were also simulated using Lagamine, a finite element code developed at the University of Liège [8]. The implicit time integration scheme was chosen here in combination with a second order shell element (COQJ4) [9]. The test part was modelled as a 45-degree segment with symmetry imposing boundary conditions at the edges. Even though the process itself is not rotationally symmetric, this approximation was found to provide useful results in the middle of the pie segment. The material model used was a Hill law with Swift-type isotropic hardening, for which the parameters were determined by means of a tensile and a Bauschinger shear test. The elastic parameters are E= MPa and ν= The yield locus is described using the Hill 1948 law with F= , G= , H= and = σ p n F = K( ε0 + ε ) Formula 2: Swift Law The hardening law is given by the Swift law (see Formula 2) with the following material parameters: K= 183 MPa, ε 0 = and n=

64 Fig. 9: Titanium cranial implant (right image courtesy of SimiCure) 5 CONCLUSIONS Fig. 6: Simulated material flow Figure 5 illustrates that the bottom of the workpiece is not as accurately predicted as the wall. The symmetry imposing boundary conditions introduce an error. It has already been shown in a previous article [10] that the bottom of a single-step cone could be predicted more accurately if the whole part was modelled. This deviation seems to accumulate when simulating a multi-step toolpath. The obtained wall geometry, the material flow (see Figure 6) and the simulated strains however correspond well with the experimentally obtained results. 4 CASE STUDIES A method for automatic multi-step toolpath generation was developed and successfully tested in a number of case studies. The part in Figure 7, a mould for composite pressure vessel production, has a vertical wall of 30 mm on top of which a hemisphere is modelled. Figure 8 illustrates that also for non-rotative geometries the multi-step approach remains applicable. The limits for achievable minimum radii between vertical walls are object of further research. Figure 9 shows an implant manufactured in 0.7 mm grade 2 titanium. A multistep toolpath made it possible to form angles up to 61 while respecting the thickness requirements. Fig. 7: Composite pressure vessel mould Fig. 8: Non-rotational part The extended process window achievable by means of multi-step SPIF can be explained by the straining of (semi-) horizontal workpiece areas that remain unaffected in conventional toolpath strategies. This allows to produce vertical walls without leading to part failure. The resulting thinning of the sheet during multi-step forming can exceed the maximum thickness reductions observed in single-step processing, implying a formability shift. The research shows a shift from a sine law like behaviour for the first step of the process to a more bending like behaviour for the following steps. REFERENCES 1. Jeswiet J., Micari F., Hirt G., Bramley A., Duflou J.R. and Allwood J., 2005, Asymmetric single point incremental forming of sheet metal. CIRP Annals - Manufacturing Technology, 54/2: Duflou J.R., Lauwers B., Verbert J., Tunckol Y., De Baerdemaeker H., 2005, Achievable Accuracy in Single Point Incremental Forming: Case Studies, Proc. of the 8th Esaform Conf. Vol. 2., pp Ham M., Jeswiet J., 2007, Forming Limit Curves in Single Point Incremental Forming, CIRP Annals- Manufacturing. Technology, 56/1: Matsubara S, 2001, A computer numerically controlled dieless incremental forming of a sheet metal, J. of Engineering Manufacture. 215/7: Young D. and Jeswiet J., 2004, Wall thickness variations in single-point incremental forming, J. of Engineering Manufacture, 18/11: Kim T.J., Yang D.Y., 2001, Improvement of formability for the incremental sheet metal forming process. Int. J. of Mech. Sciences, 42: Hirt G., Ames J., Bambach M, and Kopp R., 2003, Forming strategies and Process Modelling for C C Incremental Sheet Forming, CIRP Annals - Manufacturing Technology, V53/1, pp Cescotto S. and Grober H., 1985, Calibration and Application of an Elastic-Visco-Plastic Constitutive Equation for Steels in Hot-Rolling conditions, Engineering Computations, 2: Jetteur P. and Cescotto S., 1991, A Mixed Finite Element for the Analysis of Large Inelastic Strains, Int. J. for Numerical Methods in Eng., 31: He S., Van Bael A., Van Houtte P., Szekeres A., Duflou J.R., Henrard C. and Habraken A.M., 2005 Finite Element Modeling of Incremental Forming of Aluminum Sheets, Adv. Mat. Research, 6-8:

65 Comparing Two Robot Assisted Incremental Forming Methods: Incremental Forming by Pressing and Incremental Hammering L. Vihtonen 1, A. Puzik 2, T. Katajarinne 3 1 Helsinki University of Technology, BIT Research Centre, Po BOX 5500, FI TKK, Finland URL: lotta.vihtonen@tkk.fi 2 Fraunhofer Institute for Manufacturing Engineering and Automation IPA, Nobelstrasse 12, D Stuttgart, Germany URL: arnold.puzik@ipa.fraunhofer.de 3 Helsinki University of Technology, Laboratory of Processing and Heat Treatments of Materials, Po BOX 6200, FI TKK, Finland URL: tuomas.katajarinne@tkk.fi ABSTRACT: This paper explains and compares two different robot assisted incremental forming processes: robot assisted incremental forming by pressing and robot assisted incremental hammering. Both processes are based on robot assisted forming, but forming of the material is different. In this study, these two processes have been used to form the same test geometries. The deformed geometries have been compared and analysed. The measurements include material elongations, sheet thinning and sheet surface hardening. Key words: Incremental Forming, Industrial Robot, Incremental Hammering 1 INTRODUCTION In recent years new sheet metal forming processes have been developed and introduced to industry in order to increase the flexibility and meet the presentday challenge of manufacturing prototypes with flexible forming technologies, [1][2]. The trend in sheet metal forming industry is to manufacture more complex parts a and faster introduction of new and individual products in small lot series [3]. Incremental forming (ISF) is suitable for this kind of manufacturing and has great potential in flexible production. ISF is performed in several variations all over the world. The forming machinery varies from special incremental forming machines to milling machines and robot assisted forming. Typically the forming methods have been classified according to the number of contact points in the forming. There are two variations, that are presented in Figure 1, two point incremental forming (TPIF) and single point incremental forming (SPIF). Variations A and B describe the TPIF process, and variation C shows the SPIF process principle. In TPIF there are two contact points with the sheet: the tool and the supporting tool. In SPIF no support tools are needed. Most of the forming machinery can be used both for TPIF and SPIF processes, which creates a number of process variations. In literature all incremental sheet forming processes are considered as one, even if the conditions of the processes can be very different from each other. Figure 1. Incremental forming variations This paper concentrates on robot assisted incremental forming. It describes and compares the two different robot assisted incremental forming processes: robot assisted incremental sheet forming by pressing (RAIFP) and robot assisted incremental sheet forming by hammering (RAIFH). Both processes are based on robot assisted forming, but the way of deforming the material is different.

66 2 ROBOT ASSISTED INCREMENTAL FORMING PROCESSES 2.1 Robot assisted incremental forming by pressing RAIFP is patented by Tuominen [4] and further developed by Vihtonen et al [4]. In this method the material is deformed by pressing and sliding a forming tool on the surface of the blank, similarly to most of the incremental forming process variations. The forming equipment is shown in Figure 2. The forming method is based on a strong industrial robot, that is used to perform a TPIF process, i.e. to press the forming tool against the sheet metal along the predetermined forming path and thus forming the sheet metal into desired form. The parts are formed on the convex surface, while the blank holder descends as the forming proceeds. Also SPIF process is possible with this setup, by fixing the vertical movement of the table and changing the path generation mode. applications of concave forming, where support tools are not needed, or their need is smaller. In these applications the material tends to move to the bottom of the part and create a bump in the bottom. A support tool below the sheet blank is always required when forming on convex surface, regardless of the incremental forming method. Simple geometries can be formed using a simple support tool, such as a square bar, at the highest point of the part. With complicated geometries the support tools are met with higher demands, in some cases even a complete support. A support is always needed under the highest point of the part and under the edge of planar surfaces. If the edge is not supported, the metal bends unwantedly as the forming proceeds. Figure 3 Forming principle and a small forming table in RAIFP 2.2 Robot assisted incremental hammering Figure 2 Setup of RAIFP Tools used in forming are cylindrical poles with a polished spherical end with a diameter varying between 6 and 25 mm. In the pressing application the parts are formed from the convex surface, which makes the support tool necessary. There are also In RAIFH the deformation of sheet metal is caused by a hammer tool. The high-frequency oscillating hammer punches creates the deformation of the sheet metal. Similarly to RAIFP a strong robot is executing the movement with the interacting hammering tool above the clamped sheet metal (Figure 4). Contrary to RAIFP, RAIFH is working absolutely dieless. The sheet is clamped horizontally, with a fixed clamping fixture, and not supported beneath. By high-frequency hammering along the predetermined path the sheet metal deforms concavely to the designated shape. Additional convex details can be formed by turning the part and forming it from the reverse side. Thus combined concave and convex geometries depend on different forming strategies. If the geometry makes it necessary parts have to the rotated and formed in different forming steps. The hammering tool itself consists of an eccentric connecting rod which excites the vertical movement of the tool. In order to reach a high frequency and a stabilized system the eccentric punch of the hammer

67 is balanced by two mass rings, [5]. Since the forming tool executes hammer punches most of the deformation remains below the hammering tool because of the inertia of the sheet metal. The forces in direction of the moving path can also be reduced to a minimum. TPIF can also be used in RAIFH. In order to be able to form the largest variety of geometries and to meet the requirements to reduce tooling, and thus costs, research on SPIF is preferred.tpif was also tried out with RAIFH, but in order to be able to form the most possible combinations and varieties of geometries and to meet the requirements of the industry to reduce tooling supports and thus costs most research on SPIF was done. Table 1 shows the comparison of RAIFP and RAIFH in terms of the most important geometrical and process parameters related to this technology. Figure 4 Operating setup of RAIFH Table 1 Comparison of RAIFP and RAIFH processes Parameter RAIFP RAIFH Wall angle n depending on material Radii Working area Materials (forces) Programming Depending on material and total geometry, appr. r~2mm Machine dependent, not process limited Al 5mm Mild steel 3mm Stainless steel ~2mm Commercial CAD/CAM, Machine dependent control software Al 3mm Mild steel 2mm Stainless steel ~1mm Also other materials Commercial CAD/CAM, translator between CAM and the robot developed by IPA 3 STRAIN TESTS Two test geometries were formed with both forming methods, a circular cone with a upper diameter of 32mm (A) and a square cone with a upper side length of 40mm (D). They are shown in Figure 5. The geometries were formed with both methods, but on different side. RAIFP formed the convex surface of the parts and RAIFH formed the concave surface of the parts. The height of both geometries was 100mm, but the forming was stopped when the material fractured. A 0,75 mm thick deep drawing quality steel DC04 was used as a test material. All the sheets were marked with 2mm square grid for measuring the strains after the forming. The measurement was taken from the first sound square next to the fracture. 4 RESULTS Figure 5 The test geometries The true strains measured from test parts are presented in Figure 6 and Figure 7, each forming method in one chart. They show the known fact, that strains in ISF are significantly higher than in conventional forming. In addition to that, these results show that the robot assisted methods produce