simulation and modelling of single point incremental...

Proceedings of the 5th Manufacturing Engineering Society International Conference – Zaragoza – June 2013

Simulation and Modelling of Single Point Incremental Forming Processes within a Solidworks Environment

L.M. Gómez-López(1,3), V. Miguel(1,2), A. Martínez(2), J. Coello(1,2), A.Calatayud(1,2)

(1) Industrial Engineers School of Albacete, UCLM, Avda. España s/n 02006 Albacete, Spain, [email protected]. (2) Regional Development Institute, UCLM, Avda. España s/n 02006 Albacete, Spain (3) Industrial Development Institute, Albacete Science and Technology Park, Paseo de la Innovación 1, 02006 Albacete, Spain.

RESUMEN

Los procesos de conformado incremental de chapa en un punto (SPIF) han sido altamente desarrollados durante los últimos diez años debido a las múltiples ventajas que presentan, tal como su conocida configuración sin molde, mayor conformabilidad que la obtenida con el proceso convencional y su flexibilidad [1,2]. A pesar de esto, el proceso ha estado experimentalmente aplicado a aleaciones de materiales de no muy altas características mecánicas, como las aleaciones de aluminio. En este sentido hay múltiples variables que influyen y están relacionadas con parámetros tecnológicos como la conformabilidad del material y el fenómeno de fricción. Estos efectos no han sido suficientemente estudiados, especialmente en aplicaciones con acero. El presente trabajo es una parte de una extensa investigación futura e intenta evaluar a priori las tensiones y deformaciones existentes en la chapa y en la herramienta durante el proceso de conformado incremental de chapa de acero DC-05 en un punto. Un entorno de Solidworks ha sido creado para hacer simulaciones de este proceso por el método de los elementos finitos (MEF).

Palabras clave: SPIF, Solidworks, acero DC-05, simulación por elementos finitos, curva de Hollomon.

ABSTRACT

Single Point Incremental Forming (SPIF) process has been largely developed for the last ten years due to the multiple advantages that presents as its well known dieless configuration, the larger conformability that can be obtained with it and its flexibility [1,2]. In spite of that, the process has been experimentally applied to soft-fluent alloys, like aluminium alloys. Herein there are multiple variables taking part and related to the technological parameters, the material conformability and the friction phenomena. These effects have not been sufficiently studied, especially at steel applications. The present work is a part of a future extended research and tries to evaluate in advance the stresses and strains existing in the sheet and in the tool during SPIF of DC-05 steel. A Solidworks® environment has been created to do a FEM Simulation of this process.

Keywords: SPIF; Solidworks; DC-05 steel sheet; FEM Simulation; Hollomon curve

1. Introduction.

In previous works, other FEM Simulation software can be seen instead of Solidworks ® like Abaqus® [2, 3] or LS-Dyna [4-6] to CAE processes. There are also some works in which Solidworks® software is used for CAD-CAM stages while specific FEM software is used to the CAE phase, like Abaqus or LS-Dyna. H. Meier et al [7] uses Solidworks® for the design stage (CAD) while SolidCAM, a specific module of Solidworks® is used for the tool path generation stage (CAM) and LS-Dyna software for the analysis stage (CAE).

Therefore, the Solidworks® software never or hardly ever has been used for doing FEM simulation of Single Point Incremental Forming (SPIF) processes.

Nowadays, the Solidworks® software is being increasingly used to mechanical design and tool path generation. In the last years, Solidworks® has improved its FEM simulation module formerly named


Cosmosworks, thereby doing a good FEM simulation applied to Single Point Incremental Forming (SPIF) processes is possible.

In this work, the whole Single Point Incremental Forming (SPIF) process (CAD-CAM-CAE) is integrated in the Solidworks® software. Therefore, the design, tool path generation and analysis stages of Single Point Incremental Forming can be done in the same system, so the compatibility is guaranteed. In addition, the Solidworks Simulation module has a more friendly environment than others specific CAE software, thereby it can be used by people who are not expert in finite element method.

Now, the FEM Solidworks® module is named Solidworks Simulation® and there are some sub modules in it that can be selected depending on the system characteristics to be simulated. So, it is possible carry out different studies like static, dynamic, linear, non-linear, frequency response, thermal, buckling, pressurized tanks, fatigue and freefall.

In the case of Incremental Sheet Forming processes, the material reaches the plastic deformation and thus, the non linear zone of its Stress-Strain curve. Moreover, the force application point by the tool against the sheet changes along the time. Due to these reasons, the dynamic non linear Solidworks® module is used to do the FEM Simulation.

The goal of this paper is to do FEM simulations of a Single Point Incremental Forming (SPIF) process with Solidworks®.

2. Solidworks® Environment for Computer Aided Engineering (CAE) and FEM Simulations.

At the present time, there is a great variety of software to analyze and simulate real engineering problems that are well known under the term, Computer Aided Engineering (CAE). The stress and strains distribution of the system can be obtained using this kind of software. Solidworks® Simulation is the Solidworks® module that solves these problems through the application of Finite Elements Method (FEM).

It is well known that FEM consists of a numerical technique to find approximate solutions to partial differential equations of a system. Then, the system is divided into many subsystems producing a mesh. These subsystems are called finite elements; every finite element has a determined number of nodes in which a partial differential equation is solved.

The Single Point Incremental Forming process was simulated in Solidworks ® Simulation. The simulation consisted of a hemispherical tool that deformed a DC-05 steel sheet. The tool describes a pyramidal with squared base path. All the degrees of freedom are constrained in the sheet edges imitating, in this way, an experimental blankholder effect. The blankholder, the DC-05 steel sheet and the hemispherical tool design were created in Solidworks® CAD module.

This scenario was reproduced in Solidworks® Simulation and a dynamic and non linear study was opened. The following steps were developed to carry out the FEM Simulation:

Applying the materials of the different parts with the definition of the material properties and the material behaviour model.

Definition of the contacts between the different parts involved in the process.

Establishing the parts constraints or boundary conditions like degrees of freedom and displacements.

Applying the external loads to the system (not in this case).

To create and define the mesh for finite elements method.

Configuration of the simulation parameters and running it.

Results collection and interpretation.

The material for the hemispherical tool was AISI 420 steel whereas the material for the sheet was DC-05 steel. For them, the mechanical properties and chemical composition are shown in Tables 1 and 2, respectively.


Table 1. Material properties of the Tool and Sheet involved in SPIF simulation

Parameter AISI 420 Steel DC-05 Steel

Elasticity Modulus 2.1 e5 (MPa) 20,284.45 (MPa)

Poisson Coefficient 0.28 0.28

Shear modulus 7.9 e4 (MPa) 7,924 (MPa)

Mass density 7,740 (kg/m3) 7,850 (kg/m3)

Ultimate tensile strength 1,500 (MPa) 308.54 (MPa)

Yield 1,200 (MPa) 149.67 (MPa)

True strain at yield point - 0.007

Hardening factor - 0.348

Reference Rule AISI UNE-EN-ISO

Material Model Linear elastic

isotropic Von Mises -

Plasticity

Table 2. Chemical composition of the materials.

Material % C S Cr Mn Ni P Si

DC-05 < 0.1 < 0.02 0.08 0.12 0.014 --- ---

AISI 420 0.37 0.03 13.56 0.75 --- 0.04 0.36

In the case of DC-05 steel sheet the yield stress is exceeded, thereby the plastic deformation happens. In this way, the material behaviour reaches the plasticity zone and the Von Misses model must be used.

The experimental stress – true strain curve had to be previously obtained for being introduced to the software. This curve is usually introduced through a table format but Solidworks has a limitation about it and a table with more than 5,000 points cannot be introduced. Even, although Solidworks® only needs the points of the curve of the plastic field, this part had more than 5,000 points and thus, the curve was approximated by the Hollomon function.

The Hollomon curve is a power regression between true stress, σ, and true strain, ℰ, as indicated in Eq. (1) where the coefficients k and n are constants.

nkσ ε= ⋅ [1]

Figure 1 depicts the true stress – true strain curve that was introduced in the software. As it is said previously, only the points after yield point were introduced. In Eq. (2) the Hollomon curve is written. This expression was obtained with a regression coefficient value, R2, of 0.9996.

0.348597.6σ ε= ⋅ [2]

Figure1. Stress-strain curve for DC-05 steel sheet.


The hemispherical tool was defined as rigid body for the simulation, whereas the sheet as deformable body.

The contact between the hemispherical tool and steel sheet was simulated selecting the node to surface option, without considering any penetration and under no friction condition.

Two types of constraints were defined related to the clamping sheet and the tool displacements. The clamping sheet simulates the effect of the blankholder on the sheet; this restriction consists of blocking all degrees of freedom up to 15 mm from the sheet edges. In this way the rotations and displacements were not allowed near the sheet borders. Another constraint is the tool displacements; thereby a pyramidal path along the time must be introduced in the software by a table in which the time, t, and X, Y, Z tool positions appear.

Then, external loads have not to be introduced in the simulation because the forces are generated as a consequence of the restrictions and of the deformation work.

The mesh was defined with the following parameters: solid and quadratic high level elements, minimum element size 1.43 mm, maximum element size 4.3 mm, 10,288 elements, 20,685 nodes and 45.69 degrees of freedom.

In Figure 2 the mesh of the system and the constraints of the steel sheet and the tool can be seen. The arrows placed near the sheet edge, depict the clamping sheet. On the other hand, the arrows placed on the forming tool establish the X, Y and Z axis displacements. Apart from, the shape and dimensions of the mesh elements are showed. As smaller the elements are the more accurate system solution and longer computation time is obtained.

Figure 2. Mesh and constraints definition.

Large displacements and large deformations options were chosen for the simulation parameters. These options involve non linear geometry. The solver used was ‘Direct Sparse’ that it is recommended for systems with less than 100,000 degrees of freedom.

The collected results were stresses, displacements and strains along the sheet and the tip tool. Moreover, it is possible to know the forces in each node of the mesh.

3. Simulation Parameters and Methodology.

There are some parameters that must be defined for FEM simulation and the experimental tests. These parameters are the forming paths, tool shape, dimensions, spindle speed, feed rate and steel sheet thickness.

The simulation aim is to form a squared base pyramid by single point incremental forming process; thereby the tool pushes on the steel sheet describing squares at different depths. The tool starts at a specific depth describing a square with a side of determined length; at the second step the tool goes inward and downward from the previous path and so on until the pyramid top is reached. The path, steel sheet and the definition of the tool parameters can be seen in the Figure 4.


Figure 3. Simulation XZ section. Tool path parameters.

As it is indicated in Figure 3, L is the side length of the first square, Lc is the constrained length of the sheet, Lf is the length between the fix region tool path, Pxy is the length difference between a square and its previous square in X and Y axes;, Pz is the same as Pxy but in Z axis, e is the steel sheet thickness, Rt is the tool radius, St is the tool spindle speed, Ft is the tool feed rate, Cf is the friction coefficient at the tool tip. Tool spindle speed, St, and friction coefficient, Cf, were not considered at this first study. In a previous work [8], the friction coefficient behaviour for the steel experimented here was determined. According to that one, the coefficient of friction, Cf, in lubrication conditions is considered to be between 0.05 and 0.08. Authors assume that friction forces can be neglected in a first approximation if taking into account the aims of the present analysis. Logically friction forces will be included in later works. In addition, the time parameters must be defined too; ts is the step time, tr is the real time and tc is the computation time. The computation time obviously depends on PC characteristics. The mesh node number, nn, is also taken into account for the simulation. The selected values for these parameters can be seen in Table 3.

The FEM simulation was done in three steps:

1. The first side of the pyramid base; in this phase the tool goes to a pyramid corner, goes down along Z axis up to -2 mm and goes 90 mm along X axis.

2. The first square of the pyramid; in this phase the tool goes to a pyramid corner, goes down along Z axis up to -2 mm and repeats the first phase four times creating the first square; that is, the pyramid base.

3. The complete pyramid; the tool goes inward and downward repeating the second phase to arrive to the pyramid top. After the tool completes the first round, it goes inward the Pxy value and downward the Pz value and so until the top of the pyramid is reached.

Table 3. Simulation parameter values.

Parameter Phase 1 Phase 2 Phase 3

L 102 mm 102 mm 102 mm

Lc 15 mm 15 mm 15 mm

Lf 14.8 mm 14.8 mm 14.8 mm

Pxy - - 15 mm

Pz - - 2 mm

e 0.8 mm 0.8 mm 0.8 mm

Rt 6 mm 6 mm 6 mm

St - - -

Ft XY: 1 mm/s XY: 1 mm/s XY: 1 mm/s

Z: 0.5 mm/s Z: 0.5 mm/s Z: 0.5 mm/s

Cf - - -

nn 20,685 20,685 20,685

ts 0.25 s 0.25 s 0.25 s

tr 86 s 332 s 689 s

tc 2 h : 20’: 28’’ 9 h : 19’: 51’’ 19 h: 22’: 28’’


4. Experimental Procedure.

An instrumented blankholder is being built to experiment SPIF with different materials. One design has been carried out for measuring the forces that acts on the sheet and on the tool during the process. Based on this design, the sheet constraints were design for the simulation, Figure 4.

Figure 4. A blankholder to establish the sheet constraints and for monitoring SPIF modelled in Solidworks CAD module.

Once the blankholder was built completely, it will be coupled in a CNC milling machine for doing the Single Point Incremental Forming processes. The tool paths will be designed in Solidcam, which is a well known Solidworks® module, for creating and post processing the forming paths. The forming paths will be the same as those having simulated. In this manner, the CNC milling machine will be programmed for doing the process, what is called the CAM stage.

Anyway, the herein obtained results will be compared to those experimentally found by other authors [2, 4].

5. Simulation and Experimental Results.

Once the simulations were executed, the results were available. The stresses, displacements and strains at the steel sheet were registered during the simulation. On the other hand, the forces could be obtained at any node or at specific vertex, line or face for each simulation step time. The Solidworks® provides the results by graphics with different colours. These colours are related to the value of the parameter that is being considered.

The obtained stress simulation results can be seen in Figure 5. At this time, the tool is pushing at the top of the pyramid and the zones whose stress values are above 149.67 MPa exceeds the yield point. Those zones reach the plastic deformation at this time and will not recover its original shape. The maximum stress value is about 258 MPa at the pyramid top.

A stress versus time graphic was obtained at some nodes of the system. Figure 6 depicts stress-time registers for the three nodes indicated in Figure 5. The forces were collected when the tool was at the top of the pyramid and the resultant force value at the middle of the line 1, Figure 5, was 3,234.20 N. The corresponding values of the X, Y and Z components for that force are 9.76 N, 3,067.90 N and 1,023.60 N, respectively. This analysis was carried out in the steel sheet sides to contrast the results in a future experimental work in which load cells are foreseen to fix on each line similar to line 1.

The analysis of the stress results leads to state that the greatest stresses appear when the tool is pushing the steel up to greatest Z coordinate; that is, at the top of the pyramid as it was expected. The nodes with the maximum stresses are on the bottom plane of the sheet when the tool is passing on the front face, like, for example at node 3. At the regions near to forming tool in the front side of the sheet the stresses takes large values too, although not as much as on the back side. For this reason the node 3 reaches a higher value than node 2. Apart from that, the node 1 has several stress peaks, neither of them greater than node 2 or 3.


Figure 5. Stress simulation results. Front and rear sheet side.

Figure 6. Stress evolution versus the time at some nodes.

The displacements and strains were also studied. In this way, Figures 7 & 8 depict a diagram of them once the forming tool has separated from the sheet. It can be seen that the sheet does not take the staggered pyramid shape, probably because of the springback effect that appears in the process. Effectively, the springback phenomenon is clearly observed if the final displacement of the sheet and the tool path in Z axis are compared. The final displacement is shorter than the Z tool path and then, a elastic recovery is supposed to take place. Relating to strains, and as a first approximation, according to the strain-stress curve for the sheet, values up to 0.007 corresponds to a level of stresses below yield point and so, the material deformation will tend to be recovered. Strain values above 0.007 lead to plastic deformation according to the power shape of the Hollomon´s function, Figure 2.

The herein obtained results agree with experimental data existing in literature [2, 4] if differences of planning works are considered.

Figure 7. Displacement results.

Node 3 Node 1 Line 1

Node 2


Figure 8. True strain results.

6. Conclusions.

A methodology to simulate SPIF into the Solidworks® has been successfully devised and it has been demonstrated that this environment can be employed for a correct definition of the process variables and the material properties, especially for plastic behaviour.

The results herein obtained show that the stress values are not large and that the achieved strain should be greater from the forming goal viewpoint of Incremental Sheet Forming Processes. For this reason, the tool path should be suitably modified, increasing the Z coordinate. Anyway, the agreement of the simulation results with the experimental ones existing in literature predicts that the technique herein presented will lead to a good evaluation of the process.

Another consideration that should be taken into account in future is the friction phenomenon. The expectations that the authors have in this context are high.

7. Acknowledgements.

This work has been conducted thanks to the National Research Plan’s financial support promoted by the Spanish Ministry of Science and Innovation: Project MAT2009-13877 (the MAT subprogramme).

8. References.

[1] W.C. Emmens, G. Sebastiani, A.H. van den Boogaard. The technology of Incremental Sheet Forming. A brief review of the history. Journal of Materials Processing Technology, 210 (2010), pp. 981–997.

[2] J. Jeswiet, F. Micari, G. Hirt, A. Bramley, J. Duflou, J. Allwood, Asymmetric Single Point Incremental Forming of Sheet Metal, CIRP Annals - Manufacturing Technology, 54-2 (2005), pp. 88-114.

[3] Zemin Fu, Jianhua Mo, Lin Chen, Wei Chen, Using genetic algorithm-back propagation neural network prediction and finite-element model simulation to optimize the process of multiple-step incremental air-bending forming of sheet metal, Materials and Design, 31 (2010), pp. 267–277.

[4] Minoru Yamashita, Manabu Gotoh, Shin-Ya Atsumi, Numerical simulation of incremental forming of sheet metal, Journal of Materials Processing Technology, 199 (2008), pp. 163–172.

[5] B. Taleb Araghi, G.L. Manco, M. Bambach, G. Hirt, Investigation into a new hybrid forming process: Incremental sheet forming combined with stretch forming, CIRP Annals - Manufacturing Technology, 58 (2009), pp. 225–228.

[6] S. Thibaud, R. Ben Hmida, F. Richard, P. Malécot, A fully parametric toolbox for the simulation of single point incremental sheet forming process: Numerical feasibility and experimental validation. Simulation Modelling Practice and Theory, 29 (2012), pp. 32–43.

[7] H. Meier, J. Zhu, B. Buff, R. Laurischkat, CAx Process Chain for Two Robots Based Incremental Sheet Metal Forming. Procedia CIRP 3 (2012), pp. 37 – 42.

[8] V. Miguel, J. Coello, M. C. Manjabacas, A. Calatayud, C. Ferrer and A. Martínez. Electrogalvanized Low Carbon Steel Adhesion Tendency in Friction Processes Under Mixed Lubrication Regime. Journal of Tribology 133 (1) (2010), pp. 1-9.

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