Experimental and numerical investigation of a short, thin-walled steel tube incremental forming process

Journal of Manufacturing Processes 19 (2015) 59–66

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Technical Paper

Experimental and numerical investigation of a short, thin-walled steel tube incremental forming process J. Raujol-Veillé 1 , F. Toussaint ∗ , L. Tabourot, M. Vautrot, P. Balland Univ. Savoie Mont Blanc, Symme, F-74000 Annecy, France

a r t i c l e

i n f o

Article history: Received 21 October 2014 Received in revised form 11 March 2015 Accepted 27 March 2015 Keywords: Numerical simulation Forming process Springback study Steel

a b s t r a c t This paper concerns the forming of a short, thin-walled steel tube by means of an innovative incremental forming process close to spinning. Material characterization necessary for model calibration was carried out through tensile tests at different angles with respect to the rolling direction and simple shear tests. These data were used to identify material parameters of suitable behavior law taking into account the Baushinger effect but neglecting anisotropy. Thus, two different models were built in order to virtually reproduce the forming process. The obtained results are compared amongst themselves but also with experimental data coming from an industrial partner. It has been highlighted that the multidimensional model gives a good representation of the forming process both in terms of part geometry and applied load on tooling. The two-dimensional model is advantageous to predict qualitatively only part geometry with short CPU time. Special attention is paid to springback that occurs as a function of the studied part geometry. © 2015 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

1. Introduction Incremental forming has been used for a number of forming processes such as Single Point Incremental Forming (SPIF), Two Point Incremental Forming (TPIF), shear forming, flow forming and spinning. The reviews of the technique in use were presented by many authors [1–3]. The technique of spinning consists in clamping a metal blank on a spinning lathe and gradually forming the metal sheet onto the mandrel surface by a roller. From this point of view this technique is comparable to the process studied in this paper. There is a large number of components which can be produced by this way including art objects, musical instruments, kitchenware but also wheel discs, rims, clutch drums for automotive industry and for which manufacturing methodologies are described [4–7]. Finite element analysis (FEA) of spinning is used in order to calculate geometry of parts, loading applied on tooling, stresses and strains and to predict failures which is of great interest for industrialists when manufacturing a new part is expected. There are mainly two points which justify why further modeling conducted

∗ Corresponding author. Tel.: +33 0450 096 576; fax: +33 0450 096 543. E-mail address: [email protected] (F. Toussaint). URL: http://www.symme.univ-savoie.fr (F. Toussaint). 1 Present address: Laboratoire Brestois de Mécanique et des Systèmes – EA 4325, ENSTA Bretagne/Université de Brest/ENI de Brest, 2, rue Franc¸ois Verny, F-29806 Brest Cedex 9, France.

in this area is needed: computation time reduction and improvement of results accuracy in order to give qualitative rather than quantitative prediction. Either if three-dimensional models supplant two-dimensional-models with the increase of computational power, the difficulty lies always in finding the best compromise between scheme and time of integration, size and number of elements [8–12]. In the present study, a mixed experimental and numerical investigation of a short, thin-walled steel tube incremental forming process is proposed. The studied part is more precisely an inner race of automotive suspension thrust rolling bearing as shown in Fig. 1(a). The challenge is to replace the current manufacturing process (Fig. 1(b)) in order to minimize waste of raw material and to increase the mechanical properties of the parts. The paper begins by a presentation of material and forming process. The mechanical behaviour and model calibration are the subject of the second section. In the third one, two numerical models (a 3D and a 2D axisymmetrical models) are proposed in order to simulate the forming. In the fourth section, firstly a numerical comparison is performed between the two models. Secondly, an experimental/numerical comparison is carried out with the 3D model and measurements coming from a part manufactured by our industrial partner and the results are discussed. Then, a numerical comparison between models which used two different die geometries is carried out in order to see the springback effect during this process. Finally, conclusions of this study are drawn.

http://dx.doi.org/10.1016/j.jmapro.2015.03.008 1526-6125/© 2015 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

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Fig. 1. (a) Suspension thrust rolling bearing device, (b) current manufacturing process of an inner race.

Table 1 Chemical composition of studied material. Grade

DC03

3. Mechanical behaviour and model calibration

Chemical composition (wt%) Al

C

Mn

P

S

Si

0.052

0.035

0.202

0.013

0.012

0.003

2. Material and forming process The studied material is a low alloyed steel grade DC03 supplied in the form of 1.5 mm thick rolled coil. Well-known for its good formability by bending or stamping and widely used for the manufacturing of parts for the automotive industry, the chemical composition of the studied grade is given in Table 1. The main sequences leading to a ferrule and then to a manufactured part are presented in Fig. 2. First, a metal band is cut in the steel sheet in the rolling direction (RD). Rolling and welding by a flash butt welding process are then applied in order to form a ferrule. In comparison with the initial process (Fig. 1(b)), this technique allows to minimize wasted raw material and to align rolling grain flow with the circumferential direction of the ferrule increasing mechanical part properties. After these operations, the material is annealed for 60 min at 600 ◦ C. The final forming process consists in spinning the ferrule on a die using a roller. During the last step, the manufacturing process is carried out at ambient temperature. Thereafter, we focus exclusively on this last step for which it is important to distinguish from a kinematic point of view: (i) the part mounted in the chuck of a lathe and therefore subjected to rotation at constant speed N, (ii) the roller forming the part, moving in a rectilinear path at constant speed v. This roller is tilted at an angle ˛ to the die axis. It is also fixed to a Kistler force plate which is used to record forces acting on the roller during the forming process. These data will then be compared with the numerical calculations.

Several tests were performed to determine material behaviour. These tests were done on an INSTRON 5569 testing machine using Digital Image Correlation (DIC) method for calculation of displacement fields with 7D software [13]. A first series of tests was carried out at various angles varying from 0◦ to 90◦ with respect to the rolling direction (RD) in order to determine the plastic anisotropy ratios. Secondly, tensile tests for different strain rates were also done in order to highlight material strain rate sensitivity. Based on the results of these tests [14], it has been decided to neglect both effects in favour of kinematic hardening. In order to study the elastic behaviour of the material, other uniaxial tensile tests were also performed. In that case, to obtain an accurate measurement of the strain during the elastic loading, an INSTRON 2620-604 axial extensometer was used. Successive loading–unloading cycles were applied on a DC03 sample in order to obtain a statistical measurement of Young’s modulus. The average value of E is determined by linear regression in the elastic area. The lower limit of data used in the linear regression corresponds to 20% of the yield stress to avoid the nonlinearity at the beginning of the test and the upper limit to 80% of the yield stress to avoid microplasticity. According to this method, the average Young’s modulus is E = 208 GPa and standard deviation is 1.093 GPa. Poisson’s ratio ( = 0.3) and density ( = 7800 kg/m3 ) are data from the literature. During the process, due to the repeated passage of the roller on the ferrule, the material is stressed by loading–unloading elastic plastic cycles. As it is crucial that the experimental characterization make use of loading conditions corresponding to those imposed by the forming process, an experimental set-up for shear testing from LIMATB laboratory – France (Fig. 3) was used. Both monotonic and cyclic tests were performed for different angular deviations  ranging from 0.1 to 0.3. During the test, visible images of the samples (useful area 50 mm × 4 mm) were recorded for correlation with a high-speed camera of 1280 × 1024 pixels image resolution fitted with a 50 mm Schelder lens. The focal plane

Fig. 2. Main sequences for part manufacturing.

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61

Table 2 Plasticity parameters identified by the inverse method for DC03. Q (MPa)

b

Qx (MPa)

bx

0

1 (%)

245

10.78

138.2

5.6

192

2.7

where  0 is the yield stress, s is the deviatoric part of the Cauchy stress tensor  so that s =  − (1/3)Tr() I, R is the hardening law of the steel under consideration and X is a second-order tensor which describes kinematic hardening. The evolution of X is as follows: p X˙ = Qx ε˙ − bx X p˙

Fig. 3. Experimental device using DIC method.

of the camera lens was located at 450 mm from the surface of the sample. To apply the DIC method, the samples were painted with white paint and speckled with black paint and primary colors. The device was fitted on an Instron 8803 testing machine in order to ensure load recording during the test. Fig. 4 shows the experimental stress–strain curves coming from monotonic and cyclic shear tests. The monotonic curve displays an elastic behaviour (zone (1)), followed by a plateau (zone (2)) where Lüders bands appear, then the material hardening (zone (4)). These results were used in order to describe material behaviour in the finite element model taking into account the Bauschinger effect. The isotropic hardening behaviour of the model defining the evolution of the yield surface size as a function of the equivalent plastic strain is: R = Q [1 − exp(−b(p − 1 ))]

(1)

where Q represents the maximum change of the yield surface size, b defines the growth rate of the yield surface and p the accumulated plastic strain. When the material is formed, a plateau appears behind the elastic zone due to propagation of Lüders bands. From a phenomenological point of view, this phenomenon is not easy to simulate. A simplified approach has been chosen. Here, we introduce a deformation parameter 1 playing the role of an empirical coefficient. The kinematic contribution is non-linear and of the Armstrong and Frederick type. The pressure-independent yield surface is defined by the function



(, X, R) =

250 200

Stress τ (MPa)

150

3 (s − X) : (s − X) − 0 − R 2

Monotonic shear test (γ ≈ 0,4) Cyclic shear test (γ ≈ 0,1) Cyclic shear test (γ ≈ 0,2) Cyclic shear test (γ ≈ 0,3)

(2)

3 2

100 1

(3)

where bx represents the hardening saturation rate, Qx is the satup ration value and ε˙ the plastic strain rate tensor. Based on previous experimental data, an inverse identification method was used to determine all material parameters [15,16]. In the present case, the obtained parameter values are given in Table 2 4. Finite element analysis The aim of finite element analysis is to provide results to industrialists that fit with real processes. In an industrial context, the best model is found when the quality of the results versus cost ratio is high. In order to achieve this goal, two finite element models were developed in ABAQUS/Standard finite element code. For both models, the short tube is considered as a deformable solid with the behavioural model described in Section 3. The roller and the die (tools) are considered as analytical rigid bodies. The geometries of the different parts are given by our industrial partner. 4.1. The 3 dimensional model The 3D model built in ABAQUS does not use the same kinematics as that of the real process presented in Fig. 2. Based on the previous works of Davey et al. [17] but also Wong et al. [18] which stated that rotating the workpiece in the FE analysis tends to result in volume change and increases the computational times, the initial kinematics of incremental forming process, which is a translation of a tool combined to a rotation of the part, is reversed into a turning tool relative to a fixed part. By these means the projection of the nodes at each increment is avoided and consequently the computer time is reduced. So, the roller moves in a rectilinear path and with a double rotation. This double motion is characterized by the free rotation of the roller about its axis and repeats the rotary motion of the die. The kinematics of the roller is monitored with connectors under ABAQUS/Standard. Connectors ensure the connections between two master points. Therefore, each connector has its own degrees of freedom and the kinematic conditions can be applied in the non-constrained directions. Fig. 5 shows a schematic representation of the connectors used to apply the boundary conditions on the roller.

50 0 −50 −100 −150 −200 −250 −0,5

−0.4

−0.3

−0.2

−0.1

0

Strain γ

0.1

0.2

0.3

0.4

Fig. 4. Experimental stress–strain curves obtained by monotonic and cyclic shear tests.

Fig. 5. Schematic representation of the connectors used to impose the boundary conditions on the roller. Representation of the embedded surface of the short-tube (yellow). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Table 3 Boundary conditions of the incremental forming process. Point A: U

Point A: URy

C1: Vz

C2: UR

0

ω

v

0 if = 0, ∅ if not

Fig. 6. Part mesh with solid hexahedral 3D elements, four layers and (1/8) portion refined.

In the present case, two connectors are used. The connectors are represented by bold dotted lines, and their degrees of freedom are designated with arrows. Connector C1 which connects point A (located on the axis of the part) to point B (located on the axis of the roller) allows a translation. Connector C2 which links point B to the reference point of roller C (also located on the roller axis and ensuring the roller motion) allows the part to rotate. The boundary conditions of point A, the degree of freedom of connector C1 and the degree of freedom of connector C2 for the incremental forming process are summarised in Table 3. The ferrule is partially embedded in the die. The yellow inner surface of the chuck shows this embedment (Fig. 5). The contact between the short tube and the tools (roller and chuck) is processed by a penalty method and integrates friction via a constant coefficient of a Coulomb type law. These are the parameters which are used the most in simulating small surface contact processes [19,20]. Previous investigations [21] were done to determine the friction coefficient and an adapted mesh. Results show that the friction coefficient does not have an influence on calculations. So, the rotation of the roller about its axis of revolution is blocked. The part mesh is done using solid hexahedral 3D elements (C3D8) with trilinear interpolation, full integration and 4 layers. A representation of the short tube mesh is given in Fig. 6. Only (1/8) of this part is refined to reduce the CPU time. Therefore, the numerical profile and load applied on the roller are calculated in the refined section. 4.2. The 2 dimensional model Calculations of the 3D model are relatively time consuming since it takes about 3 days on 8-core processor2 . In order to reduce this calculation time, a 2D axisymmetrical model was built. To simulate the ferrule forming, the roller is replaced by a ring having an increasing diameter during calculation. To compare the 3D and 2D simulations, the element in the 2D and 3D models section of the deformed part are of equal number. The part is meshed with axisymmetric elements CAX4. Fig. 7 shows the axisymmetrical 2D model.

Fig. 7. 2D axisymmetrical model.

A good correlation is observed between the two profiles. However, the part curvature change is not predicted by the 2D model and a maximum difference of 120 ␮m is calculated. Moreover, the external diameter of the part predicted by the 2D model is underestimated in comparison with the 3D model, the difference being about 200 ␮m. Indeed, the kinematics of the axisymmetrical 2D model cannot calculate the deformation path during the process. The springback occurs at the end of the 2D simulation. The boundary conditions highly stressed the material and can be compared with a stamping process. Contrarily, during the studied process, contact is local and the elements in contact with the roller change all the time. The springback occurs throughout the process and not only at the end. This explains the difference between the two simulation profiles. Fig. 9 highlights the predicted accumulated plastic t p deformation p = 0 ˙ dt coming from 2D and 3D calculations. Zone 1 in Fig. 9 shows the area of the part where the roller was in contact with the inner surface of the part. In this area, the maximum accumulated plastic deformation of the 3D model is greater than the 2D model. This difference is due to the fact that there is cyclic loading–unloading imposed by the passage of roller. The same comparison was done to compare equivalent stress  eq (Fig. 10). Calculated equivalent stress coming from 3D analysis is higher than the 2D analysis. The difference between the two simulations is highlighted when the field of  11 is studied (Fig. 11). Indeed, the  11 stress calculated by 2D simulation is positive and becomes negative on the face where the roller is going to deform the part. Contrarily, the  11 stress calculated by 3D analysis is negative and becomes positive and is equal to zero around the neutral axis.

120 μm 200 μm

3D 5. Results and discussion 5.1. Comparison of the two models In order to choose the best model to simulate an industrial case, the results of the axisymmetrical 2D and 3D calculations are compared with experimental measurements. Fig. 8 shows the calculated outline for the two finite element analyses.

2 Calculations were done on a 2 Intel© Xeon© CPUs E5520 machine, 2.27 GHz frequency and 24 GB of memory.

2D

y

X Fig. 8. Comparison between the numerical axisymmetrical bidimensional and tridimensional profiles.

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63

p

y

X

Fig. 9. Accumulated plastic deformation field p coming from both 2D and 3D calculations.

σeq

MPa 526 469 412 355 297

y

240 183 126

X

11

3D

2D

68

Fig. 10. Equivalent stress field  eq coming from 2D and 3D simulations.

σ 11

MPa 304 227 151 75 -1

y

-77 -153 -230

X

2D

3D

-306 -382

Fig. 11. Stress field  11 coming from the 2D and 3D simulations.

The localized and repeated deformation generates, as the number of turns increases, a tensile stress accumulation on the inner surface and a compressive stress on the outer surface of the part. Fig. 12 shows the stress field of  11 coming from the 3D simulation during the roller passage. Three zones are highlighted: • zone (1), after roller path, • zone (2), under the roller, • zone (4), before roller path, During the passage of roller, the outer surface in front of it (zone (4)) is compressed. Then, under the roller (zone (2)), there is tensile stress and finally behind the passage of roller (zone (1)), the outer

surface is already compressed. Compression stresses in front of the roller path are lower than behind it. For each part rotation, there is a compressive stress accumulation due to the particular kinematic process. This comparison shows that the 2D axisymmetrical model is able to calculate qualitatively the geometry of the part. It could be highly advantageous when trends of part geometry with short CPU time are expected. 5.2. Comparison of calculations and measurements In order to compare the FEA results with the measurements, several parts were formed with the test equipment presented in Fig. 13.

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Fig. 12. Stress field  11 coming from the 3D calculations during the roller passage.

−27

3 −28

2

Y (mm)

−29

1

−30 −31

1 Fig. 13. Picture of test equipment used for part forming.

Table 4 Lower and upper value of process parameters.

−33 −34 −40

Experimental Simulation −38

−36

−34

−32

Z (mm) Fig. 14. Both experimental and calculated outline of the studied part.

geometry more accurately. At last, as shown in Fig. 16, the strain rate field is not homogeneous in the part and can reach high values (ε˙ = 1 × 102 s−1 ) at the contact between the roller and the part. However, tests have been conducted for strain rates really lower than the process rates. For a given strain, to take into account this sensitivity by the behaviour model will allow us to predict a higher stress level [24].

2500

Experimental Simulation 2000

Reaction force R (N)

A CNC lathe was used in order to control with accuracy the kinematic of tooling (previously detailed in paragraph 2). A significant series of tests was carried out varying process parameters such as operating speed N, angle of tilt ˛, speed v of roller. Table 4 gives the upper and lower value of these parameters. The following results are given for N = 500 rpm, v = 8 mm/s, ˛ = 4◦ , D = 77.65 mm, e = 1.5 mm and l = 10.7 mm. After the deformation, the part outline was measured using a profilometer. Observed differences between the two results are determined and error sources are discussed. Fig. 14 shows the comparison between the measurements and the calculated results. A strong likeness is observed in zones (1) and (2). However, in zone (4), the part curvature change is more prominent than the numerical profile and this generates a difference. The maximum difference location is denoted by an arrow and is about 250 ␮m. This occurs where the deformation is high. Fig. 15 shows the vari ation of the resultant R = Fx2 + Fy2 + Fz2 of the forces on the roller stemming from numerical results and measurements. Both curves show the same tendency: R increases up to a time t ≈ 0.5 s and then decreases. The maximum is reached when the distance between the roller and the die is minimum. However, the difference between the measured and calculated maximum loads is about 16%. Many hypotheses can be drawn to explain the differences observed in terms of both geometry and load applied on tooling. Quigley et al. [22] showed that tool deflection generates a major change on tooling reaction force. Yoon et al. [23] demonstrated that Young’s modulus decreases with the deformation and that taking into account this evolution can help us to predict part

−32

1500

1000

500

Parameters

Lower value

Upper value

N (rpm) v (mm/s) ˛ (◦ )

500 3 4

1500 20 45

0 0

0.5

1

Time (s) Fig. 15. Comparison of the force R obtained by measurements and simulation.

1.5

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65

Fig. 16. Strain rate during the tridimensional simulation.

5.3. Springback analysis Depending on part geometry, springback can play an important role in some cases. Two part geometries (Figs. 17(a) and 18(a)) were used to study this phenomenon. An enlargement of zone 1 is done on the external part side where springback should be greater (Figs. 17(b) and 18(b)). In these figures, the red line corresponds to the part geometry when the roller deforms the part and the blue line gives the outline of the part after unloading. Springback is calculated for these two configurations and a spread of 80 ␮m for part #1 instead of 20 ␮m for part #2. When a particular geometry is chosen, this phenomenon can be reduced (Fig. 18). Indeed, springback value is about 20 ␮m for this geometry, so one-fourth the previous one. This comparison shows that it is possible to reduce the springback only by choosing an adapted geometry. As can be expected due to the concave geometry of part #2, springback in that case is lower by one-fourth the value of part #1. A material displacement generates a stress difference during the roller passage. The bigger this difference, the lower the springback for a same displacement. Fig. 19(a) and (b) shows the equivalent stress  eq field just before the roller deforms the part and afterwards respectively for the studied case and with another geometry of die.

Fig. 19. Numerical stress field  eq during the roller passage and afterwards for (a) the reference piece and (b) a different geometry shape die.

Fig. 17. (a) Reference part #1, (b) enlargement of zone 1 showing numerical profiles before (in red) and after (in blue) unloading. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. (a) Reference part #2, (b) enlargement of zone 1 showing numerical profiles before (in red) and after (in blue) unloading. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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For the first case, the equivalent stress difference between the two states is about  = 200MPa for an 80 ␮m displacement. That means a minimum variation of equivalent stress can generate large displacement. For the second case, the maximum difference of equivalent stress between the two states is about  = 500 MPa for a 20 ␮m displacement. That means this concave geometry reduces the springback effect because a material displacement generates large . 6. Conclusion An incremental forming process for manufacturing an inner race of suspension thrust rolling bearing device was studied from a comparative experimental and numerical approach. This process is of particular interest for industrialists since it allows them to reduce raw material losses in comparison with stamping and increase the mechanical properties of parts. Due to the complexity of the tooling kinematics, process control is not easy and it appears that finite element analysis could play an important role in order to optimize the manufacturing of new parts. An experimental characterization of a steel alloy was done using tensile and simple shear tests. Based on the obtained results, an isotropic elastic–plastic mixed hardening model was used and calibrated in order to describe material behavior for finite element analysis. The numerical results of both models are well correlated together when a comparison of profiles is done. However, only the 3 dimensional model is able to predict most aspects of the forming process, such as the applied loading on the roller and thickness distribution. The two dimensional model can be a good alternative if trends for manufacturing a new part are expected with short computing time. It was highlighted that models are perfectible: deformable body for tools, behaviour law taking strain rate sensitivity into account, Young’s modulus decreasing with strain. The analysis of residual stresses during the roller passage and the study of springback show that, depending on part geometry, springback can vary from 20 ␮m to 80 ␮m. Concave geometry greatly minimizes the elastic recovery. Acknowledgements The authors wish to acknowledge the financial support of FUI in the context of competitiveness clusters proposals for this research and the contribution of NTN-SNR, CTDEC and M2O.

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