Forming strategies and Process Modelling for CNC Incremental Sheet Forming 1
G. Hirtl, J. Ames', M. Bambachl/ R. Kopp' (1) Materials Technology/Precision Forming, Saarland University, Saarbrucken, Germany 2 Metal Forming Institute, RVVTH Aachen, Aachen, Germany Submitted by R. Kopp, Aachen Germany
Abstract Incremental Sheet Forming (ISF) is a process capable of producing complex sheet components by the CNC movement of a simple tool in combination with simplified dies. Earlier work revealed two major process limits, namely the limitation on the maximum achievable wall angle, and the occurrence of geometric deviations. The work detailed in this paper focuses on forming strategies to overcome these process limits, including the processing of tailor rolled blanks. Additionally, finite element modelling of the process is presented and discussed with respect to the prediction of the forming limits of ISF. Keywords: Forming, Sheet metal, Kinematic
1 INTRODUCTION Deep drawing is a very cost-effective and well-established process for the mass production of sheet components. However, because of the high costs and long processing time for die manufacturing it is not economical for small batch production, rapid prototyping and large sheet components with a complex geometry. The incremental sheet forming process (ISF) has been developed to close the existing gap in small batch production and prototyping. It is characterised by a kinematic forming approach, i.e. a part is produced by the CNC movement of a simple tool in combination with simplified dies [I-41. Earlier work addressed aspects such as limit strains, geometric accuracy, surface quality and mechanical properties for various demonstrator components made of mild steel, stainless steel, aluminium and titanium [5-71. It has revealed two major process limits, both becoming predominant for steep part areas, namely excessive thinning, and deviations from the target geometry. In the present paper, forming strategies to overcome the existing limits will be given. In certain cases, the use of tailor rolled blanks with a varying thickness can be shown to be of positive effect. In addition, the local stress state under the action of the tool is investigated by finite element simulations as it is considered the key to understanding the forming limits observed in ISF. 2
PROCESS TECHNOLOGY
2.1 Process description The conventional forming strategy in ISF consists of a single forming stage where the tool traces along a sequence of contour lines with a small vertical pitch motion in between. Generally, a distinction can be made between 'single point forming', where the bottom contour of the part is supported by a rig, and 'two-point forming', where a full or partial positive die supports critical surface areas of the part (Figure 1).
Figure 1: Process variants 2.2 Process limit: formability In contrast to classical sheet drawing the plastic deformation zone in ISF is very small and strictly limited to the contact area between tool and workpiece. Visioplastic evaluation and optical deformation measurement of test pieces also show that the deformation mode on flat surfaces is very close to plane strain conditions [6]. Accordingly, volume constancy leads to the so-called 'sinelaw' [5] that relates the initial (to) and actual ( t 7 ) sheet thickness for a given wall angle a (Figure 1):
t 7 = to~sin(90" - a)
(1)
Due to excessive thinning, this relation limits the range of possible flange angles to approximately 60" for 1-1.5 mm A199.5 and mild steel sheets. As a consequence, the forming kinematics inherent in ISF entail the following drawbacks: the limitation on the maximum wall angle restricts the potential scope of shapes and applications the strong dependence on the feature angle can lead to an inhomogeneous thickness distributions in the final part These drawbacks motivate to investigate multistage forming strategies to be presented in section 3.1. The forming limits observed in ISF are significantly larger than expected from a typical forming limit diagram (FLD) for mild steel and strongly dependent on process parameters such as the size of the tool and the vertical pitch [6]. This influence of the process parameters on the
limit strains has been investigated by finite element simulations using a damage model (see section 4.2).
shallow wall angle (45" in this example) is produced by using the regular ISF process and a partial die.
2.3 Process limit: geometric accuracy A second process limit arises from the fact that the tool path is generated exclusively from the geometric information specified by the CAD model of the desired part. Following this tool path, the tool tries to impose the desired shape on the sheet. This strategy would only be successful if the deformation was purely plastic, but the elastic parts of the deformation entail a local 'spring back of the sheet when the tool moves on. In addition, we expect the buildup of significant residual stresses due to the cyclic plastification and unloading. In fact, depending on the tool size and vertical pitch the tool contacts an arbitrary spot on the sheet between 10 and 100 times. This can lead to considerable deviations from the target geometry, especially for complex parts (Figure 2). Consequently, strategies to control the geometric accuracy are of particular importance.
Then, a number of stages follow in which the pitch motion of the forming tool alternates from upward (Figure 3b) to downward (Figure 3c). From one stage to the next the tool path is generally designed with an increase in angle of 3" or 5". This means that a 7 to 12 stages are needed to produce components with an angle of about 80". The described forming strategy has been successfully tested for the four-sided pyramid depicted in Figure 4.
Figure 4: Preform and four-sided pyramid with a = 81". To determine the wall thinning the produced components were cut along the x-axis and the actual sheet thickness was measured (Figure 5). The measurement of a pyramid with an angle of 81" produced by using the multistage forming strategy clearly shows thinning that is less than the theoretically expected value, given by the 'sine law" (eq. (1)). Heavy thinning of the flange and consequent failure are prevented by the preforming and subsequent multistage forming, since a larger portion of sheet volume is included in the forming process.
Figure 2: Process limit: geometric accuracy 3
FORMING STRATEGIES
3.1 Multistage forming Inspired by the ideas for multistage forming strategies for axisymmetric components [8], a modified multistage forming strategy (Figure 3) has been developed for nonaxisymmetric parts.
Figure 5: Measurement of sheet thickness (81" pyramid). 3.2 Use of tailor rolled blanks (TRB) The flexible rolling process as detailed in [9] allows to produce blanks with a predefined thickness profile without joining operations. It has been designed for applications where load-adapted or load-optimised structures with a specified thickness profile are needed. In the context of incremental sheet forming, TBRs could in principle be used as an alternative to the multistage forming strategy. With an increased initial sheet thickness in steep part areas, TRBs could allow to compensate for the excessive sheet thinning. This could in some cases allow for the forming of steeper flanges and a more homogeneous sheet thickness distribution
Figure 3: Multistage forming strategy. The following stages constitute the multistage strategy: In the first 'preforming stage' (Figure 3a) the blank is clamped on the blank holder and a preform with a
First attempts were made with A199.5 blanks of the size 320 mm x 250 mm. At the Metal Forming Institute (Aachen), the initial sheet thickness of approximately 1.95 mm has been reduced to 1.26 mm in a centred layer of 70 mm width by flexible rolling. With these blanks, a pyramidal component with two different flange angles, 45" and 63", respectively, has been produced using the conventional ISF process. The shallow fsteeol side walls are located in the thin fthickl laver of the blank (Figure 6). \
I
1
of measured points of the component and the corresponding target geometry points. The deviation vector ( d ) from each measured point to the corresponding target point is calculated, inverted and scaled by a factor c. This yields the vector that points at a new trial point (Figure 9).
Figure 6: Definition of geometry and blank orientation This set up has been chosen according to the sine law in order to obtain the same wall thickness on all side walls. After forming, the sheet thickness has been measured along sections in rolling (RD) and transverse direction (TD) (Figure 7). With about 0.9 mm, an almost homogeneous sheet thickness has been achieved on all flanges despite their different wall angles. Further to that, it is worth mentioning that the use of a sheet section of 1.95 mm thickness allows to produce the 63" side walls without failure.
- c. d
Finally the cloud of trial points is imported to a CAD system and a CAD model is generated to compute the path for an improved part. The correction module can be applied several times until a specified tolerance is met.
Figure 9: Determination of corrected points A 3D comparison of an uncorrected and a corrected component after the first correction loop (Figure 10) indicates that the developed correction module leads to a drastic reduction in deviation.
Figure 7: Radial course of the sheet thickness. 3.3 Improving the geometric accuracy
Since earlier work [5] had shown that the process is very reproducible an attempt was started to develop a general correction algorithm based on tool path optimisation. The correction module engages after the regular ISF process is finished and a first component is produced (Figure 8).
Figure 10: Validation of the correction module. 4 FINITE ELEMENT MODELLING An explicit FE code (ABAQUS/explicit) has been successfully used in earlier work to simulate the ISF process [6], as it is very suitable for highly non-linear problems and the treatment of arbitrary contact surfaces and conditions. In the following, two aspects of process simulation for ISF will be considered: 0
0
Figure 8: Regular ISF process with correction module The following steps constitute the correction module: A first component is produced and measured by a coordinate measuring machine which outputs a cloud
the prediction of sheet thickness will be validated with the forming of TRBs (see section 3.2) the use of a constitutive law including damage evolution to investigate the dependence of the forming limits on process parameters such as tool diameter and vertical pitch (see section 2.2)
4.1 Simulating the forming of TRBs For the prediction of sheet thinning, a new part has been produced using a TRB as described in section 3.2. While the flange angles of 45" and 63", respectively, have been maintained, the part has been reduced in height in order to reduce the calculation time for the related FE simulation. In the FE model, the sheet has been meshed with 3,900 shell elements, with the initial sheet thickness distribution applied as nodal thickness values (Figure 11). A comparison of the sheet thickness in rolling and transverse direction (Figure 12) shows a fairly good agreement with collated experimental data.
Figure 11: Prediction of sheet thickness for TRBs
Figure 13: Damage induced by forming heads of different size for different pitch settings (f,=0.06).
Figure 12: Sheet thickness validation in RD and TD 4.2 Stress state and forming limits The stress field under the action of the tool is an important factor with respect to the formation and growth of voids that eventually lead to ductile fracture. Despite the good coincidence with experiments, the applied shell elements cannot account for the 3D stress state due to the inherent plane stress assumption. As modelling the whole sheet with brick elements is too demanding of computing resources, the local stress and strain fields during forming are investigated by means of a partial model meshed with brick elements. This set up has been used in earlier work [6] to analyse the state of stress during forming. It has revealed that a significant hydrostatic pressure is present during the immediate action of the tool. As the presence of hydrostatic pressure can have a huge impact on the damage evolution during forming, a more detailed investigation using a damage model was conducted.
Damage evolution The Gurson-Tveergard-Needleman (GTN) constitutive law available in ABAQUS [6] has been applied to examine the influence of process parameters such as the tool size and the vertical pitch on necking and the forming limits in a qualitative manner. Applying the GTN model, calculations for three different tool sizes (diameters DT of 30 mm, 10 mm and 6 mm) and values of the vertical pitch d, (1 mm and 0.5 mm) have been conducted. For these calculations, a flange angle of 65" has been chosen as this is close to the fracture limit found experimentally (see section 2.2). Figure 13 gives the damage evolution during forming for all six parameter combinations. The ordinate has been normalised by the critical void volume fraction fc that marks the onset of void coalescence. The abscissa has been normalised in order to compare calculations of different durations. Further to that, only those time ranges yielding a non-zero contribution to the damage evolution have been included. The damage evolution confirms qualitatively the experimentally obtained fact that higher forming limits can be achieved with smaller forming heads and larger values for the vertical pitch.
5 SUMMARY This paper gave an overview over recent developments in incremental sheet forming and corresponding finite element modelling. Motivated by the drawbacks of conventional ISF, two forming strategies have been put forward to help enlarge the range of potential process applications, namely a multistage forming strategy to produce steep flanges of up to 81", and a correction algorithm to enhance the geometric accuracy. Besides that, the use of tailor rolled blanks has been shown to be of positive effect in certain cases. In addition, process modelling using an explicit solver has been applied to predict the sheet thickness distribution for the forming of tailor rolled blanks. Finally, the GTN damage law helped to model the dependence of fracture limits on process parameters in a qualitative way. 6
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