Today finite element airbag simulations are standard practise in the development of restraint systems. If the inflating process has no influence on the dummy in most cases simplified scaled airbags are used. To simulate the opening behavior of an airbag cover or the dummy response in an out-of-position case with LS-DYNA it is important to obtain a realistic inflating process and therefore folded airbags must be used. For 2D airbags a regular mesh with respect to the folding lines has to be created. The folding itself then is relatively simple. However the creation of folded meshes of 3D airbags is very difficult and time consuming. The main problem is the transformation of the 3D shape to a 2D configuration, the so-called flattening of the 3D shape.

This paper gives an overview of the currently used methods to create folded airbags and shows their advantages and disadvantages in simulations. A new approach to fold a 3D shape is presented which allows the creation of a simulation model in a relatively short time.

 

INTRODUCTION

To simulate the exact deployment of an airbag in a realistic way a folded bag must be used. There are different ways to achieve a folded mesh that can be used in the simulation. While the folding of a 2D airbag is relatively simple, a 3D airbag first has to be flattened, which causes some problems.

Currently used methods

Currently used are three approaches to create a folded mesh:

1. Simulate the flatten/ folding process
2. Mesh 2D surfaces and fold the mesh
3. Mesh 3D surfaces, flatten and then fold the mesh

Simulation of the flatten/ folding process

This method starts with an arbitrary 3D mesh. An airbag is defined and using initial pressure and volume, it is deformed with punches as in reality. A selfcontact (a13 in LS-DYNA) avoids initial penetrations in the following deployment simulation. A typical example for this procedure is a driver airbag, which is sometimes not folded but simply compressed as shown in figure 1.

The flattening of a 3D passenger airbag in a LS-DYNA simulation causes several problems. The airbag is compressed between moving rigid walls to a total height of approximately 2mm. It is very difficult to achieve a folding of the side parts according to the folding pattern. Normally many random wrinkles arise from this procedure. Depending on the element size penetrations in the fully compressed mesh can occur. A very fine mesh may avoid these penetrations, but is not useful in further simulations. Figure 2 shows such a flattened mesh. For the subsequent folding it is necessary to align nodes to the folding line by moving nodes or splitting elements. This method is very time-consuming and therefore not suited for industrial projects.

Figure 1. Compression of a driver airbag	Figure 2. Flattened 3D airbag

 

Mesh 2D surfaces and fold the mesh

To fold a 2D airbag first the flat surfaces are meshed with respect to the defined folding lines. A regular fold is achieved when also the nodes on both sides of this line are on a parallel to the folding line as shown in figure 3. Different types of folds are then used, such as thin (sharp) fold, thick (smooth) fold, roll fold, tuck and double tuck fold. In figure 4 the procedure to create a thin fold is shown. This can be done in a preprocessor like EASi-CRASH, LS-INGRID or OASYS Primer. Figure 4 also illustrates that the element side length changes due to a fold.

Figure 3. 2D mesh with folding line	Figure 4. Thin fold

 

In case of a 3D airbag the flat surfaces have to be derived from the original 3D shape. If an airbag in hardware is not available this is often only possible with simplifications, which leads to incorrect volume, surface area and shape in the simulation. LS-DYNA allows the usage of reference nodes, which represent the real shape of the airbag, to equalize this difference. The problem is to find such a reference mesh, which must have the same number of nodes and elements as the initial mesh.

Mesh 3D surfaces, flatten and then fold the mesh

This approach starts with a 3D mesh of the airbag, which should be created with respect to the folding lines. It is then flattened in a preprocessor by scaling nodes e.g. in z-direction and moving other nodes outwards to avoid a large number of highly distorted elements. This flat mesh can be folded as described above. The original mesh is used as reference mesh. This method allows a flattening, but not necessarily according to the real airbag with folds inside and outside. When the mesh is scaled in z-direction all elements with a normal perpendicular to this axis are highly distorted. OASYS Primer provides this method named scrunching.

 

APPROACH

A new approach described in this paper is the ‘meshing after flattening’. This method was developed for 3D passenger airbags. It is based on the fact that these airbags often have a similar shape and therefore are flattened in a similar way.

Creation of an initial flat mesh

A study of the flattening pattern of several passenger airbags showed that they all are flattened in a similar way. Due to this a general flat passenger bag is created with several 2D surfaces, which are derived from a 3D shape. This can be used as an initial flat configuration for many passenger airbags of the shape described here. In this example the airbag is flattened with the side parts moved inwards. The geometry is reproduced with some simplifications, so that volume, surface area and shape may differ from the original airbag. Figure 5 shows the original bag, figure 6 the surfaces derived from this shape in opposite order for better visualization.

Figure 5. Original airbag	Figure 6. Surfaces derived from 3D airbag

 

Two methods are available to mesh the surfaces, as shown in figures 7 and 8: project a regular mesh on the surfaces or drop fold lines on the surfaces to split them and then mesh the subparts. While the mesh projection restricts the fold lines to be parallel to e.g. the x- and y-axis, the surface splitting enables the possibility to fold along arbitrary lines. After meshing the parts are connected to obtain a closed mesh for an airbag definition.

Figure 7. Mesh projection	Figure 8. Surface splitting

 

In a deployment simulation this airbag would differ from the real airbag shape because of the simplifications made in the general flat airbag model. Therefore the mesh is scaled in length and width direction and with this the difference minimized. To find out the scale factors a first simulation is carried out. The original 3D airbag is meshed and defined as rigid body. The flat mesh is placed inside this rigid body as shown in figure 9 and a node-to-segment contact defined between the two airbags. To allow an extension of the airbag elements a low Young’s modulus is used. After deployment the simplified airbag takes the shape of the original airbag. On the final shape the length and width of the parts can be measured as marked in figure 9 for the upper layer. The first flat mesh is scaled so that the measured dimensions are achieved. This yields the initial flat mesh, which can be folded.

Figure 9. Mesh placed inside a rigid body

 

Creation of a reference mesh

To ensure the correct volume, surface area and shape of the inflating airbag a reference mesh is used in further simulations. A second deployment simulation with the scaled flat mesh inside the rigid body is used to obtain this reference mesh. The node coordinates of the fully deployed airbag in the rigid body are taken as the reference nodes.

The scaling of the flat mesh described above gives the possibility to minimize the difference in the area of between initial mesh and reference mesh. Figure 10 shows for all airbag elements this difference between initial and reference element size. Most of the elements are about 20% larger in the reference state.

 

 

DISCUSSION OF RESULTS

The final flat mesh is folded according to the folding pattern using thin folds and a distance of 1mm between the layers. The deployment sequence of the folded airbag is shown in figure 11.

Figure 11. Deployment sequence of the folded airbag

 

To compare the volume and shape after inflation with the original airbag, the mesh used as rigid body in the above described simulation is defined as an airbag and inflated. Figure 12 shows the fully inflated airbag. Volume and surface area, summarized in table 1, correspond to the folded airbag.

 

Table1: Volume and surface area

	volume (l)	surface area (m2)
original airbag	145	1.468
folded airbag	144	1.474
difference (%)	0.7	0.4

 

Verification of the procedure with a different airbag shape

Starting with the same standard flat mesh the described procedure is applied to another passenger airbag with a different shape and volume as shown in figure 13. While the first airbag investigated is available in hardware the second airbag is only available as CAD data. The position of the inflator is changed compared with the previous example. Therefore the size of the correspondent layers is changed according to the new dimensions measured in the CAD data. The flat surfaces shown in figure 14 are created and meshed.

Figure 13. Original airbag	Figure 14. Modified surfaces to create a flat mesh

 

Again the original airbag is meshed and defined as rigid body. In the final state of the flat mesh deployed inside the rigid body (figure 15) the length and width of the different layers are measured. From this distances scale factors are calculated to modify the flat mesh. This is inflated a second time inside the rigid body to obtain the reference mesh for further simulations. Figure 16 shows the fully deployed flattened airbag. Only volume and surface area are of interest and therefore this airbag is not folded. Figure 17 shows the inflated original airbag to compare it to final state of the flattened bag. As summarized in table 2 the volume and surface area correspond to the original airbag.

Figure 15. Mesh placed inside the rigid body

 

Figure 16. Deployed flattened airbag	Figure 17. Deployed original airbag

 

CONCLUSIONS

In this paper a method is presented, which allows the creation of a folded airbag for a finite element simulation in relatively short time.

Starting with the CAD data of the airbag geometry and a standard flat configuration the airbag is simplified modeled with several surfaces. For that the standard configuration is changed using several parameters measured on the CAD drawing. This process is here called ‘parametric modeling’. The surfaces are meshed and this initial mesh improved using the results of a first simulation, in which the airbag is deployed inside the original shape of the airbag.

This airbag is then folded according to the folding pattern. It is not time consuming to fold a well prepared mesh since several software tools exist, that allow this with different fold types.

A second simulation yielded a reference mesh, which is used to achieve the correct volume, surface area and shape with the simplified airbag.

With this approach it is possible to create a folded passenger airbag, which is not there in hardware, in approximately 1-2 days. Figure 18 shows the flow chart of this method presented here. The advantage is that a reference mesh can be obtained after flat surfaces are folded.

In the future a more comfortable way to flatten an airbag should be found. A direct and exact flattening and folding of the surfaces in the CAD data would make a reference mesh unnecessary.

 

ACKNOWLEDGEMENTS

This presentation is based on the Diploma Thesis of Magnus Eriksson and Jonas Fältström, written at EASi Engineering GmbH, Germany, October 1998 - April 1999.

 

REFERENCE

EASi CRASH User’s Manual for LS-DYNA, (1999), EASi Engineering GmbH, Germany

ERIKSSON, M. and FÄLTSTRÖM, J. "Advanced Technologies for the Simulation of Folded Airbags”, Institute of Technology, Dept. of Mech. Eng., Linköping University, Sweden, 1999, No. LITH-IKP-EX-1611

LS-DYNA Keyword User’s Manual Version 940, (1997), LSTC, Livermore, California

OASYS PRIMER User Manual, (1998), Oasys Ltd.

 

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