RD-E: 0401 Driver Airbag

Deployment of a folded multi-chambered uniform pressure airbag into a head impactor.

The accurate prediction of the overall deployment phases of airbags is crucial for passenger protection in motor vehicles. Due to its specific application airbags are modeled in different ways.

The subject of this example is to demonstrate the deployment process of a simple multi-chambered airbag hitting an impactor. The airbag is initially folded along four-fold-lines and is modeled by monitored volumes using communications between chambers. The modeling is based on a uniform pressure approach, where uniform pressure distribution in the entire control volume (chamber) is applied.

The physical reality of the airbag is transferred into a very simple model by using the ideal gas equation: (1)

p V = m R T

Where,

$p$: Pressure inside of the airbag
$V$: Airbag volume
$m$: Mass of gas inside of the airbag
$T$: Gas temperature
$R$: Universal gas constant

The physical airbag with local pressure and gas velocity distribution, in each part of the bag, turns into a uniform pressure description, where the pressure and the temperature are constant in each chamber of the airbag. The gas generator will be represented by the load curves, which control the injected mass flow rate and gas temperature. Outflow takes place through vent holes or porous fabric ().

A more sophisticated method (Finite Volume Method: FVM) is the topic of another example.

The fabric of the airbag is meshed with shell elements. The fabric is assumed to be orthotopically elastic with softening in compression. The injected gas enters a central chamber via an inflator. The airflow spreads into neighboring chambers through inter-chamber openings. The chambers are inflating one after another as the airbag is deploying.

Options and Keywords Used

Units used: Mg mm s

/MAT/LAW19 (FABRI) (elastic orthotropic material for modeling airbag fabric)
/MAT/GAS/MASS (Coefficients of C_p(T) per mass unit)
/MAT/LAW0 (VOID) (Define elements to act as a void or an empty space)
/PROP/TYPE9 (SH_ORTH) (Orthotropic property shell definition)
/PROP/INJECT1 (Describes mass injected for each constituent gas)
/PROP/TYPE4 (SPRING) (Spring property with one translational DOF)
/PROP/TYPE1 (SHELL) (Shell property set)
/INTER/TYPE19 (Airbag self-contact)
/RWALL (Infinite rigid plane)
/BCS (Fix inflator)
/SENSOR (time sensor defining time to fire of the airbag)
/DAMP (Rayleigh mass and stiffness damping coefficients, applied to a set of nodes)
/MONVOL/COMMU1 (Airbag monitored volume communications)

Input Files

The input files used in this example include:

<install_directory>/hwsolvers/demos/radioss/example/04_Airbag/driver/*

Model Description

An approximately 80-liter airbag is folded along four fold lines.

The fabric thickness is 0.33 mm and is modeled using an elastic orthotropic material law (/MAT/LAW19) with the following properties:

Material Properties
Density: 0.85 x 10^-10 $[\frac{g}{m m^{3}}]$
Young's modulus: 500 $[MPa]$ in both directions
Shear modulus: 10 $[MPa]$ (G12, G23, G31)
Reduction factor: 0.001

The property set is /PROP/SH_ORTH (shell orthotropic, TYPE9), with one integration point to neglect bending stiffness of fabric material. The default 3 node tria element formulation is used.

Model Method

The model is divided into two subsets:

the fabric layers
the communication surfaces

The fabric surface is then divided into 9 subsets, one for each monitored volume. Each "monitored volume" is further divided into two parts. All the parts of the layer of the fabric have the same property and mat_ID.

The same properties apply for the communication surfaces.

The airbag is modeled using 9 communicating volumes to simulate approximately propagation of air into the folds. The communicating surfaces between the volumes are simulated using dummy membranes (Figure 4). The dummy membranes are modeled using shells with void material (/MAT/LAW0 (VOID)).

A monitored volume of each airbag chamber is defined as a collection of surfaces. The volume should be closed, the normal of the shells is directed outwards. The monitored volume used, is a COMMU1 type for airbags, using communications (chambered, with communications, of the folded airbags). For further details about monitored volumes, refer to COMMU1 Type in the Radioss Theory Manual.

Gas materials are specified in separate /MAT/GAS cards (using MASS type), which describe the gas molecular weight MW and specific heat coefficients C_pa, C_pb, etc. in the polynomial function C_p(T).

For the property, of the injector /PROP/INJECT1 is used, which describes the mass injected for each constituent gas. The final injected mass is 47 g, injected into the central chamber ( $Fscal e_{M}^{1}$ and $Fscal e_{T}^{1}$ =1). Two functions define the mass and temperature of the injected gas controlled by time (function identifiers: $fct_I D_{M}^{1}$ and $fct_I D_{T}^{1}$ ).

The main properties for this type are:

Properties
Mu (Volumetric viscosity): 0.001 (default)
P_ext (External pressure): 0.1 $[MPa]$
T₀ (Initial temperature): 296.0 $[K]$
I_ttg (Timeshift flag): 3; Only active when at least one injection sensor is specified. In the present case, it is in chamber 1. The flag determines the time shift for venting, porosity, and communication options when injection starts at a Time-to-Fire specified in a sensor.
N_jet (Number of injectors): 1
Vent hole membrane surface area: 1000 mm₂ (A_vent = 0) is immediately activated
Communication area: Total (A_com = 1 and S_com = 0); The airbag is braced on the back with additional tethers, modeled as springs. Furthermore, damping is applied (/DAMP) to reduce the movement of the airbag after inflation.

Interface

To model the airbag self-contact, the contact interface /INTER/TYPE19 is used. This contact combines surface to surface and edge to edge contact and uses surface input based on the same secondary/main surfaces. The interface's main and secondary surfaces are defined using /SURF/PART. If different contact parameters need to be used for the surface to surface contact and edge to edge contact, then this can be done by replacing the /INTER/TYPE19 contact with a /INTER/TYPE7 node to surface self-contact and a /INTER/TYPE11 edge contact.
The distance between the fabric layers before unfolding is very small. To avoid initial penetration, Inacti=6 is used to automatically reduce the contact gap thickness. There should be no initial intersections in the contact at the beginning of the simulation.
It is recommended to set I_bag=1 which stops venting through the airbag in areas where contact occurs.
A constant contact thickness similar to the fabric thickness of Gap_min=0.3 is used.

Time Step Control

Nodal time step control /DT/NODA/CST is used in the model with a typical crash simulation time step. To improve model stability, a maximum time step is set using the /DTIX. This would normally not be needed since the time step in a crash simulation would normally be controlled by other parts in the simulation.

Impactor Head

The dummy head is modeled as a simplified head of a crash test dummy and modeled as a rigid part. The head is constrained to prevent rotation in all directions. It can only translate in the z-direction.

Results

Curves and Animations

In Figure 5 the mass injected for each constituent gas is displayed. The total amount of the injected gas into the central chamber is about 47 g.

As can be observed from Figure 6, when the airbag is deploying the pressure is different in different chambers until 0.005s. When the airbag is fully deployed, the pressure distribution in each chamber is equal. This is important to represent the propagation of gas flow inside the airbag.

The final volume of the airbag after deploying is about 80 liters.

Animations