A New Method for Simulating Airbag Deployment in Abaqus Explicit

Ritwick Roy (Dassault Systemes Simulia Corp., USA)

Introduction

Airbags are vital to occupant safety in an automobile. Early usage of airbags was limited to frontal airbags. Over time, the number of airbags in a car have increased to include side airbags, knee airbags, rear curtain airbags, and even pedestrian airbags. Airbags now form an integral part of an automobile and simulating airbag deployment has become an essential part of automobile crash simulation. The Lumped Kinetic Molecular (LKM) method is a promising new numerical method in Abaqus Explicit for simulating airbag deployment.

Airbags minimize injury by cushioning the impact forces experienced by the occupant. Airbags come in different shapes and sizes, and are placed at different locations such as the steering wheel, the door trim and the side of a seat to name a few. Depending on the direction and location of impact, one or more of these airbags are deployed. Airbags consist of a flexible fabric bag, an inflator device, an electronic controller and sensors. The fabric is tightly folded or wrapped around the inflator. This makes it possible to install the airbag assembly in a confined space such as a steering wheel. During a crash, the electronic controller evaluates the signal from the sensors, and sets off a controlled explosion in the inflator. The rapidly expanding gases emerging from the inflator push open the tightly folded airbag. The duration of deployment is between 20 to 30 milliseconds. During deployment, some amount of gas is allowed to escape from vents in the airbag to enhance the cushioning effect.

The contact of an occupant with a partially deployed airbag is an important occupant safety consideration. Such a situation is called an out-of-position impact and can lead to injuries because of the large forces experienced by the occupant. The simulation of such a complex event presents several significant challenges. The rapidly changing state of contact between the layers of fabric of an unfolding airbag needs to be resolved accurately. Significant variations in the pressure and the temperature fields occur due to rapidly changing state of the gas inside the expanding airbag. Further, the expanding gas has to push its way through the narrow passages in between the folds of the airbag. Failing to capture the pressure variation in the gas and the accurate interaction of the gas with the airbag, will result in inaccurate forces being exerted by the gas on the airbag. This will result in inaccurate modelling of the forces transferred from the airbag to the occupant. It is also important to capture the location where the gas emerges from the inflator as well as the jetting of the gas. Such directional effects influence the accuracy of the solution during the early stages of the airbag deployment. These requirements present a significant set of challenges for any numerical approach to simulating airbag deployment.

Modelling gas using the Lumped Kinetic Molecular method

The lumped kinetic molecular method (LKM) is a particle method that approximates the macroscopic behaviour of a gas. It is based on the kinetic theory of gases that assumes that all gases are composed of a large number of molecules that are in a constant state of random motion. The molecules of a gas collide elastically with each other, as well as with the walls of the container. The pressure on the container wall is the result of collisions of the gas molecules with the wall. Gas is composed of an enormous number of molecules. For example, only 4 grams of helium has 6.02X10^23 atoms, each with a Van der Waals field radius of 140X10^-9 m. The presence of such a large number of molecules allows the motion of the gas molecules to be treated statistically. The average behaviour of the molecules determines the macroscopic gas behaviour. Because numerical modelling of every gas molecule is outside the reach of today’s computing capacity, the LKM method reduces the size of the problem by lumping many gas molecules into a single lumped molecule or gas particle. In the LKM method, we solve for the motion of gas particles.

The LKM method makes the following assumptions:

 ·        Lumped molecules are rigid spherical particles that collide elastically.

·        Lumped molecules obey the Maxwell-Boltzmann speed distribution.

·        Lumped molecules modeling a monatomic gas have only translational energy.

·        Lumped molecules modeling a polyatomic gas have both translational and rotational energy.

·        The temperature of the gas is low enough to ignore vibrational energy.

·        No attractive or repulsive forces exist between lumped molecules.

·        The pressure exerted by the gas on a structure is the combined result of particle collisions over time on the surface.

For elastic collisions between lumped molecules, it is essential to enforce both the energy and the momentum balance between a pair of colliding lumped molecules. The LKM method solves these equations while preserving the partition of the spin and the translational energy for polyatomic gases. The solution to the energy and momentum equations yields the post collision velocities of lumped gas molecules. Since the mass of a lumped molecule is small compared to the mass of a facet of an airbag, the above set of equations can also be used to determine the velocity of the lumped gas molecules after they collide with a facet of an airbag. 

 Cut View of a Partially Deployed Curtain Airbag with an Impactor. Zoomed view showing lumped molecules.

Key Features of the Lumped Kinetic Molecular Method

·        Captures non-uniformity of pressure during the initial stages of airbag deployment.

·        Define complex inflator configuration, including multiple injection points.

·        Control jetting angle of the injected gas.

·        Easy specification of mass flow rate and temperature data for the inflator.

·        Automatic particle sizing.

·        Ability to have delayed inflator activation.

·        Ability to switch to uniform pressure method.

·        Parallel execution.

A Side curtain airbag example

The simulation replicates an experiment designed to measure the displacement, the velocity and the acceleration of an impactor whose impact with a wall is cushioned by a side curtain airbag.

Side curtain airbag model at 0 milli-second.

The model consists of a side curtain airbag that is tightly rolled-up and attached to a fill tube. The airbag and inflator assembly are mounted on a frame. A human head involved in a side impact is modelled with a rigid impactor. The impactor is moving towards a flat rigid wall with an initial velocity. The airbag fabric has nonlinear elastic material definition. 200,000 gas particles are used to model the gas in the airbag. The LKM method is used during the early phase of deployment because the pressure in the airbag is highly non-uniform. After the bag is sufficiently inflated and the pressure inside the airbag is nearly uniform, the analysis procedure is switched from the lumped kinetic molecular method to the uniform pressure method for computational efficiency. The simulation was performed in domain parallel mode using double precision. The analysis took 9559 seconds using 8 cores on a machine with an Intel (R) Xeon (R) CPU ES-2620 v4 processor.

Airbag deformed configuration at 80 milli-second.

Conclusion

The Lumped Kinetic Molecular method is a particle-based method for solving a gas flow problem. It is based on the kinetic theory of gases. A relatively small number of elastically colliding rigid gas particles are used to model the gas flow. Modelling capabilities make it easy to define the inflator. The LKM method suitable for airbag deployment simulation.

Click on the link to watch an airbag deployment animation using this method: https://www.youtube.com/watch?v=yTsWZKtmnHA