2. Airbag geometry and folding representation
An airbag model is only as reliable as the geometry it starts from. In a deployment simulation, the fabric shell must inflate from a tightly packed, folded configuration into a fully expanded cushion within tens of milliseconds. If the starting geometry contains sliver faces, self-intersections, or an inconsistent fold topology, the solver will either fail during initialization or produce a pressure curve that looks plausible but is physically meaningless. This section covers the three-stage pipeline that turns a supplier CAD surface into a solver-ready folded airbag: CAD cleanup, shell mesh generation, and initial fold state mapping for contact.
Why the Folded State Must Be Represented Explicitly
Most airbag simulations use a control-volume (CV) or corpuscular (particle) gas model. The gas pressure acts on the fabric surface, and the fabric must unfold through contact with itself and with the occupant. The initial folded state therefore defines two critical things: the packed volume that the gas model uses to compute the initial pressure, and the contact topology that governs how the fabric layers slide against each other during the first few milliseconds.
If the folded geometry is approximated as a flat or arbitrarily crumpled surface, the initial gas volume is wrong, the contact pairs are missing, and the deployment kinematics will not match physical test data. The fold representation is not a cosmetic detail — it is a boundary condition of the simulation.
Stage 1: CAD Cleanup
Supplier CAD for airbags typically arrives as a set of trimmed surfaces, often with gaps between panels, overlapping seams, and non-manifold edges. The goal of cleanup is to produce a single, watertight, manifold shell that represents the fabric mid-surface.
Typical cleanup operations include:
- Stitch and sew: close gaps between adjacent panels to within a tolerance of 0.1–0.5 mm, depending on mesh size.
- Remove sliver faces: eliminate faces with aspect ratios above 20:1 or with included angles below 5°, which cause poor mesh quality.
- Resolve self-intersections: detect and repair overlapping surfaces, especially near the inflator opening and seam lines.
- Define the mid-surface: offset the outer and inner fabric surfaces to a single mid-surface, since shell elements carry no thickness in the geometric sense.
- Mark seam lines and tethers: preserve seam curves as edge sets so they can be constrained or merged later.
Stage 2: Shell Mesh Generation
Airbag fabric is modeled with membrane or thin shell elements. The mesh must be fine enough to capture fold curvature and contact, but coarse enough to keep the explicit time step stable. A common target is an element edge length of 5–15 mm for a driver-side airbag, with local refinement to 2–3 mm near the inflator and vent holes.
Key mesh quality criteria for airbag shells:
| Metric | Target | Reason |
|---|---|---|
| Element edge length | 5–15 mm (2–3 mm near inflator) | Balance contact resolution and stable time step |
| Aspect ratio | < 5:1 | Avoid hourglassing and inaccurate bending |
| Warpage angle | < 15° | Maintain membrane behavior |
| Jacobian | > 0.6 | Prevent negative volume at large deformation |
| Element type | 4-node quad, reduced integration | Standard for fabric membranes |
Triangular elements should be avoided in regions that will undergo large folding deformation, because they are stiffer in bending and can lock. If triangles are unavoidable near the inflator opening, use them only in a small, well-supported patch.
Stage 3: Initial Fold State Mapping
This is the most error-prone step. The flat or partially folded mesh must be mapped into the packed configuration that matches the physical folded airbag. There are three common approaches:
- Direct geometric folding: apply a sequence of rigid rotations and translations to mesh patches to reproduce the physical fold pattern (e.g., accordion, roll, or star fold). This is precise but labor-intensive.
- Implicit folding via a reference geometry: map the flat mesh onto a pre-folded CAD surface using a projection or shrink-wrap algorithm. Faster, but can introduce element distortion.
- Pre-simulation folding: run a quasi-static simulation that pushes the flat airbag into a rigid mold cavity representing the packed volume. This produces a physically consistent folded state with natural contact, but requires a separate solver run.
Regardless of method, the folded mesh must satisfy three conditions before it can be used in a deployment simulation:
- No initial penetration: all contact pairs must be free of overlap at time zero. A penetration of even 0.5 mm can cause an explosive contact force at initialization.
- Correct initial volume: the enclosed volume of the folded airbag must match the packed volume specified by the inflator curve. This is typically 2–8 liters for a driver-side airbag.
- Preserved seam and tether connectivity: seam lines must remain merged, and tethers must be attached to the correct nodes.
Worked Example: Driver-Side Airbag Fold Mapping
Consider a driver-side airbag with a flat pattern area of 0.42 m² and a target packed volume of 4.5 L. The mesh has 12,000 quad elements with an average edge length of 8 mm.
After cleanup, the shell is watertight and the surface area measures 0.418 m² — a 0.5% deviation, which is acceptable. The mesh is generated with local refinement to 3 mm around the inflator opening. The fold pattern is a star fold with six pleats, each rotated 60° about the inflator axis.
Using direct geometric folding, each pleat is rotated inward by 150° and translated 35 mm toward the center. After folding, the enclosed volume is computed by a closed-surface integration and measures 4.3 L. This is 4.4% below the target. The pleat translation is reduced to 32 mm, bringing the volume to 4.52 L. A final penetration check shows a maximum overlap of 0.2 mm at two pleat intersections, which is resolved by a 0.3 mm node offset along the surface normal.
The folded mesh is now ready for the deployment simulation. The initial contact pairs are defined between adjacent pleat surfaces, and the seam lines are constrained to remain merged.
Verification Checklist Before Deployment Simulation
| Check | Acceptance Criterion | Typical Tool / Method |
|---|---|---|
| Shell watertightness | No free edges except at inflator opening | Mesh free-edge query |
| Surface area vs. flat pattern | Within ±2% | Area calculation |
| Element quality | Jacobian > 0.6, aspect ratio < 5 | Mesh quality checker |
| Initial penetration | < 0.3 mm | Contact initialization check |
| Packed volume | Within ±5% of inflator spec | Closed-volume integration |
| Seam/tether connectivity | All merged nodes remain merged | Node merge verification |
The SVG below summarizes the three-stage pipeline and the key decision points at each stage.
The pipeline is iterative. If the folded volume is off by more than 5%, or if initial penetration exceeds 0.3 mm, return to the fold mapping stage and adjust the pleat geometry. If the mesh quality degrades after folding — for example, Jacobians drop below 0.6 — the mesh may need to be regenerated with a finer edge length in the affected region. Only when all six checks in the verification table pass should the model be promoted to a deployment simulation.