3. Airbag design variables

In an LS-DYNA airbag model, the occupant restraint outcome is not governed by a single "airbag stiffness" knob. It is the combined result of how much gas enters the cushion, how fast it enters, how much escapes through engineered vents, and how much leaks through the fabric itself. For DOE purposes we need these four physical mechanisms mapped onto controllable, monotonic, and independently parameterizable inputs. This chapter defines each factor, shows where it lives in a typical *AIRBAG_* keyword setup, and explains how to choose levels that produce a well-conditioned design matrix rather than a set of redundant or physically impossible designs.

Mass Flow Rate: The Inflator's Delivery Capability

The mass flow rate ṁ(t) describes the gas mass delivered by the inflator per unit time. In LS-DYNA the uniform-pressure airbag method (*AIRBAG_SIMPLE_PRESSURE_VOLUME, *AIRBAG_ADIABATIC_GAS, or the more general *AIRBAG_WANG_NEFSKE family) accepts either a mass flow rate curve or a pressure curve, depending on the formulation. For DOE, mass flow rate is attractive because it is a direct physical quantity: scaling it changes inflation aggressiveness without altering the shape of the deployment event.

A practical parameterization is a multiplicative factor applied to the baseline curve:

*DEFINE_CURVE
         101       0.0       1.0       1.0
     0.000    0.000000
     0.005    0.018000
     0.010    0.041000
     0.015    0.052000
     0.020    0.048000
     0.030    0.020000
     0.040    0.000000
*AIRBAG_SIMPLE_PRESSURE_VOLUME
         1         1       101       0.0

Here the curve ordinates are mass flow rate in kg/s (example values only). A DOE factor f_m in the range 0.85–1.15 is applied by scaling every ordinate. Keep the time base fixed: scaling time as well as amplitude confounds two effects and destroys the interpretability of the main effect. If the inflator model uses a tank-pressure curve instead, the equivalent factor scales pressure amplitude, and the resulting mass flow follows from the orifice equation — note that this makes the factor nonlinearly coupled to venting, which is why mass flow rate is usually the cleaner DOE variable.

Vent Hole Area: The Primary Energy Sink

Vent holes are the dominant tuning lever for cushion pressure after peak inflation. In the lumped-parameter formulations, venting is represented by a discharge coefficient and an effective area, often through *AIRBAG_SIMPLE_PRESSURE_VOLUME with a vent area or via a dedicated vent definition. The physically meaningful DOE factor is the total effective vent area:

A_eff = C_d * n * (pi/4) * d^2

where n is the number of holes, d the hole diameter, and C_d the discharge coefficient (typically 0.6–0.8 for sharp-edged fabric vents). For a baseline of two 30 mm vents with C_d = 0.7, A_eff ≈ 9.9 × 10⁻⁴ m². A DOE factor of 0.7–1.3 on A_eff corresponds to diameters of roughly 25–34 mm — a range that is manufacturable and produces measurable pressure differences. Do not vary n and d independently in the same screening study; they enter only through A_eff and will appear as perfectly correlated columns in the design matrix.

Inflator Pressure Curve Scaling: Shape Versus Amplitude

Scaling the inflator pressure curve is conceptually similar to mass flow scaling but differs in one important respect: it changes the driving pressure that the cushion sees, so the effect on occupant loading is more direct and often more nonlinear. Two distinct DOE treatments are useful:

• Amplitude scaling — multiply all ordinates by f_p. This preserves the deployment timing and the ratio of early to late output, and is the recommended single-factor treatment.
• Time scaling — stretch or compress the abscissa by f_t. This changes how quickly the cushion reaches peak pressure and is physically meaningful for inflator burn-rate studies, but it interacts strongly with venting and should be reserved for a second-stage study.

For screening, use amplitude scaling only. A factor range of 0.9–1.1 is usually sufficient; beyond ±15% the design departs from the validated inflator hardware and the DOE results lose credibility with the restraint system team.

Fabric Permeability: The Distributed Leak Path

Fabric permeability is the leakage through the cushion material itself, distinct from engineered vents. In LS-DYNA it is commonly represented by a permeability parameter or a leakage-area curve in the airbag definition, or by a fabric material model with porosity. The DOE factor is a multiplier on the permeability coefficient k (units of volume flow per unit area per unit pressure, e.g. L/(dm²·min) at a reference pressure).

Permeability is the factor most often neglected in DOE studies and the one most likely to explain unexplained scatter in validation. A coated fabric may have k ≈ 0.5 while an uncoated fabric of the same construction can exceed k ≈ 5 at the same reference pressure. Because permeability acts over the entire cushion surface, its effect grows with cushion volume and inflation time — it is not interchangeable with vent area even when the total leakage at peak pressure happens to match.

Building a Non-Redundant Factor Set

The four factors are physically distinct but not statistically orthogonal in their effect on occupant response. Mass flow rate and pressure curve scaling both raise peak pressure; vent area and permeability both lower it. A screening design that varies all four at wide levels will produce strong two-factor interactions and may show near-zero main effects for individual factors — a classic sign of confounding. The practical remedy is to fix the inflator representation to one form (mass flow or pressure curve, not both) and treat the other as a constant, then vary vent area and permeability together because they are the two leakage paths that the restraint engineer can actually tune on hardware.

A workable screening matrix for this chapter's factors, using a two-level fractional factorial in coded units (−1, +1):

These are example levels chosen to bracket realistic hardware tolerances; they are not measured values. Note that f_m and f_p are varied together in this particular resolution-IV design, which means their main effects are estimable but their interaction is aliased with the f_A × f_k interaction. If the physics suggests that interaction matters, add four axial runs or switch to a D-optimal design with the aliasing explicitly controlled.

Verification Before Running the DOE

Before committing the matrix to the solver queue, run the baseline and the two extreme corners (all factors at −1 and all at +1) and inspect three outputs: peak cushion pressure, time-to-peak, and the pressure at the moment of occupant contact. The corner runs should show a monotonic, physically sensible spread — for example, the all-low corner producing a late, soft cushion and the all-high corner producing an early, stiff one. If a corner produces a pressure trace that is flat, clipped, or identical to the baseline, the corresponding factor is not actually reaching the solver: check that the curve ID referenced in the airbag keyword matches the scaled curve, that the vent area is not being overridden by a constant in a second keyword, and that the permeability parameter is active for the chosen fabric material model. Catching these silent no-ops before the full DOE run saves an entire batch of wasted simulations and, more importantly, prevents a factor from being wrongly declared insignificant.