4. Inflator performance characterization

The inflator is the energy source of a driver airbag module, and its output determines whether the cushion deploys fast enough to protect the occupant without causing injury itself. In DAB design and CAE simulation, the inflator is not modeled as a simple pressure source; it is characterized by a set of measurable performance data that the simulation consumes directly. The three most important characterization outputs are the pressure–time (P–t) curve in a closed tank, the mass flow rate derived from that curve, and the temperature sensitivity of both. This chapter explains what these quantities mean, how they are obtained, and how they are used in a CAE model.

1. The Tank Test and the Pressure–Time Curve

Inflator performance is measured in a fixed-volume closed tank, typically 60 L or 100 L, following the general approach of SAE J2238 / AK-LV 4 style procedures. The inflator is mounted inside the tank, fired, and the internal pressure is recorded with a fast-response pressure transducer (sampling at 10–100 kHz). The result is the P–t curve: tank pressure versus time from the trigger signal.

A typical driver-side pyrotechnic inflator P–t curve has three recognizable phases:

• Initiation delay — from the electrical trigger to the first measurable pressure rise, usually 0.5–2 ms, dominated by squib and initiator burn.
• Rapid pressurization — the steep rise as the gas generant burns and gas enters the tank, typically reaching 90% of peak within 10–30 ms.
• Cool-down / decay — after peak, the gas cools against the tank wall and pressure falls toward a quasi-steady value.

The peak tank pressure P_max and the time to reach it (t_Pmax) are the two headline numbers. For a 60 L tank and a typical driver inflator, P_max may fall in the range of 200–400 kPa(g) with t_Pmax around 15–40 ms, but these values are strongly inflator-specific and must never be assumed — they come from the supplier's test data.

2. From Pressure to Mass Flow Rate

CAE solvers such as LS-DYNA (keyword *AIRBAG_...) or PAM-CRASH do not directly use the P–t curve. They need the mass flow rate ṁ(t) and the gas temperature T(t) entering the cushion. The conversion from tank pressure to mass flow uses the ideal-gas relation applied to the tank control volume:

m(t) = (P(t) · V_tank) / (R · T_tank(t))

ṁ(t) = dm/dt

where:
  P(t)      = measured tank pressure (Pa, absolute)
  V_tank    = tank volume (m³)
  R         = specific gas constant of the combustion products (J/kg·K)
  T_tank(t) = gas temperature in the tank (K)

Because T_tank(t) is not directly measured in a simple tank test, two practical approaches are used:

1. Isothermal assumption — assume the gas cools instantly to ambient, T_tank = 293 K. This overestimates mass early in the event and is only acceptable for rough work.
2. Two-temperature / adiabatic–isothermal model — the gas enters hot (T_gas ≈ 1000–2000 K) and cools with a time constant τ. The mass flow is then solved iteratively. This is the standard approach in supplier data sheets.

In practice, the inflator supplier delivers a mass flow rate table and a temperature table as functions of time, already deconvolved from the tank test. The CAE engineer imports these directly. The P–t curve is retained as the verification reference: after building the model, a "tank simulation" is run with the same 60 L volume, and the simulated P–t curve is compared against the measured one. A good match (peak within ±5%, timing within ±1 ms) confirms the mass flow input is correct.

3. Temperature Effects

Inflator output is strongly temperature-dependent because the gas generant burn rate and the gas density both change with temperature. Inflators are therefore characterized at three soak temperatures, defined by the standard:

The spread between cold and hot peak pressure is typically 15–30% for a pyrotechnic inflator. This spread is not a nuisance — it is a design constraint. The airbag must protect the occupant at −35 °C (where the cushion inflates slowly and may not reach full stiffness in time) and must not over-pressurize at +85 °C (where the cushion may become too stiff and cause injury). The CAE model must therefore be run at all three temperatures, and the restraint performance evaluated at each.

Two temperature effects must be separated in the model:

• Inflator output temperature effect — the mass flow and gas temperature change with soak temperature. This is captured by using three separate inflator input decks (cold, ambient, hot).
• Cushion material temperature effect — the fabric stiffness and permeability change with temperature. This is captured by temperature-dependent material cards (e.g., *MAT_FABRIC with a temperature scale factor).

Confusing these two is a common modeling error. A model that uses the hot inflator curve but ambient fabric properties will over-predict cushion pressure at +85 °C and may wrongly conclude the design is unsafe.

4. Practical Workflow for CAE Input

The following sequence is a reproducible workflow for preparing inflator input for a DAB simulation. The numbers below are illustrative and must be replaced with the actual supplier data.

1. Obtain the supplier data package — P–t curves at −35 °C, +23 °C, +85 °C in a 60 L tank, plus the derived mass flow and temperature tables.
2. Check the reference volume — if the supplier tested in a 100 L tank but your model uses a 60 L cushion, do not simply scale the curve. Re-derive mass flow from the 100 L data, then apply it to the 60 L model.
3. Build the inflator keyword — for LS-DYNA, define *AIRBAG_SIMPLE_AIRBAG_MODEL or *AIRBAG_WANG_NEFSKE with the mass flow rate and temperature as load curves. Example structure:

*AIRBAG_SIMPLE_AIRBAG_MODEL
$   sid   sidtyp  rbid   vsca   psca   lcmt   tsca
     1     0       0     1.0    1.0    100    1.0
$   lcmt  = mass flow rate vs time
$   lct   = gas temperature vs time
$   lca   = ambient pressure vs time (optional)
$   lcc   = cushion volume vs pressure (optional)
$   lcs   = scale factor vs time (optional)
$   lcj   = jetting factor vs time (optional)
$   lcsl  = ...

5. Reading the Results

When reviewing a DAB simulation, the inflator performance shows up in three places:

• Cushion pressure history — should track the tank curve shape but at lower magnitude due to venting and volume growth.
• Cushion volume history — the rate of volume increase is driven by mass flow; a slow volume rise at cold temperature is expected and must be checked against the occupant's forward excursion.
• Occupant contact timing — the time from trigger to occupant contact should be compared against the time to peak cushion pressure. If the occupant arrives before the cushion is pressurized, the inflator is too slow for that condition.

The figure below summarizes the relationship between the measured tank P–t curve, the derived mass flow rate, and the temperature-dependent input decks used in CAE.

The chain is straightforward: the tank test produces the P–t curve, the curve is deconvolved into mass flow and gas temperature, and those tables become the CAE inflator input. Temperature is not a single correction factor but a set of three independent input decks, each verified against its own tank test. When the simulated tank curve matches the measured curve at all three temperatures, the inflator model is trustworthy and can be used for occupant restraint simulation with confidence.