2. Restraint system fundamentals for correlation

Occupant restraint CAE correlation is not a single-model problem. A frontal impact simulation typically contains at least four interacting subsystems — the seat belt webbing path, the retractor and its pretensioner, the load limiter, and one or more airbags — plus the occupant model and the seat structure. Correlation failures are rarely caused by "the whole model being wrong." They are caused by one subsystem's force–time or displacement–time characteristic being misrepresented, and that error propagating through the occupant kinematics. This chapter establishes what each restraint component physically does, which parameters govern its behavior, and how each is represented in a CAE model so that later correlation work has a defensible baseline.

Seat belt system: geometry, routing, and slip

The seat belt is a tension structure. Its influence on the occupant comes almost entirely from three things: where the belt sits on the body (geometry), how much it stretches (stiffness), and how much it can slide through the D-ring and buckle (slip and friction). In CAE, the belt is normally modeled as a combination of 1D seat belt elements (slip rings, retractor elements, pretensioner elements) and 2D membrane or shell elements for the portion in contact with the occupant.

Two modeling decisions dominate correlation quality. First, the belt routing must match the physical hardware: anchor points, D-ring position, buckle stalk geometry, and the outboard/inboard paths. A D-ring located 15 mm too high changes the chest belt angle and shifts chest deflection by a measurable amount. Second, belt-to-occupant friction must be defined. Typical values used in correlation studies range from μ = 0.1 to μ = 0.3 for the belt-to-clothing interface; the exact value should be treated as a calibration parameter, not a fixed constant.

Belt stiffness is usually supplied as an engineering stress–strain curve for the webbing, converted into a force–strain relationship for the 1D belt elements. A representative webbing stiffness for a 48 mm polyester belt is on the order of 200–400 N per percent strain in the initial region, stiffening at higher strain. These values are illustrative; the actual curve must come from the belt supplier or a component test.

Retractor, pretensioner, and load limiter

The retractor provides the locking function and, in many systems, houses the pretensioner and load limiter. The pretensioner removes slack from the belt early in the event — typically within the first 10–20 ms — by pulling 40–80 mm of webbing back toward the retractor or buckle. In CAE this is represented as a prescribed displacement or a force–time curve applied to a pretensioner element, with a defined stroke limit. If the pretensioner is modeled as a force only, without a stroke limit, the belt will continue to tighten unrealistically and chest deflection will be under-predicted.

The load limiter is the component that caps belt force to protect the chest. It is usually a torsion bar in the retractor or a stitch pattern in the webbing. Its CAE representation is a force–displacement curve: force rises to a plateau (the limit load), then stays approximately constant while the torsion bar twists or the stitches tear. A typical limit load for a driver-side retractor is 3–5 kN, with a stroke of 80–150 mm. The correlation-critical parameters are the plateau force, the stroke at which the plateau begins, and the stroke at which the belt force begins to rise again (bottoming out).

Airbags: pressure, venting, and deployment

Airbags are modeled in CAE using one of three approaches: uniform pressure (UP), control volume (CV), or corpuscular particle method (CPM). For correlation work, the choice matters because each method represents gas flow and venting differently.

• Uniform pressure (UP): The bag is treated as a single pressure acting on the fabric. Fast, but cannot capture pressure gradients or early deployment.
• Control volume (CV): The bag is divided into chambers; pressure is computed from mass and energy balance using an equation of state (typically ideal gas or JWL). This is the standard for driver and passenger frontal airbags.
• Corpuscular particle method (CPM): Gas is represented as particles; used when jetting and fabric interaction are important, such as side airbags and curtain airbags.

The correlation-critical inputs for a CV airbag are: inflator mass flow rate versus time, gas temperature, vent hole area and discharge coefficient, fabric permeability, and bag geometry including tethers. A typical driver inflator mass flow curve rises to a peak of 2–4 kg/s within 10–20 ms and decays over 40–60 ms. Vent hole area is often 2,000–4,000 mm² total, with a discharge coefficient around 0.6–0.8. Fabric permeability is usually given as a volumetric flow rate per unit area per unit pressure difference and is a common source of correlation error because it changes with bag inflation state.

How the subsystems interact in a correlation model

The figure below shows the restraint system as a coupled signal and force chain. Each block has a defined input, a governing parameter set, and an output that feeds the next block or the occupant. The arrows indicate the direction of influence, not necessarily the direction of physical motion.

Practical correlation workflow for restraint subsystems

The following sequence reflects how restraint correlation is typically executed in a program. It is not a rigid template; the order may change depending on which subsystem is suspected of causing the mismatch.

1. Component-level validation first. Before running a full sled model, validate the belt force–strain curve against a coupon test, the pretensioner stroke against a bench test, and the load limiter plateau against a retractor pull test. If these do not match, the full model cannot be trusted.
2. Airbag static deployment check. Inflate the bag model in free space and compare the pressure–time curve and bag shape at 20 ms, 40 ms, and 60 ms against a tank test or static deployment video. Adjust vent area and permeability to match the pressure decay.
3. Belt-only sled run. Run the sled model with the airbag disabled. Compare belt force at the retractor and shoulder, and chest deflection. This isolates belt routing, pretensioner, and load limiter behavior.
4. Full system run. Enable the airbag and compare occupant kinematics. If chest deflection is now over-predicted, the bag is likely too stiff or venting too slowly; if head acceleration is over-predicted, the bag may be deploying too late or the tether geometry may be wrong.
5. Parameter sensitivity check. Perturb the most uncertain parameters — friction coefficient, vent discharge coefficient, load limiter plateau — by ±10% and record the change in chest deflection and head acceleration. Parameters with large sensitivity require tighter calibration.

Common failure symptoms and their likely causes

Each of these symptoms points to a specific subsystem, and each subsystem has a defined set of correlation parameters. The next chapter applies this framework to the actual correlation process: test data alignment, signal processing, and objective rating methods.