2. Restraint system architecture and sign-off scope

Before any MADYMO model is built, the restraint system must be decomposed into its functional elements and each element mapped to a verifiable sign-off claim. A restraint system is not a single component but a coordinated chain: seat belt webbing and geometry, retractor, pretensioner, load limiter, airbag modules, and the occupant themselves. Sign-off scope defines which of these elements are represented in the model, which are validated against physical tests, and which interactions must be demonstrated to meet regulatory and consumer-rating targets.

2.1 Functional Decomposition of the Restraint Chain

The restraint chain can be organized by energy path. The seat belt is the primary load path for the torso and pelvis; the airbag is a secondary, distributed load path for the head and chest; the pretensioner removes slack before the occupant loads the belt; and the load limiter caps the force transmitted through the belt by allowing controlled webbing payout or deformation. Each element has a distinct force–displacement or force–time signature, and MADYMO sign-off must reproduce these signatures within defined tolerances.

Element	Primary Function	Key MADYMO Representation	Sign-Off Metric
Seat belt webbing	Torso/pelvis restraint, load transfer	Finite-element belt segments with slip rings	Belt force–time, elongation
Retractor	Webbing storage, locking	Belt payout function, locking threshold	Payout vs. time, lock timing
Pretensioner	Slack removal, early coupling	Force–time or displacement–time actuator	Belt tension rise, slack removal time
Load limiter	Force capping, chest deflection control	Torsion bar or webbing payout curve	Peak belt force, payout stroke
Airbag module	Head/chest cushioning, load distribution	Gas flow model, fabric FE, venting	Internal pressure, contact force, HIC

In MADYMO, the belt is typically modeled with BELT elements and slip rings, while the retractor and pretensioner are represented by RETRACTOR and PRETENSIONER definitions. The load limiter is often a force–displacement curve applied to the retractor payout or a torsion-bar element. Airbags use GASFLOW or uniform-pressure models depending on fidelity requirements. The sign-off scope must state which of these are predictive (validated against test) and which are assumed or carried over from supplier data.

2.2 Interaction Effects That Drive Sign-Off

The most consequential sign-off issues arise from interactions, not from individual components. Three interactions dominate:

• Pretensioner–load limiter timing. If the pretensioner fires too late or the load limiter engages too early, the belt force rises before the occupant is coupled, reducing restraint efficiency. MADYMO must reproduce the relative timing within a few milliseconds.
• Belt–airbag load sharing. The airbag must not push the occupant into the belt or vice versa. The model must capture the belt path relative to the airbag deployment zone, including slip-ring friction and belt-to-occupant contact.
• Occupant–belt–seat coupling. Seat cushion stiffness and recliner behavior affect pelvis kinematics, which in turn changes belt geometry and airbag contact. Sign-off scope should state whether the seat is rigid, deformable, or represented by a validated seat model.

2.3 Defining the Sign-Off Scope in MADYMO

A practical sign-off scope is a matrix of load cases, occupant sizes, and restraint configurations. For a frontal impact program, a typical scope includes:

1. Load cases: full frontal rigid barrier at 50 km/h, offset deformable barrier at 64 km/h, and a low-speed pulse for pretensioner-only verification.
2. Occupant models: 50th percentile male, 5th percentile female, and 95th percentile male, each with validated posture and belt routing.
3. Restraint configurations: baseline (belt + pretensioner + load limiter + airbag), belt-only, and airbag-only, to isolate contributions.
4. Output metrics: HIC15, chest deflection, chest acceleration (3 ms clip), belt force, and femur load, each with pass/fail thresholds from regulation or rating.

The scope must also define the model boundary: what is imported from supplier data (airbag pressure curve, retractor payout), what is calibrated in MADYMO (belt friction, slip-ring losses), and what is validated against physical test (occupant kinematics, belt force). This boundary is the basis for the validation plan and the confidence statement in the sign-off report.

2.4 A Worked Example: Pretensioner and Load Limiter Interaction

Consider a frontal load case where the pretensioner is pyrotechnic and the load limiter is a torsion bar with a 4 kN plateau. The MADYMO model uses a PRETENSIONER with a force–time curve and a RETRACTOR with a payout curve. The sign-off question is whether the belt force stays below 4.5 kN while the pretensioner removes at least 60 mm of slack within 15 ms.

In the model, the pretensioner is activated at T=0 ms with a rise time of 5 ms. The load limiter begins payout when belt force reaches 4 kN. The observable outputs are belt force at the retractor and belt displacement at the slip ring. If the pretensioner stroke is too slow, the occupant loads the belt before slack is removed, and the force peak exceeds the limit. If the load limiter engages too early, the belt force plateaus before the occupant is fully coupled, increasing chest deflection. The sign-off criterion is therefore a window: pretensioner stroke ≥ 60 mm by 15 ms, and peak belt force ≤ 4.5 kN.

2.5 Scope Boundaries and Exclusions

Every sign-off scope must state exclusions explicitly. Common exclusions include out-of-position occupants, rear-seat interactions, and non-fired airbag cases. These are not failures of the model but boundaries of the validation. In MADYMO, an excluded case may still be simulated for sensitivity, but it cannot be used as a sign-off claim. The scope document should list each exclusion with a rationale and a risk statement.

The diagram above shows the restraint chain as a set of interacting load paths. The occupant loads the belt, the pretensioner and load limiter modify the belt force, and the airbag shares the load with the belt. The seat provides the reaction path for the pelvis. Each arrow represents a sign-off interaction that must be validated, not just modeled.

2.6 Practical Sign-Off Checklist

The following checklist is a compact, reusable scope definition for a frontal restraint sign-off. It is written as a table so it can be copied into a validation plan.

Item	Definition	Evidence Required
Belt geometry	Anchor points, slip-ring positions, belt width	CAD match, belt path photo
Retractor	Payout curve, locking threshold	Supplier curve, bench test
Pretensioner	Stroke–time, activation time	Supplier data, sled test
Load limiter	Force plateau, payout stroke	Component test, belt force
Airbag	Pressure–time, venting, fabric properties	Module test, tank test
Occupant	Size, posture, belt routing	Validation against sled test
Seat	Stiffness, recliner, cushion	Seat pull test or validated model

Each row must be traceable to a source document or test. If a row is marked as assumed, the sign-off report must state the assumption and its sensitivity. This traceability is what separates a defensible sign-off from a model that merely runs.

In summary, the sign-off scope for a MADYMO restraint model is defined by the functional decomposition of the restraint chain, the interactions that govern occupant response, and the explicit boundaries of what is validated, what is assumed, and what is excluded. The next step is to translate this scope into a validated model with calibrated belt, pretensioner, load limiter, and airbag representations.