2. Seatbelt system fundamentals

A seatbelt restraint in MADYMO is not a single entity but a chain of mechanical elements whose behavior must be assembled from geometry, routing, and constitutive definitions. Before any belt can be validated against a sled or full-vehicle test, the analyst must translate the physical belt system — webbing path, retractor, pretensioner, load limiter, and anchor points — into a consistent set of FE and discrete elements. This section establishes the physical function of each subsystem and the corresponding MADYMO modeling primitive, so that later validation work rests on a defensible baseline.

Belt Geometry and Routing

The belt geometry defines how restraint force is transmitted from the occupant to the vehicle structure. In a three-point system, the webbing runs from the retractor through the D-ring (shoulder anchor), across the chest and lap, into the buckle, and terminates at the anchor points. The path is not a straight line: it wraps around the occupant's torso and pelvis, and the contact pressure distribution depends on the local curvature of the webbing.

In MADYMO, belt geometry is represented by a chain of BELT elements. Each belt segment is defined by a sequence of nodes, and the webbing is modeled either as a discrete spring-damper chain or as membrane/shell elements, depending on the fidelity required. The recommended practice is to define the belt path using the actual CAD routing points, then project the belt onto the occupant surface using the belt fitting procedure. The fitting algorithm adjusts node positions so that the belt lies on the occupant's outer surface with a specified initial tension.

Key geometric parameters include the belt width (typically 46–50 mm for a standard three-point belt), the initial slack, and the wrap angle at each anchor. The wrap angle at the D-ring directly influences the friction force and thus the force transmitted to the shoulder. A common modeling error is to neglect the D-ring friction, which can overestimate shoulder force by 10–20% in the early phase of a crash pulse.

Retractor, Pretensioner, and Load Limiter

The retractor serves three functions: it stores the webbing, locks during a crash to prevent payout, and — in modern systems — houses the pretensioner and load limiter. In MADYMO, the retractor is modeled as a RETRACTOR element that applies a locking condition and a payout force. The locking behavior is typically defined by a time-dependent or acceleration-dependent trigger.

The pretensioner removes slack from the belt system at the onset of a crash. It is modeled in MADYMO as a force applied at the retractor or buckle anchor, with a defined force-time curve. A typical pyrotechnic pretensioner generates 2–4 kN of force over 10–20 ms, pulling 50–80 mm of webbing. The pretensioner force curve should be obtained from component tests or supplier data; using a generic curve is acceptable only for sensitivity studies, not for final validation.

The load limiter controls the maximum force transmitted to the occupant by allowing controlled webbing payout once a threshold force is reached. In MADYMO, this is represented by a force-limiting element in series with the retractor, defined by a force-displacement curve. A typical load limiter for a frontal occupant is set at 3–4 kN, with a payout of 100–150 mm. The interaction between pretensioner and load limiter is critical: the pretensioner must complete its stroke before the load limiter activates, otherwise the two mechanisms compete and the belt force profile becomes erratic.

Anchor Points and Their Representation

Anchor points are the fixed attachment locations of the belt to the vehicle structure: the retractor anchor, the D-ring (shoulder anchor), the buckle anchor, and the lap anchor(s). Their positions determine the belt angle relative to the occupant and thus the distribution of restraint force between the chest and pelvis.

In MADYMO, anchor points are defined as fixed nodes or as nodes attached to a rigid body representing the vehicle structure. The belt elements connect to these nodes. The position of each anchor should be taken from the vehicle CAD model, and the belt path should be checked for interference with the seat and interior trim. A misplaced D-ring — for example, 20 mm too low — can increase chest deflection by 5–10 mm in a 50 km/h frontal impact, which may be the difference between a pass and a fail in the injury criteria.

The buckle anchor is often modeled with a slip ring or a fixed node, depending on whether the buckle is rigidly mounted or has a flexible stalk. For a flexible stalk, a spring element can represent the stalk stiffness. The lap anchor is typically fixed to the seat frame or the floor; its position relative to the occupant's pelvis determines the lap belt angle, which should be between 45° and 65° to the horizontal for effective pelvic restraint.

Integrated System Behavior

The belt system must be modeled as an integrated chain. The retractor locking, pretensioner firing, load limiter payout, and belt routing all interact. A common validation issue is that the pretensioner force is applied at the retractor but the belt path has not been fitted with the correct initial tension, leading to a delay in belt tightening. Another issue is that the load limiter is modeled as a constant force rather than a force-displacement curve, which underestimates the payout in the later phase of the crash.

The following SVG illustrates the signal and force flow through a MADYMO belt model, from the retractor through the pretensioner and load limiter to the occupant contact.

Practical Modeling Checks

Before running a full crash simulation, perform the following checks on the belt model:

• Belt fitting: Confirm that the belt lies on the occupant surface with the specified initial tension (typically 0.5–1.0 N per element for a discrete belt).
• Anchor positions: Compare the MADYMO anchor coordinates with the CAD data. A tolerance of ±5 mm is acceptable for most applications.
• Pretensioner timing: Verify that the pretensioner force curve is applied at the correct time relative to the crash pulse (T0).
• Load limiter curve: Check that the force-displacement curve is monotonic and that the maximum force does not exceed the belt strength (typically 15–20 kN for a standard webbing).
• Energy balance: After simulation, check that the energy absorbed by the belt system is consistent with the occupant kinetic energy change.

With the belt system modeled and checked, the next step is to validate the model against physical test data. The following sections will address the validation methodology, but the foundation established here — correct geometry, correct retractor behavior, correct pretensioner and load limiter curves, and correct anchor positions — is what makes validation meaningful rather than a curve-fitting exercise.