4. Seatbelt design variables

In a restraint-system DOE, the seatbelt is not a single object but a chain of interacting design variables. Four of them dominate the occupant response in frontal and oblique loading: webbing stiffness, pretensioner force, load limiter threshold, and anchor point geometry. Each one changes a different part of the force–displacement history delivered to the occupant, and each one interacts with the others in ways that make one-at-a-time studies misleading. This chapter defines these four factors precisely enough to be entered into a DOE matrix, explains how each is represented in an LS-DYNA belt model, and shows how to choose levels and ranges that produce a well-conditioned, physically meaningful design space.

Why these four factors, and what each one actually controls

The seatbelt system performs two competing jobs: coupling the occupant to the vehicle early enough to prevent excessive excursion, and limiting the peak force transmitted to the chest and clavicle. Pretensioner force and webbing stiffness serve the first job; the load limiter serves the second; anchor geometry sets the belt path and therefore the direction and leverage of the forces. Treating them as independent knobs is convenient for a DOE but physically incomplete, because the load limiter only becomes active after the pretensioner has paid out slack and the belt has engaged the occupant.

Webbing stiffness is the axial force–strain characteristic of the belt material, usually expressed as a force per unit strain or as a force–elongation curve at a reference gage length. In LS-DYNA it is carried by the seatbelt material (typically *MAT_SEATBELT) through a load curve, with the belt modeled as 1D seatbelt elements or as shell elements with a defined width and thickness. The DOE factor is best expressed as a multiplier on the nominal force–elongation curve, for example 0.85, 1.00, and 1.15, rather than as an absolute stiffness, because the multiplier preserves the shape of the nonlinear response and keeps the factor dimensionless and comparable across belt sections.

Pretensioner force is the retraction force applied at the buckle or retractor during the early crash phase. In the model it is usually implemented as a retractor or buckle pretensioner with a defined force–time or force–stroke curve, or as a prescribed retraction via *ELEMENT_SEATBELT_PRETENSIONER. The DOE factor is the peak pretensioner force, or a scale factor on the pretensioner curve. Its effect is strongly time-dependent: it removes slack and pulls the occupant into the seat before the load limiter engages, so its influence on peak chest deflection depends on the timing of the load limiter.

Load limiter threshold is the force level at which the belt spool pays out webbing to cap the restraint force. It is modeled as a force-limiting element in the retractor or buckle path, often with a force–displacement curve that includes a breakaway or two-stage characteristic. The DOE factor is the plateau force, for example 3.0 kN, 4.0 kN, and 5.0 kN, or a scale factor on the limiter curve. This is the factor most directly tied to chest injury metrics, and it is also the one most sensitive to occupant size.

Anchor point geometry is the set of coordinates defining the retractor, D-ring, buckle, and outboard anchor positions. In the model these are node locations or rigid-body reference points that the belt elements route through. The DOE factor is best expressed as a small translational offset of one or more anchors, for example ±20 mm in the fore–aft and vertical directions for the D-ring and buckle, rather than as absolute coordinates, so that the factor is centered on the baseline geometry and the levels are symmetric.

How the four factors interact along the restraint chain

The figure below shows the restraint chain and where each factor acts. The pretensioner and webbing stiffness act early, during slack removal and belt engagement; the load limiter acts later, once the belt force reaches its threshold; anchor geometry acts throughout, because it sets the belt path and therefore the angle at which force is applied to the occupant.

The plot makes the interaction explicit. A higher pretensioner force shifts the rise earlier but does not change the plateau; a lower load limiter lowers the plateau but does not change the rise; stiffer webbing steepens the rise and slightly raises the plateau because the belt reaches the limiter sooner. If the DOE varies these factors independently, the main effect of the load limiter will be estimated cleanly, but the pretensioner × limiter interaction will only be visible if the matrix includes combined levels. That is the practical argument for a factorial or response-surface design rather than a screening design with too few runs.

Choosing levels and ranges

Levels must be physically achievable and must not push the model outside its valid range. A practical approach is to anchor the low and high levels to real hardware variants or to the tolerance band of the nominal part, then verify that the model remains stable and that the belt does not go slack or over-engage at the extremes. The table below gives an example set of levels for a mid-size sedan driver model; these are illustrative values for teaching, not measured results.

For anchor geometry, treat the offset as a two-component factor or split it into separate fore–aft and vertical factors if the DOE budget allows. A single combined offset confounds two geometric effects and makes the main effect hard to interpret. If the budget is tight, keep the fore–aft offset as the factor and hold the vertical offset at nominal, because fore–aft position has the stronger influence on belt angle and chest loading in frontal impact.

Setting up the factor definitions in the model

The cleanest way to make these factors DOE-ready is to drive each one from a single scalar parameter, so that a run is fully defined by four numbers. In an LS-DYNA keyword deck this is typically done with *PARAMETER and *DEFINE_CURVE scaling, or with a preprocessor that rewrites the relevant cards per run. A minimal pattern looks like this:

*PARAMETER
  webScale   1.00
  preScale   1.00
  limForce   4.00
  dRingX     0.00
  dRingZ     0.00
*DEFINE_CURVE
  $ webbing force–strain, scaled by webScale in the material card
*MAT_SEATBELT
  $ ... LCID references the scaled curve ...
*ELEMENT_SEATBELT_PRETENSIONER
  $ ... force curve scaled by preScale ...
*ELEMENT_SEATBELT_RETRACTOR
  $ ... limiter plateau set to limForce ...

Two practical checks matter here. First, confirm that the scale factors are applied to the correct curve and not double-applied through both the material and the element definition. Second, confirm that the anchor offsets move the belt routing nodes and the associated rigid reference points together; moving only the visual anchor while leaving the belt path unchanged produces a run that looks different but behaves identically, which silently corrupts the DOE.

What to observe and how to judge a run

For each run, extract the belt force–time history at the retractor and at the shoulder, the chest deflection and chest acceleration of the occupant, and the forward excursion of the head and chest. These responses let you confirm that the factor acted as intended before you fit any response surface. A run where the load limiter was supposed to lower the plateau but the belt force history is unchanged usually means the limiter never engaged, because the pretensioner or webbing factor kept the belt force below the threshold. That is not a modeling error; it is a real interaction, and it should be recorded as such rather than discarded.

Judge the design space by checking that the response varies monotonically and smoothly across levels. A non-monotonic response, such as chest deflection rising at both low and high limiter force, often signals that another factor has crossed a regime boundary, for example the belt going slack at low pretensioner force. Flag those runs and inspect the force history before including them in the fit. A well-conditioned DOE for these four factors typically needs at least a full factorial at two levels plus center points, or a face-centered central composite design if curvature is expected, with the number of runs driven by the interaction structure rather than by a fixed rule.

The deliverable of this stage is a factor table with defined representations, levels, and response channels, plus a validated set of baseline runs that confirm each factor moves the response in the expected direction. Once that table is stable, the DOE matrix can be generated and the response surface fitted with confidence that the factors are physically meaningful and independently controllable.