2. Correlate Seat Belt Force–Displacement with Retractor and Pretensioner Behavior

Why Belt Force–Displacement Is the Correlation Anchor

In a frontal sled correlation, the belt system is the primary load path between the occupant and the vehicle. Head and chest acceleration from the previous baseline case can look acceptable while the belt is still wrong: a retractor that spools out too early, a pretensioner that strokes too far, or a D-ring friction coefficient that is too low will all shift chest deflection without necessarily breaking the acceleration match. The reliable way to isolate these effects is to correlate the belt at the component level first — shoulder and lap belt force versus displacement, retractor spool-out, and pretensioner stroke — and only then judge chest deflection.

This case calibrates the belt system in CAE against test data using three measured channels: shoulder belt force–displacement, lap belt force–displacement, and retractor spool-out (plus pretensioner stroke where instrumented). The deliverable is a belt model whose force–displacement curves overlay the test within a defined tolerance, with belt routing and friction treated as explicit calibration parameters rather than tuning knobs applied after the fact.

Test Channels and What Each One Constrains

Before touching the model, map each test channel to the CAE parameter it constrains. This mapping prevents the common failure of adjusting friction to fix a retractor problem.

The key discipline: retractor spool-out and pretensioner stroke are kinematic constraints. Fix them first, because they set the displacement axis of the force–displacement curves. Only after the displacement history matches should friction and webbing stiffness be tuned to match the force magnitude.

Building the Belt Model for Correlation

The belt is modeled as a seatbelt element set (2D belt elements with a defined width and EA) routed through a retractor, a D-ring, a tongue/latch, and two anchor points. The retractor is a slip-ring or spool element with a lock condition and an optional pretensioner load curve. The following excerpt shows the essential parameter block for a shoulder-belt retractor with pretensioner, using LS-DYNA-style keywords as a representative example (adapt names to your solver):

*ELEMENT_SEATBELT_RETRACTOR
$  SBRID     SID1      SID2      SID3      SID4
   1001         0         0         0         0
$  Pull-out force (N), lock acceleration (g), spool inertia
   1001       2.5      3.0       0.0
$
*ELEMENT_SEATBELT_PRETENSIONER
$  SBPID    SBRID     PTYPE     TIME      STROKE
   2001     1001         1      15.0       120.0
$  Force-stroke curve (pretensioner)
$  Stroke(mm)  Force(N)
       0.0       0.0
      20.0     900.0
      60.0    1400.0
     120.0     600.0
$
*MAT_SEATBELT
$  MID       MP        LCF       EA(N)     Width(mm)
   3001       0.0        0      12000.0     48.0
$
*ELEMENT_SEATBELT_SLIPRING
$  SBSID    SBRID     Friction
   4001     1001       0.15

Two points matter for reproducibility. First, the pretensioner force–stroke curve is a calibration target, not a guess: start from the supplier curve and adjust only within its stated tolerance band. Second, the slip-ring friction (0.15 here) is the D-ring/tongue friction that will later be separated from routing effects. Keep it as a named parameter so the sensitivity study can vary it independently.

Correlation Workflow: Kinematics Before Forces

Run the sled model with the belt parameters above and extract the three channels. Compare in this order:

1. Retractor spool-out and pretensioner stroke. Overlay CAE and test webbing pay-out versus time. If the CAE spools out more than the test before lock, raise the lock acceleration threshold or reduce the pretensioner firing delay. If pretensioner stroke is short, check that the force–stroke curve is actually being applied (a common error is a pretensioner defined but not linked to the retractor SBRID).
2. Shoulder belt force–displacement. With the displacement axis now correct, compare force magnitude. A force that is uniformly low points to webbing EA or friction; a force that rises late points to routing (belt not contacting the chest early enough).
3. Lap belt force–displacement. Compare lap force onset against shoulder force. A lap force that lags indicates the lap routing is too loose or the anchor is too far forward.
4. Chest deflection. Only now evaluate chest deflection. If belt curves match but chest deflection does not, the discrepancy is in the dummy–belt contact or chest foam, not the belt system.

Isolating Routing and Friction Effects

Once the baseline belt curves are close, run a small sensitivity matrix to separate routing from friction. Vary one parameter at a time and record the change in shoulder force at peak and in chest deflection:

The diagnostic value is in the pattern, not any single number. If chest deflection is high but shoulder force matches, friction is likely too low or the D-ring is too far forward. If shoulder force is high but deflection is low, the belt is too stiff (EA too high) or the pretensioner is over-driven. This is exactly the routing-versus-friction separation the case goal requires.

Acceptance Criteria and Failure Symptoms

Define the pass condition before running the matrix, so the correlation is objective rather than visual. A workable set for this case:

• Retractor spool-out: CAE within ±10 mm of test at lock and at peak pretensioner stroke.
• Pretensioner stroke: within ±8 mm of test total stroke.
• Shoulder and lap belt force: peak within ±8% of test, onset time within ±3 ms.
• Chest deflection: within ±5 mm of test peak, evaluated only after the belt channels pass.

Common failure symptoms and their first checks: spool-out runs long before lock → verify lock acceleration threshold and that the pretensioner is linked to the retractor SBRID; shoulder force plateau too low → check slip-ring friction and webbing EA; lap force lags shoulder force → check lap anchor position and routing; pretensioner stroke zero → confirm the force–stroke curve is applied and firing time is within the event window.

Reusable Calibration Record

Keep a single record per correlation run so the routing-versus-friction conclusion is traceable. A minimal, directly fillable form:

With the belt kinematics locked and the force curves overlaid, the routing-versus-friction question is answered by the sensitivity matrix rather than by trial and error, and chest deflection becomes a verification of the belt calibration instead of a tuning target.