4. Load Limiter Force Plateau Verification via Quasi-Static Webbing Pull Test

Test Objective and Measurable Definition of the Plateau

The load limiter's job is to cap shoulder-belt force at a calibrated plateau while the webbing pays out. Verifying that plateau with a quasi-static pull test requires a precise, repeatable definition of what "plateau" means before any hardware is mounted. For this case, the plateau is defined over the effective extraction stroke: the interval from 50 mm to 90% of the total calibrated payout (for a typical 50th-percentile front-row retractor, roughly 50 mm to 180 mm of a 200 mm payout). Within that window, the measured belt force must stay inside a band of ±8% around the nominal plateau force F_nom.

Two additional acceptance criteria accompany the band check: the peak-to-peak force ripple inside the window must not exceed 5% of F_nom (this catches stick-slip), and the loading and unloading branches at the same stroke position must differ by no more than 6% of F_nom (this catches hysteresis from friction in the torsion bar seat or webbing routing). A test that only checks the average force will pass a limiter that is chattering or binding, which is exactly the failure mode this procedure is designed to expose.

Test Article, Fixture, and Instrumentation

The article is a production-intent retractor with the calibrated torsion-bar load limiter installed, webbing routed through the production D-ring and tongue geometry, and the pretensioner in its unfired state (the pretensioner is not exercised in this test; its stroke consistency is verified separately). Mount the retractor in a rigid fixture that reproduces the vehicle's retractor mounting angle within ±2°, because the webbing wrap on the spool changes with attitude and shifts the effective lever arm.

  • Actuator: servo-hydraulic or ball-screw tensile frame, 20 kN capacity, capable of 100 mm/s constant velocity with position feedback better than ±0.1 mm.
  • Load measurement: in-line tension load cell, 10 kN range, 0.1% FS accuracy, mounted between the pull clamp and the frame crosshead so it sees only belt tension.
  • Displacement: frame LVDT plus an independent string potentiometer clipped to the webbing at the D-ring exit, so spool rotation and webbing stretch are separated from crosshead travel.
  • Clamp: serrated wedge grip with a 60 mm engagement length; a slip of more than 0.5 mm invalidates the run.
  • Sampling: 1 kHz minimum on both channels, synchronized, with a 10 Hz low-pass filter applied only for reporting (raw data retained for ripple analysis).

Condition the article at 23 ± 2 °C for at least 4 hours. Record the retractor serial number, torsion-bar lot, and webbing lot on the data sheet; plateau force is sensitive to bar lot, and a mixed-lot comparison will produce misleading scatter.

Executing the Pull Profile

The profile is a displacement-controlled ramp with a hold and a return, run three times on the same article with a 60 s rest between cycles to let the torsion bar relax. Use 100 mm/s for the loading ramp — slow enough to stay quasi-static (no inertial contribution from the spool and webbing mass) but fast enough to keep the run under a minute and avoid thermal drift in the load cell.

  1. Pre-tension: pull to 200 N at 20 mm/s and hold 5 s to seat the webbing in the clamp and take up slack. Zero the displacement channel here; this is stroke position 0.
  2. Loading ramp: drive to 200 mm total payout at 100 mm/s, logging force and displacement continuously.
  3. Hold: dwell at 200 mm for 10 s. A force that decays more than 3% during the hold indicates the limiter is still yielding rather than riding its plateau.
  4. Unloading ramp: return to 50 mm at 100 mm/s, then release to the pre-tension position.
  5. Repeat steps 1–4 for cycles 2 and 3.

Do not stop the ramp inside the plateau window to "take a reading." Stopping loads the bar at a fixed strain and lets it creep, which biases the next segment and manufactures apparent hysteresis. Continuous motion is what makes the plateau measurement meaningful.

Reducing the Data and Judging the Plateau

From the raw trace, extract the loading branch between 50 mm and 180 mm. Compute the mean force F_mean, the maximum and minimum force in the window, and the peak-to-peak ripple. Then compute the plateau error as (F_mean − F_nom) / F_nom × 100% and compare against the ±8% band. For hysteresis, sample the loading and unloading branches at 60, 100, 140, and 170 mm and compute the force difference at each position; the largest difference is the hysteresis metric.

A worked example with representative numbers: suppose F_nom = 4.00 kN. A run returns F_mean = 4.12 kN, F_max = 4.21 kN, F_min = 4.03 kN over the window. The plateau error is +3.0%, inside the ±8% band. The ripple is (4.21 − 4.03)/4.00 = 4.5%, inside the 5% limit. If the unloading branch at 100 mm reads 3.94 kN against a loading value of 4.10 kN, the hysteresis is 0.16 kN = 4.0%, inside the 6% limit. This run passes all three criteria. A run with F_mean = 4.35 kN (+8.8%) fails the band even if its ripple is small — the limiter is simply set too high and needs a torsion-bar diameter or material adjustment, not a test-method change.

If the ripple exceeds 5% but the mean is centered, look for stick-slip before condemning the bar. Common causes are dry webbing routing over the D-ring, a burr on the torsion-bar seat, or a clamp that is slipping in small increments. Re-route or lubricate per the production specification and re-run; a genuine stick-slip from the bar itself will persist across all three cycles and usually shows a sawtooth pattern in the raw trace.

Reading the Force–Stroke Signature

The SVG below maps the three signatures this test is built to separate: a clean plateau, a stick-slip trace, and a hysteresis loop. The acceptance windows are drawn to scale so the pass/fail decision can be read directly off the trace shape.

Load Limiter Plateau Signatures — Force vs. Extraction Stroke A. Clean plateau — PASS stroke (mm) force ±8% band B. Stick-slip — FAIL (ripple) stroke (mm) force ripple > 5% C. Hysteresis — FAIL (loop) stroke (mm) force loading unloading Acceptance Criteria and Diagnostic Mapping Criterion Limit Signature if failed First check Plateau error ±8% of F_nom Mean shifted up/down Bar lot / diameter Peak-to-peak ripple ≤ 5% of F_nom Sawtooth trace Routing / seat burr Hysteresis ≤ 6% of F_nom Open loop, load vs unload Friction / clamp slip Hold decay (10 s) ≤ 3% of F_nom Force still falling Bar still yielding

Common Failure Symptoms and What They Point To

When a run fails, the trace shape usually identifies the cause faster than any single number. A mean that sits high or low with a clean, flat plateau is a calibration problem — the torsion bar is the wrong diameter or lot, and the fix is upstream of the test. A sawtooth ripple with a centered mean is a friction or stick-slip problem in the webbing path or the bar seat; re-route, inspect for burrs, and re-run before touching the bar. An open hysteresis loop that widens with stroke is usually clamp slip or a binding D-ring, and it will show up as a displacement mismatch between the frame LVDT and the string potentiometer — if those two channels disagree by more than 1 mm, the clamp is slipping and the run is invalid regardless of the force numbers. A force that keeps decaying during the 10 s hold means the bar has not finished yielding at 200 mm; extend the payout or check that the bar was properly stress-relieved.

Run all three cycles and report the worst-case cycle, not the average. A limiter that passes on cycle 1 and drifts out of band by cycle 3 is exhibiting work-hardening or seat wear that will only get worse in service, and averaging the three cycles hides exactly the trend the test exists to catch.

Keep a per-run data sheet with the four metrics (plateau error, ripple, hysteresis, hold decay), the three cycle values, and the pass/fail flag. Three consecutive passing cycles on the same article, with the worst-case metric inside every limit, is the release condition for this verification step.
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