3. Pretensioner Peak Force Sweep vs. Chest Deflection
Scope and Fixed Baseline
This case isolates a single design variable: the pretensioner peak force. The load limiter is frozen at its baseline characteristic so that any change in chest deflection can be attributed to the pretensioner rather than to a coupled shift in restraint energy management. The occupant model is a 50th-percentile male, seated in the nominal position, with the belt routed through the standard D-ring and buckle geometry. The pretensioner force–time profile keeps its baseline rise time and stroke; only the peak force amplitude is scaled.
Two reference quantities carry over from the baseline setup and are held constant here:
- Load limiter plateau: 3.5 kN, with a force–displacement characteristic that reaches plateau after approximately 15 mm of belt payout and holds to the end of the stroke.
- Pretensioner rise time and stroke: 12 ms to peak and 55 mm of retraction, unchanged across the sweep.
The sweep variable is the pretensioner peak force, stepped across a defined range. A practical range for a 50th-percentile male in a frontal 56 km/h barrier test is 2.0 kN to 5.0 kN in 0.5 kN increments, giving seven runs. The upper bound is chosen so that the pretensioner does not dominate the restraint response and mask the load limiter; the lower bound keeps the pretensioner from becoming effectively inactive.
Why Peak Force and Chest Deflection Trade Off
The pretensioner removes belt slack and couples the occupant to the restraint early. A higher peak force pulls the occupant forward into the belt sooner and more firmly, which reduces the time the chest spends decelerating against a loose belt. That early coupling generally lowers chest deflection because the chest is loaded more gradually relative to the sled pulse. However, the pretensioner also adds its own force into the belt path, and above a certain level the added force begins to load the chest before the load limiter has paid out enough belt to cap the force. The result is a non-monotonic response: chest deflection falls as peak force rises, reaches a minimum, then rises again once the pretensioner force exceeds what the load limiter can absorb.
Ride-down efficiency captures the same trade-off from the energy side. It is the ratio of the energy absorbed by the restraint system to the kinetic energy the occupant would otherwise carry into the barrier, expressed as a percentage. Higher pretensioner force improves early coupling and raises ride-down efficiency up to the point where the pretensioner starts to add chest loading faster than it removes slack.
Running the Sweep
The sweep is executed by scaling the pretensioner force–time curve amplitude while leaving its shape, rise time, and stroke untouched. In a typical CAE workflow this means editing the pretensioner force scale factor in the restraint model, not the curve definition itself. The load limiter characteristic file is not touched between runs. Each run produces a chest deflection time history and a belt force time history; the peak chest deflection is read from the deflection trace, and ride-down efficiency is computed from the belt force and chest displacement work.
A reproducible procedure for the seven-run sweep:
- Confirm the baseline model reproduces the reference peak force, rise time, and stroke from the baseline setup. If the baseline does not match, stop and correct the model before sweeping.
- For each peak force level in {2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0} kN, set the pretensioner force scale factor so the curve peak equals the target, run the simulation, and export the chest deflection and belt force traces.
- Extract peak chest deflection (maximum of the deflection trace) and compute ride-down efficiency as the ratio of restraint-absorbed energy to occupant kinetic energy at belt engagement, expressed as a percentage.
- Tabulate the results and identify the peak force at which chest deflection is minimized.
| Pretensioner peak force (kN) | Peak chest deflection (mm) | Ride-down efficiency (%) | Observation |
|---|---|---|---|
| 2.0 | 44.5 | 42 | Slack removal incomplete; late coupling |
| 2.5 | 41.0 | 50 | Improved coupling, deflection falling |
| 3.0 | 37.5 | 58 | Approaching optimum |
| 3.5 | 35.5 | 65 | Minimum deflection region |
| 4.0 | 36.5 | 70 | Efficiency still rising, deflection rising |
| 4.5 | 39.0 | 73 | Pretensioner loading chest ahead of limiter payout |
| 5.0 | 42.5 | 75 | Diminishing efficiency gain, deflection penalty |
Reading the Result
The sweep reveals a clear minimum in chest deflection near 3.5 kN, where the pretensioner has removed enough slack to couple the occupant early without adding chest load faster than the load limiter can cap it. Beyond that point, ride-down efficiency continues to climb but at a decreasing rate, while chest deflection rises. The engineering decision is therefore not "maximize efficiency" but "choose the peak force that keeps chest deflection at or below the injury target while capturing most of the available efficiency gain."
A practical selection rule: identify the peak force at minimum deflection, then check whether a slightly higher force buys meaningful efficiency without pushing deflection past the target. In the illustrative data, moving from 3.5 kN to 4.0 kN gains about 5 percentage points of efficiency but adds about 1 mm of deflection — a defensible trade only if the deflection margin allows it. Moving to 5.0 kN adds only 2 more points of efficiency while adding 6 mm of deflection, which is rarely justified.
Verification and Common Failure Symptoms
Verify the sweep by confirming that the load limiter plateau force is identical across all seven runs — if it drifts, the load limiter file was modified and the sweep is invalid. Confirm that the pretensioner rise time and stroke are unchanged; only the peak amplitude should differ. A quick sanity check is that the belt force trace should show the pretensioner spike followed by the load limiter plateau, and the plateau height should not move between runs.
Typical failure symptoms and their causes:
- Deflection identical across all runs: the force scale factor is not being applied, or the pretensioner is being overwritten by a later restraint definition.
- Load limiter plateau shifts between runs: the load limiter characteristic is coupled to the pretensioner scale, which violates the fixed-limiter constraint.
- Efficiency exceeds 100% or is negative: the energy reference (occupant kinetic energy at belt engagement) is computed inconsistently, usually because engagement time is taken from the wrong event.
- No minimum in deflection: sweep range mis-centered, as noted above.
Once the sweep is clean, the output is a single defensible recommendation: the pretensioner peak force that minimizes chest deflection for the fixed load limiter, together with the efficiency cost of moving away from it in either direction.