2. Column Collapse Force-Displacement Characterization
Why Characterize the Collapse Curve
An energy-absorbing steering column protects the driver by deforming in a controlled way: it must yield early enough to limit the load transmitted to the chest, yet resist hard enough to absorb the occupant's kinetic energy over the available stroke. The single most useful descriptor of that behavior is the axial force–displacement curve obtained from a quasi-static compression test. From this curve you extract the parameters that feed an occupant model — initial collapse force, mean crush force, stroke, and the shape of the plateau — and you can judge whether the element will behave as intended before committing to a sled test.
This case builds a complete, reproducible quasi-static test procedure for a representative steering-column energy-absorbing element (a corrugated steel crash tube, a common sacrificial component), then reduces the raw data into the parameters an injury model needs. All numeric values below are illustrative example parameters chosen to make the procedure concrete; they are not measured results.
Test Object and Instrumentation
The specimen is a thin-walled corrugated tube, 180 mm long, 60 mm outer diameter, 1.5 mm wall, low-carbon steel. It is loaded axially between a fixed base plate and a moving platen. The test article is mounted in the same orientation it would occupy in the column assembly so that the fold pattern develops as in service.
- Load measurement: a uniaxial load cell (≥ 50 kN capacity, ≤ ±0.5 % full-scale linearity) in series with the platen.
- Displacement measurement: a linear displacement transducer referenced to the platen, plus an independent crosshead encoder for cross-check.
- Rate: quasi-static, 10 mm/min crosshead speed, so inertial effects are negligible and the curve represents the structure's static crush resistance.
- Sampling: ≥ 100 Hz; log load, platen displacement, and time to a single file.
Before the run, zero the load cell with the specimen just touching the platen (preload ≤ 50 N) and record the initial gauge length L₀ between the base and platen reference faces. This defines the displacement origin; every subsequent displacement is measured from this contact point.
Running the Compression
- Mount the specimen, verify axial alignment (platen parallel to base within 0.5 mm over the face), and set the preload.
- Start acquisition, then command the platen down at 10 mm/min.
- Continue until the tube has collapsed to roughly 70 % of its original length or until load drops below 20 % of the peak, whichever comes first — this captures the full plateau and the onset of densification.
- Stop, unload, and export the time-history. Photograph the deformed specimen to correlate fold formation with features on the curve.
Reading the Force–Displacement Curve
A typical corrugated tube produces a curve with four recognizable regions, shown in the figure below: an elastic rise to an initial peak, a load drop as the first fold forms, a long oscillating plateau where successive folds develop, and a final rise as the collapsed stack densifies. The parameters that matter for occupant modeling are read directly off this trace.
Deriving the Injury-Model Parameters
Reduce the trace with the following definitions, applied consistently across all specimens:
| Parameter | Definition | Example value |
|---|---|---|
| Initial collapse force, Fpeak | First local maximum after the elastic rise | 28 kN |
| Mean crush force, Fmean | Average force over the plateau, from first fold to onset of densification | 16 kN |
| Effective stroke, S | Displacement from Fpeak to the point where load rises above 1.2·Fmean (densification onset) | 62 mm |
| Absorbed energy, E | Integral of force over displacement across the plateau | ≈ 0.99 kJ |
| Load ratio, Fpeak/Fmean | Peakiness of the curve; high values mean a harsh initial spike | 1.75 |
Compute Fmean as the trapezoidal integral of force over the plateau divided by the plateau length, not as a simple average of samples — the sampling density must not bias the result. The absorbed energy is the same integral without dividing by length. For the example trace, the plateau integral gives E ≈ 0.99 kJ over 62 mm, consistent with Fmean ≈ 16 kN.
Feeding the Occupant Model
In a lumped-parameter or FE occupant model, the column is represented as a force element whose resistance follows the measured curve. Two practical mappings:
- Rigid-plastic idealization: replace the plateau with a constant force equal to Fmean acting over stroke S. This preserves absorbed energy and is adequate for chest-deflection estimates when the curve is reasonably flat.
- Tabulated curve: import the measured force–displacement pairs directly as a nonlinear spring. Use this when Fpeak/Fmean exceeds about 1.5, because the initial spike drives peak chest acceleration and a constant-force idealization would underestimate it.
Whichever mapping you choose, verify that the model's absorbed energy matches the measured E within a few percent; a mismatch usually means the stroke or the plateau bounds were misread.
Verification and Common Failure Symptoms
Pass criteria for the test itself: three specimens with Fmean within ±10 % of each other, Fpeak within ±15 %, and no specimen showing asymmetric folding (visible in the post-test photograph and as an abnormally jagged plateau).
- Curve starts at nonzero load: preload was not zeroed — re-zero with the platen just touching and re-run.
- Plateau drifts upward steadily: axial misalignment causing progressive binding; check platen parallelism.
- Single sharp spike then flat line: specimen buckled globally instead of folding; the tube is too slender for the fixture or the wall is too thin.
- Noisy, spiky plateau: fold formation is irregular; inspect for wall-thickness variation or a seam that should have been oriented away from the load path.
Once the curve is clean and the parameters are extracted, they become the input to the occupant model in the next stage of the countermeasure design — the column's job is to convert occupant kinetic energy into controlled deformation, and this test is how you prove it will do so before anyone is in the seat.