Force–Displacement Corridor and Average Stiffness

Description

Vehicle Analysis → Force–Displacement Corridor puts the force–displacement profiles of two or more load-cell-wall tests on one displacement grid. It plots the profiles, their average and a residual corridor. It then calculates initial stiffness and Kw400 from the average curve.

When this feature is available

Force–Displacement Corridor becomes available when the current curve selection or at least two loaded vehicle tests meet the requirements, and the settings are valid.

For each test to pass:

• The loaded test must be a vehicle test.
• At least one body acceleration channel must have units G'S, an X axis, and an attachment containing SEAT, FLOORPAN, or SILL, or an attachment of VEHICLE CG.
• At least one wall force channel must have units NEWTONS, sensor type LOAD CELL, and an X axis or an axis of NOT APPLICABLE.
• Both channel types must have sensor location NOT APPLICABLE, data status AS MEASURED or QUESTIONABLE DATA, and channel status PRIMARY or REDUNDANT.

For manual selection, select channels from at least two tests. Select exactly one body acceleration channel and at least one wall force channel per test. Select only one channel for each wall load cell and axis; do not select both primary and backup channels. An invalid selection keeps the button disabled.

With no selection, WebSAT picks a left seat, sill or floorpan accelerometer, then the right one, then the vehicle CG, then another qualifying body channel. It selects qualifying wall forces and prefers primary channels over redundant channels for the same wall load cell and axis. Automatic selection skips tests whose qualifying body channels belong to more than one vehicle.

WebSAT uses one profile per test and requires at least two qualifying tests. Each selected vehicle must also have a positive test speed in its vehicle information before the calculation can run.

Settings

Setting	Default	Effect
Corridor Type	Standard Deviation of Residuals	Selects standard-deviation or residual-coverage bounds
Number of Standard Deviations (1–3)	1	Integer from 1 through 3; shown for a standard-deviation corridor
Coverage (%)	90	Normal coverage from 0% to below 100%; shown for a residual-coverage corridor
Remove Acceleration Bias	Off	Removes acceleration bias before filtering
Force Time Shift (ms)	0	Moves force later in time for positive values or earlier for negative values

How WebSAT processes the data

1. Filter each wall force at CFC 60 and sum them. Filter the acceleration at CFC 180 (SAE J211, Table 1) [1].
2. Integrate the acceleration two times from time zero, with the test speed as the initial velocity.
3. Keep the part of the curve from time zero while displacement increases. Make the force positive in compression. Resample at 1 mm.
4. Interpolate all profiles onto their common displacement range at 1 mm.

Load Cell Analysis uses steps 1 to 3 for its stiffness values.

Corridor

The average is the mean force at each displacement. For each profile, the residual is the profile minus the average. The half-width is the mean of the residual standard deviations, times the SD count or the coverage z-score.

Stiffness of the average curve

Initial stiffness is the slope of the longest qualifying straight-line fit to the average curve. A fit must start within the first 200 mm, span at least 150 mm, and have an absolute correlation coefficient |r| > 0.95. WebSAT tests 150 mm segments and longer segments that end in the first half of the resampled profile. The fitted line can have a nonzero intercept.

Method note: Wiacek et al. (2015) describe an initial-stiffness method with R² > 0.95 [3]. WebSAT uses |r| > 0.95 to reproduce published reference results. With the test data for the 14 initial-stiffness values in Summers and Prasad (2005), Table 4, the current WebSAT calculation reproduces every value within 1% [4]. Changing only the threshold to R² > 0.95, with the same prepared profiles and search limits, reproduces none within 1%; one profile has no qualifying fit. This comparison supports WebSAT's criterion for reproducing those published results.

Kw400 is the stiffness of a linear spring with the same energy from 25 mm to 400 mm [2]:

$$K_{w400}=\frac{2{\int }_{25}^{400}F(x)\mathrm{d}x}{400^2-25^2}$$

How to interpret the results

The force and the acceleration must have the same time zero. When the force at 0 mm is 5% of the peak force or more, WebSAT shows a warning. A force time shift moves the force later in time (positive values) or earlier (negative values).

A profile with a constant offset from the average adds no corridor width.

Results

The results are organized into three sections:

• Average Curve Stiffness reports the profile count, common displacement range, residual standard deviation, initial stiffness, Kw400, and fit details.
• Force–Displacement Corridor plots the aligned profiles, average force, corridor bounds, and initial stiffness fit when available.
• Contributing Tests and Channels identifies each test, vehicle, body acceleration channel, and wall force channel. Check this table after an automatic selection.

Each section has an export control for its table or profile data.

The average profile must cover 0–150 mm for initial stiffness and 25–400 mm for Kw400. If it does not, the value shows N/A with the reason. Initial stiffness also shows N/A if no qualifying fit is found. The corridor results remain available when a stiffness value cannot be calculated.

References

[1] SAE International. Instrumentation for Impact Test—Part 1—Electronic Instrumentation, SAE J211/1, Table 1.

[2] Patel, S., Smith, D., Prasad, A., and Mohan, P. “NHTSA's Recent Vehicle Crash Test Program on Compatibility in Front-to-Front Impacts.” 20th ESV Conference, Paper 07-0231, 2007.

[3] Wiacek, C. et al. “Evaluation of Frontal Crash Stiffness Measures from the U.S. New Car Assessment Program.” 24th ESV Conference, Paper 15-0257, 2015, “Linear Initial Stiffness,” p. 4.

[4] Summers, S. and Prasad, A. “NHTSA's Recent Compatibility Test Program.” 19th ESV Conference, Paper 05-0278, 2005, Table 4.