Surface Distortion and Diminishing Area

Surface Distortion and Diminishing Area

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Surface Distortion and Diminishing Area

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The folding process introduces some distortion to initial geometry.  The outer surface becomes "lengthened" and the inner surface becomes "shortened". It is useful to evaluate the influence of a fold on the airbag surface in order to avoid a situation wherein the airbag, after folding and inflating, is quite different from the original one.


Figure 30: Symbols used in formula for surface reduction.

As an introduction to some symbols (see Figure 30), let L be the width of the tilted part of the airbag, let G/2 be the half gap, and let E be the airbag's thickness.

There are two extreme cases to examine: In the first one, the airbag is not yet folded. In this case it is very thin and the value of L is known as it is supplied by you. The relative shortening (with respect to L) is found with the formula, hc_img74 where hc_img75 (relative thickness) and hc_img76 (relative gap). It is assumed that there are only two layers of the airbag.


Figure 31: The relative shortening of the folded part as a function of relative gap (for different relative thickness values - case 1.

Figure 31 shows the dependence of the shortening of the folded part on the relative gap for several relative thickness values. The conclusion in that case is that it is better to have a very thin airbag and give a possibly high gap value in order to have the smallest surface difference after folding.


Figure 32: The relative shortening of a layer as a function of relative distance from the mid-plane (for different hc_img1 values) - case 2.

In the second case, the airbag is thick and the value of L depends on gap, airbag's thickness, and the maximum hc_img37 value by the formula, hc_img79.

In this case, it is not possible to use the same formula with normalized variables because L is no longer a constant. But note that for a given hc_img80 value, the length increase of a layer distant of d from the symmetry plane (dot-dashed line on the Figure 30, hc_img82) is a linear function of d (see also the Figure 32): hc_img83

The global effect of a fold on the airbag's surface will be null if this function is 0 at mid-distance between G/2 and hc_img84, that is, at hc_img85. This gives the following condition for the angle hc_img1: hc_img86 which can be transformed to (for hc_img87): hc_img88.

As for actual airbags hc_img89, this means that hc_img90, that is, the global shortening effect is small for angle hc_img91. Thus, the best value of the parameter hc_img37 is about hc_img16 if the global surface of the airbag is to be maintained.

Figure 31 shows that in the first phase of folding, a shortening of the surface is very hard to avoid. It may be useful to choose the hc_img37parameter larger than hc_img16 in order to compensate for the surface shortening that occurred during the first phase of folding by a surface increase during the second phase (Figure 32).


To summarize what has been previously discussed in terms of choice of folding parameters values and initial geometry:

The initial geometry of an unfolded airbag should be as thin as possible. The only limiting factor should be the Engine's interface performance.
The gap should be as large as possible. In practice, its value will be limited by the final airbag's thickness.
The L value has no effect on surface conservation. It is determined by the minimum time step condition.
The hc_img37 value should be about hc_img16 in order to preserve surface during the folding process, or a little larger in order to compensate for the surface loss occurred during the first phase of folding.