Simcenter Madymo - Scalable driver airbag model

The driver airbag model includes a circular container made of MB surfaces (ellipsoids for the contour and a plane for the backside) and the airbag cushion made of membrane elements inflated by a user-defined gas generator. The airbag is defined as an include (DAB_inc.xml) and its position and design are controlled by DEFINE variables.

Fig. 1 - Driver airbag model

Positioning parameters

The airbag can be attached to any existing rigid body in the user's input deck and positioned using the positioning parameters listed above. The airbag mount positioning parameters position the center of the plane at the backside of the container in the local coordinate system of the attachment body. Both airbag fabric layers are distant by 4mm from each other and the back face of the cushion is set to 1mm above the plane by default. The mesh density is about 10mm when the airbag is scaled to a diameter of 560mm (mesh reference size). The back face of the airbag consists of a circular panel (diameter user-defined) and a center circular portion of 80mm diameter (constant and independent from the outer diameter of the cushion) which is supported to the airbag's attachment body. A concentric circle of 40mm diameter (also constant and independent from the outer diameter of the cushion) is used as venting port* to exhaust the gas inflated by the gas generator. An additional part Leakage_par was included to represent possible gas leakage through the sews and module. The front face of the airbag consists of a circular panel (diameter user-defined) that is stitched at its periphery to the rear panel. The fabric thread directions (MATERIAL.FABRIC_SHEAR) of the rear panel are turned 45° relative to those of the front panel. The center part of the front panel is connected to the rear panel by straps (1D element connection between front and rear panel facing nodes) along a circle of 80mm diameter.

*the venting port is defined on purpose in the area which is not subject to scaling when varying the airbag diameter, making the CDEX calculation easier. Note here that this is a single chamber airbag model, using the uniform pressure method for thermodynamics calculations. This means that the actual location of the vent hole(s) on the fabric is not critical in itself. For correlation purposes, the user can use additional parameters (see below in the section Design parameters ) to allow the exhaust from a certain point of time to mimic the fact that the vent holes are normally located in a folded portion of the airbag (see later in the Initial Settings section).

Fig. 2 - Airbag mesh

Design parameters

The design parameters allow to vary the size of the airbag container, the diameter of the flat airbag fabric panels, the diameter of the two vent holes and the output of the gas generator. These are:

• AB_moduleinnerdia; this sets the inner diameter of the circular module in which the airbag is contained.
• AB_moduleheight; this parameter sets the height of the container walls w.r.t the backside plane.
• AB_dia; this parameter defines the outer diameter of the circular panels. This parameter does not affect the diameter of the center circular supported portion (80mm constant).
• AB_ventdia; this defines the diameter of each circular vent holes (2), normally cut in the fabric to allow venting of the inflated gas. The vent hole elements being however defined on the module part of the airbag (not scaled), the vent hole has a constant size over time. To do not allow immediate venting after trigger of the inflator, the user can tune the two next parameters, which are linked to the CDT function of the MATERIAL.HOLE definition (outflow scaling vs. time function).
• AB_exhauststartdelay; this defines the duration after trigger as of when the outflow through the vent hole is enabled.
• AB_fullexhaustduration; this defines the duration of the ramp up from start of exhaust to full exhaust (linear behavior assumed between AB_exhauststartdelay and AB_fullexhaustduration).

Alternatively, the outflow through the vent holes can be controlled by over-pressure using the two next parameters AB_ventdpex and AB_ventdtex, for instance to model a membrane tearing at a certain over-pressure. In that case, use very small values for AB_exhauststartdelay and AB_fullexhaustduration (the values must be strictly greater than zero), so that the function equals to 1 as soon as the airbag is triggered. The outflow will nevertheless start as soon as the below mentioned conditions are satisfied.

• AB_ventdpex; over-pressure condition to start outflow through the vent holes. The default value is 0.
• AB_ventdtex; over-pressure duration condition to start outflow through the vent holes after the over-pressure condition above has been satisfied. The default value is 0.
• AB_leakagedia; this defines the diameter of a fictive circular vent hole through which outflow of gas leakage through sews, inflator etc. is possible. Contrary to the regular vent holes cut in the fabric, the outflow is enabled as soon as the relative pressure in the airbag chamber exceeds AB_leakagedpex.
• AB_leakagedpex; over-pressure condition to start outflow for leakage. Set value to 0 to activate outflow all the time.
• AB_straplength; this parameter sets the untensioned length of the straps connecting both panels to each other.
• AB_refscale; this parameter is automatically calculated to scale the coordinates of the nodes located outside the center circular surface of 80mm to reach the desired outer diameter* (reference state mesh).
• AB_iniscale; this parameter is also automatically calculated to further scale the coordinates of the nodes located outside the center circular surface of 80mm to fit the airbag inside the container (initial mesh state) with a gap of 5mm between the contour of the airbag and the inner wall of the container*.
• AB_inflatedgasmass; this represents the total gas mass inflated into the airbag chamber. This parameter effectively applies a scaling factor in Y on the default mass flow rate vs. time function.
• AB_perm; permeability constant factor of airbag fabric used in permeability model 1.

*in this model, the nodal coordinates are expressed in cylindrical coordinates to allow a simpler implementation of the size scaling.

Note: a none-exhaustive list of parameters can be defined as simulation parameters such as permeability factor. Also, inflated gas definition and/or inflator characteristics (output temperature and mass flow rate functions) can be taken out from the include file if these latter ones are part of the variation parameters.

Initial settings

The initial setting parameters available are:

• AB_ttf; this parameter defines when the airbag inflator is triggered. The switch referring to this event also switches on the contact between the airbag and the module and change the state of the FE fabric mesh from rigid to deformable.
• AB_selfcnt; this parameter allows to activate the self contact for the airbag fabric elements; OFF disables the self contact (less CPU consuming) whereas ON activates it after the inflator is triggered.

Please contact your local Madymo Support organization for further questions/details on this topic.