Simcenter Madymo Simcenter Madymo - Buckle pretensioner modelling using gas inflation

The demonstrator consists of a sled set-up with rigid bench and footrest, an occupant (Hybrid-III 50th percentile male dummy) restrained by a conventional 3-point seat belt, a simplified seat belt retractor (only featuring load limitation) and a buckle pretensioner. Instead of modelling the pyrotechnical pretensioner using a joint restraint representing a pre-loaded spring (see related article), this pretensioner model proposes a more realistic approach using gas inflation which requires less tuning compared to the joint restraint approach (force-stroke characteristic), therefore most suitable for simulation versus test correlation purposes. Similarly to the model using joint restraint, the pyrotechnical pretensioner is defined in a separate SYSTEM.MODEL which does not only allow user-friendly exchangeability between the two modelling approaches but also can be used in any applications where a linear pyrotechnical pretensioner would be used.

Fig. 1 - Demonstrator with MB/FE buckle pretensioner model

The kinematic chain and switch logic is identical to the model using joint restraint, apart from the characteristic (force-stroke based) defined in the joint restraint (PyrotechnicalPretensioner_Piston_rst) which has been removed and replaced by an airbag chamber in combination with a gas inflator. Like any airbag modelled in Madymo, the pyrotechnical pretensioner requires the definition of the inflated gas, a gas mass flow rate and exit temperature functions (usually obtained from so-called tank tests) and a closed chamber. The Uniform Pressure method is used in this model. The combustion chamber is modelled as such:

• the FE mesh of the combustion chamber consists of 8 nodes and 6x2 triangular elements (2 per face)
• the face of the airbag chamber on the gas inflator side (4 nodes) is fully supported to the fixed body PyrotechnicalPretensioner_Attachment_bod. 1 element among on this face is used as a vent hole to model the over-pressure release valve (with a pressure threshold defined to enable outflow through the hole)
• the opposite face (4 nodes) is fully supported to the body PyrotechnicalPretensioner_Piston_bod, itself connected to the body PyrotechnicalPretensioner_Attachment_bod with a translational joint.
• when the inflator is triggered, the pressure will increase in the combustion chamber and will move the piston, also expanding the combustion chamber.
• all nodes being supported to rigid bodies, the elements are defined as facet elements (MATERIAL.NULL) and no permeability is allowed, except through the over-pressure release valve.

In the Sled_sys SYSTEM.MODEL, a load case including a pre-crash longitudinal braking phase at 0.8g immediately followed by a crash pulse (25g) at T0 is defined. The buckle assembly and the pyrotechnical pretensioner are defined in two separate SYSTEM.MODEL's, so that that pretensioner system can easily be exchanged. The positioning of the buckle assembly and the pretensioner was facilitated using referencing to a coordinate system (CRDSYS_OBJECT.MB) for which all the positioning parameters are listed as a set of DEFINE parameters in their respective local GROUP_DEFINE's. For the positioning and design parameters and the initial settings of the buckle assembly, refer to the related article.

Specific design parameters for the pyrotechnical pretensioner using gas inflation are made available to the user. See the list below.

Fig. 2 - Design parameters for pyrotechnical pretensioner

The design parameters are:

• PP_pistonmass: mass of the moving piston, excluding the mass of the cable
• PP_pistonfric: static friction load between the piston and the cylinder's inner wall. The dynamic friction load is defined at 0.8x the static friction load.
• PP_maxstroke: maximal stroke of the piston after which the piston joint will lock
• PP_pistondiameter: diameter of the pretensioner tube (visual only)
• PP_effectivepistonsurface: effective surface of the piston on which the pressure will longitudinally apply 
• PP_chamberinitialvol: initial volume of the combustion chamber
• PP_inflatorexittemp*: exit temperature of the gas inflator - assumed constant over time
• PP_inflatedgasmass*: total gas mass provided with the gas inflator. The mass flow rate function is defined as it follows:

Fig. 3 - Mass flow rate function

• PP_overpressurethreshold: over-pressure w.r.t ambient required to open the release valve
• PP_overpressurevalvedia: hole diameter of the over-pressure release valve through which the gas outflows.

*the user can alternatively replace the existing temperature and mass flow rate functions with physical data. And if different as defined in the provided as default, the user must also update the gas mixture of the inflated gas. The GAS.MIXTURE element can be found in the AIRBAG.CHAMBER under INFLATOR.DEF.

Fig. 4 - Definition of inflated gas

A few output definitions related to the pyrotechnical pretensioner are predefined such as the piston velocity and travel (pull-in) signals, the pressure and temperature inside the combustion chamber, the volume of the combustion chamber, outflow through over-pressure release valve, etc.

Fig. 5 - Available outputs for pyrotechnical pretensioner

A session file with the above-mentioned signals is provided in the attachment as an example and is shown below.

Fig. 6 - Example of signal analysis

Notes:

1) In the belt forces plots, the forces in the two cable segments (red and green) are shown to illustrate the force distribution around the cable guide. These forces remain constant after the pretensioner has locked since the joint CablePortion_Collapse_jnt and the piston joint PyrotechnicalPretensioner_Piston_jnt share the same state switch logic. The buckle head force signal (purple) in the plot actually represents the total force applied by the occupant to the buckle system.

2) since the pressure in the combustion chamber does not exceed the threshold necessary to open the over-pressure release valve, the pretensioner operates at its maximal pull-in capacity.

3) note that as there is no heat transfer modelled through the tube, the pressure inside the chamber remains constant after all the gas has been inflated.

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