4. Restraint system components in MADYMO

In MADYMO, a restraint system is not a single object but a coordinated set of FE and multibody elements whose timing, geometry, and force characteristics determine occupant kinematics. This chapter examines the four core components — seat belts, airbags, pretensioners, and load limiters — from the perspective of how each is represented, parameterized, and tuned inside a MADYMO model. The goal is to move from "what the component is" to "how it behaves numerically and how to configure it so the simulation reflects physical reality."

Seat Belt Modeling: FE Belts vs. Multibody Belts

MADYMO offers two principal belt representations. The multibody belt (MB belt) discretizes the webbing into a chain of rigid segments connected by belt elements with defined stiffness and damping. It is computationally cheap and well suited to parameter sweeps and concept studies. The FE belt uses membrane or shell elements and captures local deformation, slip over the pelvis and thorax, and interaction with the seat and airbag surface. For crash pulse sensitivity studies where belt routing and slip matter, the FE belt is generally preferred, but the MB belt remains useful for rapid iteration.

Key belt parameters include:

  • Belt stiffness — typically defined as a force–strain curve. A common example value is 20–40 kN at 10% elongation for a standard polyester webbing, but this must be matched to the actual belt specification.
  • Belt routing — defined by a series of points (D-ring, lap anchor, buckle, retractor) that control the belt path over the occupant.
  • Friction coefficient — governs slip between the belt and the occupant or seat. Values around 0.2–0.4 are typical for belt-to-clothing contact.
  • Retractor behavior — locked, unlocked, or with a defined locking threshold.

In a typical MADYMO input deck, a belt system is defined using BELT and BELT_SEGMENT cards, with the routing specified through POINT and BELT_PATH definitions. The belt is then attached to the occupant model via BELT_ANCHOR and BELT_SLIP definitions. A common mistake is to define the belt path without accounting for the D-ring height and the retractor position, which shifts the belt loading on the chest and changes the chest deflection by several millimeters.

Airbag Modeling: Geometry, Gas Flow, and Contact

Airbags in MADYMO are typically modeled as FE membranes with a defined gas flow model. The bag geometry is imported as a mesh, and the inflation is driven by a GAS_FLOW or INFLATOR definition. The key parameters are:

  • Bag volume and shape — determines the contact area with the occupant.
  • Mass flow rate — the rate at which gas enters the bag, often given as a time-dependent curve.
  • Vent hole area — controls the pressure decay after peak inflation.
  • Internal pressure — the resulting pressure that acts on the occupant.

A typical driver airbag might have a volume of 60–70 liters, a peak pressure of 200–300 kPa, and a vent hole diameter of 20–30 mm. In MADYMO, the inflator is defined with a GAS_FLOW table that specifies mass flow versus time. The bag membrane is defined with a FABRIC material model that includes Young's modulus, Poisson's ratio, and damping. Contact between the bag and the occupant is handled by CONTACT definitions, with a penalty stiffness that must be tuned to avoid numerical instability.

Practical tip: When the airbag is modeled as an FE membrane, the time step is governed by the smallest element size. A bag mesh with 5 mm elements will require a time step of roughly 1–2 microseconds, which can make the simulation expensive. For sensitivity studies, a coarser mesh (10–15 mm) with a slightly higher penalty stiffness is often acceptable.

Pretensioners: Reducing Slack and Controlling Timing

A pretensioner removes slack from the belt system at the onset of a crash. In MADYMO, it is modeled as a belt retraction applied at a specific anchor point. The pretensioner is defined by:

  • Trigger time — typically 10–20 ms after the crash pulse starts.
  • Retraction distance — the amount of belt pulled in, often 50–100 mm.
  • Retraction speed — the rate of pull-in, which affects how quickly the occupant is coupled to the belt.

In MADYMO, the pretensioner is implemented using a BELT_PRETENSIONER definition that applies a displacement or force boundary condition to the belt anchor. The retraction profile is usually defined as a time–displacement curve. A common example is a 60 mm retraction over 15 ms, which corresponds to an average speed of 4 m/s. The pretensioner must be synchronized with the airbag deployment; if the pretensioner fires too late, the occupant may already be out of position, and the belt will not engage the pelvis effectively.

Load Limiters: Controlling Belt Force

A load limiter caps the force transmitted through the belt to the occupant. In MADYMO, it is modeled as a force-limiting element in series with the belt. The load limiter is defined by a force–displacement curve, often with a plateau at a specified force level. Typical load limiter forces range from 2.5 kN to 4.5 kN, depending on the occupant size and the desired chest deflection.

The load limiter interacts directly with the pretensioner and the airbag. If the load limiter force is too high, the chest deflection increases; if it is too low, the occupant may move too far forward and contact the airbag with excessive velocity. In MADYMO, the load limiter is defined using a BELT_LOAD_LIMITER card with a force–displacement table. The force plateau is typically reached after 20–30 mm of belt payout.

Restraint System Signal and Force Chain in MADYMO Occupant Head Thorax Pelvis Belt (FE / MB) Pretensioner Retraction 60 mm Trigger 15 ms Load Limiter Force plateau 3.5 kN Payout 25 mm Airbag Volume 65 L Peak P 250 kPa Vent 25 mm MADYMO Outputs to Monitor • Belt force at shoulder / lap • Chest deflection (mm) • Head acceleration (g) • Airbag pressure (kPa) • Occupant forward excursion (mm) • Belt payout (mm) • Pretensioner stroke (mm) Compare against injury criteria: HIC, chest deflection, femur load Timing: Pretensioner fires first (10–20 ms) → Load limiter engages (20–30 ms) → Airbag peak pressure (30–50 ms)

Integrating the Components: A Worked Example

Consider a 50th percentile male occupant in a frontal impact with a crash pulse of 40 g peak at 50 ms. The restraint system is configured as follows:

  • Pretensioner: 60 mm retraction over 15 ms, triggered at 12 ms.
  • Load limiter: 3.5 kN plateau, reached after 25 mm of payout.
  • Airbag: 65 L volume, peak pressure 250 kPa at 35 ms, vent hole 25 mm.

In MADYMO, the simulation is set up with the occupant model positioned according to the seating reference point. The belt is routed over the chest and pelvis, with the pretensioner attached to the retractor anchor. The load limiter is placed in series with the belt at the buckle side. The airbag is positioned in front of the occupant, with the inflator defined by a mass flow curve.

After running the simulation, the following outputs are examined:

Output Example Value Judgment
Peak chest deflection 42 mm Below 50 mm threshold — acceptable
Peak belt force 3.8 kN Slightly above load limiter plateau — check belt routing
Head acceleration (3 ms) 55 g Below 80 g — acceptable
Occupant forward excursion 180 mm Within airbag contact zone — verify no bottoming out

If the chest deflection exceeds the threshold, the first parameter to adjust is the load limiter force. Reducing it from 3.5 kN to 3.0 kN typically reduces chest deflection by 5–8 mm but increases forward excursion. The second parameter is the pretensioner trigger time; advancing it by 2–3 ms can improve belt coupling and reduce chest deflection without increasing excursion. The airbag vent hole size also matters: a larger vent reduces pressure after peak, which can lower chest deflection but may allow the head to contact the bag too late.

Common pitfall: Do not tune the load limiter and pretensioner independently. They interact strongly. A late pretensioner combined with a low load limiter force can cause the occupant to submarine under the lap belt. Always check pelvis displacement and lap belt force together.

Verification and Sensitivity Checks

After the baseline simulation, run a sensitivity study by varying one parameter at a time. For example, vary the load limiter force from 2.5 kN to 4.5 kN in 0.5 kN increments and record chest deflection and forward excursion. Plot the results to identify the trade-off curve. In MADYMO, this can be automated using the PARAMETER and SWEEP features, or by scripting multiple runs with a shell script that modifies the input deck.

Check that the belt does not slip excessively over the shoulder; if slip is more than 20 mm, increase the friction coefficient or adjust the D-ring position. Verify that the airbag does not bottom out against the steering wheel or instrument panel; if it does, increase the bag volume or reduce the vent hole size. Finally, confirm that the pretensioner stroke is fully consumed before the load limiter engages; if not, the pretensioner is firing too late or the retraction distance is too small.

By treating each component as a parameterized element with clear physical meaning, and by systematically examining the outputs against injury criteria, you can build a restraint model that is both numerically stable and physically representative. The next step is to apply these components to a full crash pulse sensitivity study, which is covered in the following chapter.

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