4. Belt routing and contact definition

In MADYMO, a seatbelt is not a single rigid body but a chain of belt segments connected by slip rings and retractors. The accuracy of any frontal or side impact validation depends less on the belt material model than on how that chain is routed and how its contacts are defined. A belt that geometrically passes through the correct points but has wrong friction or missing seat contact will produce a plausible-looking animation with physically wrong occupant kinematics. This section covers the practical construction of belt routing, the three contact families that matter, and the friction parameters that govern load transfer.

Belt Routing as a Constrained Chain

MADYMO represents the belt with the BELT element, composed of BELT_SEGMENT members joined at BELT_SLIPRING points. Each segment carries stiffness (force–strain) and damping, while each slip ring defines a point where the belt can slide and change direction. Routing therefore means placing slip rings at the physical anchor, buckle, D-ring (upper guide), and any seat-integrated guide, then ordering segments between them.

A typical three-point routing for a 50th percentile male occupant is:

BELT / belt_3pt
  SEGMENT 1: anchor_outboard -> slipring_Dring      (lap-to-shoulder transition)
  SEGMENT 2: slipring_Dring  -> slipring_buckle     (shoulder belt)
  SEGMENT 3: slipring_buckle -> anchor_inboard      (lap belt)
  RETRACTOR at anchor_outboard, pull-out force 2.5 N, locking 0.5 g

Two routing rules dominate quality. First, the shoulder segment must pass over the clavicle and sternum, not through the neck or off the shoulder; a slip ring placed too far inboard causes the belt to slide off during forward excursion. Second, the lap segment must sit on the pelvis, below the anterior superior iliac spine (ASIS). If the lap belt is routed above the ASIS, the occupant submarines under it in a frontal pulse. In MADYMO this is controlled by the initial coordinates of the buckle and anchor slip rings relative to the pelvis body, and it should be verified by inspecting the belt–pelvis contact at t = 0.

Slip Ring Behavior and Friction at Guides

A slip ring is not frictionless by default. The BELT_SLIPRING card accepts a friction coefficient that resists sliding of the belt through the ring. This matters most at the D-ring, where the shoulder belt changes direction by roughly 60–90°. With zero friction, the belt tension equalizes across the D-ring and the retractor force is transmitted almost directly to the lap belt. With realistic friction (μ ≈ 0.1–0.2 for a polymer-coated D-ring), the shoulder and lap tensions decouple, which is exactly what happens in a real vehicle.

Practical guidance: set slip-ring friction explicitly rather than leaving the default. A common validated range is μ = 0.05–0.15 at the D-ring and μ = 0.1–0.3 at the buckle, depending on whether the buckle is a sliding latch plate or a fixed stalk. If the model shows the lap belt going slack while the shoulder belt loads up, the D-ring friction is likely too low or the retractor pull-out force is mis-set.

Belt-to-Occupant Contact

Belt-to-occupant contact is defined with CONTACT between belt segments and the occupant's facet or ellipsoid surfaces. The belt is treated as a line or narrow surface, so the contact model must use a small contact thickness and a stiffness high enough to prevent penetration but low enough to remain stable. Typical values for a belt–torso contact are:

The friction coefficient between belt and occupant is the single most sensitive parameter in this group. For a bare torso, μ ≈ 0.3–0.5; for clothing, μ ≈ 0.2–0.3. During validation, a model that predicts excessive forward excursion often has μ set too low, allowing the shoulder belt to slide laterally off the shoulder. Conversely, a model that shows the belt "sticking" and the occupant rotating unnaturally may have μ too high.

Belt-to-Seat Interaction

Belt-to-seat contact is frequently omitted in early models and then added during correlation. It matters because the lap belt bears against the seat cushion and the shoulder belt may contact the seat back or head restraint during rebound. In MADYMO, define contact between the belt segments and the seat cushion/back surfaces using the same contact card family, but with a lower friction coefficient (μ ≈ 0.3–0.5 for belt–foam) and a softer stiffness to reflect foam compliance.

Two failure modes are common. If belt–seat contact is missing, the lap belt can pass through the cushion and the pelvis loads unrealistically. If the seat contact stiffness is too high, the belt appears to "bounce" off the cushion, producing a spurious load spike. A practical check is to plot belt tension at the buckle and compare the timing of the peak with the seat cushion compression; they should be physically consistent.

Friction Parameters: A Consolidated View

Friction appears in three places: slip rings, belt–occupant, and belt–seat. They are independent and must be set separately. The following table summarizes a validated starting set for a frontal 50 km/h pulse with a 50th percentile male.

Worked Example: Diagnosing a Shoulder-Belt Slide-Off

Suppose a frontal simulation shows the shoulder belt migrating off the outboard shoulder at approximately 60 ms, with the occupant's chest rotating toward the buckle. The steps to diagnose and correct are:

1. Plot the lateral position of the shoulder belt relative to the shoulder joint over time. A monotonic inboard drift indicates slide-off.
2. Check the D-ring slip-ring friction. If it is at the default (often 0), raise it to 0.10 and re-run.
3. Check the belt–torso friction. If below 0.25, raise to 0.30.
4. Verify the initial D-ring position. If it is more than 30 mm inboard of the shoulder joint, move it outboard.
5. Re-run and confirm the belt remains on the shoulder through peak chest deflection (typically 80–100 ms).

If the slide-off persists after these changes, the issue is likely geometric: the shoulder segment is too short, or the retractor is pulling at an angle that encourages lateral migration. In that case, adjust the retractor anchor position rather than increasing friction further, which would introduce non-physical load transfer.

Verification Checklist

• Belt passes over the clavicle and sternum, not the neck.
• Lap belt sits below the ASIS at t = 0.
• Slip-ring friction is explicitly set at D-ring and buckle.
• Belt–occupant contact stiffness and friction are within validated ranges.
• Belt–seat contact is defined for lap and shoulder segments.
• Belt tension at the buckle peaks consistently with seat cushion compression.
• No penetration of the belt through the occupant or seat surfaces.

The diagram above shows the routing chain and the five friction interfaces that must be defined. The load path runs from the retractor through the D-ring, down the shoulder belt to the buckle, and then splits into the two lap segments. Each interface has its own friction coefficient, and each must be validated independently against test data before the model can be considered predictive.