3. Belt geometry parameterization

Belt geometry robustness begins with a defensible parameterization. Before any variation study can be meaningful, the restraint system must be described by a small set of physically interpretable parameters whose values can be traced from the vehicle package through the CAD assembly into the CAE deck. This section defines those parameters, establishes the sign and coordinate conventions used throughout the course, and shows how each parameter is represented consistently in CAD and in a restraint CAE model.

Coordinate Convention and Reference Frame

All geometry in this course is expressed in the vehicle coordinate system: X positive forward, Y positive to the occupant's right (vehicle right), Z positive upward, with the origin at the vehicle datum. Angles are measured in degrees. Belt routing angles are defined as the angle between the belt segment direction vector and the forward (+X) axis, projected into the relevant plane; a positive angle rotates toward +Y. This convention must be stated explicitly in the CAE model header and must not be redefined between CAD and CAE, because a sign flip in the shoulder belt angle silently mirrors the routing and invalidates every downstream robustness conclusion.

The Anchor Set

Five anchor points fully define a three-point belt for a given seating position. Each is a point in vehicle coordinates, and each carries a small tolerance envelope that represents manufacturing and adjustment variation.

• D-ring (shoulder anchor, upper outboard): the guide through which the shoulder belt passes. Its Y and Z positions dominate shoulder belt angle and the height at which the belt crosses the occupant's shoulder. On adjustable systems, the D-ring has a travel range; the parameterization must capture both the nominal position and the adjustment range.
• Buckle (inboard stalk end): the latch point on the inboard side. Its X and Z positions set the lap belt angle and the inboard lap anchor location.
• Outboard lap anchor: the fixed lower outboard attachment, typically on the seat frame or rocker. Its X and Z positions set the outboard lap belt angle.
• Inboard lap anchor: the lower inboard attachment, usually coincident with or near the buckle stalk base. It defines the inboard end of the lap belt path.
• Retractor / ELR spool (optional but recommended): the point at which the shoulder belt leaves the retractor. Including it allows the model to represent the belt path from spool to D-ring, which matters for pretensioner and load-limiter behavior.

In addition to the anchors, two derived points are required: the shoulder reference point (the point on the occupant's shoulder where the belt is intended to cross) and the lap reference point (the midpoint of the lap belt path across the pelvis). These are not anchors; they are targets against which the anchor geometry is judged.

Routing Angles

Three angles carry most of the geometric information:

Shoulder belt angle is the angle, in the frontal (X–Z) plane, between the shoulder belt segment (D-ring to shoulder reference point) and the horizontal. A typical design target is 30°–45° from horizontal, but the exact value is occupant- and seat-dependent. A steeper angle increases the tendency of the belt to load the neck; a shallower angle increases the risk of the belt slipping off the shoulder.

Lap belt angle is the angle, in the side (X–Z) plane, between the lap belt segment and the horizontal, measured at the outboard anchor. A typical target is 45°–65°. Too shallow and the belt can submarine over the iliac crest; too steep and it loads the abdomen.

Belt routing angle (plan view) is the angle, in the X–Y plane, between the shoulder belt segment and the vehicle centerline. This angle controls how far inboard the belt crosses the chest and is the parameter most sensitive to occupant anthropometry, because a larger occupant moves the shoulder reference point outboard and changes the effective routing.

Representation in CAD and CAE

In CAD, the anchors are typically modeled as datum points or coordinate systems on the seat frame and body-in-white, and the belt is a swept solid or a centerline spline through the anchors and reference points. The parameterization should be driven by a design table or a parameter set so that anchor coordinates and angles can be varied without rebuilding geometry. In CAE, the same anchors become node sets or point masses, and the belt is a seatbelt element chain (1D elements with defined slip rings at the D-ring and buckle). The critical consistency requirement is that the CAE belt path must be generated from the same anchor coordinates and the same angle definitions as the CAD model; a common failure is a CAE deck that was meshed from an older CAD revision, producing a shoulder belt angle that differs by several degrees from the current design intent.

The following parameter block is a representative, illustrative example of how the anchor set and angles can be captured in a form that both CAD and CAE can consume. The values are plausible teaching values, not measured data.

# Belt geometry parameter set — illustrative example, not measured
# Frame: vehicle XYZ, X fwd, Y right, Z up; angles in degrees
anchor.D_ring        = ( 980.0,  380.0, 1420.0)   # mm
anchor.buckle        = ( 620.0, -180.0,  260.0)
anchor.lap_outboard  = ( 700.0,  360.0,  240.0)
anchor.lap_inboard   = ( 640.0, -170.0,  250.0)
anchor.retractor     = ( 300.0,  400.0,  900.0)

ref.shoulder_point   = ( 850.0,  200.0, 1300.0)
ref.lap_midpoint     = ( 660.0,   90.0,  250.0)

angle.shoulder_deg   = 38.5    # D-ring -> shoulder point, X-Z plane
angle.lap_deg        = 55.0    # outboard anchor -> lap midpoint, X-Z plane
angle.routing_deg    = 12.0    # D-ring -> shoulder point, X-Y plane

tol.anchor_mm        = 15.0    # per-axis manufacturing tolerance
tol.angle_deg        = 2.0     # assembly/adjustment tolerance

With this block, a robustness study becomes a controlled perturbation: vary each anchor within its tolerance envelope, recompute the three angles, and observe how the belt path and the resulting occupant loading change. The angles are derived quantities, not independent inputs, which is exactly what makes the parameterization useful — it keeps the anchor coordinates as the single source of truth and prevents the CAD and CAE models from drifting apart.

Practical Consistency Checks

Before a parameter set is released to a robustness study, three checks catch most representation errors. First, recompute the three angles from the anchor coordinates and confirm they match the values stored in the parameter block to within 0.1°; a mismatch indicates that the angles were entered manually rather than derived. Second, verify that the CAE belt path passes through the same anchor node sets as the CAD datum points, and that the D-ring slip ring is located at the D-ring coordinate, not at the shoulder reference point. Third, confirm that the tolerance envelope is applied to the anchors, not to the angles — perturbing angles directly decouples the study from the physical manufacturing variation the anchors represent.

When these checks pass, the parameterization is ready to support the anthropometry variation studies that follow: each occupant size moves the shoulder and lap reference points, which changes the derived angles, which in turn changes the belt path and the loading. Because the anchors remain the single source of truth, the effect of occupant size and the effect of anchor tolerance can be separated cleanly rather than being confounded in a single geometric perturbation.