4. Function analysis of the load limiter

The load limiter is the second half of the pretensioner–retractor safety chain. Where the pretensioner removes slack and couples the occupant to the restraint system within the first tens of milliseconds, the load limiter governs what happens next: it caps the belt force transmitted to the occupant's chest and shoulder so that the restraint system absorbs energy instead of the human body. In DFMEA terms, the load limiter is a function carrier whose failure modes are almost entirely functional rather than structural — the part rarely breaks, but it can limit at the wrong level, limit inconsistently, or fail to limit at all. This chapter decomposes the load-limiter function into three analyzable sub-functions: torsion-bar deformation, the force-limiting profile, and energy absorption, and shows how each becomes a DFMEA line item.

4.1 The torsion bar as the force-limiting element

In the dominant design, the spool is split into two coaxial sections — the locking section (held by the locking pawl or web-locking mechanism during a crash) and the belt-carrying section (which rotates with the webbing) — joined by a hardened torsion bar. During normal use the bar transmits retraction torque as a rigid shaft. During a crash, once the locking section is grounded, further webbing payout forces the belt-carrying section to rotate relative to the locking section, and the only load path between them is the torsion bar, which twists plastically.

The governing relation is straightforward torsional mechanics. For a solid circular bar of diameter d and shear yield strength τ_y, the torque at which plastic flow begins is:

T_y = (π · d³ / 16) · τ_y

and the belt force at the spool follows from the torque balance F_belt = T / r_spool, where r_spool is the effective webbing wrap radius. As a worked example (illustrative values, not measured data): a bar with d = 6.0 mm, τ_y = 1200 MPa gives T_y ≈ 50.9 N·m; with r_spool = 25 mm the belt force at first yield is about 2.0 kN. This is the physical origin of the "limit level" — it is set by bar diameter, material, heat treatment, and spool radius, and every one of those is a DFMEA-relevant characteristic.

Two deformation regimes matter for function analysis. In the elastic regime the bar behaves as a spring and the belt force rises steeply with payout; in the plastic regime the torque plateaus near T_y (with modest strain hardening) while the bar continues to twist through many revolutions. The plateau is the useful part: it converts webbing payout into controlled, roughly constant force. The total twist angle before fracture, θ_max, sets the maximum payout the limiter can supply — typically several hundred degrees, corresponding to a defined length of webbing released at the spool radius.

4.2 The force-limiting profile

The force-limiting profile is the belt-force-versus-payout curve produced by the limiter. A single-stage torsion bar produces a characteristic shape: a steep elastic rise to the limit level, a plateau, and a terminal rise or drop as the bar approaches fracture or as the spool geometry changes (the effective radius grows as webbing unwinds, so belt force at constant torque actually decreases slightly with payout — a second-order effect worth capturing in the analysis).

Modern systems rarely use a single plateau. Multi-stage limiters switch the effective stiffness mid-event: a pyrotechnic or mechanical switch may release a second load path (a parallel bar, a friction clutch, or a stepped spool) at a defined payout or time, dropping the limit level for smaller occupants or raising it for larger ones. The DFMEA consequence is that the profile is now a function of a switching event, and the switching threshold itself becomes a characteristic to be analyzed — a switch that fires early or late changes the force the occupant sees, even if the bar itself is perfect.

For DFMEA purposes the profile should be decomposed into analyzable parameters rather than treated as a single curve:

4.3 Energy absorption characteristics

The purpose of the plateau is energy absorption. The energy absorbed by the limiter over a payout s is the integral of belt force over payout:

E_abs = ∫ F_belt(s) ds  ≈  F_plateau · s_effective

For the illustrative bar above, a plateau of 2.0 kN sustained over 150 mm of payout absorbs about 300 J. That number is the design currency of the load limiter: it must be large enough to keep chest deflection and acceleration within occupant-protection targets, yet small enough that the occupant does not "bottom out" against the belt and strike the interior. The energy balance is therefore a window, not a maximum — too little absorption and the occupant loads spike; too much and the occupant travels too far forward.

This is where the DFMEA becomes genuinely interesting. The failure mode "limits at too high a force" and the failure mode "limits at too low a force" have opposite physical causes but both degrade the same function, and the severity depends on occupant size and crash severity. A high limit level protects a large occupant but over-loads a small one; a low limit level protects a small occupant but allows excessive excursion for a large one. The function analysis must therefore state the limit level as a target with tolerance, tied to a defined occupant and crash matrix, not as a single nominal value.

4.4 From function to DFMEA line items

The function analysis above translates directly into DFMEA structure. The load limiter's primary function is stated as: "Limit belt force transmitted to the occupant to a defined profile within tolerance across the specified payout range, and absorb a defined amount of energy without fracture before maximum payout." Each clause of that sentence becomes a failure mode when negated:

• Limits at too high a force — bar diameter oversize, τ_y high from heat treat, spool radius small, friction low. Effect: elevated chest loading, possible rib deflection exceedance for small occupants.
• Limits at too low a force — bar undersize, τ_y low, spool radius large. Effect: excessive payout, occupant excursion, possible interior contact.
• Fails to limit (bar fractures early) — ductility low, surface defects, stress concentration at fillet. Effect: loss of force control, sudden force drop, uncontrolled payout.
• Stage switch mistimed — threshold drift, tolerance stack, charge variation. Effect: profile deviates from the occupant-specific target.
• Inconsistent limit across units — friction variation, bar runout, bearing drag. Effect: unit-to-unit scatter in occupant response, reduced robustness margin.

Each of these is a functional failure mode with a measurable detection path: bench torsion testing of the bar, spool-level force-payout characterization on a belt-force test rig, and sled or component-level verification against the occupant matrix. The DFMEA should record the profile parameters from the table in 4.2 as the design characteristics that prevent or detect these modes, and should tie the limit-level tolerance to the occupant and crash matrix that defines "correct" in the first place.

Finally, note the coupling to the pretensioner analyzed earlier. The pretensioner determines when the occupant couples to the belt; the load limiter determines how much force the coupled system delivers. A pretensioner that fires late leaves the limiter to absorb energy over a shorter payout, effectively raising the force the occupant sees even if the bar is nominal. This interaction is a legitimate DFMEA interface line item and should be captured as a cross-function failure mode rather than analyzed in isolation.