Dimensionless complementarity modelling for disengagement screening of a spring-loaded railway pawl latch under vibration and shock

A novel complementarity-based screening framework is developed for vibration- and shock-induced disengagement of a spring-loaded self-locking pawl latch used for remote handling of a portable railway wheel chock. The engagement geometry is treated explicitly. The critical opening angle is derived from the engagement depth and the engagement radius, and a retention factor κ carries the wear, tolerance and elastic-approach allowances. Contact forces and moments are formulated for the locked and the incipient-opening configurations, and the equivalent-wedge self-locking condition is recovered only as their plane-flank limit. Because the catch element is a cylindrical pin, the retention condition within the planar rigid-contact model is tan ψ ≤ μ , in which ψ is the same angle that fixes the critical opening angle; the wedge form understates the required friction coefficient by a factor of approximately 2.4 for the stated worked-example dimensionless proportions ( α = 5° and δ / a = 0.208). The latch is then treated as a unilateral-contact system governed by five dimensionless groups: the frequency ratio, the damping ratio, the severity number Λ , the pulse duration Θ , and a preload number Π = M 0 /( k φ φ c r ) introduced here. Three cases are separated. For the seated latch the criterion is loss of contact, Λ < Π . The preload-free oscillator is retained as an explicitly labelled upper-bound idealisation. The seated latch with a lift-off threshold is formulated as a linear complementarity problem. Numerical integration of that model over 0.1 ≤ Π ≤ 40 supports the conservative algebraic screening bound Λ < 0.6( Π + κ ). The damping ratio moves this boundary by less than 4 %, and the worst frequency ratio is sub-resonant, so the critical damping ratio of the preload-free model does not describe the preloaded latch. Reproducible Euler-Bernoulli and Rayleigh calculations for an explicitly defined reduced shaft model place the first bending frequency between 3.2 and 62.0 Hz, which identifies the grip-to-pivot amplification, rather than the damping ratio, as the measurement of highest value. For the nominal set of the worked example the model predicts a lift-off acceleration of 1389 m/s 2 ; at the worst corner of the parameter domain it predicts 167 m/s 2 , and a conditional guard-banded screening calculation at β = 1 excludes that corner under the assumed input uncertainties. All quantities are model predictions conditional on assumed parameters; no experimental validation is claimed.