Speed dependence, scale fidelity, and three-dimensional effects in the dynamic asymmetry of train-collision energy absorption

In a 1/8-scale, one-dimensional train collision test at 22.8 km/h and matching multibody simulations, Shao et al. (2016) found that the moving train's energy-absorbing structures absorb more collision energy than the stationary train's symmetric counterparts, and that this dynamic asymmetry, quantified by a coefficient $a$ fitted to simulations at 10-36 km/h and inserted into the energy-absorption design equation, decreases with increasing collision speed. The open problem is to establish this speed dependence on experimental evidence, determine whether it and the improved-model predictions hold at other scale factors and at full scale, and quantify how three-dimensional effects modify the partitioning of collision energy between the two trains, so that the scaling-law-based design of train-collision energy dissipation rests on validated evidence rather than a single-speed, single-scale, one-dimensional simulation fit. The literature since 2016 (Refs. 3-16) leaves the speed dependence of the asymmetry coefficient and its cross-scale and three-dimensional validation unresolved.

Background

Rail-vehicle crashworthiness design must ensure that when a train collides, the impact energy is dissipated in a controlled way by sacrificial energy-absorbing structures (collapsible tubes, metal honeycomb blocks, buffers) at the ends of the cars rather than by deformation of the passenger space. The European standard EN 15227, which also anchors Chinese practice, prescribes design collision scenarios such as a moving train striking an identical stationary train. Because full-scale train-to-train impact tests are extremely expensive, two cheaper tools dominate the field. One is multibody dynamics (MBD): each car is modeled as a rigid mass and the inter-car connections and end structures are represented by force elements, such as nonlinear springs or force-crush curves, which makes whole-train computations far faster than the finite element (FE) method. The other is scaled model testing: by dimensional analysis (the Buckingham $\pi$ theorem), similarity factors are assigned to geometry, mass, force, and time so that a small-scale model reproduces the dynamic behavior of the full-scale prototype.

A widely used design rule due to Lu (2002) prescribes the energy $E_d$ that a head car must be able to absorb, $E_d=\frac{R_1}{2f_d}\cdot\frac{1}{2}M_1v^2$, where $R_1$ is the fraction of kinetic energy absorbed at the collision interface, $f_d$ is a dynamic amplification factor (suggested value 1.2), $M_1$ is the head-car mass, and $v$ is the impact velocity; the factor 2 in the denominator encodes the assumption that the collision energy is split evenly between the two colliding head cars.

Shao, Xu, Yao, Peng, Li, and Zhao (2016) tested this assumption with a 1/8-scale, one-dimensional (longitudinal) train-collision model, in which car bodies were iron blocks, the energy absorbers were honeycombs, and the inter-car buffers were rubber, with a moving consist striking a stationary one at 22.8 km/h. They simulated the test in the commercial multibody package ADAMS with a traditional method model (TMM, one force element per inter-car junction) and an improved method model (IMM, a nonlinear spring for the inter-car connection plus separate equivalent forces for the energy-absorbing structures). Both agreed with the test, but the IMM additionally resolved the deformation at both ends of each car and revealed an unexpected effect: although the two trains are geometrically symmetric about the collision interface, the moving train's structures absorb more energy than the stationary train's symmetric counterparts. Quantified by a dynamic asymmetry coefficient $a$, defined as the ratio of the moving head car's share of the absorbed interface energy to the even-split share of one half, the asymmetry decreases with collision speed: $a$ falls from about 123% at 10 km/h to about 108% at 36 km/h in IMM simulations, while the excess of the moving head car's share over the even half-split, which the source reports as a percentage of the total absorbed interface energy, falls from 11.69% at 10 km/h to 3.60% at 36 km/h. The authors folded this into an improved design equation $E_d=\frac{R_1}{2f_d}\cdot\frac{1}{2}M_1v^2\,a$ with $a=(-0.025v^2+0.566v+120.3)$ percent, $v$ in km/h, obtained by second-order polynomial fitting of IMM results at 10, 22.8, and 36 km/h; as in the source's Eq. (11), the percent-valued coefficient enters the design equation as its numeric fraction, i.e. $E_d=\frac{R_1}{2f_d}\cdot\frac{1}{2}M_1v^2\cdot\frac{-0.025v^2+0.566v+120.3}{100}$.

The evidence base for this speed dependence is thin and indirect. The physical test covered a single speed (22.8 km/h), a single scale factor (1/8), and one dimension: vertical and lateral loads and the torques about all three axes present in real collisions were not modeled, which the authors held responsible for the simulations overpredicting the absolute deformations and absorbed energies. The $a(v)$ relation is a fit to simulations, offered as a conservative, provisional estimate pending verification by further tests and higher-fidelity (three-dimensional or FE) simulation.

Problem Statement

Determine, on experimental evidence and validated higher-fidelity modeling, how the dynamic asymmetry of collision energy absorption between the moving and stationary train depends on collision speed: validate, refine, or replace the IMM-fitted relation $a=(-0.025v^2+0.566v+120.3)$ percent, with $v$ the collision speed in km/h, for the dynamic asymmetry coefficient (which, being quoted in percent as in the source's Eq. (11), enters the corrected design equation as the numeric value $a/100$) from tests spanning speeds beyond the single experimental point at 22.8 km/h, and establish whether this asymmetry and its speed dependence, predicted at 1/8 scale by the improved multibody model, transfer to other scale factors and to full-scale prototypes. Included in the same objective is quantifying how three-dimensional effects, vertical and lateral loads, out-of-plane torques, and the associated override (one carbody climbing over another) and lateral interaction, modify the partitioning of collision energy between the two trains relative to the one-dimensional treatment. The overarching goal is to put the scaling-law-based prediction of train-collision energy dissipation distribution, and the asymmetry-corrected energy-absorption design equation $E_d=\frac{R_1}{2f_d}\cdot\frac{1}{2}M_1v^2\,a$, on a validated footing for crashworthiness design.

References

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