On Determining the Stability of an M1-Category Vehicle with an O2-Category Trailer During Braking

Abstract

The paper investigates the braking stability of an M1–O2 road train composed of a light commercial van (Mercedes-Benz T1N Sprinter) towing a dual-axle trailer (ПВБФ 15). Particular attention is paid to how the simultaneous action of axle-side brake-force non-uniformity, trailer payload and the vertical position of the combined centre of gravity (CoG) affects both deceleration efficiency and directional safety. A coupled, non-linear six-degree-of-freedom model of the articulated combination was solved numerically; the brake forces on each wheel were varied parametrically so that the imbalance coefficient kₙ covered the range 0.50–1.00. Three performance criteria were adopted: braking distance Sᵦ, mean deceleration jₓ and the stability coefficient ηᵧᵢ, defined as the ratio of the lane width required for stable braking to the statutory limit.

The simulation demonstrates that the UNECE R-13 requirement of j ≥ 6 m s⁻² at an initial speed of 60 km h⁻¹ is met only when the trailer-axle imbalance does not exceed kₙ = 0.82. Global loss of stability is governed by the towing vehicle: it becomes laterally unstable at kₙ ≈ 0.70, whereas the trailer retains stability down to kₙ = 0.53. Raising the trailer payload from 0.6 t to 2.8 t improves ηᵧᵢ by 12–18 %, while increasing the relative CoG height from 0.35 to 0.50 halves stability.

Scientific novelty lies in the integrated assessment of simultaneous axle-side brake-force imbalance and mass-distribution parameters, which yields a more realistic forecast of road-train behaviour in emergency braking. The practical value consists in formulating admissible imbalance limits and cargo-placement guidelines that can be incorporated into maintenance regulations, driver-assist warnings and onboard monitoring algorithms.

Keywords: road train; braking stability; brake-force imbalance; directional stability; centre of gravity; payload distribution; mathematical modelling.