Synthesising spatially repeatable tyre forces from axle load probability distributions

Abstract

Spatially repeatable dynamic tyre forces arise because heavy trucks are similar in weights, dimensions and dynamic characteristics and they travel at similar speeds. It is important to be able to model the statistical and spatial characteristics of dynamic tyre forces, using efficient algorithms, when studying the effects of vehicle–road interaction. Pitch-plane vehicle models derived from ‘per-vehicle’ weigh-in-motion (WIM) data of US ‘Class 9’ vehicles were used to generate a Virtual WIM vehicle fleet for spatial repeatability calculations. Four methods were investigated for simulating dynamic tyre forces with a level of spatial repeatability similar to the Virtual WIM fleet: (i) randomised pitch-plane models, (ii) randomised quarter car models (both derived from axle load probability distributions), (iii) phase-shifted quarter car models and (iv) phase-shifted pitch-plane models. Of these four methods, the best was found to be the phase-shifted pitch-plane models, which required four orders of magnitude less computation time than the Virtual WIM case, while approximating the spatial repeatability of the Virtual WIM fleet with reasonable accuracy.