Dynamic Modeling and Lateral Stability Analysis of Long Combination Vehicles

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Tech


This study provides a comprehensive modeling evaluation of the dynamic stability of Long Combination Vehicles (LCVs) that are commonly operated on U.S. highways, using multibody dynamic simulations in MATLAB/Simulink®. The dynamic equations for a tractor with two trailers connected by an A-frame converter dolly (A-Dolly) are developed. The dynamic model is used for running MATLAB® simulations, with parameters that are obtained through measurements or obtained from other sources. The simulation results are verified using track test data to establish a baseline model. The baseline model is used for parametric studies to evaluate the effect of trailer cargo weight, center of gravity (CG) longitudinal location, and trailer wheelbase. The dynamic model is further used to analyze both single-trailer and double-trailer trucks through nondimensionalization. The nondimensionalization method has the added advantage of enabling studies that can more broadly apply to various truck configurations. The simulation results indicate that increasing the trailer wheelbase reduces rearward amplification due to the damping effect of the longer wheelbase. A larger momentum ratio due to increased trailer gross weight increases rearward amplification. The detailed models of pneumatic disc and drum brakes in LCVs, including the airflow delay and thermal characteristics, are also developed and are coupled with the articulated vehicle dynamic models. The disc and drum brake braking performance are evaluated and compared in straight-line braking and combined steering and braking at a 150-ft J-turn maneuver. In straight-line braking, the simulation results indicate that disc brakes provide significantly shorter braking distance than drum brakes at highway speeds on a dry road, mainly due to their larger braking torque. On a slippery road surface, however, the greater braking torque causes more frequent wheel lockup and ABS activation at higher speeds, and disc brakes do not provide a substantially shorter braking distance than drum brakes. The simulations also point out that the disc brakes' cooling capacity is higher than the drum brake, with the cooling efficiency heavily dependent on the airflow speed. At higher driving speeds, the airflow accelerates to a turbulent flow and increases the convection efficiency. For braking in-turn maneuvers, at higher entering speeds, disc brakes decelerate the vehicle slightly sooner and then scrub speed faster, resulting in better roll stability when compared with drum brakes.



Long Combination Vehicle Dynamic Stability