MATHEMATICAL PREDICTION OF CRITICAL MOTION MODES OF VEHICLES WITH LIQUID FILLING

Abstract

The aim of the work is to create a mathematical apparatus and algorithms for the operational prediction of the occurrence of critical modes (loss of directional stability, rollover) of vehicles with liquid filling. The study used a comprehensive approach: methods of classical mechanics, hydrodynamics of an ideal incompressible fluid, variational methods, numerical integration of differential equations of motion in the MATLAB/Simulink environment, as well as the second Lyapunov method for analyzing the stability of nonlinear systems. Additionally, elements of computational hydrodynamics were used to verify the results. It was found that the addition of one longitudinal partition reduces the amplitude of oscillations by 35–40%, and the combination of a longitudinal and two transverse ones by 60%, increasing the threshold of the occurrence of a critical mode by 25–30% in lateral acceleration. The scientific novelty consists in improving the mathematical apparatus for assessing the dynamic states of vehicles with liquid cargo by introducing the S(t) criterion and the Lyapunov function for identifying bifurcation points in real time. The practical value of the work lies in creating an algorithm that can be integrated into on-board active safety systems to prevent overturning of road tankers, tank containers and railway tank cars. The results can be used in the development of international safety standards for the transportation of dangerous goods. The proposed model allows for the quantitative assessment of the risk of loss of stability with an advance of up to 1.4 s, which is sufficient for automatic braking. It is proven that incomplete filling (40–60%) is a critical risk factor, and the installation of partitions significantly increases safety. Further research will be aimed at taking into account the viscosity of petroleum products at low temperatures and the use of neural networks to reduce computational costs