Physical foundations of vehicle stability when moving uphill and at longitudinal roll back

Abstract

Problem. The determination of the stages of stability for vehicles as technical systems when moving uphill on an inclined section of the road and their possible longitudinal roll back is considered. The considered stages ensure the safe operation of vehicles in various conditions and with various combinations of the values of the parameters that are included in the proposed equations characterizing the stability of the vehicle. Goal. The purpose of the paper is to improve the method of researching the physical foundations of the stability of vehicles when moving uphill on an inclined plane, the formation of mathematical models, which allows to significantly improve the mathematical support of the methods of calculating the stability of two-axle vehicles (cars, trucks, tractors, special and specialized vehicles, etc.) Methodology. The approaches adopted in the work to achieve the set goal are based on the classical laws of the mechanics of free-standing or moving objects, namely: the principle of possible movements, where calculated dynamic and mathematical models with their solutions are able to preserve the given conditions and parameters, and characterize the state of stability of the vehicle in case of its longitudinal roll back. Results. It was established and confirmed by a numerical examples that the longitudinal stability of a vehicle moving uphill depends on the longitudinal road slope, the vehicle design, the elasticity of the road surface, the critical overturning angle of the vehicle and its weight parameters. Originality. The proposed mathematical model of the longitudinal stability of the vehicle when moving uphill showed that its solution significantly depends on the values of the geometric parameters of the uphill and the vehicle, and also depends on the position of the center of gravity of the vehicle relative to the surface of the road surface. Practical value. The obtained equations for determining the values of the stability parameters of the vehicle when moving uphill on an inclined road section make it possible to specify the parameters for ensuring the logistics of vehicles in the conditions of their operation on uphill.