Mathematical Modeling Features of the Wheeled Vehicle Movement with an Automated Braking Control System

Most vehicles: cars, buses, motorcycles, airplanes, etc. are currently equipped with an automated braking control system. Its purpose is to shorten the braking distance while maintaining vehicle stability and controllability. The presence in the design of a wheeled vehicle of an automated braking control system leads to the need to simulate movement taking into account this system. Because the real change in time of vehicle motion parameters is continuous, and the calculated is discrete, the problem of verifying such models arises. The purpose of this work is to maintain solution accuracy and ensure solution stability of equations in the numerical simulation of the vehicle movement with an automated braking control system. A selection has been made of a validated mathematical model of vehicle motion equipped with an automated braking control system and its software implementation. Calculation experiments were carried out to verify the mathematical model of vehicle movement. Its motion parameters in different modes were obtained and their correspondence to experimental values was determined. It has been established that the integration step of the calculated motion parameters significantly affects at the calculating results then vehicle trajectory parameters in braking modes (straight-line and curvilinear). The direction of this influence is ambiguous. It is determined that the solution instability is given by: the equation for calculating the longitudinal wheel slip and the related equation of the every braking wheel. This is especially true for small value of slip in the wheels-road contact, which are critical in accordance with the algorithms automated control system. A method for obtaining the objective function as a result of solving the problem of choosing a integrating step for the motion parameters of a wheeled vehicle with an automated braking control system has been developed and implemented while ensuring the necessary solution accuracy and solution stability. The study results can be used in design modeling of the vehicles movement on elastic wheels. 

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