Modeling the functioning process of the steering system of a truck during parking maneuvers

The article discusses the development of a mathematical model for the steering system of a truck equipped with a screw-and-rack steering mechanism with power assistance. Special attention is given to modeling the system's operation during parking maneuvers, characterized by large wheel turning angles, vari-able steering linkage ratios, and nonlinear resistance to wheel turning. The model includes descriptions of the main components of the steering system: the pump, pressure pipeline, rotary valve, hydraulic cylinder, steering linkage, tires, and steered wheels. Key assumptions and equations used for modeling the mechanical and hydraulic subsystems are presented. The features of the rotary valve's operation and the variation in the characteristics of throttle openings depending on the torsion bar twist angle are examined. The dynamics of the hydraulic cylinder and steering linkage, as well as the resistance moments for wheel turning, are analyzed. A kinematic analysis of the steering linkage is performed, and equations for calculating the linkage ratio and the angular velocities of its elements are derived. To describe the wheel turning resistance moment, a model considering hysteresis phenomena is employed. Numerical solutions of the model equations in the Matlab/Simulink environment, under sinusoidal input to the steering wheel, confirmed that the model's response corresponds to the expected characteristics of the steering system.