MATHEMATICAL JUSTIFICATION OF STABILITY OF STEERING BRIDGE OF WHEELED TRACTOR

Abstract

The article deals with the influence of wheel oscillation and the micro-profile of the road surface on the stability of the wheel tractor axle movement. The reasons for the oscillations of the steered wheels, the design diagram of the controlled axle of the tractor and the sequence for determining the oscillation frequency of the axle of the tractor are presented. The reasons for the oscillation of the steered wheels are collisions with bumps, imbalance of the wheels and a double connection with the tractor frame through the steering system and the fastening of the steering axle beam. The most common functions for describing road irregularities that affect the movement of a tractor are the mathematical expectation and the average value of the ordinates of the micro-profile, the variance or standard deviation of the ordinates, the correlation function characterizing the relationship of various implementations of the micro-profile functions along the length of the road section and spectral density. Oscillations of the steered wheels have a side effect on the stability of the tractor, which leads to oscillations of the steered axle due to the presence of an additional degree of freedom (turning around the pivot) in comparison with uncontrolled ones. In addition, the steered wheels are interconnected by a steering linkage, which is damped due to clearances. Oscillations of the wheels can also occur due to the fact that the radial (normal) stiffness of the tires around the circumference is not the same. When such a tire rolls, the wheel begins to oscillate in a vertical plane. Such oscillations, performed due to changes in the parameters of the oscillatory system, are called parametric. Self-oscillations of the steered wheels cause significant dynamic loads on the steering parts, intense tire wear and lead to a loss of tractor controllability and driving stability. One of the main reasons for the occurrence of oscillations of the steered wheels is the presence of a gyroscopic relationship between the angular oscillations of the beam of the steered bridge in the transverse plane and the rotation of the wheels of this bridge relative to the pins. The article also discusses the physical essence of the processes occurring during self-oscillations of the tractor's controlled wheels.