THEORY OF VERTICAL VIBRATIONS AND SUSTAINABILITY OF MOTION OF COMBINED MACHINE-TRACTOR UNIT

The purpose of this study is to develop the theoretical foundations of the vertical oscillations of the combined arable-grinding machine-tractor unit and to justify the stability of its movement in the longitudinal-vertical plane. The studies used methods for constructing mathematical models of the functioning of agricultural machines and machine units based on the theory of the tractor, the theory of oscillations, the theory of automatic control and stability of motion, and methods of programming and numerical calculations on a PC. The dynamics of the vertical oscillations of this unit is investigated on the basis of the analysis of the amplitude-frequency characteristics of the unit as a dynamic system that reacts to external disturbances in the form of irregularities in the soil surface. As a result of the conducted analytical studies, an equivalent circuit of this combined machine-tractor unit was constructed in the longitudinal-vertical plane, its characteristic points were determined, linear and angular displacements were specified, and active forces were applied. Each pneumatic wheel of the unit, presented in the form of an elastic-damping model, has a point contact with the unevenness of the soil surface, which are given by the corresponding heights. Using the initial equations of Lagrange form of the 2nd kind, first generalized coordinates, expressions for kinetic and potential energies, dissipative functions and generalized forces were determined and after the necessary transformations a system of four differential equations of motion of the dynamical system under consideration was composed. Next, for the obtained system of differential equations, Laplace transformations were performed, which made it possible to obtain a system of equations in operator form and prepare them for a form convenient for numerical calculations using a compiled program on a PC. According to the results of numerical calculations, graphs of the amplitude and phase frequency characteristics of the tractor’s vertical oscillations with different stiffness coefficients of its steerable wheels, amplitude-frequency characteristics of chopper vibrations depending on its mass and stiffness coefficient of the tires of the support wheels, as well as the characteristics of its oscillations field pneumatic support wheel.

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