## Study of the oscillation processes of a front-mounted haulm harvester when it moves on the inequalities of the ground surface

In the article the calculated mathematical model of oscillations of the haulm-harvesting machine frontally attached to a wheeled tractor is constructed. A nonlinear differential equation is obtained, which describes the oscillations of a haulm-harvesting machine in the longitudinal-vertical plane during the movement of its pneumatic copying wheels along the unevenness of the soil surface. On the basis of the received theoretical results rational constructive and kinematic parameters of the front-mounted hoisting machine which provide decrease in amplitude of the specified fluctuations are defined. So, at translational speed of movement of the haulm-harvesting unit V = 3.0 m∙s–1, the amplitude of oscillations of the rotor of the haulm harvester decreases in 1.2…1.5 times in comparison with height of roughnesses of a surface of the field o h = ± 0.04 m. At the amplitude of oscillations of the lower ends of the knives of the rotary cutting device up to 4 cm, the loss of the tip does not increase significantly. However, when increasing the values of the amplitude of these oscillations to 7 cm or more, the loss of the branch increases significantly and the maximum values of which exceed 12%.

## Development of mathematical model of plane-parallel movement of trailer harvesting machine

This paper presents the basic principles of building a mathematical model of trailer harvesting, for which an example of a trailed combine harvester is considered. To develop this mathematical model, all the components are given, starting with the assembly of an equivalent scheme of plane-parallel movement of this harvesting unit, which consists of a wheeled aggregate tractor of classic layout and trailed behind the combine. And behind the combine is attached a cart for the harvest. Differential equations of relative motion of the collecting unit are compiled and solved on the basis of the Lagrange equation of the second kind.

## Theory of vertical oscillations of a frontally mounted tops harvesting machine

To establish influence of kinematic and constructive parameters of tops-harvesting machine on quality of a continuous cut of the massif of tops at oscillations in the longitudinal-vertical plane of its tops-cutting device at frontally mounted machine on a wheeled row-crop aggregate tractor. Used modeling methods based on higher mathematics, theoretical mechanics, solving a system of differential equations and compiling programs and numerical solutions on a PC. An equivalent scheme has been developed for a tops-harvester mounted on a wheeled tractor in front of it on its oscillations in the longitudinal-vertical plane, considering all the forces that arise, taking into account the kinematic excitation that occurs when moving along soil surface definitions also due to the elastic-damping properties of its support-copying wheels. For the specified equivalent scheme, on the basis of application of initial equations in the form of Lagrange of the 2nd kind, on the chosen generalized coordinates, the system of two nonlinear differential equations of oscillatory motion of the tops-harvesting machine is received. According to the analytical transformations, the solution of this system was obtained, which made it possible to obtain the f inal expressions for determining the amplitude and circular frequency of natural and forced oscillations of the tops-harvesting machine. Numerical calculations of the received expressions on the made program on the personal computer are carried out . According to the results of numerical simulation, the final expression was obtained, which allowed to determine the vertical displacements of the end of the rotary cutting unit during the oscillations of the topping machine in the longitudinal-vertical plane. Numerical calculations on the PC of the received expression gave the chance to construct graphic dependences which establish dependences of amplitude of the specified oscillations depending on constructive parameters of the tops-harvesting machine, and also characteristics of roughnesses of a soil surface and elasticdamping properties of copying wheels.

## Mathematical model of root head cleaning machine with vertical drive shaft

The operation of the machine attached to the back of the tractor to clean the heads of root crops from residues in the case of using copying pneumatic wheels causes oscillations of the tops harvester in the vertical plane, which significantly affects the quality of the process. Accordingly, the movement of the horizontal working body will depend on many structural and kinematic factors. Therefore, the development of a mathematical model that will describe the movement of the working body of such a unit is an important task. To solve which the method of construction of calculated mathematical models of functioning of agricultural machines and machine units, on the basis of theoretical mechanics and higher mathematics was used in the work.. Using which the equivalent scheme of movement of the unit is developed and the system of two nonlinear differential equations for detailed research of oscillations of the cleaner of heads of root crops in the longitudinalvertical plane at movement of its pneumatic copying wheels on roughnesses of a surface of soil is received. The mathematical model of movement of the cleaner with a horizontal cleaning shaft developed on the basis of initial equations of dynamics in the form of Lagrange of the 2nd kind allowed to establish depedencies between constructive and kinematic parameters of the car and its oscillatory characteristics. The found dependences created preconditions for the further mathematical modeling of parameters of the rear-mounted cleaner of heads of root crops, with a horizontal clearing shaft. Using the developed calculation model it is possible to optimize the values of angle B and coordinates у that characterize the oscillations of the machine in the longitudinal-vertical plane.

## MODELING OF A CYLINDRICAL BODY MOTION ON A VIBRATING SURFACE

Mathematical Modeling, Vol. 3 (2019), Issue 4, pg(s) 105-108

The problems of continuous motion of a cylindrical body with a displaced center of mass along vibrating horizontal and inclined surfaces are considered.
The analytical solutions of the motion equations were obtained by the method of partial discretization of nonlinear differential equations [1] and graphs of changes in the rotation angles of a cylindrical body were constructed for various cases.

• ## SCHEMATISATION THE STUDY PROCESS OF MULTIBODY ROAD VEHICLE MODELS DESCRIBING RIDE COMFORT – PART II. METHODS OF MATRIX MECHANICS

The objective of this study is investigation possibilities to obtain main parameters of road vehicle ride comfort using formal matrix approach. The automobile is modeled as a dynamic system consist masses interconnected by springs and dampers with linear characteristics. The procedure is applied about four to eight wheel models. The engine, transmission, passengers and loads are presented like a simple masses suspended on a single springs. In the paper are written the main principles of calculation procedure for formal modeling typical vehicle dynamic system.

• ## SCHEMATISATION THE STUDY PROCESS OF MULTIBODY ROAD VEHICLE MODELS DESCRIBING RIDE COMFORT – PART I. METHODS OF CLASSICAL MECHANICS

The objective of this study is investigation possibilities to obtain main parameters of road vehicle ride comfort using formal matrix approach. The automobile is modeled as a dynamic system made of masses interconnected by springs and dampers with linear characteristics. The procedure is applied about four to eight wheel models. The engine, transmission, passengers and loads are presented like a simple masses suspended on a single springs. In the paper are written the main principles of calculation procedure for formal modeling typical vehicle dynamic system.

## MATHEMATICAL MODEL OF INTERACTION OF THE FLEXIBLE CLEANING BLADE WITH ROOT CROP HEAD

Modern technologies of harvesting sugar beet tops provide solid preliminary cutting and collecting its harvest at the increased altitude and subsequent additional root crops heads cleaning from tops residues on a root. This last operation also defines quality of root crops of beet before their digging up. Objective of this research is improvement quality of root crops heads cleaning from tops remains, by development of interaction theory of flexible cleaning blade with a spherical surface of root crop head. In the theoretical study were used methods of modeling, higher mathematics and theoretical mechanics, as well as programming and carrying out numerical calculations on the PC. As a result of the conducted theoretical research the interaction theory of flexible cleaning blade with a root crop head surface in the course of its cleaning from tops remains is developed. On the basis of the received differential equations of blade movement which is pivotally mounted on the drive shaft with a horizontal axis of rotation, new mathematical dependences which justify basic parameters of this technology process are given.