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.
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