Mathematical model of the system “manual vibration shock shaker – fruit branch”

• Published in: Mehanization and electrification of agricultural no. 9(108); pp. 210 - 223
• Main Authors: R., Krupych, I., Nishchenko, R., Shevchuk, S., Krupych
• Format: Journal Article
• Language: Ukrainian
• Published: 2019
• ISSN: 0131-2189; 2707-0751
• DOI: 10.37204/0131-2189-2019-9-27

Purpose. Development of mathematical model of oscillating system “manual vibration shock shaker – fruit branch” for the purpose of theoretical substantiation of the parameters of the shaker. Methods. The basic positions of mathematics, theoretical mechanics, mathematical modeling, program development and numerical calculations on the PC using methods of constructing mathematical models of functioning of agricultural machines are used. Results. The paper proposes a mathematical system model “manual vibration shock shaker – fruit branch” of six differential equations describing the motion of five separate masses (the mass of branch and four masses of individual shaker strings) and differential equations of the transverse and rotational motion of the system as whole. The mathematical system model determines the regularity of the motion of all masses, as well as the reactions of the viscals of the oscillatory system to the impact and after the impact that is generated in the shock mechanism. The proposed nonlinear, complex system of differential equations solves the numerical Runge-Kutta method of the fourth order of accuracy. On the basis of the calculated data the theoretical regularities of change of movement, speed and acceleration of a branch in the place of capture are received, which confirm that in the case of interaction of the cups of the shock mechanism there is blow that is accompanied by an increase in the acceleration of the branch, which is 4–5 times greater than the acceleration of the vibration mode of operation. Conclusions 1. The mathematical model of oscillating system “manual vibration shock shaker – fruit branch” is proposed in the form of system of six differential equations that allows to theoretically substantiate the basic modes of work of the manual shaker in the vibration shock mode to provide the agrotechnical necessary extraction completeness. 2. The received theoretical regularities of change of displacement, speed and acceleration of branch at the place of capture confirm the effectiveness of the vibration shock mode of the shaker. Due to the vibration-shock mode, the acceleration of the branch at the point of transmission of disturbing forces is 4–5 times higher than the acceleration of the vibrational operation mode. Keywords: manual shakes, vibration shocking process, oscillation oscillators, mathematical model, fruit branch, harvesting.