ДИНАМІЧНА МОДЕЛЬ ПРИСТРОЮ ДЛЯ КЕРУВАННЯ ЗМІНАМИ ШВИДКОСТІ ІЗ ЗУБЧАСТИМ ДИФЕРЕНЦІАЛОМ І ЗАМКНУТОЮ ГІДРОСИСТЕМОЮ ЧЕРЕЗ ВОДИЛО

Abstract

The purpose of the study is to build a dynamic model of the speed change device including a differential gear and a closed-loop hydraulic system, where the driving link is a sun gear driven by an electric motor, while a closed-loop hydraulic system is connected to the carrier and can change its speed due to changes in system’s throughput, the ability of the fluid to move across the hydraulic system, so that the necessary law of motion on the driven link - the ring gear can be obtained. The analysis of recent publications has revealed that the research of new speed control devices with a differential gear and a closed-loop hydraulic system through the carrier pays much attention to their structure, principle of operation, and the change in speed, that has been confirmed by analytical and graphical dependences. In addition, energy efficiency and self-braking of such devices has been studied by determining the coefficient of performance efficiency. The dynamics of such devices is waiting to be resolved. It will allow us to develop methods to reduce the impact of dynamic loads on the mechanical drives of machines when changing speed. The article proposes a mathematical model of the movement of a mechanical system for new devices for changing the speed using a differential gear with a closed-loop hydraulic system through the carrier. For this purpose, the equation of dynamics by the Lagrange method of the second kind has been used and the equation of kinetic energy of the system has been formed. Since there is a relationship between the speeds of all links in the differential gear, the expression for the kinetic energy of the system has been described by the speed of the driving and driven links, i.e., by the speed of the sun gear and the ring gear. The result of solving the Lagrange equation in partial derivatives is a system of two differential equations with unknown derivatives of the velocities of the sun gear and the ring gear. The obtained results are the basis for further computer simulation and quantitative analysis to assess the performance of such devices and select the necessary closed-loop hydraulic system to control speed changes. Based on the dynamic model, it is possible to compose and solve the equations of dynamics for typical cases of changes in the torque resistance: long-term shock, short-term shock and significant overload, up to the stop of the machine.