On developing structural and technical solutions to ensure the vibratory displacement of the working medium

Abstract

A research study into using vibration technologies for the transport of granular working medium was carried out. A vibration testing machine, whose calculation model includes a mechanical vibration system having two degrees of freedom with a rigid body on elastic supports, was selected as an object of research. The study involved analysing the variation in the system vibrations by using the structural theory for vibration isolation systems, where a dynamic equivalent represented by a structural diagram of an automatic control system is compared to the initial calculation model. The structural diagram of the system is based on the motion equations in operator form obtained using Lagrange differential equations of the second kind. The Laplace transform was used to transform the initial data for the system of differential motion equations. The paper addresses the characteristics of a new structural and technical solution in the field of vibratory displacement of a granular working medium using the working body of a vibration technological machine, which involves introducing a number of additional weights, levers, springs, and hinges. Here, springs comprise generalised structures containing both elastic elements and vibration dampers. To connect the coordinates of the endpoints in the working body of the vibration technological machine, analytical relations were obtained. It was established that varying the parameters of the elements within the elastic-lever blocks allows the dynamic state of the vibration technological machine to be controlled. In addition, it was shown that the obtained structural diagram helps to derive mathematical expressions for transfer functions, comprising the ratio between the motion coordinates of a technical object and an external force disturbance. On the basis of these expressions, the transfer function for the ratio of the motion coordinates of the vibration technological machine was formulated. A mathematical model of a vibration technological machine was obtained in the form of a transfer function, including a large number of additional elastic and massinertial elements, where the parameters of vibration displacement can be adjusted automatically. The research results will allow the existing technical solutions in the field of technological engineering to be modernised.