Classical approach to determining the natural frequency of continual subsystem of three-mass inter-resonant vibratory machine

Abstract

Problem statement. The three-mass vibratory system can be defined by five basic parameters: inertial parameters of the masses and stiffness parameters of two spring sets. Unlike the classical discrete system, the discrete-and-continual one consists of two rigid bodies connected by one spring set that form the discrete subsystem, and of the reactive mass considered as deformable (elastic) body characterized by certain stiffness and inertial parameters, which are related with one another. Purpose. The main objective of the paper consists in determining the first natural frequency of the continual subsystem of the three-mass discrete-and-continual vibratory machine. Methodology. While carrying out the investigations, it is used the classical theory of oscillations of straight elastic rods. Findings (results). The engineering technique of determining the first natural frequency of the continual subsystem of the three-mass vibratory machine is developed and approved by means of analytical calculations and numerical simulation. Originality (novelty). The optimal diagram of supporting the continual subsystem (elastic rod) is substantiated. The possibilities of exciting the vibrations of the three-mass discrete-and-continual mechanical system using the eccentric drive are considered. Practical value. The obtained research results and the developed calculation techniques can be used be engineers and designers dealing with various technological and manufacturing equipment that use vibratory drive. Scopes of further investigations. While carrying out further investigations, it is necessary to develop the model of combined discrete-and-continual system of three-mass vibratory machine, and to carry out the numerical simulation of the system’s motion under different operational conditions.