The widespread use of vibrating tables in industry motivates researchers to develop new, efficient designs that can increase production profitability. For this purpose, the authors present a new schematic design of a vibrating table with an inertial drive, proposed to be powered by a hydraulic coupling. The principle of operation is as follows: the driving shaft of the hydraulic coupling is rotated by an electric motor, while its driven shaft is connected to an unbalanced mass. In this case, it is assumed that the rotor of the induction electric motor reaches its nominal operating mode, and the unbalanced speed “locks” near the resonant peak due to processes associated with the Sommerfeld effect. This enables the automatic maintenance of the forced oscillation frequency near the pre-resonant regime, thereby implementing energy-saving operating modes in the vibration system of the vibrating table, without the need for expensive control systems.
A problem arises because the implementation of such a design requires a clear justification of the inertial, stiffness, and force parameters of the oscillatory system. In addition, it is necessary to analyze the dynamic characteristics of the oscillatory system. This will enable a priori verification of the design's operability with the required technological parameters.
This article addresses the issues discussed. For this purpose, the authors present the methodology for determining the inertial, stiffness, and force parameters of a two-mass resonant vibrating table with an inertial drive. For the specified operating mode, analytical expressions are given for determining the amplitudes of mass oscillations, stiffness coefficients of elastic elements, the amplitude of the excitation force, and unbalance parameters. The dynamic parameters of such an oscillatory system, namely the dynamic coefficients of the oscillating masses, are analytically derived and analyzed. A specific example demonstrates the application of the proposed approach to calculating a two-mass oscillatory system with a force disturbance from a reactive mass. The amplitude-frequency characteristic of the oscillatory system is constructed and analyzed.
The value of this article lies in presenting a comprehensive methodology for calculating the vibration systems mentioned. A distinctive feature of this methodology is that it provides refined analytical expressions for setting the parameters of the vibration system. The material is accompanied by clear visualization. The presented methodology can be used by engineers when designing vibration technological equipment of this type.
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