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Vibration technological machines with self-synchronized unbalanced vibration exciters (vibrating conveyors, vibrating screens, vibrating crushers, etc.) are widely used in modern industry. Despite drive construction simplicity throughout exploitation of such machines a number of nonlinear dynamics effects can be observed. Most of such effects are related to machine drive and elastic suspension interaction and appear while passing through resonant frequencies. Nowadays the idea of resonant vibrating machines creation got a second breathe. The distinctive feature of such machines is the automated system for maintaining resonant mode of machine. Creation of such automated systems requires accurate mathematical models of vibrating machines that can reflect its most important features. The aim of this work is to create a spatial mathematical model and determine the dynamic system unknown parameters of a vibrating screen experimental sample with two self-synchronizing unbalanced vibration exciters that can create the working body spatial motion. The mathematical model motion equations are derived using the Lagrange equations of the second kind. Using the obtained experimental data (natural frequencies and logarithmic damping decrement), the mathematical model mass-geometric parameters and the damping parameters values were calculated. The investigation result is a verified mathematical model of a vibrating screen sample with two self-synchronizing unbalanced vibration exciters.

The article provides a comparative analysis of the energy consumption required for the implementation of the resonant and beyond-resonant modes of vibrating technological machines working body’s oscillations. An algorithm for selecting parameters of an electric drive based on an asynchronous electric engine to provide the specified amplitude and frequency of the working body oscillations for both modes of vibration is presented, taking into account frequency regulation, losses arising in the elastic suspension of the machine and in bearings of engine, the occurrence of reactive power and changes in the energy conversion efficiency.

A model of a vibrating jaw crusher (VJC) with self-synchronizing unbalanced vibration exciters is considered with account of the impacts between the jaws and the material being processed. Numerical modeling is used to establish the influence of the initial gap between the jaws and the material and of the velocity recovery factor upon impact on the synchronization of vibration exciters rotation and jaw vibrations, on the excitation frequency ranges of stable periodic vibroimpact regimes, and on the impact velocities between the jaws. The analysis results indicate that a change in the conditions of contact between the jaws and the material being processed leads to a change in the frequency ranges of the stable antiphase synchronization of vibration exciters rotation, as well as in the excitation frequency ranges of steady single-period vibroimpact regimes for the motion of the system, considered as the main operating modes of the VJC. The impact-like nature of the interaction between the jaws and the material being processed suggests the possible multimodality of the system, which explains some of the effects observed in practice and manifested in changes in the periodicity of the vibroimpact regime and in the vibration mode of the jaws at a constant excitation frequency. Therefore, the vibroimpact-based model proposed for the VJC and its dynamics analysis results may be used to design and improve vibrating jaw crushers with the selection of reasonable design parameters and the most effective vibration excitation conditions. The work was carried out with the financial support of the RFBR, project No. 18-08-01491_a.