The crushing equipment is characterized by a significant energy-consuming system during the crushing workflow. The current trend in the development of such processes puts forward requirements for the development of new or improvement of existing energy-saving equipment. The essence of the solution to the problem in this work is determined by using resonant modes, which are inherently the most effective. The practical implementation of the resonance mode has been achieved taking into account the conditions for the interaction of the resonant vibration crusher with the material at the stages of its destruction. The degree of the stress-strain state of the material is taken into account, which was a prerequisite for identifying the potential for the development of a vibration load. Composed equations of motion based on a substantiated discrete-continuous model of a vibration crusher and processing material. An approach is applied to determine the stepwise destruction of the material with the determination of the required degree of energy. This methodological approach made it possible to reveal the nature of the process of material destruction, where energy costs at the stages of crack formation, their development and final destruction are taken into account. It was revealed that the greatest energy consumption during the operation of crushers goes into the kinetic energy of the crushing plates and the potential energy of deformation of the springs. The proposed model is common for any design of a vibration machine and its operating modes. The stable resonance mode has made it possible to significantly reduce the energy consumption for the course of the technological process of material grinding. The results obtained are used to improve the calculation methods for vibratory jaw and cone crushers that implement the corresponding energy-saving stable zones of the working process.

The necessity of solving the problem of increasing the efficiency and reducing the energy intensity of the working process of the vibration machine movement is substantiated. A new principle is proposed for transferring energy from the shape-forming surfaces to the processing medium by implementing highly effective modes and parameters. A constructive scheme and a definite mathematical model of the frame of the vibration machine have been developed, realizing complex spatial oscillations. The oscillations of this shape-forming surface are investigated using the finite element method. The finite element model is composed by approximating all load-bearing elements of the frame with beam end elements. Loads created by pneumatic centrifugal exciters of high-frequency oscillations are determined. The basic waveforms of the shape-forming surfaces that are realized at 18.79 Hz, 18.89 Hz and 19.71 Hz, respectively, are investigated and determined. The distribution of the vibration amplitudes along the perimeter of the frame is estimated at the excitation frequency of 182.5 Hz. The rational values of the amplitude of oscillations for the realization of an effective process of concrete mixture compaction are found. The amplitude of the oscillations is 0.0002...0.0005 m. The obtained vibrations show the presence of the multimode operation of the vibration machine. A definite direction of the purposeful use of one of the forms of natural oscillations is the shape-forming surfaces. The approach for creating high-performance vibration machines of a new generation is proposed. The ideology of implementing such regimes can be successfully applied in road construction for the construction of concrete roads

The process of a vibration concrete mixer has been investigated. Well-coordinated equations of motion of the system «mixer – concrete mixture» and their solutions have established the regularities of changing the parameters of the mixer at different angles of inclination. An experimental design of vibration-gravitational mixing has been developed and manufactured, and studies of the working process of mixing efficiency have been carried out on it. Research carried out at three warehouses of concrete mixtures confirmed the assumptions accepted in the work, the assumption and the selected physical and mathematical model of the «Mixer – concrete mixture» system. The use of a vibration concrete mixer made it possible to reduce the duration of mixing by 2.5–3 times in comparison with conventional free mixing concrete mixers. Provides the preparation of hard concrete mixtures and improving the quality of concrete mixtures due to the destruction of defective aggregates and a more uniform distribution of the binder throughout the volume of the mixed mixture. An algorithm and method for calculating the main parameters of a vibration concrete mixer have been developed.

This paper considers the influence of higher harmonics in dynamic action systems due to their complex movement in the process of interaction with the technological load. The object of research is the process of propagation of oscillations in complex dynamic systems. One of the problems in the application of oscillatory processes is the consideration of higher harmonics in the overall movement of systems. To solve the problem, the idea of using a hybrid model that takes into account both discrete and distributed parameters was proposed. The resulting mathematical discrete model in the analytical equations of motion of the dynamic system preserves continuous properties in the form of wave coefficients. These coefficients in their analytical form take into account the contribution of higher harmonics of both the reactive (elastic-inertial) and active (dissipative) components of the resistance force. The studies were carried out on a model of a plant with a multimode spectrum of oscillations and a nonlinear dynamic system, which is a system with piecewise linear characteristics.A series of experimental studies with a wide variation of the change in the frequency of oscillations was carried out on the installation with a multimode spectrum of oscillations. Zones of manifestation of higher harmonics along the vertical axis of force action were revealed. The given spectrum at the exciter frequency of 35 Hz showed the manifestation of the spectrum component (around 70 Hz) along the X axis, which is an important result for practical application. For a system with piecewise linear characteristics, the manifestation of multimode, which manifests itself in the form of subharmonic and superharmonic oscillations, was determined. The contribution of each harmonic is determined by applying the obtained dependences. The results were used in the development of algorithms and calculation methods of a new class of dynamic action systems taking into account the contribution of higher harmonics

Determination of the workflow of energy-saving vibration unit with polyphase spectrum of vibrations

Due to the continuous development of the building-and-construction industry, it is necessary to design new or modify outmoded industrial equipment. Using jaw crushers with the impact action of crushing plates on material is a perspective line of developing crushing equipment. Purpose. Developing a mathematical model of a vibratory jaw crusher and studying the operational process which is based on the mathematical model in order to design new crushers. Methodology. Definition of the crusher working process is based on the main statements of the theory of mechanical oscillations and the theory of continuous environment. In the motion equations of the crusher the material is taken into account on the basis of a discrete model by a continual parameter. Findings. A physical model is developed on the basis of which motion equations are derived, which include three main conditions of the efficient operation: 1) the elasticity of the second vibrating element must exceed or be equal to crushing force; 2) vibrations of the first and the third vibrating elements must be in phase, and vibrations of the second vibrating element must be in antiphase; 3) the summarized displacement of the second and the third crushing plates must ensure crushing of material. Graphs of the effect of the vibrating elements and elasticity coefficients of elastic systems on the amplitudes of vibrations are plotted and analyzed. On the basis of the motion equations, with consideration for the optimal parameters of the crusher vibrating elements and for the elasticity coefficients of the elastic systems, the amplitude-frequency characteristics of the crusher for different frequency ranges are determined. Set up is an equation describing the displacement of material in the crushing chamber for a time interval required for the crushing plates to be separated. Presented are graphs of dependency of the amplitude of vertical vibrations of the crusher casing on the elasticity of the isolating elastic system, and provided are recommendations for selecting and calculating vibration isolation. Originality. A mathematical model of an experimental vibratory jaw crusher and the characteristics of the experimental crusher are presented, on the basis of which recommendations are given for the selection of energy-efficient operating modes of the crusher. Practical value. Knowledge on the rational values of the frequency ranges for operation of the studied vibratory jaw crusher makes it possible to determine the optimal level of power consumed by the crusher and efficiency in processing materials of different hardness.