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.

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