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 rolling of a flat figure in the form of an equilateral polygon on a curvilinear profile is considered. The profile is periodic. It is formed by a series connection of an arc of a symmetrical curve. The ends of the arc rely on a circle of a given radius. The equation of the curve, from which the curvilinear profile is constructed, is found. This is done provided that the centre of the polygon, when it rolls in profile, must also move in a circle. Rolling occurs in the absence of sliding. Therefore, the length of the arc of the curve is equal to the length of the side of the polygon. To find the equations of the curve of the profile, a first-order differential equation is constructed. Its analytical solution is obtained. The parametric equations of the curve are obtained in the polar coordinate system. The limits of the change of an angular parameter for the construction of a profile element are found. It is a part of the arc of the curve. According to the obtained equations, curvilinear profiles with different numbers of their elements are constructed.