Mathematical Modeling and Multi-Criteria Optimization of Design Parameters for the Gyratory Crusher

Abstract

There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times.

Technogenic Reservoirs Resources of Mine Methane When Implementing the Circular Waste Management Concept

“…The data obtained from the previous studies [60,61] were presented in the form of a generalized regression model (Figure 3), in order to compare them with the options intended for creating two-dimensional models.…”

“…The data obtained from the previous studies [60,61] were presented in the form of a generalized regression model (Figure 3), in order to compare them with the options intended for creating two-dimensional models. The analysis of the generalized trend line allows the conclusion that the methane release intensifies after the longwall passage, and can transit into an emission component The analysis of the generalized trend line allows the conclusion that the methane release intensifies after the longwall passage, and can transit into an emission component due to the roof subsidence in the mined-out space.…”

Reuse and Mechanochemical Processing of Ore Dressing Tailings Used for Extracting Pb and Zn

“…If the waste is reactivated in order to improve the properties of the filling mass, as the study [107] mentions, the strength of the samples can be increased two times. Even using the copper tailings as an additional cement material can be environmentally justified [108][109][110]. In our previous studies concerning this type of tailings, the backfilling strength was found to be 8-9 MPa [84].…”

Transient Stability Analysis for Grid-Forming VSCs Based on Nonlinear Decoupling Method

“…The effective utilization of renewable energy is a crucial step in promoting energy reform and alleviating environmental pressures. Various renewable energy systems are used to save energy expenses and reduce dependence on grid energy [3][4][5][6][7][8]. However, unlike conventional synchronous generators (SGs), distributed resources are commonly integrated into the power utility through power electronic devices, such as voltage source converters (VSCs).…”