Building a model of the impact grinding mechanism in a tumbling mill based on data visualization

Abstract

A mathematical model was built based on data visualization for the impact grinding mechanism in a tumbling mill, which is mainly implemented during coarse grinding. The determination of impulse interaction parameters is problematic due to the difficulty of modeling and the complexity of hardware analysis of the behavior of intramill loading. Conceptually, it was envisaged to identify the relative dynamic parameters of the impact action as components of the model, which are criteria for the similarity of the loading movement and the grinding process. Impact power was taken as an analog of grinding performance. The initial characteristic of the impact was considered to be the averaged vertical component of the speed of loading movement in the flight zone at the boundary of contact with the shear layer. The formalization of the model revealed the effect on the performance of the mass fraction of the flight zone and the reversibility of loading. The method of numerical modeling was applied, based on experimental visualization of the behavior of granular loading in the cross section of a rotating chamber. The influence of the rotation speed on the performance at a chamber filling degree of 0.45 and a relative particle size of a milling load of 0.0104 was estimated by experimental simulation. The maximum productivity value was found at the relative speed of rotation ψω=1–1.05. A rational condition for impact grinding at ψω=0.75–0.9 has been established. The test proved the effectiveness of using visualization to evaluate dynamic loading interaction analogs. Verification of modeling results was implemented by comparison with the data of the technical standard. The use of similarity criteria unifies approaches to modeling different mechanisms of destruction. The model built makes it possible to predict the rational parameters of the grinding processes by impact, crushing, and abrasion

Building a model of the abrasion grinding mechanism in a tumbling mill based on data visualization

“…On the basis of data visualization, patterns of loading movement in the rotating drum chamber at κ = 0.45 were obtained [11]. Separate obtained patterns of steady movement of loading in the chamber of a stationary rotating drum are shown in Fig.…”

“…Visualization was carried out by registration through a transparent end wall and further processing of pictures of loading movement in the cross-section of the chamber. The algorithm for implementing the data visualization method consists in the sequential implementation of a number of stages [10,11]. The calculation scheme of the pattern of the three-phase mode of movement of loading in the cross section of the rotating chamber is applied (Fig.…”

“…The vertical distance from the highest to the lowest point on the free surface of the flight zone h fr was adopted in [11] as a visual input parameter that approximately determines the impact interaction (Fig. 2).…”

“…Video recording of the behavior of the shear layer of the ball milling loading of the tumbling mill under the cascade mode of movement is given in [11]. However, quantitative characteristics of the shear interaction in this zone were not established in [11].…”

“…Mathematical models for two grinding mechanisms in a tumbling mill were built on the basis of data visualization. In work [11], the mechanism of destruction by breaking under the action of the impact loading mechanism was established. In [10], the mechanism of crushing failure under the action of the compression loading mechanism was revealed.…”