This article concerns the issues of modeling and the optimizational approach for the performance of ore comminution circuits. A typical, multi-stage comminution circuit was analyzed with the high-pressure grinding rolls unit operating at a fine crushing stage. The final product of the circuit under investigation was, at the same time, a flotation feed in which particle size distribution initially determined the effectiveness of flotation operations. In order to determine the HPGR-based comminution circuit performance, a suitable mathematical model was built wherein the target function was linked directly with the effectiveness of the flotation processes. The target function in the presented model considers the issue in terms of the flotation operation’s effectiveness. The particle size distribution of individual comminution products and resulting from the weight recoveries of individual size fractions were criteria determining the quality of the comminution product. Weight recoveries of individual size fractions, in turn, were tied with the technical operating parameters of individual comminution devices. In the first model, profit maximization was the target function, while the second variant of the model took into account maximization of the useful mineral weight recovery in the concentrate. The HPGR application into ore processing circuits also results in energy saving benefits which were presented in a comparative analysis of the energy consumption of two comminution circuits – the first based on conventional crushing devices, and the second on the HPGR unit application which replaced the rod mills. The main benefit of such a modernization was almost two times lower energy consumption by the fine crushing stage and a decrease in the ball mills’ grinding operations load through bypassing a part of the material directly for the rough flotation operations.

This paper describes comminution processes using the theories of limiting states, elasticity, and plasticity to explain some effects observed in the process of crushing brittle materials. It further describes the phenomena occurring during crushing in high-pressure roll presses and analyzes the effects of selected factors upon crushing results. The evaluation of the usefulness of various hypotheses for interpretation of the crushing process in the high-pressure grinding roll was carried out by means of experimental investigations. A series of laboratory crushing tests were also conducted in which limestone samples were pressed in a hydraulic piston-die press. Comminution conditions in this press are similar to those observed in the working chamber of HPGR presses. The limestone aggregate, placed in a steel cylinder, was exposed to pressure exerted by the stamp of the press. Samples had various particle size distributions, and experiments were conducted for two values of pressing force. Operating pressure was the main parameter influencing the obtained comminution effects, but the particle size distribution also has an impact on the process effects. A comparison of the results of the investigations indicated that there exists a significant potential for adjusting the operational parameters of high-pressure grinding rolls. Internal stresses are a derivate of crushing actions such as compression, impact, bending, and shearing. The result of crushing in a particular crusher depends on the strength properties of particles reacting to a specific type of crushing actions. In every crusher there are many crushing actions out of which one is dominating due to the crusher type. Impact is a dominating factor in impact or hummer crushers. Various actions of crusher elements on the crushed material are beneficiary. For example, the shape of the jaw surface in jaw crushers, cone surface in cone crushers, or roll surface in roll presses are important.