This work concentrates on the energy consumption and grinding energy efficiency of a laboratory vertical roller mill (VRM) under various operating parameters. For design of experiments (DOE), the response surface method (RSM) was employed with the VRM experiments to systematically investigate the influence of operating parameters on the energy consumption and grinding energy efficiency. The prediction models of energy consumption ($E_{cs}$) and grinding energy efficiency (η) were established respectively with the operating parameters (loading pressure, rotation speed and moisture content). Analysis of variance (ANOVA) was performed to obtain useful knowledge in designing operating parameters. Moreover, the multi-objective optimization design (MOD) method was conducted to seek out the optimal parameters of the VRM, and a set of optimal parameters was gained based on the desirability approach by Design-Expert. It is proved that the optimized prediction results match the experimental results well, which indicates this research offers a reliable guidance for reducing energy consumption and improving grinding energy efficiency.

PDC (polycrystalline diamond compact) drill bits are widely employed for rock-breaking in many industries like underground engineering and building constructions. The cutter layout would directly affect the overall performance of the drill bits. Field applications show that the staggered cutter layout strategy of dual-cutter can increase the drilling efficiency of the PDC bit. In order to explore the rock breaking mechanism of this type of drill bit, a numerical model of a dual-cutter and rock breaking with damage evolution based on a hybrid finite and cohesive element method (FCEM) has been established in this work. The model is verified through Brazilian disk tests. The rock breaking processes of this type of bit have been analyzed, including crack initiation, propagation, and the formation of rock debris. Moreover, the effects of horizontal and vertical offset of the back cutter on the MSE (mechanical special energy) have been investigated. Results demonstrate that the dual-cutter can prominently reduce the MSE compared to a single-cutter. The vertical offset of the back cutter has a minor effect on the MSE, while the horizontal offset is of great significance on the MSE. On this basis, the relationships between the MSE and both the vertical and horizontal offset coefficients have been built based on the response surface methodology (RSM). Finally, an optimized layout solution, with optimal vertical and horizontal offset coefficients of 0.641 and 0.497, is determined via the Gray Wolf algorithm.

Vertical stirred mills (VSM) are widely used for powder processing in many situations like mechanical alloying preparation and raw material crushing and shaping. Many structural and operational parameters like stirrer helix angle and rotating speed have great significance on VSM performance, especially in a large industry-scale situation. Therefore, it becomes essential to investigate these parameters systematically to obtain high energy efficiency and good product quality. In this work, the discrete element method (DEM) was used to examine the effects of stirrer helix angle ($\alpha$), stirrer diameter (d), and rotating speed (n) on the grinding performance in an industrial VSM, and then the response surface method (RSM) was employed for multi-objective optimization in the VSM. It is found that a media vortex phenomenon may happen near the stirring shaft. The media collisions are significantly influenced by $\alpha$, d, and n. Through multi-objective optimization design (MOD), the power consumption (P) of the stirrer reduced by 8.09%. The media collision energy (E) increased by 9.53%. The energy conversion rate (R) rises by 20.70%. The collision intensity and frequency are both improved. This optimization method can help determine good operating parameters based on certain structures.