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Article

Simulation and Parameter Optimisation of Edge Effect in Ore Minerals Roll Crushing Process Based on Discrete Element Method

by
Ruijie Gu
1,2,
Wenzhe Wu
1,
Shuaifeng Zhao
1,*,
Hao Xing
1 and
Zhenzhong Qin
1
1
School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang 471003, China
2
Longmen Laboratory, Luoyang 471000, China
*
Author to whom correspondence should be addressed.
Minerals 2025, 15(1), 89; https://doi.org/10.3390/min15010089
Submission received: 19 December 2024 / Revised: 10 January 2025 / Accepted: 15 January 2025 / Published: 18 January 2025
(This article belongs to the Section Mineral Processing and Extractive Metallurgy)
Browse Figures
Versions Notes

Abstract

:
The edge effect is caused by poor use of confinement systems, different roll aspect ratios, operating conditions and other factors, which result in uneven pressure distribution between the two crushing rolls along the roll width direction, affecting the overall roll crushing process. To reduce the edge effect, this paper investigates the simulation of the edge effect and parameter optimisation in the roll-crushing process of ore materials based on the discrete element method (DEM). Firstly, the parameters of the iron ore crushing model are experimentally calibrated, and the working process of HPGR is simulated by DEM. Secondly, the effects of roll speed, roll gap, roll diameter and roll width on edge effect and crushing effect of HPGR are analysed by the one-factor experiment. Finally, the roll pressure optimisation model is established based on the Response Surface Methodology (RSM) to obtain the optimal roll pressure parameters. The results show that, with the roll speed and roll diameter increase, the edge effect also increases, the roll gap shows the opposite trend, and the roll width has less influence. The change in roll diameter has the greatest influence on the crushing effect, roll gap is second, and roll speed and roll width have less influence on the crushing effect. When the feed particles are iron ore with a particle size of 32 mm, the optimisation results show that the edge effect and crushing effect of HPGR are significantly improved when the roll speed is 1.25 rad/s, the roll gap is 38 mm, the roll diameter is 2000 mm and the roll width is 742 mm.

1. Introduction

The High-Pressure Grinding Roll (HPGR) is an important piece of equipment in the ore processing system, which has high-throughput, energy-saving and high-efficiency features. Therefore, it is widely used in various mineral processing, including the crushing of diamonds, gold, copper, iron and many other minerals [1,2,3]. With the ore quality decline and overall operating costs increasing, pushing the development of the mining industry towards a more energy-efficient direction is a global trend [4,5,6].
So far, the edge effect of the HPGR is difficult to solve in the actual rolling process. The edge effect is caused by the uneven pressure distribution between the edge portion and the centre portion of the HPGR, where the material is subjected to more pressure in the centre of the roll and less pressure in the edge region [7]. The existence of the edge effect will lead to low crushing efficiency, severe roll wear, and increased energy consumption of HPGR. So, it has an important engineering significance to research the edge effect of HPGR.
The cheek plates have a great influence on the edge effect of the HPGR by preventing the material from leaving the working area from both ends of the roll and reducing the pressure difference between the edge region and the centre region of the roll. Rodriguez et al. [8,9] modelled the effects of lateral restraint, roll aspect ratio, and wear state on HPGR performance by using the Discrete Element Method (DEM)–Multibody Dynamics (MBD)–Particle-Role Model (PRM) method, and found that the product size of the roll was more constant and the throughput was higher when side baffles and studs were installed. Knorr et al. [10] studied the innovative measures of HRCTM technology in reducing the edge effect, including improved roll mill design, optimised material flow paths and the adoption of an advanced control system, and the results showed that the application of HRC™ technology significantly reduces the edge effect, resulting in a more homogeneous milling process and higher overall efficiency. Nagata, Y. et al. [4] investigated the effect of roll diameter on the processing capacity of HPGR by the DEM, focused on simulating the effect of different roll diameters on the material flow and crushing efficiency, and the results showed that selecting the appropriate roll diameter can improve the overall performance of the equipment. Paul W. Cleary et al. [11] investigated the axial pressure distribution, material flow behaviour and crushing effect in HPGR by the DEM method, and the results showed that the crushing effect in the middle region of HPGR rolls was higher than in the edge region of rolls. Ralph van Rijswick et al. [12] used a wide range of feed material conditions, roll aspect ratios and flanges. The results show that flanging can have a positive effect on throughput, but the size/energy ratio is not necessarily increased. Moreover, this effect seems to be very dependent on the aspect ratio of the rolls. Baawuah, E. et al. [13] investigated and compared the release characteristics of selected size fractions of the products obtained from SFC and HPGR using Quantitative Evaluation of Minerals by SCANning electron microscopy (QEMSCAN™) and magnetic separation, and the results showed that SFC generated finer product particles compared with HPGR, which was attributed to the presence of edge effects. Due to the presence of edge effects, the wear mode of the roll was concave, and the maximum wear occurred at the centre of the roll [14]. Due to the wear profile at the centre of the rolling mill being greater than that at the edges [15], the question was whether there was a difference in the material discharge size between the centre and edge areas of the rolling mill. Mohsen Izadi-Yazdan Abadi et al. [16] investigated the impact of hydraulic pressure, roll speed, material level inside the hopper, and operation gap on HPGR performance. Furthermore, the effect of these variables on the HPGR discharge in the centre and edge of the rolls was assessed on an industrial scale. Despite the extensive research conducted by scholars on the edge effect through experiments and simulations [17,18,19], there is a paucity of studies that enhance the crushing efficacy of HPGR by modifying the process parameters and the multi-factor coupling of equipment design. Therefore, this paper carries out the study of the edge effect in the roll-crushing process.
In summary, to reduce the edge effect, this paper investigates the simulation of the edge effect and parameter optimisation in the roll-crushing process of ore materials based on the DEM. Firstly, the parameters of the Tavares Universidade Federal do Rio de Janeiro (UFRJ) Breakage model are calibrated through extensive experiments and the operating process of the HPGR is simulated using the DEM [20,21]. Secondly, the effects of each parameter, such as roll diameter, roll width, roll speed and roll gap, on the edge effect and crushing effect of HPGR are systematically analysed by the one-factor experiment and response surface method. Finally, the optimisation model of HPGR performance is established, which reduces the edge effect under the premise of ensuring the crushing effect, improves the overall performance of the HPGR, and offers a theoretical foundation for the design of rolls.

2. Materials and Methods

2.1. Simulation Models

According to a certain industrial grade HPGR, with a roll diameter of 2000 mm and a roll width of 1000 mm, a simplified model of the roll press is established, as shown in Figure 1a, and the parameter settings of the HPGR are shown in Table 1. It mainly includes moving roll, fixed roll, studs, cheek plates and feeding device. To prevent the material in the edge region from being extruded by the roll producing lateral movement and leaving the working area from the edge of the roll, this paper adopts cheek plates as the restraining device, where the gap between the cheek plates and the roll is 10 mm, and the working parameters of the HPGR are shown in Table 1. The working principle of the HPGR is shown in Figure 1b [22,23]. The one-factor method was used to investigate the effect of different factors on the edge effect, all other factors were kept the same as the base case (Table 1) in the one-factor experiment, and the diameter-to-width ratios of the HPGR were kept within the interval of 1.33–2.86.

2.2. Discrete Element Method Analysis

The DEM is a numerical simulation method based on the interaction forces and equations of motion between particles, and it is a suitable method for describing the mechanical behaviour of granular materials [24]. EDEM is used for roll crushing simulation, and the crushing models in EDEM are divided into two types: the bonded model and the Tavares UFRJ fracture model. The bonded model effectively simulates the adhesive forces and breakage behaviour between particles, making it particularly suitable for modelling materials with significant particle–particle interactions. Its limitations include the simplified assumptions regarding particle shape and size distribution, as well as the neglect of complex contact mechanics and fracture mechanisms [25]. The Tavares UFRJ Breakage model effectively describes the particle breakage process using an energy balance approach and provides accurate predictions of particle size distribution. However, the model overlooks the heterogeneity of the particles, the irregularity of their shapes, and the complex interactions between particles [21]. So, the Tavares UFRJ Breakage model was used in this paper.
The Tavares model describes the adaptation of a detailed fracture mechanism for brittle materials and accounts for the variability and size dependence of the fracture probability, as well as attenuation by repeated application of stress, and provides the final size distribution of the material.
By establishing suitable fracture energy parameters, how the material fractures during the simulation can be regulated. Fracture energy is the energy property of a material that undergoes fragmentation under force, each particle exhibiting a distinct fracture energy [26]:
P E = 0.5 1 + erf   [ ( ln ⁡ E ∗ − ln ⁡ E 50 ) / 2 σ ]
E ∗ = E m a x E / ( E m a x − E )
where P ( E ) is the fracture probability of the particles; E is the fracture energy distribution of the particles, which is the maximum stress energy it can withstand during the collision process; E m a x is the peak value of the particle fracture energy distribution; E 50 and σ are the median and standard deviation of the particle’s fracture energy distribution, respectively; and the median specific fracture energy of the particle can be expressed by Equation (3):
E = E ∞ / 1 + k p / k s t 1 + d 0 / d p φ
where E ∞ , d 0 , and φ are model parameters that must be fitted to experimental data. d p is the particle size, k p is the stiffness of the particle and k s t is the stiffness of the steel.
When the particle is subjected to the squeezing force of the two rolls or the interparticle interaction force without damage, the particle generates a new fracture energy, which is lower than the previous fracture energy. This can be expressed by Equation (4):
E f ′ = E f 1 − D
D = 2 γ / 2 γ − 5 D + 5 · e E k / E f 2 γ / 5
where E f is the fracture energy of the particles; D is the damage; e E k is the specific stress energy generated by the collision; γ is the damage accumulation coefficient used to characterize the damage accumulation of materials under repetitive loading; and e is the proportion of energy in the collision, which is represented by the following Equation (6):
e = 1 / 1 + k p / k s
where k p is the stiffness of the particles, whereas k s is the surface stiffness of particle contact, when particles of the same material collide k p = k s ; that is, the kinetic energy is distributed equally between the two particles. The degree of particle fragmentation can be represented by the parameter t 10 , which is the percentage of offspring that is less than 10% of the initial average particle size [21].
t 10 = A 1 − e x p − b e E k / E f
where A and b are the model parameters through experiment. In particular, A is the maximum value of t 10 that can be achieved when the material is damaged in a single impact event [27].

2.3. Ore Parameter Calibration Experiment

The ore used in this experiment is an iron ore (A certain iron ore plant in China) with a solid density of 3948 kg/m3 and humidity is below 5%. The ore was put into the vibrating sieve machine (Henan, China) for screening, each layer of the sieve is a grain level, as shown in Figure 2, 9.5–16 mm, 16–19 mm, 19–26.5 mm, 26.5–31.5 mm, and 31.5–37 mm were selected to screen 30 ores for each grain level, and the screened ore particles of each grain level were weighed and recorded.
The five selected ore samples were subjected to uniaxial compression experiments, as shown in Figure 3. The force–displacement curves of particles with different grain sizes were recorded, and the fracture energy of each particle was calculated by integrating the curves before the maximum crushing point. Due to the irregularity of the ores, the force–displacement curves could be roughly classified into three categories, as shown in Figure 4. During the experimental process, the time for determining the main body failure of particles can be mainly divided into three points: Firstly, it is essential to continuously monitor the real-time status of the particles. Secondly, the force–displacement curves generated in real time by the data acquisition system should be observed. Thirdly, attention must be given to the sounds emitted during the particle loading process. Upon hearing a significant crushing noise, one must promptly assess the situation based on the observed actual state of the particles. The fracture energy of the particles was divided by their mass to obtain the fracture-specific energy of all the particles, the fracture energy of each particle size was arranged in ascending order, and its fracture probability was calculated. The fracture probability can be expressed by Equation (8):
P = i / N + 1
where N is the total number of samples, while i is the ascending ranking of the fracture energy of particles at each particle level.
The particle crushing probability-crushing specific energy curves for each grain size were fitted to Equation (1), and the fitted curve is shown in Figure 5. Let A be ln ⁡ E 50 and B be σ and change Equation (1) to:
P E = 0.5 1 + e r f ln ⁡ ( x ) − A / 2 B
The value of A is fitted to find e A , which is the median specific energy of fracture for that particle size, and the B value is the standard deviation of the fracture energy.
The median fracture toughness for each particle size is fitted to Equation (3), and based on the fitted curve, the values of E ∞ , d o , and d p are determined to be 92.27, 13.2, and 2.08, respectively.
The same vibrating sieve machine was used to screen the particles in three grades, and each grade screened 30 particles and was divided into three groups. Each group of particles was crushed with energy of 0.25 kw/h, 1 kw/h, and 2.5 kw/h, respectively. The crushed particles in each group were then sieved and weighed, and the mass and size of the broken particles of different particle sizes and energies were determined, as shown in Figure 6. Thus, the percentage of offspring with particle sizes smaller than 10% of the initial average particle size was obtained, which is the value of t 10 under different energy conditions for different particle sizes [28], as shown in Figure 7. Equation (10) is valid to describe the breakage of particles at moderate-to-high impact energies, such that all particles break at the first impact. The parameter fitting was performed using Equation (10).
t 10 = A 1 − e x p − b E c s
The values of the parameters A and b are determined to be 42.13 and 0.38, respectively, which are then used to assess the particle’s degree of fragmentation.
The parameters of the Tavares model, derived from uniaxial compression experiments and falling weight experiments, are presented in Table 2.

2.4. Parameters of the Simulation

The edge effect of the HPGR and the roll structure, operating parameters, material properties and other factors were found to have a significant relationship. The following factors were considered to ascertain the effect of changing the roll speed, roll gap, roll diameter, and roll width on the edge effect: Modification to the roll speed, roll gap, roll diameter, roll width and other parameters was conducted by the simulation model, and the experimental arrangement is shown in Table 3, The standard values were set as a roll speed of 2.25 rad/s, a gap of 38 mm, a diameter of 2000 mm and a width of 1000 mm. When one factor was varied, the other parameters were kept at their standard values. The rolls and discharge opening were divided into the sampling region of the SP1–SP9 interval in turn, which is shown in Figure 8. The force exerted by material particles in disparate regions of the SP1–SP9 rolls and the particle size distribution after crushing were taken into account during the simulation midpoint. In this paper, the terms particle size distribution and crushing effect are both defined in terms of the proportion of the material’s mass that is less than 6 mm in size following the crushing process. The contact parameters of materials and material characteristic parameters in EDEM 2023 software are shown in Table 4. Since the Tavares UFRJ Breakage Model supports the simulation of the breakage of spherical particles, the material particles were assumed to be spherical to ensure that the stability and accuracy of large-scale particle breakage simulations were not significantly affected. The particle size of the feed material was obtained through sieving and statistical analysis. To better reflect real-world conditions, the particles of the sieved ore were measured, and the percentage of the total mass corresponding to each particle size fraction was calculated. Based on this, the feed particle size in the discrete element simulation software was precisely modelled, as shown in Table 5. The total simulation time is 10 s, the total mass of the generated ore and the mass of the generated ore per second follow the condition factors, and it is guaranteed that the generated ore can form a certain layer of material in the compression zone.
While changing the size of the roll diameter, to ensure that the roll surface has the same linear velocity, the corresponding angular velocities under different roll diameter conditions are 2.81 rad/s, 2.65 rad/s, 2.5 rad/s, 2.37 rad/s, 2.25 rad/s, 2.14 rad/s, 2.05 rad/s, 1.96 rad/s, 1.88 rad/s, 1.8 rad/s.

3. Results and Analyses

3.1. Effect of Different Factors on Edge Effect and Crushing Effect

The force on material particles in different regions of the SP1–SP9 rolls during the working process of HPGR and the crushing effect of the particles after crushing were determined by simulating the experimental arrangement in Table 3. Then, the influencing factors of edge effect and crushing effect in the roll crushing process of ore materials were analysed.
In Figure 9a, when the roll speed increases, the material force in each region of SP1–SP9 increases: the material force in the region of roll SP5 increases by 300 kN, and the edge region of SP1 and SP9 increases by 150 kN and 128 kN, respectively. From Figure 9b, it can be seen that the variance of the material force in the different regions of SP1–SP9 does not increase with the increase in roll speed. When the roll speed increases to 2 rad/s and 2.75 rad/s, the variance of the force in different regions on the material is relatively reduced; that is, the overall force fluctuations in the SP1–SP9 region are reduced. When the roll speed increases to 3.25 rad/s, the variance of the force in different regions of the material tends to stabilise, and the fluctuations of the force in the SP1–SP9 material are the largest.
In Figure 9c, with the roll speed increasing, the mass ratio of crushed material with a diameter below 6 mm continuously decreases. However, this growth is gradual, with the highest expansion reaching approximately 2%.
In Figure 10a, when the roll gap increases, the force of the material in each region of SP1–SP9 decreases, and the force of the material in the centre SP5 region is reduced by 213 kN, and in the edge SP1 and SP9 regions, it is reduced by 87 kN and 82 kN, respectively. The variance change curve in Figure 10b shows that the variance of the force exerted on the material in different regions does not continuously decrease with the increase in the roll gap; the variance of the force in different regions on the material of SP1–SP9 tends to be stable when the roll gap is 38–40 mm, and fluctuates the least when the roll gap is 42 mm. The roll gap has a great influence on the force of the material in each region.
In Figure 10c, with the roll gap increasing, the mass ratio of crushed material with a diameter below 6 mm continuously decreases. This is observed in both the central and edge regions: the central area has decreased by about 4.1% and the edge area has decreased by more than 3%.
With the roll diameter modified, the quantity of material subjected to compression is also altered. Consequently, when evaluating the force exerted on the material in each area, it is essential to multiply the roll diameter coefficient, which is the standard roll diameter divided by the roll diameter. In Figure 11a, when the roll diameter increases, the material experiences increased stress within the SP1–SP9 zones. The greatest increase is observed in the central SP5 region, where the force rises by 774 kN. In the SP1 and SP9 regions, the rise is 334 kN and 305 kN, respectively. Figure 11b illustrates that as the roll diameter increases, the variance of the force on the material in different regions decreases. In particular, for roll diameters between 2000 mm and 1600 mm, the variance of the force on the material in different regions is smaller and tends to stabilise. Additionally, the edge effect is less pronounced.
In Figure 11c, with the roll diameter increasing, the mass ratio of crushed material with a diameter below 6 mm demonstrates a positive correlation. The central area exhibits an approximate 7.5% increase, while the edge region demonstrates a 6.7% increase. The influence of roll diameter on the edge effect is significant; therefore, selecting the appropriate roll diameter is of great significance.
The roll width is identical to the roll diameter and must also be multiplied by the roll width coefficient, which is the standard roll width divided by the roll width when considering the material force situation. In Figure 12a, with the roll width increasing, the material force in each area of SP1–SP9 does not change much, and the impact on the force of the material is also minimal. From Figure 12b, it can be observed that the variance in the material’s stress distribution across different regions shows little change. When the roll width exceeds 1193.5 mm, the variance in the material’s stress in the centre-edge region of the roll increases. The impact of roll width on the material’s stress in different regions is minimal, and the overall variance in stress between the centre and edge of the roll remains relatively stable. Therefore, the edge effect is minimally influenced by the roll width.
Figure 12c illustrates that with the roll width increases, the proportion of materials with a diameter less than 6 mm does not change significantly, which means that the roll width factor has a minimal impact on the overall process.
In summary, it is clear that as the roll diameter increases, the roll gap decreases, the roll speed increases the force on the material in each region, and the crushing effect increases. However, the edge effect also increases.

3.2. Optimisation of HPGR Performance Based on Simulation Results

3.2.1. Box–Behnken Design Methods

The preceding study has enabled the influence of each factor on the edge effect of the HPGR to be determined. To guarantee the crushing effect, this Section will investigate the impact of roll speed, roll gap, roll diameter and roll width on the crushing effect and edge effect of the HPGR through the response surface method, to optimise the performance of the HPGR. RSM primarily explores the relationship between multiple input variables and one or more response variables by fitting a mathematical model. It analyses, predicts and optimises the response through the development of a mathematical expression for the response surface [29,30]. The edge effect is represented by the variance of the material force in the SP1–SP9 region, while the crushing effect is represented by the proportion of material with a diameter less than 6 mm after crushing.
This paper considers four factors, namely, roll speed (A), roll gap (B), roll diameter (C) and roll width (D). The highest and lowest levels of each factor are determined by one-factor experiments, which are shown in Table 6. Four-factor, three-level experiments are designed by the Box–Behnken Design (BBD) method. The scheme is shown in Table 7, with a total of 29 experiments and 5 repeated experiments at the centre point. To maintain consistency in the linear speed of the rolls across different diameter sizes, it is essential to adjust the roll speed of the 1600 mm and 1800 mm rolls.

3.2.2. Analysis of Variance

The significance of the response surface model on the experimental results is verified by ANOVA; the results are shown in Table 8. The results of the ANOVA are as follows: when the p-value is greater than 0.05, the result is not significant; when the p-value is less than 0.05, the result is significant; when the p-value is less than 0.01, the result is extremely significant; the p-value of the model is less than 0.0001 and the p-value of the misfit term is greater than 0.05, which indicate that the model accurately reflects the relationship between the experimental results and the experimental variables, and has a good fit. The compound correlation coefficient of the edge effect regression model, R 2 = 0.9815 , and the corrected compound correlation coefficient, R A d j 2 = 0.9631 , demonstrate that the regression model is an excellent fit with the simulation results, with 98.28% of the variation in the response values explained by the model. The variation in the response values can be explained by this model. The discrepancy between R P r e 2 and R A d j 2 is less than 0.2, which indicates that the discrepancy between the simulation results and the prediction results is within an acceptable range.
In addition, according to Table 7, the effects on edge effect are that factors AB, BD, B2, and D2 have insignificant effects, factors AD, BC, and A2 have significant effects and factors A, B, C, D, AC, CD, and C2 have highly significant effects. This indicates that these factors studied in this paper have a significant effect on the edge effect of HPGR.
As indicated in Table 9, the p-value of the model is less than 0.0001, while the p-value of the misfit term is greater than 0.05. This suggests that the model is capable of effectively reflecting the relationship between the experimental results and the experimental variables, which exhibits a good fit. The crushing effect regression model’s compound correlation coefficient is R 2 = 0.9941 , and the corrected compound correlation coefficient is R A d j 2 = 0.9881 , which indicates that this regression model fits well with the simulation results, and 99.03% of the variation in the response value can be explained by this model. The difference between R P r e 2 and R A d j 2 is less than 0.2, which indicates that the error between the simulation results and the prediction results is within the permissible range.
In addition, factors A, B, C, and D had highly significant effects on the crushing effect of the HPGR, but factors AB, AC, AD, BC, BD, CD, A2, B2, C2, and D2 had insignificant effects.

3.2.3. Interaction Response Surface Analysis

In accordance with the edge effect regression model, the edge effect response surface plot and contour plot, as illustrated in Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18, is constructed. When the steepness and inclination of the surface plot are higher, it is indicative that the coupling of the two factors exerts a more pronounced influence on the experimental outcomes. Furthermore, when the contour lines of the contour plot are more densely distributed or exhibit an elliptical shape, it is indicative that the coupling of the two factors plays a pivotal role.
Through the above response surface and contour plots, it can be seen that Figure 14, Figure 15, Figure 16 and Figure 18 have steeper surfaces and denser contours than the other plots. Figure 14 illustrates that the interaction between roll speed and roll diameter is significant when the roll speed falls between 1.25 rad/s and 1.5 rad/s and the roll diameter is between 1600 mm and 1650 mm, the variance of the material force in the SP1–SP9 zone is the smallest edge effect. Figure 15 illustrates that the interaction between roll speed and roll width is significant. The edge effect is observed to be minimal when the roll speed ranges from 1.25 rad/s to 1.5 rad/s and the roll width falls within the interval of 742 mm to 800 mm. Figure 16 illustrates the significant interaction between the roll gap and roll diameter, with the edge effect being minimal when the roll gap falls between 38 mm and 39 mm and the roll diameter between 1600 mm and 1650 mm. Figure 18 illustrates the interaction between roll diameter and roll width is significant, and the edge effect is minimized when the roll diameter falls between 1600 mm and 1650 mm and the roll width falls between 742 mm and 800 mm.

3.2.4. Construction and Optimisation of Predictive Models

This study aims to investigate the influence of roll speed, roll gap, roll diameter and roll width on the performance of HPGR. Initially, the study will ensure that the crushing effect of HPGR is effectively demonstrated in practice. Subsequently, the edge effect will be considered, and a prediction model will be established to assess the edge effect performance of HPGR. The importance weight of the fragmentation effect is five, while that of the edge effect is three. Then, the corresponding optimisation function can be expressed as shown in (11):
f m o b X 1 , X 2 , X 3 , X 4 = f B 5 X 1 , X 2 , X 3 , X 4 · f E 3 X 1 , X 2 , X 3 , X 4 1 8 1.25 < X 1 < 2.25 38 < X 2 < 42 1600 < X 3 < 2000 742 < X 4 < 1000
A quadratic regression model for optimising HPGR performance is established using the principle of multiple nonlinear regression, as demonstrated by Equation (12):
y = f X 1 , X 2 , X 3 , X 4 = B 0 + ∑ j = 1 4 B j X j + ∑ i < j B i j X i X j + ∑ j = 1 4 B j j X j 2
where y is the simulation result that is the response value of the regression model, X 1 is the value of roll speed, X 2 is the value of the roll gap, X 3 is the value of roll diameter, and X 4 is the value of roll width. B is the regression coefficient, which is defined as follows:
B 0 = 1 N ∑ k = 1 N y k B j = ∑ k = 1 N X k j y k / ∑ k = 1 N X k j 2 B i j = ∑ k = 1 N X k j X k i y k / ∑ k = 1 N X k j X k i 2 B j j = ∑ k = 1 N X k j 2 − 1 N ∑ k = 1 N X k j 2 / ∑ k = 1 N X k j 2 − 1 N ∑ k = 1 N X k j 2
where N is the number of simulations.
Subsequently, the corresponding optimisation objective function for the edge effect and the crushing effect of the HPGR can be expressed by Equation (14):
y 1 = f B X 1 , X 2 , X 3 , X 4 = 0.258381 + 0.009495 X 1 − 0.005527 X 2 + 0.000110 X 3 + 0.000016 X 4 y 2 = f E X 1 , X 2 , X 3 , X 4 = 114,317 − 6743.73 X 1 − 261.272 X 2 − 90.6683 X 3 − 97.52 X 4 + 12.8652 X 1 X 3 +   9.25524 X 1 X 4 − 1.98489 X 2 X 3 + 0.0844086 X 3 X 4 − 2199.92 X 1 2 + 0.0277005 X 3 2 1.25 < X 1 < 2.25 38 < X 2 < 42 1600 < X 3 < 2000 742 < X 4 < 1000
The process conditions aim to achieve better crushing performance and minimise edge effects following roll press comminution. The regression model predicts a crushing effect of 12.86%, with a minimum variance of 10,218.3 kN2; at this time, the roll speed is 1.252 rad/s, the roll gap is 38 mm, the roll diameter is 1991.995 mm and roll width is 742.031 mm. To meet the actual requirements, the predicted process conditions are adjusted to a roll speed of 1.25 rad/s, roll gap of 38 mm, roll diameter of 2000 mm and roll width of 742 mm. During the simulation process, deviations in the results may arise due to the simplifications made regarding the motion of the rolls, the shape of the particles, and the use of the DEM (Discrete Element Method) analysis. Five groups of DEM simulation experiments are repeated under these conditions, and the crushing effect obtained is 12.82%, the minimum variance is 10,334.5 kN2, and the results of the simulation experiments are verified as shown in Figure 19.
The optimised edge effect reaches 97.08% of the expected effect, which is superior to the expected effect. Similarly, the crushing effect reaches 100% of the expected effect, and the fit between the expected effect and the actual effect is enhanced. This optimisation result is therefore deemed to be reliable. As illustrated in Table 7, an inverse relationship exists between the HPGR’s crushing effect and the fluctuation of the material along the roll width. Specifically, when the crushing effect is superior, the material exhibits greater fluctuation along the roll width. Conversely, when the crushing effect is inferior, the material displays reduced fluctuation along the roll width. Under the condition of basically the same crushing effect, the comparison of the force fluctuation along the roll width direction of the material is shown in Figure 20. The crushing effect, throughput, and power of the HPGR before and after optimisation are shown in Table 10.

4. Conclusions

This paper presents a calibration of the Tavares model parameters through uniaxial compression and drop hammer impact experiments. The DEM is used to simulate the comminution process of iron ore under HPGR, aiming to optimise the edge effects and crushing efficiency of the HPGR. In this simulation, the moving roll of the HPGR is simplified as a fixed roll, and the ore particles are simplified as spherical particles.
(1)
The distribution of pressure exerted on the material in the centre and edge regions of the roll under single-factor conditions is investigated. The result demonstrates that as roll speed and roll diameter increase, the material force in each region of SP1–SP9 rises. Additionally, the pressure difference between the material in the edge region of the roll and the centre region exhibits an overall upward trend. Conversely, the roll gap and other factors display the opposite trend, and the change in roll width has a negligible impact on the material force. Therefore, the influence of each factor on the edge effect is in the following order: roll diameter > roll speed > roll gap > roll width.
(2)
The effect of single factors on the crushing effect of materials is studied. The findings indicate that the alteration of roll diameter has the most significant influence on particle size distribution, with roll gap as the secondary factor, and roll width exerts a comparatively lesser influence on particle size distribution.
(3)
Based on the influence of different factors on the crushing effect and edge effect of HPGR, the optimisation model of roll press performance is established by the response surface method. The optimisation results demonstrate that when the roll speed is 1.25 rad/s, the roll gap is 38 mm, the roll diameter is 2000 mm, the roll width is 742 mm, the material force variance in different areas is 10,334.5 kN2, and the crushing effect is 12.82%. Compared with the previously optimized HPGR, the variance of material force in different areas was reduced by approximately 48.5%. Furthermore, the edge effect of the HPGR has been significantly enhanced.
To address the overall performance issues of HPGR, it is essential to monitor indicators such as throughput, power consumption, roll stress, particle size distribution of the discharge and roll wear, based on actual operating conditions. This will provide real operational data, which can be used to further optimise and enhance the performance of the HPGR. Additionally, validating the accuracy of the HPGR simulation model will offer valuable insights for the design of HPGR rolls.

Author Contributions

R.G.: Conceptualization, Supervision, Paper reviewing and editing. W.W.: Conceptualization, Data generation, Result analysis, Draft paper writing. S.Z.: Data generation, Result analysis, Paper editing. H.X.: Result analysis, Paper editing. Z.Q.: Data generation, Result analysis, Paper editing. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by a grant from the Longmen Laboratory Project (LMQYTSKT036), Ministry of Industry and Information Technology Special Projects (TC220H05V-W03), and Henan Provincial Department of Science and Technology (231111221000).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Figure 1. (a) Simplified model of HPGR; (b) HPGR Working Principle.
Figure 1. (a) Simplified model of HPGR; (b) HPGR Working Principle.
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Figure 2. Vibrating machine and screen.
Figure 2. Vibrating machine and screen.
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Figure 3. (a) Uniaxial compression experimental machine (Henan, China); (b) Force–displacement curve for ore crushing; (c) Crushed ore.
Figure 3. (a) Uniaxial compression experimental machine (Henan, China); (b) Force–displacement curve for ore crushing; (c) Crushed ore.
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Figure 4. Experimental force–displacement curves for three types of irregular particles: (a) Type I curve; (b) Type II curve; (c) Type III curve.
Figure 4. Experimental force–displacement curves for three types of irregular particles: (a) Type I curve; (b) Type II curve; (c) Type III curve.
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Figure 5. The Lognormal fitting curves of five particle size fractions of ore: (a) −16 + 9.5; (b) −19 + 16; (c) −26.5 + 19; (d) −31.5 + 26.5; (e) −37 + 31.5.
Figure 5. The Lognormal fitting curves of five particle size fractions of ore: (a) −16 + 9.5; (b) −19 + 16; (c) −26.5 + 19; (d) −31.5 + 26.5; (e) −37 + 31.5.
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Figure 6. Particles after impact crushing with different energy for different particle sizes.
Figure 6. Particles after impact crushing with different energy for different particle sizes.
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Figure 7. The particle size distribution of iron ore comminution progeny at different impact energies and particle sizes. (a) The particle size distribution of the crushing product at 0.25 kWh/t.; (b) The particle size distribution of the crushing product at 1 kWh/t; (c) The particle size distribution of the crushing product at 2.5 kWh/t.
Figure 7. The particle size distribution of iron ore comminution progeny at different impact energies and particle sizes. (a) The particle size distribution of the crushing product at 0.25 kWh/t.; (b) The particle size distribution of the crushing product at 1 kWh/t; (c) The particle size distribution of the crushing product at 2.5 kWh/t.
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Figure 8. SP1–SP9 iso-interval region.
Figure 8. SP1–SP9 iso-interval region.
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Figure 9. (a) Influence of roll speed on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll speeds; (c) Influence of roll speed on Crushing effect.
Figure 9. (a) Influence of roll speed on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll speeds; (c) Influence of roll speed on Crushing effect.
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Figure 10. (a) Influence of roll gap on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll gaps; (c) Influence of roll gap on Crushing effect.
Figure 10. (a) Influence of roll gap on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll gaps; (c) Influence of roll gap on Crushing effect.
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Figure 11. (a) Influence of roll diameter on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll diameters; (c) Influence of roll diameter on Crushing effect.
Figure 11. (a) Influence of roll diameter on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll diameters; (c) Influence of roll diameter on Crushing effect.
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Figure 12. (a) Influence of roll width on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll widths; (c) Influence of roll width on Crushing effect.
Figure 12. (a) Influence of roll width on material force; (b) The average force variance of the material in the middle time period of SP1–SP9 area under different roll widths; (c) Influence of roll width on Crushing effect.
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Figure 13. The response surface and contour plots for the interaction of roll speed and roll gap.
Figure 13. The response surface and contour plots for the interaction of roll speed and roll gap.
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Figure 14. The response surface and contour plots for the interaction of roll speed and roll diameter.
Figure 14. The response surface and contour plots for the interaction of roll speed and roll diameter.
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Figure 15. The response surface and contour plots for the interaction of roll speed and roll width.
Figure 15. The response surface and contour plots for the interaction of roll speed and roll width.
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Figure 16. The response surface and contour plots for the interaction of roll gap and roll diameter.
Figure 16. The response surface and contour plots for the interaction of roll gap and roll diameter.
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Figure 17. The response surface and contour plots for the interaction of roll gap and roll width.
Figure 17. The response surface and contour plots for the interaction of roll gap and roll width.
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Figure 18. The response surface and contour plots for the interaction of roll diameter and roll width.
Figure 18. The response surface and contour plots for the interaction of roll diameter and roll width.
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Figure 19. The verification results of simulation experiments.
Figure 19. The verification results of simulation experiments.
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Figure 20. The optimisation comparison results.
Figure 20. The optimisation comparison results.
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Table 1. Parameter settings for the HPGR.
Table 1. Parameter settings for the HPGR.
VariableSymbolValueVariableSymbolValue
Roll diameter (mm)D2000Roll gap (mm)X038
Roll width (mm)L1000Studs diameter (mm)Dst28
Roll speed (rad/s) ω 2.25Studs height (mm)Hst7
Table 2. Parameters of the Tavares model.
Table 2. Parameters of the Tavares model.
ParameterValueUnit
Damage Constant5-
E Infinity92.27J/kg
D013.2mm
Phi2.08-
Std Deviation2.62-
Alpha Percentage42.13-
b0.38-
Table 3. Experimental arrangement of different factors.
Table 3. Experimental arrangement of different factors.
Groups12345678910
Factor
Roll speed
(rad/s)		1.251.51.7522.252.52.7533.253.5
Roll gap
(mm)		34353637383940414243
Roll diameter
(mm)		1600170018001900200021002200230024002500
Roll width
(mm)		742806.5871935.510001064.511291193.512581322.5
Table 4. Material and contact parameters used in DEM simulations.
Table 4. Material and contact parameters used in DEM simulations.
ParameterValue
DEM settingsIndividual parametersoresteel
Density3948 kg/m27800 kg/m2
Shear stiffness1.6 × 107 pa7 × 1010 pa
Poisson’s ratio0.250.3
Contact parametersore-oreore-steel
Coefficient of restitution0.10.1
Coefficient of static friction0.50.53
Coefficient of rolling friction0.10.1
Table 5. Particle size distribution and mass percentage of feed material.
Table 5. Particle size distribution and mass percentage of feed material.
Particle Size (mm)17.622.427.228.83233.635.2
Mass ratio (%)125107255
Table 6. Experimental factors and their levels.
Table 6. Experimental factors and their levels.
FactorsRoll Speed
(rad/s)		Roll Gap
(mm)		Roll Diameter
(mm)		Roll Width
(mm)
Low levels1.25381600742
High levels2.254220001000
Table 7. Experimental programme and its results.
Table 7. Experimental programme and its results.
Experiment NumberRoll Speed X1 (rad/s)Roll Gap
X2 (mm)		Roll Diameter
X3 (mm)		Roll Width
X4 (mm)		Edge Effect
(kN2)		Crushing Effect
(%)
11.753818007428422.150.119353
22.2538180087114,406.710.123066
31.7540160010005101.460.100675
41.753816008716706.400.106481
51.7540180087112,353.830.113916
61.754216008715307.830.093166
72.2540180074210,826.440.113247
81.254018007426648.660.108158
91.253818008717499.810.118452
101.7542200087115,176.30.120060
111.75402000100018,123.50.128555
121.2540200087111,7160.122009
131.2540180010008098.510.111799
141.7540180087110,507.070.113609
151.75381800100012,848.880.120726
162.25401800100013,346.610.117662
171.7540180087110,163.120.114377
181.754218007429977.480.107014
191.7540180087111,1620.110987
202.2542180087112,570.620.110368
211.754016007425905.540.09918
221.75421800100010,204.350.109181
232.2540200087120,5470.130256
241.7538200087120,257.620.134296
251.254016008713381.350.097231
261.7540200074214,945.620.125963
271.254218008717809.480.105228
281.7540180087111,060.960.113562
292.254016008716614.910.102309
Table 8. Results of ANOVA for edge effect.
Table 8. Results of ANOVA for edge effect.
FactorsF-Valuep-ValueFactorsF-Valuep-Value
Model53.14<0.0001BC4.830.0453
A130.52<0.0001BD6.280.0252
B9.820.0073CD5.650.0323
C544.88<0.0001A25.570.0333
D14.360.0020B20.32880.5755
AB1.640.2212C22.430.1411
AC11.160.0049D23.950.0668
AD0.40800.5333Lack of Fit1.010.5453
R2 = 0.9815R2Adj = 0.9631R2Pre = 0.9157Adeq Precision = 27.9104
Table 9. Results of ANOVA for crushing effect.
Table 9. Results of ANOVA for crushing effect.
FigureF-Valuep-ValueFactorsF-Valuep-Value
Model167.39<0.0001BC0.17650.6808
A80.38<0.0001BD0.13110.7227
B415.34<0.0001CD0.25460.6217
C1823.71<0.0001A20.19590.6648
D17.070.0010B23.120.0991
AB0.05760.8138C20.10560.7500
AC2.090.1702D20.00380.9514
AD0.12470.7292Lack of Fit0.55380.7956
R2 = 0.9941R2Adj = 0.9881R2Pre = 0.9762Adeq Precision = 50.6274
Table 10. Comparison of the data before and after optimisation.
Table 10. Comparison of the data before and after optimisation.
Before OptimisationAfter Optimisation
Crushing effect12.8%12.82%
Throughput14.5 kg/0.025 s10 kg/0.025 s
Net power2 × 41 kW2 × 20 kW
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MDPI and ACS Style

Gu, R.; Wu, W.; Zhao, S.; Xing, H.; Qin, Z. Simulation and Parameter Optimisation of Edge Effect in Ore Minerals Roll Crushing Process Based on Discrete Element Method. Minerals 2025, 15, 89. https://doi.org/10.3390/min15010089

AMA Style

Gu R, Wu W, Zhao S, Xing H, Qin Z. Simulation and Parameter Optimisation of Edge Effect in Ore Minerals Roll Crushing Process Based on Discrete Element Method. Minerals. 2025; 15(1):89. https://doi.org/10.3390/min15010089

Chicago/Turabian Style

Gu, Ruijie, Wenzhe Wu, Shuaifeng Zhao, Hao Xing, and Zhenzhong Qin. 2025. "Simulation and Parameter Optimisation of Edge Effect in Ore Minerals Roll Crushing Process Based on Discrete Element Method" Minerals 15, no. 1: 89. https://doi.org/10.3390/min15010089

APA Style

Gu, R., Wu, W., Zhao, S., Xing, H., & Qin, Z. (2025). Simulation and Parameter Optimisation of Edge Effect in Ore Minerals Roll Crushing Process Based on Discrete Element Method. Minerals, 15(1), 89. https://doi.org/10.3390/min15010089

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