研磨体形状对水泥熟料破碎参数的影响

为探讨研磨体形状对破碎参数的影响,采用钢球和钢段两种形状研磨体对水泥熟料进行粉磨,通过对粉磨产物的筛分处理,分析其粒度分布情况,研究粉磨过程中粉磨动力学方程的表述形式,最后运用非线性拟合技术进行回归分析。结果表明:采用上述两种形状研磨体,水泥熟料的粉磨均遵循一级粉磨动力学方程。钢段的破碎速率高于钢球的破碎速率,钢段粉磨物料可以在较短时间内达到预定细度。进一步研究证实:破碎分布函数基本不受研磨体形状的影响,与进料粒度有关。     

Experimental investigation of the impact breakage characteristics between grinding media and iron ore particle in ball mills

The particle breakage of the ball mill is an extremely complicated breakage process. It is difficult to quantify and describe the particle breakage behavior. In this study, a drop-ball experimental setup was developed to demonstrate the impact process of grinding media on ore particles. The quantitative analysis of the effects of particle size, impact energy, and the number of impacts on particle breakage behavior was performed separately. The results show that the breakage probability model and product size distribution model used can be excellent to predict the particle breakage behavior for the single-particle impact experiments. The breakage probability of particles is highly sensitive to impact energy and particle size, exponentially increasing with the increase of impact energy. In addition, the application of the t_n-t₁₀ relationship provides a convenient means to characterize and predict the particle size distribution. In multi-layer particle impact experiments, the captured thickness of ore particles is approximately 2 layers during the crushing process. The broken mass of iron ore particles is proportional to the number of concessive impacts at different impact energies. This paper provides theoretical and methodological support for the evaluation and optimization of particle breakage in ball mills.     

Evaluating the effect of feed particles size and their hardness on the particle size distribution of semi-autogenous (SAG) mill’s product

The main target of this research was to provide the optimal size of mills’ feed with acceptable accuracy, in order to find the size range of particles to achieve the maximum grinding product. Nowadays, experimental semi-autogenous (SAG) mill and drop-weight test are used for evaluation of grinding circuit regarding changes in feed particle size distribution, size of the ball, speed of mill, prediction of energy required, and product size distribution for complete grinding in AG and SAG mills. In this study, the effect of initial size ranges of feed (+13.2–315?mm) on the amount of grinding product and its size distribution has been evaluated, in order to find the size range of particles to achieve the maximum grinding product. The results showed that the feed size range of 19–22.4?mm had the highest amount of grinding product and breakage index number in different energy levels and the validity of results was evaluated with ball drop-weight test, as well.     

DEM Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

DEM Simulation of Particle Comminutionin Jet Milling

A combined discrete element method (DEM) and CFD numerical model was developed to simulate particle comminution in a jet mill. The DEM was used to simulate the motion of the particles in the gas flow. For this, the compressible Reynolds Averaged Navier-Stokes (RANS) equations were used to describe the gas flow field inside a given size's jet mill. Ghadiri's models for breakage and chipping were implemented in the simulation to define the reduction of the particle's size during jet milling. The size distributions of the particles after grinding were obtained numerically. The prediction of the numerical simulation for the median particle size d 50 after grinding was qualitative compared with experimental results for the different operating conditions (i.e., feed rate, angle of grinding nozzles, volumetric rate of grinding air, etc.). The comparison shows good agreement with the experimental observation. The results shows that the feed rate, angle of feeding nozzle, and feeding air's flow rate have more influence on the breakage and chipping of particles in jet milling. In addition, a parametric study was performed to obtain the desired operation conditions.     

A population balance model for the chocolate roller refining process

A study was performed to analyze the evolution of particle size distribution in the chocolate roller refining process. A mathematical model based on the continuity and population balance equations was developed to interpret industrial data. The industrial data were provided for chocolate pastes with powder/crystalline sugar particles at low/high shear rates. The parameters of the breakage frequency and fragment distribution function were estimated using industrial data. After parameter fitting, the model shows good agreement with the experimental results for varying conditions with a single consistently chosen set of parameters. This provides confidence that the general model structure is suitable for process evaluation. The population balance model was used to analyze the influence of changing some process variables on the efficiency of grinding. The results show that there might exist optimum values of the roll’s diameter and rotational velocity for a specific configuration of the equipment.     

Scale-up procedure of parameter estimation in selection and breakage functions for impact pin milling

This paper presents a scale-up procedure of parameter estimation in the selection function and breakage function from single particle impact breakage to inform the predictions at the process scale of an impact pin mill. The selection and breakage functions used in population balance model (PBM) for particle breakage in the literature are briefly reviewed. Single particle breakage tests are conducted in a vertical impact tester subject to varying impact velocities. The single particle breakage results further serve to provide the database for the parameter estimation in Vogel and Peukert model (Vogel and Peukert, 2005). The estimated parameters in the particle level are upscaled in an impact pin mill using the population balance model, which is implemented in the software gPROMS (Process Systems Enterprise, UK) (gPROMS® 4.1 Release Notes, 2016). The impact milling tests were carried out in an impact pin mill UPZ100 subject to four feed rates, providing the dataset for model validation. The sensitivity analysis of the PBM parameters was conducted to help identify their leverage on the particle size distribution. The scale-up procedure by specifying the parameters from single particle level to the process level of PBM demonstrates an approach to help predict the size reduction process subject to the prevailing mechanism in an impact pin mill and other milling processes alike.     

Simulation of particle bed breakage by slow compression and impact using a DEM particle replacement model

The present work introduces a particle replacement model implemented in the commercial software EDEM to describe breakage of particles. Several model parameters were initially estimated on the basis of single-particle breakage tests on iron ore pellets. The model was then used to simulate breakage of particle beds by both slow compression and impact. Model predictions were compared to experiments in terms of compressive force versus packing density, breakage probability of the particles versus compressive force applied to the bed, and the product size distribution in compression and impact. The model showed the expected trends as well as some agreement with the measured product size distributions both from confined and unconfined stressing conditions of the bed of particles, being a simple and effective approach to describe breakage in systems where particles are stressed as assemblies.     

Evaluation of the relationship between energy input and particle size distribution in comminution with the use of piecewise regression analysis

It is known that the single linear Gates–Gaudin–Schuhmann (GGS) model is in some cases unable to fully describe the particle size distribution of comminution products. In order to overcome this shortcoming, piecewise regression analysis was used to predict the size distributions derived, after grinding for various periods four mono-sized fractions of quartz and marble in a laboratory ball mill. The single line was divided into two straight lines, which indicate the presence of two domains of particle sizes and therefore the involvement of two distinct breakage mechanisms. The obtained GGS model parameters were used to determine the evolution of particle size distribution as a function of the energy input.

In addition, the existing relationships between energy input and particle size distribution were improved, by taking into account the effects of the feed size and material type. The new relationships obtained can be used for a more accurate estimation of the required energy for breakage.     

Fracture mechanisms and particle shape formation during size reduction of a model food material

The importance of particle shape to powder properties warrants examination of the effect of size reduction on particle shape formation. In this study, a model food material (dried gelatinized starch) was comminuted in an impact breakage gun, a hammer mill (with and without a screen) and in a blender. After sieving, particle shape at selected sizes was assessed as deviation from sphericity. Generally, particle shapes were elongated at smaller size, except for those produced by unscreened hammer milling. Particle shapes were unaffected by impact velocity in the gun, but were rounded by increased milling. Fractography was used to demonstrate how elongated particles formed. During fracture, fracture fronts were disturbed by air holes in the material, creating cleavage steps. Subsequent undercutting of the steps as fracture planes spread released the elongated particles. Such particle formation mechanisms may account for anomalous size distribution results at early stages of grinding. Particle shape differences between mills and single impact breakage were ascribed to particle selection mechanisms surmised to be operating in the mill. Both material properties and the size reduction method were shown to affect particle shape, thus fracture progress in a given material should be studied if particles of specific shapes are to be produced by comminution.     

Material characteristics and the breakage parameters in a circular fluid energy mill

Towards analyzing the breakage behavior of materials with respect to their physical properties in the context of simulation and modeling of the process of comminution in a circular fluid energy mill, the present work was taken up to characterize the effect of material hardness on the breakage process of the mill. The breakage parameters of a range of materials, chosen based on their hardness, were analyzed by estimating them using the G-H solution for the size discretized batch grinding equation, with corrections to account for the deviation from first-order kinetics during the initial stages of grinding and a back-calculation scheme. All the operating variables of the mill were kept the same while collecting the primary breakage data using a single-size feed for six successive passes through the grinding chamber of the mill. The breakage distribution values could be related to particle size with the sum of two power function equations, while the breakage rate could be expressed as a power function of the dimensionless particle size and the top size interval disappearance. The coefficients of these functions for different materials indicated inconsistent behavior with respect to the hardness for softer materials, while medium and harder minerals showed specific trends.     

Prediction of iron ore mineral liberation behavior using the Andrews–Mika diagram and beta distribution

A combined grinding and liberation model was studied to predict the liberation characteristics of iron ore comminuted by a ball mill. Comminution characteristics were obtained using the one-size-fraction method; then, the iron ore samples were crushed and separated into several narrow-size fractions by screening. The size fractions were further divided into three classes by magnetic separation, namely concentrate, middling, and tailings. Subsequently, various size classes were subjected to ball milling, and the results were analyzed in the kinetic grinding model. The mineralogical textures of the ground products were analyzed using mineral liberation analysis. The beta distribution and Andrews–Mika diagram characterized the distribution of the iron content within the size fractions. The breakage characteristics of the iron ore samples varied slightly with the iron content. However, the liberation characteristics were well-described by adjusting the four parameters of the beta distribution. The variation in grinding kinetics with composition and liberation model parameters was used in the combined liberation–comminution model to predict the evolution of the size–composition matrix as grinding proceeded. The predicted results align with the experimental results. The developed model can construct a yield–recovery graph and calculate the liberation efficiency to determine the size reduction threshold for efficient separation.     

Analyses of the energy-size reduction of mixtures of narrowly sized coals in a ball-and-race mill

Mixture breakage of particles in various sizes is common in industrial mills, and breakage behavior is influenced by size composition. But studies on particle breakage are conducted to narrowly sized samples. In this paper, tentative works are made to investigate interaction among super clean coal in mixture breakage from aspects of breakage rate, energy consumed characteristics and energy split factors. Experimental results demonstrate that breakage rate of coarse particles in mixture breakage increases if compared with that in single breakage. Particle size is modelled into classical breakage equation, and the modified model is successfully applied to mixture breakage. Energy split factor of component is determined based on the balance of specific energies of components in heterogeneous breakage and energy-size equation, and consumed energy (W) of component in multi-component grinding is calculated. Calculated energy split factors of components are all above one in various mixed conditions, so energy efficiency (value of product t₁₀ at the same specific energy) decreases if compared with that of single breakage. Energy split analyses are also conducted for mixture breakage of middling coals, which illustrates that the method is robustness for energy-size reduction process influenced by associated minerals in coal.     

搅拌磨中研磨介质大小对氧化锌超细研磨的影响

采用2种直径分别为0.4⁰.6、0.80.6、0.8¹.0 mm的氧化锆球,研究研磨介质大小对湿法研磨过程中氧化锌粒径的影响,并利用粉磨动力学模型分析研磨过程中的破碎机理。结果表明,采用直径为0.41.0 mm的氧化锆球,研究研磨介质大小对湿法研磨过程中氧化锌粒径的影响,并利用粉磨动力学模型分析研磨过程中的破碎机理。结果表明,采用直径为0.4⁰.6 mm的研磨介质研磨30 min时,氧化锌粒径可达到最小,即d50为0.9μm,d90为2.41μm;研磨介质直径为0.40.6 mm的研磨介质研磨30 min时,氧化锌粒径可达到最小,即d50为0.9μm,d90为2.41μm;研磨介质直径为0.4⁰.6 mm时的破碎速率明显大于直径为0.80.6 mm时的破碎速率明显大于直径为0.8¹.0 mm时的破碎速率,且破碎颗粒分布在较小的粒径范围内;在研磨过程中冲击破碎和摩擦破碎同时存在,研磨介质直径为0.41.0 mm时的破碎速率,且破碎颗粒分布在较小的粒径范围内;在研磨过程中冲击破碎和摩擦破碎同时存在,研磨介质直径为0.4⁰.6 mm时摩擦破碎的比例大于直径为0.80.6 mm时摩擦破碎的比例大于直径为0.8¹.0 mm时的比例。     

An investigation on the breakage behavior of olivine sand particles: An attainable region technique

This study investigates the breakage behavior of olivine sand particles to identify optimal operating parameters to get products in three different define particle size classes. This was achieved by a Los Angeles abrasion test with different numbers of steel balls (up to 12), weights of steel balls (up to 0.441 kg), and different grinding durations (up to 200 mins). The data obtained were then analyzed using a model-free and equipment-independent attainable region (AR) technique. The findings revealed that the required product fineness is a function of the grinding time, numbers and weight of steel balls, and feed material size. Using 9 steel balls of 0.441 kg, a higher mass fraction of materials in the fine-sized class (?75 μm) was obtained after grinding for 200 mins. The AR technique proved to be a practical approach to optimize olivine particle size during breakage, with a potential application in sustainable soil stabilization projects.     

Influence of impact velocity on fragmentation and the energy efficiency of comminution

Comminution processes such as crushing and grinding are essential stages in mining and mineral processing operations to reduce the size of ore and rock, and to liberate the valuable mineral for beneficiation. Comminution is energy-intensive and responsible for most of the energy used during mineral recovery. Energy efficiency is very low since almost all the energy is dissipated as heat instead of generating new surface area. This paper reports on studies conducted on strain rates achieved by various velocities of impacts that enhance energy efficiency and mineral liberation. The research focuses on understanding comminution fracture mechanics and on quantifying the distribution of energy with respect to generating new surface area. In interpreting breakage energy phenomena, accurate measurements of surface roughness and surface area are essential. A novel approach to measure surface roughness and surface area based on a fractal analysis procedure has been developed. Changes in surface roughness of broken specimens under variable loading rates were studied using a laser probe to generate 3D topographical maps of the fracture surfaces. The results indicate that surface roughness and hence, specific surface area, increase with increasing loading rate by several orders of magnitude as particle size decreases to 1 μm. Below this limit, surface roughness begins to diminish from particle–particle attrition. An apparatus to measure the quantitative parameters of impact at different velocities on aggregated rock samples is proposed. Experiments are being carried out at projectile velocities up to 500 m s⁻¹ utilizing a compressed-air device. The results suggest possible efficiency improvements in breakage under the velocity of impact.     

Dry grinding in planetary ball mills: Evaluation of a stressing model

Planetary ball mills at laboratory scale are widely used for grinding and alloying processes. However, in contrast to other mill types, no applicable mechanistic model exists to describe the stressing conditions and their effect on particle breakage, so that processes are empirically evaluated so far. Within this study, the stressing conditions are determined by simulations based on the discrete element method including the contact model of Hertz and Mindlin. The contact model parameters are carefully calibrated by a series of experiments, so that it is finally possible to validate the simulation results by comparison of measured and calculated power values. The correlation of stressing conditions and breakage rates of alumina powder demonstrates the effect of stressing on breakage kinetics and breakage mechanism. It allows calculating the active mass in dependence on process parameters by an extension of Schönert’s active mass model.Altogether, the presented stressing model features analytical functions for the mill-related stressing conditions and highlights the importance of stressing intensity as process determining parameter, which defines the required number of material-related stressing events and the specific energy.     

Evaluation of Particle Degradation Due to High-Speed Impacts in a Pneumatic Handling System

Particle degradation can be a significant issue in particulate solids handling and processing, particularly in pneumatic conveying systems, in which high-speed impact is usually the main contributory factor leading to changes in particle size distribution (comparing the material to its virgin state). However, other factors may strongly influence particles breakage as well, such as particle concentrations, bend geometry, and hardness of pipe material. Because of such complex influences, it is often very difficult to predict particle degradation accurately and rapidly for industrial processes. In this article, a general method for evaluating particle degradation due to high-speed impacts is described, in which the breakage properties of particles are quantified using what are known as “breakage matrices.” Rather than a pilot-size test facility, a bench-scale degradation tester has been used. Some advantages of using the bench-scale tester are briefly explored. Experimental determination of adipic acid has been carried out for a range of impact velocities in four particle size categories. Subsequently, particle breakage matrices of adipic acid have been established for these impact velocities. The experimental results show that the “breakage matrices” of particles is an effective and easy method for evaluation of particle degradation due to high-speed impacts. The possibility of the “breakage matrices” approach being applied to a pneumatic conveying system is also explored by a simulation example.     

Understanding production of fines in batch ball milling for mill scale-up design using the population balance model

The rate of production of fine material in the batch mode of grinding operation forms the basis for determination of the grindability parameter of the Bond approach and the breakage distribution function of the population balance model (PBM) approach to the mill scale-up design. For a given set of mill operating conditions, the rate of production of fines is determined by the breakage characteristics and production history of the material being ground. Another important aspect is the variation in the rate of production of fines with grinding time. With a view to developing a clear understanding of these aspects, a detailed analysis of variations in the rate of production of fines was carried out using the PBM framework and two well-known functional forms for the specific breakage rate and breakage distribution parameters. In this paper, it has been shown how the results of this analysis can be used for: (i) obtaining more accurate estimates of the breakage distribution parameters by performing just one short-duration batch grinding experiment, and (ii) explaining variation in the Bond Work index with the product size in terms of the exponent of particle size in the expression for the specific breakage rate function: $k_j=A^1{x}_j^{\alpha }$.     

BREAKAGE KINETICS USING MULTI-PASS GRINDING

To understand the mechanism of material breakage in a mill, it is important to first study the breakage kinetics. This is often done by experimental methods which Involve batch grinding a size fraction of the material and measuring the amount of the original size fraction remaining at various grind times. If the mill can not be used as a batch grinder, It Is difficult to experimentally study the breakage kinetics. The Szego mill is one such example of a mill which can be used only as a continuous grinder.

This paper deals with the method of using multi-pass grinding to determine the breakage kinetics. The experimental procedure Involves measuring the fraction of the top √2size Interval of material remaining after each pass through the mill at steady-state conditions. The model for steady-state, open-circuit grinding is extended for multi - pass grinding and it is shown how breakage kinetics can be determined from multi-pass grinding data under certain conditions. In this method the error resulting from a plug flow assumption of the material transport in the mill is also discussed. An application to multi-pass, dry grinding of coal with the Szego mill is described.