Cone crusher chamber optimization using multiple constraints

The chamber geometry is one of the key factors that influences the performance of a cone crusher. The design of the chamber geometry should take product quality and crushing efficiency into account. In this paper the kinematics of rock material in a crushing chamber, as interparticle breakage occurs, has been analyzed and the chamber division is achieved. Based on the chamber division and a population balance model, the method for chamber geometry design is presented. Combining the empirical model for predicting particle shape with the size distribution model, a flakiness prediction model is proposed. With the size reduction model and flakiness prediction model as constraints, an optimization of the crushing chamber is achieved. Finally, the validity of the crushing chamber optimization model has been verified by an appropriate prototype test.     

Parametric study of the smooth‐joint contact model on the mechanical behavior of jointed rock

The smooth‐joint contact model based on distinct element method has been widely used to represent discontinuity in the simulation of fractured rock mass, but there is rare efficient guidance for the selection of proper parameters of smooth‐joint contact model, which is the basement for using this model properly. In this paper, the effect of smooth joint parameters on the macroscopic properties and failure mechanism of jointed rock under triaxial compression test is investigated. The numerical results reveal that the friction coefficient of smooth joint plays a dominant role in controlling mechanical behaviors. The stiffness of smooth joint has a relative small influence on the mechanical behaviors. Poisson ratio decreases with the reduction of normal stiffness but increases with the reduction of shear stiffness. The reduction of smooth joint strength, which is determined by normal strength, cohesion, and friction angle of smooth joint, contributes to the breakage of bonded smooth joint and ultimately decreases the strength of the specimen. We proposed a detailed calibration process for smooth‐joint contact model according to the relationship between smooth‐joint parameters and mechanical properties. By following this process, the numerical results are validated against corresponding experimental results and good agreement between them can be found in stress‐strain curves and failure modes of different joint orientations. Further analyses from the microperspective are performed by looking at transmission of contact force, the nature and distribution of microcracks, and the particle displacement to show the failure process and failure modes.     

颗粒破碎效应对堆石坝应力变形的影响

颗粒破碎对堆石体的变形有重大影响,颗粒破碎除与母岩强度有关外,与应力状态密切相关,高堆石坝堆石体的大部分变形正是高应力场下颗粒破碎的反映。沈珠江院士提出的南水双屈服面模型虽可以较全面地反映堆石体的变形特性,但未充分考虑颗粒破碎引起的剪缩特性,因此坝体变形计算结果往往偏小,适用于中低堆石坝的分析中。本文的计算方法在南水双屈服面模型的基础上,考虑了堆石体在一定应力状态下颗粒破碎引起的应变,较真实地反映了堆石体的变形特性,可为堆石坝尤其是高堆石坝的应力变形研究提供更为合理的结果。     

Discrete element modeling for predicting breakage behavior and fracture energy of a single particle in a jaw crusher

In the present study, Discrete Element Method (DEM) technique was applied to model the fracture behavior of a single spherical and cubic rock in a laboratory jaw crusher. The rocks studied were modeled as granular assemblies located between two jaws, and their fracture mechanism was studied. To verify the obtained results, the spherical and cubic specimens produced from Dokoohak Limestone and Dehbeed Granite were studied and the energy applied by the jaws was compared to those of the fracture energy estimated by the single particle breakage analysis. There is fairly good agreement between the energy acquired from the DEM model and the single particle fracture energy of the spherical rocks. It appears that DEM is a suitable method for predicting the crushing energy of the spherical rocks in the jaw crusher. The fracture behavior of the crushed rocks was examined and compared by the results obtained from the DEM model. The tensile mode of fracture occurring in the spherical rocks is well presented by the discrete element modeling. However, the DEM technique is not capable of modeling the delamination mode occurring in the cubic rocks.     

Modeling the effect of wetting on the mechanical behavior of crushable granular materials

It is well known that the compressibility of crushable granular materials increases with the moisture content,due to the decrease of particle strength in a humid environment.An existing approach to take into account the effect of grain breakage in constitutive modeling consists in linking the evolution of the grain size distribution to the plastic work.But how the material humidity can affect this relationship is not clear,and experimental evidence is quite scarce.Based on compression tests on dry and saturated crushable sand recently reported by the present authors,a new non-linear relationship is proposed between the amount of particle breakage and the plastic work.The expression contains two parameters:(1)a material constant dependent on the grain characteristics and(2)a constant depending on the wetting condition(in this study,dry or saturated).A key finding is that the relationship does not depend on the stress path and,for a given wetting condition,only one set of parameters is necessary to reproduce the results of isotropic,oedometric,and triaxial compression tests.The relationship has been introduced into an elastoplastic constitutive model based on the critical state concept with a double yield surface for plastic sliding and compression.The breakage ratio is introduced into the expression of the elastic stiffness,the critical state line and the hardening compression pressure.Incremental stress-strain computations with the model allow the plastic work to be calculated and,therefore,the evolution of particle crushing can be predicted through the proposed non-linear relationship and reintroduced into the constitutive equations.Accurate predictions of the experimental results in terms of both stress-strain relationships and breakage ratio were obtained.     

Modeling for critical state line of granular soil with evolution of grain size distribution due to particle breakage

Determination of the critical state line(CSL)is important to characterize engineering properties of granular soils.Grain size distribution(GSD)has a significant influence on the location of CSL.The influence of particle breakage on the CSL is mainly attributed to the change in GSD due to particle breakage.However,GSD has not been properly considered in modeling the CSL with influence of particle breakage.This study aims to propose a quantitative model to determine the CSL considering the effect of GSD.We hypothesize that the change of critical state void ratio with respect to GSD is caused by the same mechanism that influences of the change of minimum void ratio with respect to GSD.Consequently,the particle packing model for minimum void ratio proposed by Chang et al.(2017)is extended to predict critical state void ratio.The developed model is validated by experimental results of CSLs for several types of granular materials.Then the evolution of GSD due to particle breakage is incorporated into the model.The model is further evaluated using the experimental results on rockfill material,which illustrates the applicability of the model in predicting CSL for granular material with particle breakage.     

An empirical model for predicting flakiness in cone crushing

A fundamental understanding of the factors influencing particle shape is of central importance for optimisation of the output quality from crushing plants for aggregate production. The literature reports that the wear on and setting of a cone crusher influence particle shape, The fact that wear on and the setting of a cone crusher influence particle shape is considered common knowledge and is also reported in the literature. To date, no mathematical model for predicting particle shape has been presented.     

Wet grindability of an industrial ore and its breakage parameters estimation using population balances

The grindability of a diasporic ore was studied by wet grinding in a laboratory ball mill and its breakage parameters were determined based on the population balance model (PBM). Four different feeds with unnatural size distributions were designed to save grinding and sieving work. It was found that three size-intervals fitted the first-order breakage, but the coarsest interval did not. The non-first order breakage was most probably caused by the heterogeneity of the material. The heterogeneity was then confirmed by experiments. The breakage rate and the breakage distribution parameters were back calculated by treating the non-first order breakage as two linear segments according to the grinding time. The back-calculated breakage rates were in good agreement with the values calculated directly from the experimental data, and non-normalizable breakage distribution was observed. The model with the obtained parameters simulated the experimental product size distributions with good accuracy. These findings are valuable to the simulation and optimization of the industrial grinding processes of diasporic ores.     

Relationship between breakage parameters and process variables in ball milling — An industrial case study

The performance of the secondary ball mill at the New Broken Hill Consolidated Ltd. concentrator is analysed using the perfect mixing model and an ore-specific breakage distribution function. This function was determined from single-particle breakage tests using a computer-monitored twin pendulum apparatus.The ratio of the breakage rate to the normalized discharge rate, r/d^*, determined for the ball mill using the ore-specific breakage distribution function for a range of grinding conditions is related to the mill power consumption. The mill power consumption is related to the percentage of mill volume occupied by the ball charge and to the percentage of solids in the mill feed.     

Role of feed moisture in high-pressure roll mill comminution

The application of high-pressure roll mills (HPRM) for industrial comminution has been growing, particularly because of its energy efficiency. Many aspects of HPRM comminution have not been fully characterized because the performance of the machine is affected by numerous parameters that still need to be investigated and optimized. The present paper is concerned with the effect of feed moisture on HPRM performance. The comminution of minus 8-mesh dolomite feed at several different moisture levels was conducted with a laboratory HPRM to delineate the effect of feed moisture on product characteristics, specific energy consumption, and such mill operating parameters as applied load, roll gap and roll speed. The results showed definite effects of moisture on these parameters and the product size distribution, most likely because of lubrication of the particles in the compacting bed as they pass through the roll gap.     

结构性黄土二元介质本构模型在局部化剪切带中的应用

基于破损力学理论,将结构性黄土抽象成具有一定结构强度的结构块和摩擦带组成的二元介质模型。对结构性黄土体来说,局部化剪切带问题也是土体的破损问题,剪切带萌生发展的实质就是结构块向摩擦带转化的动态过程。应用结构性土的双参数破损率二元介质本构模型,采用数值分析方法模拟了平面应变压缩条件下结构性土中局部化剪切带萌生、扩展的过程,研究了不同缺陷方案下局部化剪切带的形态、特性与规律,发现结构性土中局部化剪切带的发展起初是由一段段不连续的微小局部破坏区域在外荷载逐步作用下渐进扩展连接贯通而形成整体剪切带的破坏形式。二元介质本构模型和常规有限元的结合,形象生动地再现了局部化剪切带萌生、发展的过程。     

Modelling the performance of industrial ball mills using single particle breakage data

Ball milling is an energy-intensive unit operation and usually consumes a major proportion of the power drawn by a typical mineral processing plant. Hence, substantial economic benefits can be achieved by optimal design and by operating ball milling circuits under optimum process conditions. This requires an accurate ball mill modelling technique.In the multi-segment ball mill model, the size-dependent material transport within the mill varies systematically with the amount of coarse particles present in each segment. The ore-specific breakage distribution function can be determined from single particle breakage tests conducted using a computer-monitored twin pendulum apparatus. When the ore-specific breakage distribution function is used in the multi-segment, a constant relationship between the breakage rate parameters and mill diameter is observed. Thus, the performance of an industrial ball mill can be adequately described using the ore-specific breakage distribution function together with the systematic variation of the material transport and the breakage rate functions with process conditions and mill diameter, respectively.This ball mill modelling technique is illustrated using a case study on the design of a ball milling circuit for a particular grinding requirement and another case study on modelling the performance of an industrial ball milling circuit.     

考虑颗粒破碎影响的粗粒土本构关系

粗粒土在较大的应力条件下容易产生颗粒破碎现象,而现有的大多数模型都没有考虑剪切过程中的颗粒破碎。模型将塑性功引入土体受力变形过程的能量方程中,推导得到土体流动法则。采用直线型屈服轨迹和非相关联流动法则,利用不排水应力路径计算得到硬化函数,建立了一个考虑颗粒破碎的粗粒土本构模型。对比分析表明：该模型对粗粒土在各种围压下的应力-应变和体应变计算结果与试验曲线吻合较好。     

基于三维矿化域模型的泥河铁矿床动态储量估算

基于泥河铁矿床矿体地质特征的详细研究,本文结合边界品位指标以及样条曲线方法对矿体边界进行简化平滑处理,并通过对各剖面的矿体解译边界进行圆滑渐变处理建立控制矿化边界的矿化域模型.基于矿化域模型,用于储量估算的样品分析数据具有更好的连续性和全面性,避免了双指标圈矿带来的矿体形态过度复杂和在三维空间内不可避免的空间占位现象.基于矿化域模型进行的储量估算,可以更快速、合理地获取矿体品位的空间分布特征,从而提高金属矿床储量估算结果的准确性和合理性.     

粘土的双硬化模型

本文中建议了一个包含塑性体应变和偏应变两个硬化参数的封闭屈服面模型，可以同时应用于正常固结土和超固结土。该模型沿用了剑桥模型的参数测定方法，而大大拓展其适用范围。通过正常固结试样、超固结试样和应力路线转折条件下计算与试验曲线的对比，说明该模型有较广泛的适应性。     

Validation of a model for impact breakage incorporating particle size effect

Investigation of a breakage probability model published by Vogel and Peukert [Vogel, L. and Peukert, W., 2004. Determination of material properties relevant to grinding by practicable labscale milling tests. Int. J. Miner. Process., 74S, 329–338.] has led to a modification of their model to describe the degree of impact breakage, t₁₀. The modified model takes a form similar to the JKMRC prior art breakage model, but with particle size and breakage properties incorporated explicitly in the model.     

A Fragmentation Modelling Framework for Underground Ring Blasting Applications

Empirical approaches for predicting fragmentation from blasting continue to play a significant role in the mining industry in spite of a number of inherent limitations associated with such methods. These methods can be successfully applied provided the users understand or recognize their limitations. Arguably, the most successful empirical based fragmentation models have been those applicable to surface blasting (e.g., Kuz-Ram/Kuznetsov based models). With widespread adoption of fragmentation assessment technologies in underground operations, an opportunity has arisen to extend and further develop these type approaches to underground production blasting.

This paper discusses the development of a new fragmentation modelling framework for underground ring blasting applications. The approach is based on the back-analysis of geotechnical, blasting and fragmentation data gathered at the Ridgeway sub level caving (SLC) operation in conjunction with experiences from a number of surface blasting operations.

The basis of the model are, relating a peak particle velocity (PPV) breakage threshold to a breakage uniformity index; modelling of the coarse end of the size distribution with the Rosin-Rammler distribution; and modelling the generation of fines with a newly developed approach that allows the prediction of the volume of crushing around blastholes.

Preliminary validations of the proposed model have shown encouraging results. Further testing and validation of the proposed model framework continues and the approach is currently being incorporated into an underground blast design and analysis software to facilitate its application.     

粗粒料颗粒破碎数值模拟研究

粗粒料在外力作用下存在明显的颗粒破碎特性,研究颗粒破碎过程是当前研究的热点问题之一。基于粗粒料单颗粒破碎机制,考虑单颗粒破碎强度与直径的变化规律,采用非线性接触H-Z模型和密度控制法建立了粗粒料颗粒破碎数值模型。开展粗粒料双轴剪切试验数值模拟研究,并与室内试验结果进行对比分析。研究表明：建立的粗粒料颗粒破碎数值模型能够较好地模拟粗粒料偏应力与轴向应变和体积应变与轴向应变的关系;数值模拟获得的粗粒料颗粒破碎率与室内试验结果基本一致;去除试样制备过程和固结过程引起的颗粒破碎,不同围压条件下的颗粒破碎率归一化后基本重合,且可以近似地采用双曲线函数进行拟合。颗粒破碎率随着围压的增大,逐渐增大,试验级配趋于Einav提出的颗粒破碎的最终级配（分维数等于2.6）     

土石混合体块石破碎影响因素的颗粒流数值研究

颗粒破碎是土石混合体的一种基本属性,机理复杂,影响因素众多。鉴于室内试验受设备、材料等因素限制且费时费力,本文采用Monte Carlo思想构建了能够真实反映块石破碎过程的PFC2D颗粒离散元数值模型,在室内直剪试验和筛分试验基础上进行了数值剪切试验,系统性探究土石混合体块石破碎特性的影响因素及基本规律。结果表明:在法向应力作用下,剪切后试样出现明显的块石破碎现象以分散应力;块石粒径对块石破碎程度影响显著,块石粒径越大,破碎势越大,越易破碎;块石浑圆度较小时,颗粒间接触面积较小,应力集中显著,破碎率较大;颗粒级配连续、良好时,颗粒间咬合充分接触完全,接触受力点较多,碎裂更不易发生;试样初始孔隙率对破碎率影响较小,相同法向应力下,随着孔隙率增大,块石破碎程度呈现轻微增大趋势。