球磨机钢球抛落运动中的第四种最优转速率研究

球磨机钢球抛落运动中落点的径向动能起主要碎磨作用,已经在文献中详加论证。进一步研究证明:抛落钢球落点的切向磨剥作用并非由切向分速度(绝对速度)直接来完成,而是决定于它相对于圆运动钢球的相对速度。这个相对速度形成的动能与径向分速度形成的动能之和才是真实的磨矿总动能,它比传统意义上的总动能大得多。由这样的总动能最大值求出对应的转速率才是真实的最优转速率。笔者把研究的重点落实在抛落钢球落点的切向分速度和它相对于圆运动钢球的相对速度的分析上,并以特定球磨机为例,重点阐明了一种优化的计算方法。     

Comparison of energy efficiency between ball mills and stirred mills in coarse grinding

Stirred mills are primarily used for fine and ultra-fine grinding. They dominate these grinding applications because greater stress intensity can be delivered in stirred mills and they can achieve better energy efficiency than ball mills in fine and ultra-fine grinding. Investigations were conducted on whether the greater performance of stirred mills over ball mills in fine grinding can be extended to coarse grinding applications. Four different laboratory ball mills and stirred mills have been tested to grind seven ore samples with feed sizes ranging from 3.35 mm to 150 μm. A case study on full scale operations of a 2.6 MW IsaMill replacing the existing 4 MW regrind ball mill at Kumtor Gold Mine in Kyrgyzstan is also included. This paper summarizes the major findings from these investigations.     

地下选矿厂磨机(半自磨机)机械振动研究综述

地下选矿厂磨矿硐室(半自磨机硐室)需要承受磨矿设备筒体内矿石、介质和筒体交互冲击产生的机械振动作用。对国内外学者及工程技术人员针对与半自磨机类似的球磨机、磨煤机等设备,从数据采集及分析方法、改进设备作业效率、监控设备运行性能及保持设备基础稳定方面取得的研究成果进行了综述,总结了磨机(半自磨)机械振动信号采集、分析识别方法、仿真反演及实际应用等方面研究成果,具有较高的借鉴意义。     

Product size distribution in stirred media mills

A study on the control of particle size distribution (PSD) of the ground carbonate product in stirred media mills (wet Drais stirred bead mill and dry Sala Agitated Mill) is presented in this paper. The results indicated that the slope of product size distribution can be controlled by altering some operating parameters, such as size of grinding media and tip or peripheral speed. The profile of product size distribution from the stirred media mills was found to follow most closely the Rosin-Rammler-Bennett (RRB) model.     

Grindability of binary ore blends in ball mills

The understanding of how blends of materials grind is of great relevance in both the minerals and the cement industries. If benefits and challenges associated to it are properly understood, then decisions can be made on blending prior to grinding or grinding additives in separate during cement production, as well as different ores fed to mills in a processing plant. The paper investigates the size reduction of blends of materials with different grindabilities in a Bond ball mill, as well as in a continuous pilot-scale mill. The accumulation of the harder (tougher) component in the mill charge as grinding progresses is analyzed and a simple empirical model that describes this phenomenon has been proposed. It is found that the accumulation of hard component in the mill increases with the decrease in the ratio of Bond work index values of the individual soft and hard components, and with the increase in the circulating load ratio. It is also concluded that the Bond work index of the mixtures is often higher than the weighed-average value of the individual components in the mixture. As such, an expression is proposed for calculating the value for blends based on this modeled accumulation effect and has been found to remove the bias from predictions made on the basis of the weighed-average values from the feed.     

The shape of product size distributions in stirred mills

This paper presents the results of an extensive laboratory and pilot stirred milling testwork program conducted using different types of mills, fed with different types of materials and operated at different conditions. The results indicate that the slope of the product size distribution (PSD) curve remains relatively unchanged in the coarse product size range but decreases in the fine product range (less than about 20 μm size), regardless of the type of stirred milling technology used for grinding. This work therefore confirms that a narrower product particle size distribution than the feed size can be achieved independent of the type of stirred milling technology used for fine grinding below 20 μm. The change in the PSD width in fine grinding is due to the change in the material breakage properties and a change in the mill operating conditions which affect the breakage process. In the normal operating range of grinding media size, the effect on the PSD shape is not significant.     

橡胶衬板在特大型球磨机中的应用

介绍了德兴铜矿大山选矿厂球磨机 ( 5 .5 m× 8.5 m)使用橡胶衬板的情况 ,与锰钢衬板对比的考查结果及在生产实践中发现的优缺点。     

Modeling breakage rates of coarse particles in ball mills

Breakage rates of coarse particles in ball mills generally follow non-first-order kinetics and the distribution products from batch milling are often characterized by significant contributions of abrasion besides breakage by impact, which are not well described using traditional size–mass balance formulations. Under such conditions, particles are often subject to impacts of insufficient magnitude to produce breakage in each stressing event, so that they are broken by a combination of abrasion and impact and also particles undergo weakening due to unsuccessful stressing events. The paper presents a mathematical model of batch grinding which takes into account the distribution of stressing energies in the mill, the distribution of fracture energies of particles contained in the charge, describing breakage by impacts from grinding media producing catastrophic breakage, abrasion and weakening from repeated impacts. The model has been applied to describe the rate of disappearance of two materials in batch grinding with good results.     

橡胶衬板在特大型球磨机中的应用

介绍了德兴铜矿大山选矿厂球磨机(5.5 m×8.5 m) 使用橡胶衬板的情况,与锰钢衬板对比的考查结果及在生产实践中发现的优缺点.     

The application of a simplified approach to modelling tumbling mills,stirred media mills and HPGR’s

Most modern population balance models for comminution invoke the concept of a specific breakage rate function and a breakage distribution function to describe breakage kinetics. One of the difficulties of this approach is that these functions are very difficult to measure directly. Consequently, it is usual to assume that these functions can be represented by simple equations with parameters that can easily be estimated from test data using back-calculation techniques. However, these estimates can be very sensitive to small measurement errors and are usually subject to very large variances. This paper presents a simplified approach to modelling comminution processes that invoke the concept of an energy-based cumulative breakage rate function to describe breakage kinetics. This function can be estimated directly from plant data and is well-suited to multi-component modelling of individual rock types and mineral species. Examples of the application of this simplified modelling approach are described for the treatment of platinum ores using ball mills, AG/SAG mills, HPGR’s and stirred media mills.     

Dynamic modelling and simulation of semi-autogenous mills

This paper presents a dynamic simulator of the semi-autogenous grinding operation deduced from first principles coupled to an on-line parameter estimation scheme able to simulate industrial operations for control purposes. Model equations are based on conventional non-stationary population balance approach to develop the necessary dynamic model of the semi-autogenous mill operation. The model is able to predict the time-evolution of key operating variables such as product flow rate, level charge, power-draw and load position, as function of other important variables such as mill rotational speed and fresh feed characteristics. The set of ordinary differential equations was solved using MATLAB/SIMULINK as a graphic programming platform, a very helpful tool for understanding the grinding phenomenon.Using an on-line parameter estimator, the simulator was tested and validated at an 1800 t/h copper–ore mill showing the effectiveness of the system to track the dynamic behaviour of the variables. It is now being used for the study of advanced control schemes.     

Power draw estimations in experimental tumbling mills using PEPT

Positron Emission Particle Tracking (PEPT) was employed to reconstruct the motion of mono-sized glass beads in an experimental tumbling mill run in batch mode. In each case, the derived trajectory field of a representative tracer particle was used to determine the charge power draw at steady state operation. Two approaches for calculating power draw were considered: the torque of the centre of mass about the mill centre, and the time averaged torque contribution per discrete grid cell summed over the volume of the mill. Results were compared across different operating conditions and particle sizes to measured power.     

Control of the mill charge behavior in dry tumbling mills

Powder filling of a dry mill has a large influence on grinding capacity and wear rate of grinding media and liners. In particular low powder filling levels can cause extensive wear rates. This paper discusses the influence of some operating parameters of the mill circuit on powder filling, when airflow through the mill is applied. An method of warning against low powder filling levels inside the mill is shown, a piezoelectric strain transducer installed on the mill shell accomplishing this task.     

A mechanistic model for slurry transport in tumbling mills

We describe a modelling approach to slurry transport in dynamic beds. Volume and time averaging are combined to obtain a dynamic replacement for the static Ergun equation. Solutions of the resulting dynamic equation are exhibited for a simple charge-motion model, which serves as the prototype for a practical slurry transport model.     

A new predictive model of lifter bar wear in mills

The cost of mill relining and the influence of the liner profiles on mill performance provide a strong motivation to improve liner selection. However, the capability to predict liner life and progressive profile is poorly developed in the industry. A new model has been developed to predict the rate of liner wear based on the main parameters affecting the wear process such as; ore type, relative velocity between the ore and the liners, liner hardness and friction conditions. The resultant model is capable of determining the wear as a function of mill operating and discharge conditions based on the variation of specific gravity of mill contents, geometrical characteristics of the mill and mill velocity. The results from this model are in good agreement with the measured data from the SAG mill at Sarcheshmeh Copper Complex, Iran.     

立磨机磨矿关键影响因子研究

立磨机因为能耗低,效率高的特点,逐渐取代球磨机成为细磨和再磨的主要设备。但立磨机的磨矿基本理论研究还不够完善,设备的设计、介质球的匹配等还依赖于工程经验和试验探索,存在着成本高、效率低的问题。针对立磨机的两个结构参数:环形间隙,螺径比和三个运行参数:螺旋外缘线速度,介质球直径,介质充填率,以石英作为试验矿样,基于实验室KLM-10立磨机,设计了五因素四水平正交试验,以磨矿能耗与时间作为考核指标,探索影响立磨机磨矿效果的关键结构参数和工业运行参数,得到了单因素对于磨矿效果的影响规律,以及运行参数与结构参数的最佳匹配方案,为立磨机的设计运行提供理论依据。     

Calculation of two-fraction mixture porosity

A method is proposed for calculating porosity of two-fraction mixtures that are composed of irregularly compacted convex particles slightly differing in sizes in three orthogonal directions. A comparison of calculated results and the known experimental data is presented and indicates their consistency both for the irregular-shaped and rounded particles.Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 4, pp. 29–34, July–August, 2004.     

Tracer studies and breakage testing in pilot-scale stirred mills

A tracer technique is used to provide parameters that describe mixing and breakage in stirred mills. The results are also used to test the accuracy of mixing and breakage models.Tracer studies have been undertaken using a 39-litre vertical Sala agitated mill and a 4-litre horizontal Netzsch mill. The experimental residence time distribution (RTD) of the mills is analysed both in terms of a single mean residence time and a non-linear least squares fit to an optimal number of perf ect mixers of unequal size in series. Results show a strong dependence of RTD on flow rate, minimal dependence on stirrer speed, and support the concept that the RTD's of liquid tracers and solid tracers subject to breakage are similar. A very accurate match to the experimental RTD curves car be achieved with the multiple uneven mixers in series model.Size distribution results from solid tracer tests are used to determine the breakage characteristics of the pilot-scale Sala mill. The population balance model for a single perfect mixer with steady state hold-up is used as the basis for solution of a constrained non-linear optimisation inverse problem for mill breakage rate and breakage function. Experimental results indicate that the breakage rate is first order as hypothesised. The population balance model using optimal breakage parameters provides a reasonable fit to experimental data for cumulative passing percentage as a function of particle size for discrete times. Both the breakage rates and cumulative breakage functions are roughly power law dependent on particle size. Analysis of the size distribution of breakage products indicates that the mode of particle breakage, as indicated by the tracer breakage parameters, is a function of time. This demonstrates that the assumption of time independent breakage parameters in the population balance model may not be valid. Accurate determination of breakage parameters is strongly influenced by the transport characteristics of the slurry through the mill.The work shows that particle breakage in pilot-scale stirred mills is a complex function of both particle and specific mill characteristics. Therefore, in order to gain insight into the appropriate physical processes at work in an industrial scale mill, it is important to perform experiments with and analyse a system that matches the real mill as closely as possible.     

Determination of the rate of crushing of material in drum mills

Conclusions The author determines for the kinetic-probabilistic model of particle fracture in a drum mill the probability of particles coming within the zone of impact of the crushing bodies, and the probability of fracture of these particles. On the basis of several experiments in a laboratory mill with the material being ground, the equation of the crushing rate of the particles permits prediction of the crushing rate of this material under any operating conditions of mills of different sizes. The introduction of crushing rate equation (24) and batch crushing equation (23), together with use of the functions of the material residence time distribution in the mill, will permit subsequent prediction of the continuous crushing process. Sibénergotsvetmet, Krasnoyarsk. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 2, pp. 48–55, March–April, 1980.