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英文翻译改进了的锥体破碎机流量和压力模型摘要锥体破碎机的破碎被广泛用于采矿业来破碎石料.被最早发展的模型是用来推测锥体破碎机的磨损尺寸的.在那个模型中,实际值和真实值存在着许多不一致的地方.针对这种差异,一个有影响力的解释是:流量模型不能准确地判定出衬板的压力和磨损量.这次研究中,一个优化了的流量模型被展示,目的是为了更好的推测压力和磨损量.在这个新的模型中,发生的几种运动形式和旧的模型一致,而不同在于:破碎机阻塞点的以下部分. 阻塞点的以下部分的向下运动的物料认为被挤压的石料颗粒阻挡.为了确定阻塞点以上的尺寸分配和容积密度,一个反复的计算过程是必要的.1.介绍锥体破碎机的破碎被广泛用于采矿业来破碎石料.两个重要的破碎部件是定锥和动锥.动锥主轴的上端被悬吊在一上呈球状辐射的轴承上.下端固定在一个离心装置中.而汽压缸通过推力轴承来支承主轴.这种汽压缸的压力被称为液压.由于离心轴的作用而使得石料在两轴衬中间被挤压和破碎.(见图一)沿着破碎腔通岩石颗粒会经历几次破碎.一个生产者和典型工艺流程见图二.被炸开的岩石被输送到一个初级破碎装置中,通常是颚式或者旋回破碎机.通过一次破碎的石料被送往地次破碎装置中.在图二中,经过一次破碎的产品,在一次破碎和二次破碎之间有一个送料斗,经过二次破碎后,通常有一系列筛分、传送和三次破碎装置。物料经过筛分成不同大小的颗粒，接着输送到消费者那里。在许 采矿过程中，往往有一个研磨阶段。圆锥破碎机多用于二次破碎和三次破碎中。先前的研究使得模拟现有的圆锥破碎机的工作情况成为可能。破碎腔的几何形状对于工作情况的分析非常关键。由于衬板的几何形状的磨损是变化的，因此破碎机的工作性能也会随之变化，总是处于不利地位。所以它们被希望随着衬板的磨损来仿真尺寸和工作性能的变化。基于这种目的的模型被最早发明出来。这种方法是建立在基础上。这种模型中于破碎腔的上部，磨损量的仿真值和真实值之间存在着差异。关于差异的几种解释被提出来了：有人认为衬板材料的硬化可能依靠其应力。在最近的研究中，被证实破碎腔的磨损模型中使之产生装差异，而使它在工作硬化过程中是个变量。另一些人解释说压力和磨损之间是非线性关系，物料和衬板之间的剪切力取决胜于物料颗粒的大小，磨损率以及估算出的大致压力。在这些有影响力的解释当中，衬板的压力估算被认定为是一个重要因素。而且现有的模型可以准确无误地估算出它的磨损量，但是不能准确地反映液力和功耗。为了进一步正确估算压力，这需要发展流量模型。目前工作和目的是改善现有的流量和压力模型 。2锥体破碎机的模拟流量早在2000年Evretsson就介绍了锥体破碎机的模型。这个模型包含了一个流量模型和一个压力模型，它的流量模型是建立在质量守恒的基础上的，而且它只有单一的模型参数，假设物料颗粒在动锥上部被释放。这时会有三种运动会发生，滑动、自由物料颗粒落体和物料颗粒和衷共挤压。滑动发生在固体物料颗粒接触动锥时，并且发生滑落。如果说物料颗粒速度足够高，物料颗粒会加速离开动锥。然后会自由落体。被模拟的冲击波力是完全可以改变的。例如，速度的法线分量会逐渐消灭，正切分量则会保持。当接触动锥的截止区，物料颗粒会被挤压。在这个阶段，速颗粒会随着动锥转动。计算的结果是一个颗粒穿过破碎机的规迹，其它颗粒也认为按着这规迹运动。（见图三）。在一个行程内颗粒下落的距离称为一个破碎区间。例如，第一个破碎区刘取决于破碎机的容量。运行中正常的离心速度下，物料会因动态和边界的影响而不完全进入这个区域。Evertsson引进了一个模型参数：容量填充率A1时，是因为这种影响。容量填充率由此减少，大量物料进入破碎区域，它也影响材料的压缩量。容量填充量在这个反复的过程中被计算出来。容量填充率之所以第一个被选出，是因为在一定程度上在破碎腔中其容积密度将要达到物料的固体密度。容量填充率是一步步慢慢减少的，直到破碎腔中的物料在没达到物料密度的情况下完全通过。A可以由测量来证实。这种模型被证明是非常准确模拟容量和磨损的模型。在模拟磨损时，有必要计算出动锥所有点上来自物料的压力。它所用到的Evertsson流量模型，这种模型的破碎腔上端的压力是下可预测的。流量模型除不适合磨损预测外，还有其它缺点。如上所述，流量模型意在选一个合适的容量填充率。而使得容积和功耗可以准确地估算出来。例如，很难同时准确地估算出CSS、容量、功耗、液力。22改进的流量模型破碎腔的横截面在不同的高度是变化的，见图四。在横截面积最小的那个高度点被称为阻塞点。这个点被认为是阻塞大量物料通过破碎机的点。在C模型中，认为是动锥末端这个点是阻塞点。在新的模型中，认为物料在阻塞点处受到挤压，从而限制了阻塞点以上物料的流量。模型之所以用到阻塞点。以下的部分，是为了计算在阻塞点处的质量流量，容积密度。而且这个过程是反复的，直到到达阻塞点。（见图五各图六）如果 ,那最初关于判断太少了会增加，直到，是以一个恰当的步骤在增加，它们的乘积是关于V的函数，曲线图就可以绘出，用插值法可以求出一个恰当的V，见图七。在阻塞点以上物料向下流动的原因不同的模型。在阻塞点的下面，随着物料向下的流动，横截面积是增加的，而且随颗粒的进一步下落，它们之间的空间会越来越大，在阻塞点以下，EverSSon的模型还是有效的。因为在阻塞点物料容积不是预先知道的，所以有必要采取反复计算的过程，这个计算过程见图八。23 模型参数一个健全的模型可以根据不同的CSS推定出容量，液力，功率，满足不同破碎腔的设计需要。为了满足这些需要，引进了一个比例因子，也是为了配合压缩率和压力分配角，见图九。在切线方向材料的流量两个参数是物理相关量，当材料被挤压时，压力分配点的材料流量会相应的增加，可用的压力将减少，因此这两个新的比例因子的压缩率物料和压力分配角是成比例的。见图九到十一。这两个因子对空间没有任何影响，但可以明显减少压缩率和压力分配角相对于近似形状来说如果材料的流量在挤压过程中上升或下降很小时，其容量也不会有大的变化，那些增加的面积可有图十一估算出。假定两个箱体的容积是一样的，箱体的长度因其系数F而改变，相应受挤压的大小为S，压缩率可以定为S/b bld=(b-s)fld f= （1）近似压力分配角是，近似分配角的一部分在破碎时是否可以利用，取决于有效行程和近似行程的比值。随着物料的挤压度的增加，压力分配角可以这样计算， (2) 压力分配角取决于和的乘积，所以模型参数可以表示，和。由于容积填充率只影响其空间大小，所以当它达到合适的测量数据时会变大。5、结论 新的流量模型为模拟锥体破碎机破碎提供了工具，见图十三、十四它安装了两个新的标准装置,H3000F和H3000MC.这些破碎腔有着明显的不同, H3000F的破碎非磨蚀性物料,而MC是来破碎磨蚀性物料(见图十二)。这些东西被记载于南瑞典的一个采矿厂里，可以看出操作参数的容积量，液力，及功耗是CSS的函数，也可以预测不同的CSS。轴和轴承的负载通过模拟是计算不出的。在独立承载中功率的损失和压力的损益被认为是20KW和0.2MPa。对每一个尺寸和每一个破碎腔的模型参数进行优化，两种破碎腔最优化的模型参数已列入表格一中。在图十三十四中，当改变功耗、液力、容积时，可以得到不同的CSS，作为一个对照比较，以前的容积模型是为了得到准确的模型参数。而产生了功耗为964KW，压力为9.6mm的HF3000模型。很明显它与真实值有几个百分比的差异 。它们是非线性关系，所以压缩时产量是会变化的。这项研究最根本的目标是改善破碎腔的磨损量。在图十五中展示了以前流量模型和新的流量模型的真实磨损和模拟磨损量。以前的模型在破碎腔的上部存在系统误差。针对这些新的模型会有所改善。图十六展示了名义上和新的模拟量的破碎腔尺寸的磨损。这些适合于不同的功耗。最大破碎腔的磨损量是在四十五个小时内的磨损量。4 讨论如果破碎腔的尺寸有微小变化，如图十三十四中，改变CSS值，这个模型照样可以计算出容积，液力，功耗。这些显示范区这些模型在破碎腔变化很小时也是有效的。表一中可以看出，两种破碎机最人优化有模型参数只有微小差别，发展这种模型最要的是其灵敏度。研磨磨蚀性和非磨蚀性物料的差别看起来很小，但是石料的的挤压是非线线性的。用这种模型来长时间预测操纵参数会出问题的。图十三中有关于它的变化，破碎腔的尺寸和CSS的值有微小变化时，这种模型仍然是有效的。但是如果用了错误的模型参数，你会有趣的发现其运转的好坏。图十七显示了H3000F破碎腔真实的模拟的液力。两个附加的显示了对于这两种破碎腔利用普通模型参数其值偏离真实值大约达到百分之二十五。这种情况表明不同的破碎腔需要不同的模型参数。5 结论和下一步的工作新的流量模型发改善了它的工作参数 ：容积和功耗。几何磨损量也会有相应的改善。如果破碎腔的几何尺寸有微小变化，其参数也会有相应的变化。如果选择了不同的破碎腔，其模型参数也会有相应的变化。一个处理非磨蚀性物料和 磨蚀性物料就有差别。许多关于文章都倾向于进一步的研究。例如颗粒的大小和磨损量之间，轴承压力项对磨损率的影响。Improved flow- and pressure model for cone crushersAbstractCone crushers are used in the aggregates and mining industries to crush rock material. A model was previously developed to predict the worn geometry of a cone crusher. In that model there was some disagreement between predicted and measured geometry. A suggested explanation for the discrepancy is that the flow model used is not accurate enough to predict the pressure and wear on the liners. In this study an alternative flow model is presented that is better adapted for pressure and wear prediction. In the new model, the same mode of motion as in the old model is assumed to occur but only below the choke level of the crusher. Above the choke level it is assumed that downward flow is stopped by other particles that are squeezed further down. To determine the size distribution and bulk density above the choke level, an iterative process was necessary. Simulation results show that the new flow model has improved the accuracy in the prediction of operating parameters of the rock crusher, such as hydraulic pressure, power draw, and close side setting, CSS. There is also some improvement of the prediction of worn geometry as compared to the old model. 1. Introduction Cone crushers are widely used in the mining and aggregates industry to crush blasted rock material. The two main crushing parts are the mantle and the concave. The main shaft of the mantle is suspended on a spherical radial bearing at the top and in an eccentric at the bottom. A hydraulic cylinder supports the bearing that carries the thrust force on the main shaft. The hydraulic pressure in this cylinder is called the hydro set pressure. As the eccentric is turned the rock material will be squeezed and crushed between the liners (see Fig. 1). Along its path along the crushing chamber, a rock particle will be subjected to several crushing events. A typical process layout for an aggregates producer is shown in Fig. 2. The blasted rock is hauled to a primary crusher, usually a jaw- or gyratory crusher. After the primary crusher the rock is fed to a secondary crusher. In the example in Fig. 2 there is also a hopper between the primary and the secondary crushers since the output from drilling/blasting and primary crusher fluctuates. After the secondary crusher there is usually a system of screens, conveyors and tertiary crushers. The rock material is separated by screens into different size distributions and then transported to customers. In many mining applications there is also a grinding step. A common type of machine used as secondary and tertiary crushers, is the cone crusher. Previous research (Evertsson, 2000; Gauldie, 1953) has made it possible to model the behavior of a given cone crusher. The geometry of the crushing chamber is crucial for the performance. Due to wear the geometry of the liners will change, and hence the crusher performance will also change and usually suffer. Therefore it is desirable to simulate the change of geometry and performance as the liners wear. A model for this purpose was previously developed (Lindqvist and Evertsson,)2003a,b). That method was based on the results of Evertsson (2000). In the model for wear prediction there was some discrepancy between the simulated geometry and measured geometry in the upper part of the crusher chamber. Several explanations of this discrepancy were suggested. It was first assumed that the work hardening behavior of the liner material might depend on the applied pressure. In a recent study, it was concluded that it was not a variation in work hardening in the chamber that caused the discrepancy in the wear model (Lindqvist and Sotkovski, 2003). Other suggested explanations are nonlinear dependency between pressure and wear, shear stress at the interface between rock and liner, dependency between particle size and wear rate and inaccurate pressure prediction. Among the other suggested explanations, the prediction of pressure on the liners is assumed to be an important factor. The existing model is suffciently accurate to predict breakage and capacity, but not as accurate in predicting hydro set pressure and power draw. To predict the pressure more accurately it is necessary to further develop the flow model. The aim of the present work is to improve the existing flow- and pressure model.2. Modelling flow in cone crushers2.1. Previous research A model for cone crushers was presented by Evertsson (2000). That model comprises a flow model and a size reduction model. The Evertsson flow model is based on mass balance and it has a single model parameter. A particle is released at the top of the mantle. Three modes of motion can occur: sliding, free-fall and squeezing. Sliding occurs when a particle is in contact with the opening mantle and slides downwards. If the eccentric speed is suffciently high, the mantle surface will accelerate away from the particle that will fall freely. The impact is modelled fully plastic, i.e. the normal component of the velocity is annihilated and the tangential component is preserved. Upon contact with the closing mantle the particle will be squeezed. During the closing phase the particle will follow the mantle. The result of this computation is the path of a single particle through the crusher. All other particles are assumed to move in a similar way (see Fig. 3). The distance a particle falls during a stroke is called a crushing zone. The amount of material that enters the inlet zone, i.e. the first crushing zone, determines the capacity of the crusher. During operation at normal eccentric speeds the material does not entirely fill the inlet zone due to dynamic and boundary effects. Evertsson (2000) introduced the model parameter volumetric filling ratio 1 to account for this effect. The volume eccentric filling ratio hence reduces the amount of material that enters each crushing zone and it also affects the compression of the bed of material. The volumetric filling can be computed in an iterative procedure: is first selected so that the bulk density will reach the solid density of the rock at some point in the crushing chamber. The filling ratio is then decreased in small steps until the material can pass through the crusher without reaching the solid density anywhere in the crushing chamber. can also be verified through measurements. The Evertsson model has been proven to be suffciently accurate for modelling capacity and breakage in cone crushers (Evertsson, 2000). When modeling wear it is necessary to compute the pressure from the bed of rock material at all locations on the mantle. A previous study by Evertsson and Lindqvist (2003) where the Evertsson flow model was used, revealed that the wear and probably also the pressure is under predicted in the upper part of the crushing chamber. The flow model used had also other drawbacks than unsatisfactory wear prediction. As mentioned, the flow model is tuned by selecting an appropriate value for the volumetric filling ratio so that either capacity or power draw is accurately predicted. When adjusting for accurate capacity prediction the power draw will not be as accurately predicted, i.e. it is diffcult to accurately predict all the variables CSS, capacity, power draw, and hydro setpressure at the same time.2.2. Development of improved flow model The cross sectional area of the crushing chamber varies at different levels of the chamber, see Fig. 4. The level where the cross section is at a minimum is called the choke level. The cross sectional area at this level is assumed to limit the amount of material that can pass through the crusher. In the Evertsson model it was assumed that it was the closing of the mantle that limited downward transportation. In the new model, it is assumed that the material squeezed at the choke level restricts the flow of material above the choke level. The Evertsson model is hence used from the choke level and down. In order to compute the mass flow, the bulk density at the choke level is needed. This is not known a priori, so an iterative procedure is necessary. The volume of the first crushing zone is guessed. Since the feed size distribution is known it is possible to compute the bulk density and the inlet zone mass. This amount of material is crushed using the size reduction model developed by Evertsson (2000). The material is then poured into the next crushing zone and the process is repeated until the choke level is reached (see Figs. 5 and 6). If V1 q1 . If V1 is increased in appropriate steps a graph showing V1 q1 and as a function of V1can be plotted and the appropriate V1 can be interpolated according to Fig. 7. The factors limiting the downward flow above the choke level are thus different from those in the Evertsson model. Below the choke level the cross sectional area increases, as the material move down ward, and there is more and more space between particles as they fall further down. Below the choke level, it is assumed that the Evertsson model is still valid. Since the bulk density of the material at the choke level is not known a priori, it is necessary to adopt an iterative procedure. The computational procedure is shown in Fig. 8.2.3. Model parameters A robust model would be able to predict capacity, hydro set pressure and power draw at different for a large variety of chamber designs. To achieve this, another two scaling factors were introduced in order to be able to scale compression ratio and pressure distribution angle (see Fig. 9). There is a physically relevant reason for these new parameters: flow of material in the tangential direction. When the bed of material is squeezed the material will flow in the tangential direction resulting in an increase in the pressure distribution area and a decrease in utilised compression.Hence the two new scaling factors will scale the compression ratio and the pressure distribution angle (see Figs. 911). These factors do not have any impact on the capacity, but will clearly reduce the compression ratio and pressure distribution as compared to what is expected from the nominal geometry. The model parameter scaling the compression ratio is here denoted K1 and the utilized compression ratio is hence computed as (1) If the material flow up/downward during squeeze is assumed to be small, and that the volume of the material does not change much, the increase in area can be estimated according to Fig. 11. The volumes of the two boxes are assumed to be equal. The box changes its length by the factor f as the material is squeezed the distance s. The compression ratio is as usual defined as s/b. (2) The nominal pressure distribution angle is p/2. The fraction of the nominal angle that is utilised for crushing is determined by the ratio between utilised stroke and nominal stroke. As the bed of rock material is squeezed the angle increases, and it is scaled by the factor. The pressure distribution angle is hence computed as (3)Note that the pressure distribution angle is dependent on both K1 and K2. The model parameters are hence de- noted K1, K2 and . Now that the volumetric filling ratio only affects capacity it may become larger than 1when tuned to fit measured data.3. Results The new flow model was implemented in the crusher simulation programmer. Figs. 13 and 14 show the correlation between simulations and data from observations on a SANDVIK H3000 crusher equipped with two sets of new standard liners: H3000 F and H3000 MC. These chamber designs are considerably different; the F chamber is designed for fine crushing and the MC chamber is a coarse crushing chamber (see Fig. 12). The recordings were made in a quarry in Dalby in southern Sweden. As can be seen, the operating parameters capacity, hydro set pressure and power draw as a function of CSS are well predicted for different. Losses in bearings, gears etc. are not computed by the simulation programmer and loss in power draw and hydro set pressure were assumed to be 20kW and 0.2MPa respectively and independent of loading. The model parameters were optimised for each measurement and for each crushing chamber separately. The average optimal model parameters for the two chambers are given in Table 1. As can be seen in Figs. 13 and 14, the operating variables power draw, hydro set pressure and capacity are well predicted for different. As a comparison, the previous flow model tuned for accurate capacity prediction yielded a power draw of 964kW and a hydro set pressure of 38MPa at CSS 9.6mm for an H3000 F chamber, a deviation of several hundred percent. Note that the pressure response is a nonlinear function of compression therefore the output is very sensitive to changes in compression. The ultimate objective of this study was to improve the wear prediction. Fig. 15 shows the measured wear, simulated wear using the old flow model and simulated wear using the new flow model. The old model resulted in a systematic under prediction of wear in the upper part of the crushing chamber (Lindqvist and Evertsson, 2003a). With respect to this, the new model is improved as compared to the old model. Fig. 16 shows nominal new and simulated worn chamber geometries. The simulation was run with constant power draw. The most worn chamber corresponds to about 45h of operation in strongly abrasive4. Discussion If the chamber geometry is slightly changed, such as a change of CSS as in Figs. 13 and 14, the model still predicts capacity, power draw and hydro set pressure well.This suggests that the model is suitable for wear prediction where the change in chamber geometry is small. As seen in Table 1, the optimal model parameters for two different crushing chambers differ sligh
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