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锥式破碎机的发展M.Lindqvist,C.M.Evertsson戴玉贵译摘要:现在矿产业等领域广泛的应用圆锥破碎机,主要用其对石料进行破碎。以前研究了一种模型预测耐磨几何学在圆锥破碎机中的使用,根据那些模型,在实际测量中和预测几何学中产生了不同意见,一些影响被提出用于解释在这个模型中的差异。研究表明,在这个模型中剪切力在破碎机表面的作用是可以实现的。模拟法和测量法相比得出的是两个不同的破碎腔。结果展示了一个具有重要意义的进步是关于测量和模拟几何是存在差异的。测量法是在粗破碎腔内进行的,同时也是追踪那些热定型参数压力,能量和容量等,还有就是对衬板的安装了。模型的操作参数表现出了一些和测量法得到的数据的相同的地方,但是破碎机并不是一直在理想工作状态下运行的。1介绍圆锥破碎机被广泛的应用于矿产业等领域,主要用来破碎爆破后的石料。破碎机两种主要的部件是动锥和定锥,动锥的主要传动轴上端悬挂于顶部的横梁上,下端插入偏心套筒中,一个液压装置支撑着大齿轮,用于抵消来自于主轴的负载力,这个液压装置可以升高主轴,以补偿动锥和定锥的磨损。液体在液压缸内所产生的压力支撑来自于主轴的偏心力,这个称为液压。当偏心轴转动时,石料就会因为挤压而破碎。当石料通过破碎腔的时候,一个大块的石料会被破碎为几个小块,在通过破碎腔的最短距离被称为边缘接近设定CSS。对于破碎机的运行这是一个很重要的可以变化的数值。控制系统会连续的将CSS保持在一个固定值。在以前关于破碎机模型中所作的研究中认为这个方法是可行的。Evertsson发明了一种动态模型,一个缩小了的压力反应模型。破碎腔的几何学对于破碎机的运行是极其重要的。出于对耐磨性的考虑衬板的几何将会改变。对于困扰了破碎机有害的影响也将会被改变。这个对于衬板的形状的改变的磨损是合意的。以前曾经做过这个方面的研究。这个模型是建立在Evertsson的研究基础上的。在这个模型中在破碎腔的较高的位置上对于磨损的预测在模拟几何和测量中是有一些差异的。好几种对于差异的解释被提出。第一个假设是由于直接压力使工作表面衬板的材料变得更为坚硬。在一项研究中,一位学者将其归结为:在破碎腔内工件表面变硬使其不再是一个可变量,导致了在磨损模型中的差异。在其它的一些对于差异的解释中,有一些是由Lindquist和Evertsson共同提出的,在衬板上对于压力的预测被假设为一个很重要的因素。通过这些,一个提高了的,动态压力模型被Lindqvist和Evertsson提出,这个模型在预测操作规范CSS中显示了一个重要的进步,破碎强度和破碎的容量,但对于好的破碎机的工作腔的磨损预测只是一个较小的改进。其它的解释是附属于压力和摩擦间的非线性关系的。在无聊和破碎工作面的剪切力的大小,主要由无聊的大小和摩擦率决定。在一个光滑磨损的实验中Chenje和Radziszewski证明了破碎力和磨损率之间的非线性关系,如果Chenje的结果同样能在圆锥破碎机中适用那么非光滑摩擦至少在某种程度上解释了这种差异。在当前的研究中,以这种技术去测量衬板类似于Rosario对于这种技术的使用,他在旋回式破碎机中制定了衬板的磨损标准。在那么多可能的却又达不成一致的解释中,物料和衬板之间的剪切力是唯一在所有的文章中涉及到的。2.方法2.1磨损原理Archard提出了破磨原理,他认为磨损是由破磨的距离和所产生的力等特性所决定的。在以前的研究中作者也提出了磨损即使石料和衬板间没有滑落运动它也会发生的,这是圆锥破碎机的一种情况,动锥空转时也会与石料的基座发生相对运动至少在一个方面,在那个时候的动锥平衡,在动锥和基座间有一个纯粹的转动在其它方面,下滑运动是很小的。当定锥被设计为一个理想的圆锥和将动锥悬挂在横梁上。Archard提出的磨损模型认为磨损率的特性是由快速下滑所决定,如果一个损坏的破碎机衬板被检查过,没有沟槽被发现,那么在石料的基座和衬板的表面就不会有由于压迫而产生的相关的运动,当石料被破碎后重新分布,但这种运动的分布是随意的。由Archard提出的破磨模型是依靠圆锥破碎机中快速下滑的情况而作出的,相当于无磨损。Lindqvist和Evertsson采纳了破磨模型并将其使用于圆锥破碎机。这个模型对于磨损的预测,根据Lindqvit和Evertsson的描述猜测在破碎事件发生时,磨损的数量在单一破碎运动中对于最大平均压力值P来说是想称的。在这W是等同于磨损的持续作用一种物质的参数对于每个混合起来的岩石和钢都是独一无二的。磨损W的单位是mm压力单位是N/vmm2,将其进行转化得到磨损的持续单位是N/mm3。平均压力在Eq的解释中包含有大量的在刚体表面所产生的接触载荷,磨损的发生在机器的刚体上是它的一个功能。大量的表面载荷以及形状和岩石颗粒的机械特性。磨损持续作用W是由岩石和钢的机械特性所决定的,它会在实验中或大范围测量中改变。Eq在先前的研究中发现磨损持续参数是94kn/mm3.石英与锰钢的结合有很高的研磨作用。这表明在那个研究中,磨损模型和破碎模型的结合使对于破碎腔上部的磨损可以进行预料。这里的目标是提出一个模型可以对差异进行解释。如图6所示,如果一个颗粒在斜面上受压,剪切力会和啮合角一起增大,在几个涉及以及部分调查的原因中,剪切力在接触面被假设改变表面的压力单元和提高磨损率。正如提到的,这是不可能在磨损的衬板表面发现任何一个沟槽。这表示没有滑落运动,在石料和钢表面摩擦力并没有充分被应用。如果一个颗粒在斜面上被挤压在其接触表面的剪切力是可而已计算出来的。如图7所表示的那样颗粒在两斜面间被挤压。石料没有下落,摩擦力并没有完全被使用。图中的摩擦力Ft可以被分解为摩擦因素f和普通力N。因为摩擦力并未完全应用。所以f=u,u是摩擦力的有效因素。如图7所示,平衡要求。如果计算出的因素f超过有效摩擦那么物料就会下落。在这破碎模型中,Evertsson和Lindqvist提出了压力是可以通过压力反馈模型计算出来的。压力反馈和压缩率以及颗粒的尺寸等的变化有一定的关系。第二步的主要体现在两个变化(压缩和尺寸的变化)是符合证明结果的。全压Ptot也能通过压力反馈模型计算出来。所以在物体表面的剪切力Pshear和一般压力Pnormal可以通过式子(6)和(7)解出来。这里的Ptot是从压力反馈模型计算出来的全压,因此假设的磨损模型可以看作k在这里表示一个新的参数,表示当无下滑运动产生时剪切力的作用。在相同的负载下,下滑磨损在鄂式破碎机中比单纯的压力磨损快36倍。2.2磨损的测量测量设备在以前的圆锥破碎机中被用来测量损坏的程度。这种方法和以前 Rosario用过的方法相似。当探测工具检查工具检查到动锥和定锥的表面的一个地点时,破碎机就会被停止。这个装置被作为一个结构依附于破碎机的主轴上,步进电机通过一死杠的转动传递一个载荷。然后传到探测器,窜动的数值会被送到步进电机的一个位置也就是测量的那个结构,当该结构接触到衬板控制系统会停机,并将跳动数据记录,这些跳动数据接着将会被转换到坐标系中。这次的测量是在NCC,这地方离开Goteberg,Sweden大约往东70km。这是一台二手的SANDVIK H6800型的破碎机,有一个粗破腔,送入其中的无聊是32250mm的已经在鄂式破碎机中破碎过的。3.结果3.1测量将坐标中的数据进行传输,这测量结果通过CAD工具显示如图10,同部分截面相比较,显示了一个破损的几何图形。3.2破损的积累测试在破碎模型中,破损衬板的数据常被运用其中。图11表示破损的动锥数据在不同时间,有两种不同的磨损的模型。左边的那数据显示,破损的旧的几何形状主要是由于剪切力所造成的,右边的数据显示磨损的是新的剪切应力造成的。对于上破碎腔的磨损,有两种截然不同区别存在于这两种模型中,无摩擦剪切力的作用是连续的积累所以能被测量。破损模型中,参数k在式(8)中被选择为了使磨损能在衬板上的两点被正确预测,在动锥的底部附近是最大磨损发生的地方。另一点是在衬板的顶部附近,在破碎腔中的顶点往下三分之一处。当k=50是最为恰当的,一剪切力的破损因素也许看起来高了点,但剪切力磨损因素f在式子(5)是小了点,因此和衬板的夹角也小了一点。图12表示在H6800的动锥上的磨损积累,磨损在一般新的和磨损过的上面得出的数据是不同的,从七一般的表面测量来说。从图12中可以看出,和旧的模型相比,新的磨损模型破碎腔上部的比预测的要严重的多,在这使用的反馈性是由Lindqvist提出来的。图13表示的是一个破损的SANDVIK H3000 MF定锥破碎腔中的磨损积累。这一测量是由Lindqvist和Evertsson来完成的,高强度石英被破碎,这一过程和在Evertsson提出的反馈模型中完成的,这一模型和在这里使用的有一点不同。图12表示的是Sandvik,H6800破碎机上动锥的磨损,而图13标号司的是Sandvik,H3000 MF定锥上的磨损。动锥和定锥有不同的坐标系统,因此在y坐标中这是不同的。3.3参数测量压力和粉磨可以从控制面板上读出来,当出料口被石料堵塞的时候,就应该进行处理。对于圆锥破碎机来说,这实际一个惯用的方式,读数表示应该进行一般的操作, 例如喂入的石料一般是经过初破以后的32250mm的石料。磨损模型和次数并无大小的关系,磨损率在积累方面被夸张了,为了节省次数,Lindqvist和Evertsson在研究中发现,当超过4700次的时候,磨损速度就会加快,例如喂入的石料一般是经过处破以后的32-250mm的石料。 图14表示了粉末和压力之间的关系对于自动和破碎压力的要求一些参数被证实。在这所作的统计,选择的模型的参数对粉末和压力的预测尽可能像平均值那样精确。粉末和压力是不可能在遗漏数据的情况下如此精确的。这样情况的发生在圆锥破碎机中主要是由电机转速提高而导致的,带驱动齿轮由主轴驱动,这种遗失发生在齿轮的顶部,其它的都是由齿轮来传动的,通过机器特性这种破碎机一般有3035kw的驱动力。大部分主轴的压力在0.28MPa。为了减少压力损失,负荷应该加一些常数来进行平衡。一个连续的负载丢失35kw,被加到负载丢失,经计算,区分七一般能量从点能量中,其中的能量转化率59%,在电机带轮,主轴,齿轮,这些传输过程中能量的遗失大约为10%。Lindqvist在一台H3000MC的破碎腔中发现这两种模式的参数是K1=0.3590和K2=1.2387. 通过读上图一般一天清理一次。这些都是非常特别的数据,每天每小时每个破碎机的操作都会被记录,当然在8小时以下。这意味着一个不精确的记录,少于8小时,正如数据的积累那样,正如测量的那样,在坐标中生产那些相同数量的最大磨损在动锥上被记录。最大模拟磨损坐标直接指向模拟时间,在最后的测量中动锥的磨损是48mm。在破碎机工作的那天,测量的容量就已经全部记录下来了,这一破碎机是一个二手货,当设计一个破碎装置,在其组合中是存在瓶颈的,这意味着接下来的安装,将会多次不恩能够正常工作,也许他将不恩能够进行清理,因此测量容量是很麻烦的。这就是产量和预测不符合的原因。在一些移动中,被安置破090的材料在二手破碎中,在其它的一些移动,读数是行不通,这些移动是不可能涉及的,对于大多数机器的一般用途,少于10%的破碎机被用来破099mm的材料。4.讨论这个研究的目的是提高破碎机模型产量,通过增加一个剪切力将其整合在磨损模型中。正如提到的在以前的研究中,在破碎腔的上部的磨损在模型和实际中是存在差异的。在Lindqvist的研究中,在一个扩大了的反馈模型中被提出,粉末产量和压力等都被认为提高了。对于破碎腔完好的破碎机来说,对于预测的磨损会有所提高。在一粗破腔内运行模型时,这时显然被估计下破碎腔上部的磨损将更糟糕。在实际与模型中的不同点是由破碎腔引起的,当啮合角变大时。结论是在以前的反馈模型中的不精确并不是什么导致了差异,甚至,那些操作参数在预测中的提高。另一种假设的解释是差异是由颗粒大小,数量以及其与表面接触时发生的,更多的。动锥的主轴在旋转时与岩石的相对运动发生在破碎腔的上部,不管这些因素,在粗破碎腔中,和好的破碎腔的,因为动锥和破碎腔的类型差不多,然后定锥的形状和衬板间的啮合角应和破碎腔的类型有所不同。这是题目首先所涉及的。一个重要的问题是模型的参数是否如Lindqvist和Evertsson所描述的那样,依然衬板的破损,粉末和压力的测量如图15和16那样,这些波动不可以通过磨损来解释,例如在8月份读取的数据关于粉末和压力的都比一年中的其它时期要高。没有明显的产量优势可以被看见。可能的原因是岩石的特性在这时期发生了变化。当石料经过爆破以后被运进破碎机,不一样的地方的石头的特性是不同的。破碎机是不可能总是进行清理的。这解释了低于预测的容量,在少于10%的破碎机,被用于破碎090mm的材料,那意味着产量,粉末和压力都提高了,我们可以知道粉末和压力并没有在这工作条件下发生,在那时,磨损的方式也许是不同的。这时期不一样的操作条件少于10%的时间会在模型中被忽略。5.结论和展望在圆锥破碎机中通过增加一个剪切力的因素在模拟和实际中对于达成一致的是产量增加了。对于操作参数中的粉末和压力的预测是令人满意的。但这两参数还是波动的。如在秒年米毫秒年的部分涉及到的那样,也许有其它的可能的原因,解释模型总的差异,例如颗粒大小,压力和磨损率之间的非线形关系。这个破碎模型在这个模型中可以被表示为一个“灰盒子”模型。介绍更多的参数去描述更多的现象,也许最终会找到客观的模型参数。虽然这模型在这被提出,成功的解决了涉及到的问题,将来的工作需要全面理解其它方面变化的重要性。12Wear xxx (2006) xxxxxxDevelopment of wear model for cone crushersM. Lindqvist, C.M. EvertssonDepartment of Applied Mechanics, Chalmers University of Technology, SE 412 96 G oteborg, SwedenReceived 30 March 2005; received in revised form 2 November 2005; accepted 12 December 2005AbstractConecrushersareusedintheaggregatesandminingindustriestocrushrockmaterial.Amodeltopredicttheworngeometryofconecrusherswaspreviouslydeveloped.Inthatmodeltherewassomedisagreementsbetweenpredictedandmeasuredgeometryandseveraleffectsweresuggestedtoexplainthediscrepancyinthemodel.Inthisstudytheeffectofshearforcesalongthecrushingsurfaceswasimplementedinthemodel.Simulationswere compared to measurements on two different crushing chambers. The results show a significant improvement with respect to the discrepancybetween measured and simulated geometry. Measurements were made on a coarse crushing chamber where the operating parameters hydrosetpressure, power draw and capacity were tracked during the lifetime of the set of liners. The simulated operating parameters show some agreementwith measured data, but the crusher was not run under ideal conditions at all times. 2005 Elsevier B.V. All rights reserved.Keywords: Comminution; Crushing; Modelling; Abrasive wear; Cone crusher1. IntroductionCone crushers are widely used in the mining and aggregatesindustry to crush blasted rock material. The two main crushingparts are the mantle and the concave. The main shaft of themantle is suspended on a spherical radial bearing at the top andin an eccentric at the bottom. A hydraulic cylinder supports thethrust bearing that carries the thrust force of the main shaft. Thehydraulicsystemcanraisethemainshaftinordertocompensatefor the wear of the mantle and concave. The hydraulic pressurein the cylinder that supports the thrust force from the main shaftis called the hydroset pressure. As the eccentric is turned therock material will be squeezed and crushed between the liners(see Figs. 14).Along its path through the crushing chamber, a rock parti-cle will be subjected to several crushing events. The shortestdistance across the crushing chamber is called the closed sidesetting,CSS,andisanimportantvariablefortheperformanceofthe crusher. The control system is calibrated regularly to main-tainaconstantCSS.Previousresearch1,2hasmadeitpossibleto model the behaviour of a given cone crusher. Evertsson 1Corresponding author. Tel.: +46 31 772 13 76; fax: +46 31 772 3872.E-mail addresses: mats.lindqvistme.chalmers.se (M. Lindqvist),cmemvs.chalmers.se (C.M. Evertsson).developed a flow model, a size reduction model and a pressureresponse model.The geometry of the crushing chamber is crucial for the per-formance. Due to wear the geometry of the liners will change,and hence the crusher performance will also change and some-times suffer. Therefore it is desirable to simulate the change ofgeometry and performance as the liners wear. A model for thispurpose was previously developed 3,4. That model was basedon the results of Evertsson 1. In the model for wear predictionthere was some discrepancy between the simulated geometryand measured geometry in the upper part of the crushing cham-ber3.Severalexplanationsofthisdiscrepancyweresuggested.It was first assumed that the work hardening behaviour of theliner material might depend on the applied pressure. In a studyby the author 5 it was concluded that it was not a variation inwork hardening in the chamber that caused the discrepancy inthe wear model.Among the other explanations for the discrepancy, that wereproposed by Lindqvist and Evertsson 3, the prediction ofpressure on the liners was assumed to be an important fac-tor. To address this, an improved flow- and pressure modelwas presented by Lindqvist and Evertsson 6. That modelshowed a significant improvement in prediction of the oper-ating parameters CSS, power draw and capacity, but only aslight improvement of wear prediction for a fine crushingchamber.0043-1648/$ see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.wear.2005.12.010WEA-97899;No. of Pages 82M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxxFig. 1. Cone crusher, schematic image.Fig. 2. Operating principle of cone crusher.Fig. 3. An H8800 hydrocone crusher. This particular model is nearly 5m high.Fig. 4. A new set of crusher liners, mantle and concave.Other suggested explanations are non-linear dependencybetween pressure and wear, shear stress at the interface betweenrock and liner, dependency between particle size and wear rate.ChenjeandRadziszewski7showedthattherewasanon-linearrelationship between applied force and wear rate in a slidingwear experiment. If Chenjes 7 results were also applicablefor the case of non-sliding wear in cone crushers, they would, atleast in part, explain the discrepancy. The technique used in thepresentstudy,tomeasurethegeometryoftheliners,issimilartothe technique used by Rosario 8. He has made measurementsof liner wear on gyratory crushers.Among the possible explanations of the disagreement in themodel, shear forces in the contact between rock and liner is theone that is addressed in this paper.2. Method2.1. Wear modelThe wear model presented by Archard 9 suggests that wearis proportional to sliding distance and applied pressure. In theprevious work carried out by the author 10 it was found thatwear occurs even if there is no macroscopic sliding motionbetweenrockmaterialandliner.Thisisthecaseinaconecrusherwhere there is no macroscopic sliding motion between liner androck. The mantle is free to roll against the bed of rock mate-rial. On at least one point, the point of moment equilibrium forthe mantle, there is pure rolling between the mantle and bedof material. At other points the relative sliding motion is verysmall,sincetheconcaveisdesignednearlyasanidealconewiththe generatrix of the mantle intersecting the pivot point of themain shaft (see Fig. 5).The wear model presented by Archard 9 suggests that thewear rate is proportional to sliding velocity. If a worn crusherliner is inspected, no ploughing grooves can be observed. Thewearmechanismissqueezingwearwithoutmacroscopicrelativemotion between the bed of rock particles and the steel surface.On a small scale there is of course some relative motion sinceM. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx3Fig. 5. Mantles are designed nearly as an ideal cone whose generatrix intersectsthe pivot point of the main shaft.particles are rearranged as they are crushed, but the direction ofthis motion is random. A wear model like Archards 9 that isdependentofslidingvelocitywouldinthecaseofconecrushers,yield no wear. Therefore, Lindqvist and Evertsson 3 adaptedthe wear model used for cone crushers.In the model for wear prediction, described by Lindqvist andEvertsson 3 it is proposed that the amount of wear in a singlecrushing action is proportional to the maximum average pres-sure p that occurs during the crushing event (see Eq. (1). Inthis constitutive equation W is the wear resistance coefficient, amaterialparameteruniqueforeachcombinationofrockmaterialand steel. Wear w is here expressed in mm, pressure in N/mm2,and hence the unit for the wear resistance will have the unitN/mm3.?w =pmaxW(1)The “average pressure” expressed in Eq. (1), consists of alarge number of contact loads of different magnitude actingon the steel surface. The wear that occurs is a function of themechanical properties of the steel, the number and magnitudeof the contact loads, and the shape and mechanical propertiesof the rock particles. The wear resistance coefficient W is deter-mined by the mechanical properties of the steel and rock, and isverified in experiments or in full-scale measurements.The wear resistance parameter W in Eq. (1) was found to be94kN/mm3in a previous study 3. The material was highlyabrasive quartzite in combination with austenitic manganesesteel. It was shown in that study that the wear model in com-bination with the crusher model yielded an under-prediction ofwear in the upper part of the crushing chamber. The objectivehere is to present a model that will address this discrepancy.If a particle squeezed between oblique surfaces, as in Fig. 6,the shear force increases as the nip angle increases. Among sev-eralmentionedandpartlyinvestigatedreasons,ashearforceinaFig. 6. The nip angle between the liners is larger for a coarse crushing chamber(left) than for a fine chamber (right).contactishereassumedtochangethestressstatearoundthecon-tact and increase the wear rate. As mentioned, it is not possibleto observe any ploughing grooves on a worn liner surface. Thisindicates that there is no macroscopic sliding motion betweenthe rock particles and the steel surface and that friction is notfully developed.If a particle is squeezed between oblique surfaces, the shearforce in the contact can be computed. Consider the particlesqueezed between two oblique surfaces in Fig. 7. Since the par-ticle does not slip, the friction is not fully developed.The tangential frictional force Ftcan be decomposed as theproduct of a frictional factor f times the normal force N. Sincefriction is not fully developed f where is the coefficientof friction. With reference to Fig. 7, equilibrium require thatN = F cos2(2)fN = F sin2(3)Fig. 7. Shear forces are present when a particle is squeezed between obliquesurfaces.4M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxxFig. 8. Simulated pressure distribution on a mantle used with an H6800 ECconcave.: fN cos2= N sin2(4)f = tan2(5)If the computed factor f exceeds the coefficient of friction,the particle will slide.In the crusher model, the pressure is computed accordingto the pressure response model presented by Evertsson andLindqvist 4. The pressure response model relates compres-sion ratio (i.e. the compressive engineering strain of the particlebed: deformation/original thickness), and variational coefficientof the particle size distribution to crushing pressure. A second-degreepolynomialintwovariables(compressionandvariationalcoefficientofsizedistribution)wasfittedtotestresults.Thetotalpressureptotiscomputedusingthepressureresponsemodel(seeFig. 8).So the shearstress pshearand normal pressure pnormalat thesurface is hence computed according to Eqs. (6) and (7).pnormal=1?1 + f2ptot(6)pshear=f?1 + f2ptot(7)where ptotis the total pressure computed from the pressureresponse model. The proposed wear model hence looks as:?w =1W(pnormal+ Kpshear)(8)Here K is a new model parameter that scales the effect of theshear force when there is no slip. Sliding wear in a jaw crusherhasbeenfoundtobethreetosixtimesfasterthansqueezing-onlywear, at the same crushing load 10.Fig. 9. Measurement rig.2.2. Wear measurementsA measurement rig that was previously developed for mea-suring the worn geometry of cone crushers was used. Themethod resembles the one used by Rosario (2004). The crusheris stopped and a probe detects the location of the surfaces ofthe mantle and concave. The device is made of a frame that isattached to the main shaft of the crusher (see Fig. 9). A stepmotor moves a carrier by turning a threaded rod. Small steppingmotors send out probes. The number of pulses sent to the stepmotor corresponds to a certain position relatively to the measur-ing frame. When a probe contacts the liner the controller stopsthe motor and the number of pulses is registered. The numberof pulses is then converted into geometric coordinates.The measurements were carried out at the NCC quarrylocated approximately 70km:s east from G oteborg, Sweden.The crusher was a secondary SANDVIK H6800 crusher, witha coarse crushing chamber. The material fed to the crusher was32250mm granite that had previously been crushed in a pri-mary jaw crusher.3. Results3.1. MeasurementsThe coordinates from the measurements were transformed,andthemeasuredgeometrywasenteredintoaCAD-tool.Fig.10Fig. 10. Measured geometry compared with a 3D-CAD model of mantle andconcave.M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx5Fig. 11. Simulated geometry of a worn mantle profile at different times, usingtwo different wear models.showsthemeasuredworngeometry,comparedtoacrosssectionof the nominal CAD-geometry.3.2. Simulation versus measurement of wearThe worn liner profiles were computed using the crushermodel. Fig. 11 shows worn mantle profiles at different times,using the two different wear models. The left profile shows theworn geometry obtained using the previous wear model that isindependent of shear forces. The right profile shows the worngeometry from the new shear-dependent wear model. There isan obvious difference between the two models in prediction ofwear in the upper part of the chamber. The effect of non-slidingshear force is scaled so that simulations fit measured data. Thewear model parameter K in Eq. (8) was selected so that the wearwas correctly predicted at two points on the liner: where themaximum wear occurs, near the bottom of the mantle, and ononepointlocatednearthetopoftheliner,one-thirdofthecham-berheightfromthetop.K=50givesthebestagreement.Ashearwear factor of 50 may seem high, but the shear force factor f inEq. (5) is small, since the angle between the liners is small.Fig.12showsthemeasuredandsimulatedwearonanH6800mantle.Theweariscomputedasthedifferencebetweennominalnew and worn geometry, measured in the normal direction ofthe surface. As can be seen in Fig. 12, the new wear modelsignificantlyimprovesthewearpredictionintheupperpartofthecrushing chamber compared to the old model. The flow modelused here was presented by Lindqvist 6.Fig. 13 shows simulated and measured wear on the concaveof a worn SANDVIK H3000 MF chamber. The measurementin Fig. 13 was made by Lindqvist and Evertsson 3. Highlyabrasive quartzite was crushed. The simulation in reference 3Fig. 12. Simulated and measured amount of wear on the mantle of an H6800EC liner set. The geometry was measured in the normal direction of the surfaceafter 385h of operation.was made with the flow model presented by Evertsson 1. Thatmodelisslightlydifferentfromtheoneusedhere.Fig.12showsthe wear on the mantle of a Sandvik, H6800 crusher, Fig. 13shows the wear on a Sandvik H3000 MF concave. The mantleand the concave have different local coordinate systems in thesimulator, hence the difference in y-coordinate.3.3. Simulation versus measurement of operatingparametersHydroset pressure and power draw were read off the controlpanel of the crusher once every day. When the inlet bin of thecrusher is entirely filled with rock material, the crusher is saidto be choke fed, and this is the preferred way to operate a conecrusher. Readings were taken during normal operation of thecrusher, i.e. choke fed conditions. The feed was between 32 and250mm and came from the primary crusher.Fig.13. SimulatedandmeasuredwearonaconcaveofaSANDVIKH3000MFchamber. Measurements were made by Lindqvist and Evertsson 3.6M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxxFig. 14. Correlation between power draw and hydroset pressure.The wear model is indifferent to how time is scaled, and thewear rate is exaggerated in the simulations, to save computa-tion time. The wear was accelerated by a factor of 4700 times,as compared to the wear rate found by Lindqvist and Everts-son 3. If the wear rate is accelerated too much, the simulatedworn geometry will deteriorate as compared to the measuredgeometry.Fig. 14 shows the correlation between power draw andhydroset pressure. The model for flow and crushing pressurerequire a validation of some model parameters 7. In the sim-ulations made here, the model parameters were selected so thatpower draw and hydroset pressure were predicted as accuratelyas possible with respect to average measured data. Power drawand hydroset pressure cannot be predicted accurately withouttakinglossesintoaccount.Lossesinaconecrusherarisemainlyin the electric motor, the belt drive, the roller bearings support-ing the driveshaft. Frictional losses occur in the top bearing, theeccentric bushings and the spherical thrust bearing who are allboundary lubricated plain bearings. According to the machinemanufacturer, this particular crusher usually has an idle powerdraw of 3035kW. The mass of the main shaft corresponds toa hydraulic pressure of 0.28MPa. To adjust for losses, loaddependent and load independent losses were simply added tothe nominal data to make simulations match measured data. Aconstantloadindependentlossof35kWwasaddedtothepowerdraw and the load dependent loss was computed by dividing thenominal power draw by the total efficiency. The efficiency usedhere was 59%. If the losses are subdivided onto electric motor,beltdrive,driveshaft,bevelgearandeccentricbushing,theaver-age efficiency of each of these power-transmitting componentswillbeabout90%.ThetwomodelparametersforanH3000MCchamber that were found by Lindqvist 6 were K1=0.312 andK2=1.01. For this crusher, which is much larger, K1=0.3590and K2=1.2387.Readings of power draw and hydroset pressure were takenduring normal choke fed conditions once every day (seeFigs. 15 and 16). The time of these readings were only specifiedby date. The number of hours per day each crusher was in oper-ation was recorded, and was below 8h every day. This meansFig. 15. Power draw, simulation and measurement.there is an inaccuracy of less than 8h as for when each read-ing was made. Simulated time has here been expressed as dates.Simulated time corresponds to the time it takes for the modelto produce the same amount of maximum wear on the mantleas is measured. In other words, maximum simulated wear cor-responds directly to simulated time. The maximum wear on themantle was 48mm in the last measurement.The measured capacity of the crusher was computed as thedaily output divided by the number of hours the crusher was runthat day. The crusher is a secondary crusher. When designing acrushing plant the components are generally over-dimensionedandtheplantbottleneckisplacedlateintheprocess.Thismeansthat the rest of the plant, at times will be under-utilised, and thecrusher may not be choke fed. The measured capacity hencefluctuates. This is the reason why the capacity is generally overpredicted.During some shifts, the plant was set to crush 090 materialin the secondary crusher, and during those shifts readings ofpower and hydroset pressure were not taken. Those shifts areFig. 16. Hydroset pressure, simulation and measurement.M. Lindqvist, C.M. Evertsson / Wear xxx (2006) xxxxxx7not representative for the most common use of the machine,which is set to crush 090mm material less than 10% of thetime.4. DiscussionThe aim of this study was to improve the crusher model byaddingashearforcedependentcomponentinthewearmodel.Asmentioned,inapreviousstudy,therewasadiscrepancybetweensimulationandmeasurementintheupperpartofthechamber4.In the study by Lindqvist 6, an enhanced flow model was pre-sented and the prediction of power draw, capacity and hydrosetpressure improved considerably. There was a slight improve-ment in prediction of wear for a fine crushing chamber. Whenrunning simulations with the new flow model on a coarse cham-ber,itbecameapparentthattheunder-predictionintheupperpartof the chamber was even worse (see Fig. 11). The disagreementbetweenthemodelandmeasurementwasthusmorepronouncedforthecoarsechamber,wherethenipanglebetweenthelinersislarger.Theconclusionisthattheinaccuracyinthepreviousflowmodel was not what caused the discrepancy, even though therewasanimprovementinpredictionofotheroperatingparameters.Another proposed mechanism that could explain the discrep-ancy is that wear is dependent on particle size and number ofcontactpointsthatoccur.Furthermore,therotationofthemantledeviates from ideal rolling against the rock in the upper part ofthe crushing chamber (see Fig. 5). None of these effects how-ever, are likely to be more pronounced in a coarse chamber thanin a fine crushing chamber, since the mantle does not differmuch between the chamber types. The shape of the concavehowever, and the nip angle between the liners does indeed differbetweenthechambertypes(seeFig.6).Thereforethisissuewasaddressed first.An important question is whether the model parametersdescribed by Lindqvist and Evertsson 6, remain valid as lin-ers are worn. The measured power draw and hydroset pressurefluctuatesconsiderably(seeFigs.15and16).ThesefluctuationsFig. 17. Simulated and measured capacity.cannotbeexplainedbywear;considerforexamplereadingsdur-ing August when power draw and hydroset pressure is higherthan during the rest of the period. No corresponding trend incapacity can be seen. The likely reason is that the properties ofthe rock have changed during this time. The rock is blasted andhauled to the crushing plant from different locations in the pit,and rock properties generally differ between different locations.The crusher was not run choke fed at all times. This explainsthe under-prediction of capacity (see Fig. 17). During lessthan 10% of the crushers operating time, it was set to crush090mm material, which means that cap
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