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中期汇报表学生姓名XX专 业XX学 号20140601406设计（论文）题目矿山简摆颚式破碎机的设计毕业设计（论文）前期工作小结前期我主要完成了与课题相关的分析工作，通过对相关文献的资料进行收集,分析，和总结，选出了与设计相关的资料备用，分析一些关于绘画简摆颚式破碎机的结构和要求。对整体结构进行了系统的分析，寻找最佳的设计方案，按时完成了前期的工作计划，并开始为下一阶段做好准备。以下是我前期完成的工作：(1) 收集整理中英文参考文献，对命题有了初步认识(2) 通过与老师的商量探讨确定了论文的设计大纲(3) 通过文献的通读研究撰写了论文初稿(4) 对外文文献进行了外文翻译工作指导教师意见签名： 年 月 日中期情况检查表 学院名称： XX 检查日期：2018 年 4 月 22 日学生姓名XX专 业XX指导教师XX设计（论文）题目矿山简摆颚式破碎机工作进度情况1. 收集整理中英文参考文献，对命题有了初步认识；2. 通过与老师的商量探讨确定了论文的设计大纲3. 通过文献的通读研究撰写了论文初稿4. 完成了任务书以及开题报告的提交5. 对外文文献进行翻译工作 是否符合任务书要求进度是 能否按期完成任务能 工作态度情况(态度、纪律、出勤、主动接受指导等) 质量评价(针对已完成的部分) 存在问题和解决办法 检查人签名 教学院长签名 ARCHIVESOFMETALLURGYANDMATERIALSVolume 582013Issue 3DOI: 10.2478/amm-2013-0092S. WOLNYDYNAMIC BEHAVIOUR OF A VIBRATING JAW CRUSHER FOR DISINTEGRATION OF HARD MATERIALSDYNAMIKA WIBRACYJNEJ KRUSZARKI SZCZKOWEJ DO ROZDRABNIANIA MATERIAW TWARDYCHOne of the trends in design solutions of crushers ensuring the crushing ratio of about 30 involves the application of thevibratory-impulse action to the material to be crushed. Crushers utilising these effects are referred to as vibratory crushers.During the vibratory crushing the material to be disintegrated is subjected to the action of fast changing shearing forces, whichleads to the material being crushed either by applied impulses or by fatigue action, unlike conventional crushers where thestructure of the material is damaged by the applied pressure.A dynamic analysis of the vibrating jaw crusher operation is provided and its potential application to crushing hardmaterials, such as alloy materials containing iron and slag from metallurgical processes are explored.Keywords: crusher, dynamic, disintegrationJednym z kierunkw poszukiwa rozwiza konstrukcji kruszarek w ktrych uzyskuje si stopie rozdrobnienia okoo30 jest wykorzystanie efektu udarowo wibracyjnego oddziaywania na kruszony materia. Kruszarki wykorzystujce tzasad dziaania nazywa si kruszarkami wibracyjnymi. Zasada wibracyjnego rozdrabniania polega na poddaniu rozdrabnianegomateriau dziaania szybko zmiennych si ciskajcych, co w rezultacie powoduje rozdrobnienie materiaw udarem, wzgldziena zasadzie zmczeniowej, a nie jak w klasycznych kruszarkach, niszczenie struktury materiau zgniotem.W opracowaniu po przedstawieniu analizy dynamicznej pracy kruszarki wibracyjnej wskazano na moliwoci jejwykorzystania do rozdrabniania materiaw trwaych, w tym elastostopw oraz uli metalurgicznych.1. IntroductionJaw crushers are widely used crushing machines. Theyare used for disintegration of hard and medium-hard materialsto obtain various product size. They are robust, their designand construction is relatively simple, they are easy to oper-ate and maintain. Alongside those obvious advantages, theyexhibit a number of drawbacks, too, including: low crushingratio (of the order of 5), large inertia loading to foundations,large mass.One of the trends in design solutions of crushers ensur-ing the crushing ratio of about 30 involves the application ofthe vibratory impulse action to the material to be crushed.Crushers utilising these effects are referred to as vibratingcrushers. During the vibratory crushing the material to bedisintegrated is subjected to the action of fast changing shear-ing forces, which leads to the material being crushed eitherby applied impulses or by fatigue action, unlike conventionalcrushers where the structure of the material is damaged by theapplied pressure.A dynamic analysis of the vibrating jaw crusher operationis provided and its potential application to crushing hard ma-terials, such as alloy materials containing iron and slag frommetallurgical processes are explored.2. Dynamic analysis of a jaw in a vibrating jaw crusherThe analysis of design solutions used in vibrating jawcrushers reveals that in most cases jaw vibrations are inducedby two- or four-mass inertia vibrators 2, 3. Vibrating jawcrushers operate mostly below the range of natural frequencies0/ = 0.6-0.8 (0 natural frequency of vibrations) so thejaw lead increases with an increase in the jaw vibration fre-quency, in accordance with the first branch of the resonancefrequency plot 4 for induced vibrations of a single DOF(degree-of-freedom) system.The jaw in a vibratory jaw crusher (Fig. 1) complete withsprings constitutes a vibrating system, which can be approxi-mated by a model of a single DOF system, shown in Fig. 2.The requirement stipulating high frequencies of jaw crushersvibrations encourages the use of steel springs, with a verylow damping ratio. Therefore, the damping in the consideredvibrating system can be neglected. The equation of motion ofa jaw in a vibrating jaw crusher shown schematically in Fig 2can be written as 2:J000+kz l2sin = b P0sint(1)where:AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY. FACULTY OF MECHANICAL ENGINEERING AND ROBOTICS. DEPARTMENT OF STRENGTH AND FATIGUE OF MATERIALS ANDSTRUCTURES, AL. A. MICKIEWICZA 30, 30-059 KRAKW, POLANDBrought to you by | China University of Mining & Technology,BeijingAuthenticatedDownload Date | 3/12/18 8:20 AM884J0hkg m2i total inertia moment of the jaw with respectto the axis of rotation,00hs1i angular acceleration,khNm1i equivalent elasticity factor of the battery ofcompressions, rad angle of jaws rotation,lm distance between the spring attachment points andthe jaws rotation axis,P0N amplitude of the excitation force, s1 frequency of the applied excitation force,t s time,b m distance between the point of force applicationand the rotation axis.Since the angle of the jaws rotation in this type ofcrusher machines does not exceed 0.085 rad (5), it can beassumed that:sin ? (2)Fig. 1. Schematic diagram of a vibrating jaw crusher with jaws fixedon lower jointsFig. 2. Physical model of a jaw in a vibrating crusherSubstituting (2) into 1) yields the differential equation ofthe jaws motion with respect to the rotation axis:J000+kz l2 = b P0sint(3)For the steady-state motion, the solution to the differentialequation (3) is the function: = 0sint(4)Substituting (4) and into (5) and multiplying by l” yieldsa formula expressing the vibration amplitude at the springattachment point during the idle run:Ak=aP0l?kzJ0l22?(5)As shown in Fig. 2, the amplitude of jaw vibration on the levelof the discharge can be expressed by the formula:Ae=rlcos Ak(6)Substituting (6) into (5) yields the formula expressing the am-plitude of jaw vibration on the level of the discharge opening.Ae=aP0rl2?kzJ0l22? cos.(7)Substituting the following expressions:P0= m0r02(8) = 2n(9)where:m0r0kg m product of undefined mass and its radiusns1 frequency of the jaws vibrationinto (7) yields the formula governing the vibration am-plitude “Ae” on the level of the discharge:Ae=42al m0r0n2rl2?kzJ0l242n?(10)The constructional parameters of the crusher beingknown, the equation (10) can be applied to find the amplitudeof the jaws vibration on the level of the discharge dependingon frequency of the jaws vibration.Relationships (4) and (5) give the angular velocity of thejaw whilst formula (10) has relevance to the crushers perfor-mance.3. Defining the necessary conditions to initiate thevibratory or impulse crushing processIn order to define the conditions necessary to induce thestresses capable of crushing the material it is necessary todetermine the motion of the mass of material to be crushedand variations of stress in time in the cross-section x = 0 andx = l until the instant the jaws get separated from the crushedmaterial (Fig. 3). This motion is governed by the followingequation 1 5:2u(x,t)t2 a22(x,t)x2= 0(11)Brought to you by | China University of Mining & Technology,BeijingAuthenticatedDownload Date | 3/12/18 8:20 AM885with the initial conditions:u(x,o) = 0u(x,t)t|t=0=0 dla x 0V0dla x = 0(12)and the boundary conditions:m2u(o,t)t2= AEu(x,t)x|x=0,(13a)u(h,t) = 0.(13b)The general solution to equation (11) is given as:u(x,t) = ?t xa?+ ?t +xa?.(14)Substituting (14) to the boundary condition (13.b), we obtain: t +ha!= t ha!.(15)As t can assume any arbitrary value, it can be thus written: (z) = z 2ha!,(16)where the argument z may assume any value.Recalling (16) and (14) and replacing z by relevant argu-ments from (14), we get the displacement formula:u(x,t) = ?t xa? t +xa2ha!(17)Substituting (17) into the boundary condition (13a) and rear-ranging, we get:”(t) +AEma0(t) = ” t 2ha!AEma0 t 2ha!.(18)Using the relationship (18) and the initial conditions, the formof the function is gradually defined and, recalling (14), themotion of particular cross-sections of the rod 1 5 can beexpressed as:0 6 t 62hau(x,t) =V0EA,1eEAmaV0t,(19)(x,t)= Eu(t, x)x= aV0eEAmat.(20)To emphasise the qualitative effects of the impulse action,let us briefly analyse the stresses at characteristics points.For t = 0 and x = 0, recalling (17) we get:0= aV0.(21)Fig. 3. Geometric diagram of the jaw at the instant it touches thecrushed materialIt appears (see 21) that stress at the moment of appliedimpulse is not related to the mass of the impacting body. Ofmajor importance is the velocity V0to which the stress isproportional. It can be concluded, therefore, that there existssome critical impulse velocity Vkat which the yield point ofthe material gets exceeded. For example, let us calculate Vkfor a specified material:a =sE(22)Vk=H a=HE(23)for t =ha, x = h (the point where the stress wave meets theopposite end) is obtained from formula (20b) 1, yielding: = 2aV0The stress experienced by the material next to investigatedwalls increased two-fold in relation to the initial level.To achieve the required crushing effect, the geometricand operational parameters of the jaw crushers should be con-trolled such that at the instant the jaw hits the material, itsperipheral velocity should become V0= VK.4. Crushing capacity of vibrating jaw crushersTo confirm the adequacy of the applied crushing method,the efficiency of the vibrating jaw crusher was tested in thelaboratory set-up (Fig. 4).Brought to you by | China University of Mining & Technology,BeijingAuthenticatedDownload Date | 3/12/18 8:20 AM886Fig. 4. Vibrating jaw crusherThis study is limited in scope and hence the presentedresults are restricted to the crushers capacity in the functionof jaw vibration frequency during the crushing of chamottebricks with the grain size 4050 mm in relation to the dimen-sion of the discharge (Fig. 5).Fig. 5. Crusher capacity in the function of jaw vibration frequencyfor chamotte brick with the grain size 4050 mmThe dependence of a jaw crusher capacity in the functionof jaw vibration frequency is shown in Fig. 6, for two gradesof sulphur ores (grade 4030 plot 1), (grade 5040 plot2) and for the fixed size of the discharge.In the case of chamotte bricks, the maximal crushing ca-pacity for the investigated discharge size e0” coincides withthe range of jaw vibration frequencies n = 3031 s1. Sim-ilar patterns are obtained for sulphur ores. In both cases themaximal capacities would coincide with the frequency rangen = 30,332s1. Such narrow frequency ranges indicate thatthe effect of the discharge size on the optimal performance isminimal for the frequency range n = 3031 s1, at which theoptima are registered for the chamotte bricks, the jaw lead dur-ing the idle run would fall in the interval Se= 0,80,925 min.Fig. 6. Crusher capacity in the function of jaw vibration frequencyfor sulphur ore5. Summing-upThe final effect of the research efforts is to determine thecapacity of vibratory crushers for the practicable and feasiblefrequency ranges. For that purpose the dynamic analysis wasperformed of the crusher jaw behaviour and the necessary con-ditions were defined that would trigger the vibratory-impulseprocess. These considerations allowed for estimating the re-quired technical parameters of a vibratory jaw crusher, neces-sary to implement the crushing process. The vibratory crusherbeing designed and fabricated, crushing tests were performedon various materials, including the crushing capacity tests.Results of laboratory testing of operational and construction-al parameters of vibratory jaw crushers required for effectivedisintegration of various types of materials are provided andcrushing capacity can be determined accordingly.REFERENCES1 S. K a l i s k i, i in., Drgania i fale w ciaach staych. PWN.Warszawa 1966.2 R.K o b i a k a,Wpywparametrwdynamicznychikonstrukcyjnychnawydajnowibracyjnychkruszarekszczkowych. Praca doktorska AGH, Krakw 1978.3 Patent nr 69785 PRL.4 K. P i s z c z e k, J. Wa l c z a k, Drgania w budowie maszyn.PWN Warszawa 1975.5 S. Wo l n y, Dynamic Loading the Pulley Black in a Hoist-ing Installation in Normal Operating Conditions. Archives ofMining Sciences 54, 9, 2, Krakw 2004.This article was first presented at the VI International Conference ”DEVELOPMENT TRENDS IN MECHANIZATIONOF FOUNDRY PROCESSES”, Inwad, 5-7.09.2013Received: 20 January 2013.Brought to you by | China University of Mining & Technology,BeijingAuthenticatedDownload Date | 3/12/18 8:20 AMDYNAMIC BEHAVIOUR OF A VIBRATING JAW CRUSHER FOR DISINTEGRATION OF HARD MATERIALS关于振动颚式破碎机的动态特性用于硬材料的破碎的重要问题摘要压碎机的设计解决方案的一个趋势是，30左右的破碎比要求将振动脉冲作用应用到材料上。利用这些效应的破碎机被称为振动破碎机。在振动粉碎过程中，材料的分解受到快速变化的剪切力的作用，这导致材料被应用脉冲或疲劳作用压碎，不像传统的破碎机，材料的结构被施加的压力破坏。介绍了振动颚式破碎机的动态分析，并探讨了其对硬质合金材料的潜在应用，如含铁和炉渣的合金材料。关键词:破碎机、动态、解体搜索破碎机结构解决方案的方向之一 - 其中破碎程度达到约30 - 是对破碎材料使用冲击振动效应。使用这种操作原理的破碎机被称为振动破碎机。振动粉碎的原理在于使磨碎的材料经受快速变化的压缩力的作用，这基于疲劳原理通过冲击导致材料破碎，而不是像传统破碎机那样通过破碎破坏材料结构。在阐述中 - 在介绍振动破碎机工作的动态分析之后 - 指出了其用于研磨耐用材料（包括凝胶粉和冶金渣）的可能性。1. 介绍颚式破碎机是广泛使用的破碎机。 它们用于分解硬质和中等硬度的材料以获得各种产品尺寸。 它们坚固耐用，设计和施工相对简单，易于操作和维护。 除了这些明显的优势之外，它们还具有许多缺点，包括：低破碎比率（约5），对基座的大惯性负载，大质量。 破碎机设计解决方案中的一个趋势确保破碎比率约为30，这涉及到对待粉碎材料施加振动 - 冲击作用。 利用这些效应的破碎机被称为振动破碎机。 在振动破碎过程中，待破碎的材料受到快速变化的剪切力的作用，这导致材料通过施加的冲击或通过疲劳作用而被破碎，这与传统的破碎机不同，破碎机的材料结构被施加损坏 压力。 提供了振动颚式破碎机操作的动态分析，并探讨了其在粉碎硬质材料（例如含冶金过程的铁和渣的合金材料）中的潜在应用。2. 振动颚式破碎机中颚的动态分析振动颚式破碎机的设计解决方案的分析表明，在大多数情况下，下颌振动是由两个或四个质量惯性振动器引起的2，3。 振动颚式破碎机主要在自然频率0/= 0.6-0.8（0-振动的固有频率）的范围内工作，因此根据共振频率的第一个分支，钳口引线随着钳口振动频率的增加而增加 绘制单自由度（自由度）系统的感应振动曲线4。振动颚式破碎机（图1）中的弹簧构成一个振动系统，它可以近似为单自由度系统的模型，如图2所示。对颚式破碎机振动的高频率的要求鼓励 使用钢弹簧，阻尼比非常低。 因此，所考虑的振动系统中的阻尼可以忽略不计。 图2中示意性示出的振动颚式破碎机中颚的运动方程可写为2： (1)其中：- 钳口相对于旋转轴线的总惯性力矩-角加速度 -压缩电池的等效弹性系数-钳口旋转角度 -弹簧连接点与钳口旋转轴之间的距离-激振力的幅度- 施加的激励力的频率-时间 - 施力点与旋转轴之间的距离由于在这种类型的破碎机中爪的旋转角度不超过0.085弧度（5），因此可以假设： 图1.振动式颚式破碎机的示意图，在下部接头处固定有颚板 图2.振动破碎机中颚的物理模型将（2）代入1）得出下颌运动相对于旋转轴的差分方程： (3)对于稳态运动，差分方程（3）的解是函数： (4) 将（4）代入（5）并乘以“l”得到的表达式表示怠速运行期间弹簧连接点处的振动幅度的公式： (5)如图2所示，放电水平下颌振动的振幅可用下式表示： (6) 将（6）代入（5）得到表达在排放口水平上的颌振动幅度的公式。 (7)代入以下公式： (8) (9)其中：-未定义质量及其半径的乘积 -钳口的振动的频率由（7）得出控制放电水平振动幅度“Ae”的公式： （10）破碎机的结构参数是已知的，方程式（10）可用于根据下颌振动的频率找出下颌面在放电程度下的振动幅度。关系（4）和（5）得到的钳口而式（10）的角速度有相关性到破碎机的性能。 3.启动振动或冲击粉碎过程的必要条件为了确定引起能够粉碎材料