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任务书任务下达日期：20* 年 2 月 28日毕业设计日期：20* 年 3 月 7 日至 20* 年 6 月 10 日毕业设计题目：直线振动筛设计毕业设计专题题目：毕业设计主要内容和要求：设计主要内容： 自同步直线振动筛设计了解振动筛的工作过程及原理。对比各种振动筛的工作原理，设计一台自同步直线振动筛。设计参数：处理量 200t/h 给料粒度 100振幅 35mm 振动频率 16Hz筛分粒级 251.根据相关参数完成自同步直线振动筛的运动学参数和工艺参数；2.完成振动筛整体设计、激振器的选择；3.完成主要传动组件,零件的工作图设计；4.完成振动筛工作图设计；5.编写完成整机设计计算说明书。院长签字： 指导教师签字：英文原文Dynamics and screening characteristics of vibrating screen with variable elliptical traceAbstract: The ideal motion characteristics for the vibrating screen was presented according to the principle of screening process with constant bed thickness. A new vibrating screen with variable elliptical trace was proposed. An accurate mechanical model was constructed according to the required structural motion features. Applying multi-degree-of-freedom vibration theory, characteristics of the vibrating screen was analyzed. Kinematics parameters of the vibrating screen which motion traces were linear, circular or elliptical were obtained. The stable solutions of the dynamic equations gave the motions of the vibrating screen by means of computer simulations. Technological parameters, including amplitude, movement velocity and throwing index, of five specific points along the screen surface were gained by theoretical calculation. The results show that the traces of the new designed vibrating screen follow the ideal screening motion. The screening efficiency and processing capacity may thus be effectively improved.Keywords: variable elliptical trace; screening process with constant bed thickness; dynamic model; motion characteristic; screening characteristics1 IntroductionScreening operations are an important part of coal processing. The vibrating screen is one of the most extensively used screening tools. Vibrating screens, such as linear vibrating screen, circular vibrating screen or elliptical vibrating screen, have a simple translational motion. The motion follows the same path everywhere on the screen and so the screen has constant transport velocity and throwing index, which leads to low screening efficiency. Augmenting the throwing index to improve the processing capacity breaks the exciting motors or lowers the working intensity.In this paper, we report on the design of a new vibrating screen with variable motion traces that is based on the principle of screening process with constant bed thickness. Different parts of the vibrating screen traverse different elliptical traces and the resulting motion agrees well with the ideal motion. Thus the screen processing capacity and efficiency can both be improved.2 Ideal motions for a screen surface and the proposal of a vibrating screen with variable elliptical trace2.1 Screening characteristics of common vibrating screensVibrating screens commonly work at fixed vibration intensity. Material on the screen surface moves by throwing, rolling or sliding motions. For common screeners, material granularity is widely distributed at the feed end. The energy imparted to the material particles from the vibrating screen is severely dissipated. Consequently, a large number of particles become laminated only a short distance from the feed end. The material penetrates the screen within the first 1/4 to 1/2 of the screen, which affects screening and lowers processing capacity. The decrease of fine-grained material causes the ratio of particles close in size to, or larger than, the mesh to increase. Thus, the screening efficiency declines dramatically. The material granularity simultaneously becomes uniform and the energy imparted from the vibrations to the material suffers little loss .Hence, the amplitude and velocity of the material particles increase. This causes the material bed depth at the feed end to be thick while at the discharge end it is thin. This kind of motion leads to an asymmetrical penetration along the screen surface, which influences the screening efficiency and processing capability. Common screening characteristics are shown in Fig.1.2.2 Ideal motion for screen surface and implementing schemeThe ideal motion for screen surface is described below, according to the principle of screening process with constant bed thickness. The feed end of the screen has a bigger throwing index and a higher material delivery velocity, which makes bulk material quickly penetrate and causes rapid de-laminating. Earlier lamination of material increases the probability of fine-grained material passing through the mesh. The screen has an appropriate throwing index and a little higher material delivery velocity in its middle part. This is of benefit for stabilizing fine-grained materials and for penetrating uniformly along the screen length. A lower throwing index and material delivery velocity near the discharge end causes the material to stay longer on the screen and encourages more complete penetration of the mesh.Two methods are currently used to improve screening efficiency. The first is to add material to the screen from multiple feed ports. This is troublesome in practical use especially in terms of controlling the distribution of differently granulated materials. Hence it is rarely used in practical production. The second way is to adopt new screening equipment like, for example, a constant thickness screen. The motion of the new screen surface causes material to maintain the same, or an increased, thickness. It achieves a rather more ideal motion.The main problem with the constant thickness screen is that it covers a bigger area and that the structure is complicated and hard to maintain. A simple structure with good screening efficiency is still a necessity. We have designed a new vibration screen with a variable elliptical trace that is based upon an ideal screen motion for use in raw coal classification. The size of the vibrating screen is, the feed granularity is 0 to 50 and the classification granularity is 6. Elliptically vibrating screens combine the basic advantages of both circular and linear vibrating screens. The long axis of the ellipse determines material delivery and the short axis influences material loosening, to be exact.3 Dynamics model analysis of vibrating screen with variable elliptical traceWe made the exciting force deviate from the center of gravity, to change the motion pattern of the new vibrating screen. The stiffness matrix of the vibration isolation spring was not zero under these circumstances and the vibrating system had multiple degrees of freedom. Minor transverse wagging was neglected to simplify the research. The motion was considered to be a linear vibration of a rigid beam in the longitudinally symmetrical plane. At each point the vibration is a combination of the translation of the center of gravity and the screen pitching about the center of gravity. Previous studies neglected the influence of elastic forces in the horizontal and vertical direction on the swing of the vibrating screen. An accurate dynamic model consisting of three differential equations that include coupling of degrees of freedom in the vertical, horizontal and swing directions is proposed.The mathematical model of the vibrating screen is shown in Fig.2.The center of gravity O, is taken as the origin of a rectangular coordinate system at static equilibrium, in accordance with rigid motion on the plane12.Simultaneous differential equations in generalized coordinates using center of gravity coordinates,(x, y),and the swing declination angle,may be written as （1）where M is the mass of the vibrating screen; J the moment of inertia of M relative to the center of gravity, O; x and y the displacements in the x and y directions; x and y the velocities in the x and y directions; x and y the accelerations in the x and y directions; is the swing angular displacement;the installation angle; , and the damping coefficients in the and directions; and the stiffness coefficients of the supporting spring along the x and y directions; the amplitude of the exciting force, given by , where r is the radius of eccentricity, m the mass of the eccentric block and the exciting angular frequency; 1 L and L2 the distances between each supporting spring and the center of gravity; l the distance between the rotating center of the eccentric block and the center of gravity; and, the included angle between the l and x directions. The damping force is rather small and can be neglected. Then Eq. (1) can be simplified to Eq. (2).4 Motion and screening effect analysis of a vibrating screen with variable elliptical trace4.1 Analysis of the motion parametersMultiple degree-of-freedom vibration theory was used to find a stable solution for the forced vibration, as follows:Substituting the parameters in Eq. (3) into Eq. (2) allows a stable solution to be found.Suppose the coordinate of one point at the screen body is D (). The equations of motion areAssuming that , ， and , Eq.(4) may be simplified to Eq. (5).Using mathematical methods to eliminate the time parameter, t, in Eq. (5) gives the result shown in Eq. (6). When, the trace of point D is a line. When E =S and C =H the trace of point D is a circle. In general, Eq. (6) expresses the equation of an ellipse. The coordinate was rotated degrees anticlockwise to give a new set of coordinates .A standard elliptical equation was then obtained after eliminating 、 in Eq.(7).and is the included angle between the major elliptical axis and the x axis, expressed asFrom this we know that some points on the screen move in a line or a circle while others move in an ellipse. As long as the relative position of the rotating center of the eccentric block and the center of gravity are properly adjusted, variable elliptical motion of the screen will be obtained. This provides a reasonable throwing index and material delivery velocity and improves screening efficiency.4.2 Analysis of motion trace and screening efficiencyThe stable solution of a vibrating system, in terms of the vibrating screen, can be given byThe equations of motion for any point on the vibrating screen areEq. (8) shows that the center of gravity traces an approximate circle and that the amplitude in the horizontal and vertical directions is between 3.5mm and 5mm .Fig.3 shows how the center of gravity moves in three degrees of freedom.Fig.3 gives the angular phase difference between the horizontal and vertical directions as well as the amplitude of the swing angle.We can acquire traces showing the motion, and vibration characteristics, of each point of a large mono-axial vibrating screen in three degrees of freedom, shown in Fig.4.These are found by applying the stable solution for forced vibration. In Fig.4,O is the center of gravity; V is the exciter; A A is the linked axis between the center of gravity and the axis of the exciter. Analyzing the motion of different points in Fig.4 we find that:1) The motion of the center of gravity is approximately circular. If the stiffness coefficients, 、 k and , of the supporting spring satisfy the condition k x =k y=k then the motion is circular with a radius, of2) BB is normal to the line A A. The motion of each point along line BB is approximately linear. The motion of all the points at the screen is distributed symmetrically and is centered on the line BB. If the distance between the center of gravity and the line BB is S1 then the radius of inertia of the vibrating screen is and the distance between the axis of the exciter and the center of gravity is l. Then can be expressed as 3) The motion of different points on the vibrating screen is predominantly elliptical with paths having different sizes, shapes and obliquity angles, , The obliquity angle, , of the ellipses along the line A- A are identical and the length of the minor axis of these ellipses are close to .4) The path of an elliptical trace is longer at the feed end, which means that the long axis of the ellipse is bigger. The length of the major elliptical axis gradually becomes shorter from the feed end to the middle part of the screen. This length determines the material delivery rate. The results show that the feed end has a strong ability to deliver material, which makes material of wide granularity move forward with enough energy. This is useful for lamination of material and for increasing the probability that material penetrates the mesh. This enhances the screening efficiency.5) Eq.(4)allows the velocity of a point to be expressed as Five specific points along the screen surface, as shown in Fig.5, were chosen to study the change in path motion when moving from the feed end to the discharge end of the screen. Because the velocity is cyclic the maximum velocity and is taken as a measure of the material transport capacity. We mainly consider, and regard a reference, when using the horizontal velocity to predict material transport. From Table 1 we know that the velocity of material decreases from the feed end to the discharge end along the screen surface. This agrees well with the ideal motion characteristic of a screen surface. Thus, it is possible to maintain an appropriate bed thickness along the surface, which enhances the screening effect.6) The throwing index, of the screen represents the magnitude of the throwing acceleration as it acts on material granules. can be expressed asEq. (13) shows that the throwing index is related to the amplitude and is one of the main factors influencing the lamination effect. From Fig.4 and Table 1, we know that the throwing index is larger at the feed end and gradually becomes smaller from the feed end to the middle part of the screen. This assures that different segments of the screen have reasonable throwing index. The purpose is to intensify the screening effect. Eq. (13) predicts that the throwing index at the feed end is 3.91, while the translational ellipse is 3.17 with the same specifications, a 18.93% increase. This effectively promotes thicker material laminating in the segment.The results shown in Table 1 indicate that the vibration angle, , of the elliptical path gradually becomes smaller from the feed end to the discharge end of the screen. The screening effect is strengthened by a proper, , which makes fine grained material laminate and penetrate the mesh with a thinner material bed: this improves the actual service efficiency of the screen surface.5 Conclusions1) A new vibrating screen with variable elliptical motion trace was proposed according to the principle of screening process with constant bed thickness. Different points on the vibrating screen trace different elliptical paths. The motion pattern agrees well with the ideal motion characteristic for a screening surface. Thus, screening capacity and process efficiency can be increased.2) A theoretical kinematic analysis of the vibrating screen was done to study how varying different parameters affects the motion of the screen. Kinematics parameters of the vibrating screen that motion traces are linear, circular or elliptical are obtained.3) Motion traces of total vibrating screen were gained through computer simulations. Screening technological parameters, including amplitude, velocity and throwing index, of five specific points along the screen surface were calculated. These parameters are related to screening efficiency. The results show that the motion pattern of the designed vibrating screen conforms to an ideal screening motion and that the design is able to effectively improve screening efficiency.4) The position of the exciter axle center, relative to the center of gravity of the vibrating screen, is extremely important for screening efficient. Thus, we can design a vibrating screen with higher processing capacity without increasing power consumption by adjusting the relative position of the axle center. This is a point that requires further study.中文译文椭圆振动筛动力学与筛选特色随时间变化的追踪何小妹，刘楚生机电工程，中国矿业大学，徐州，江苏221116，中国大学摘要：理想的振动筛运动特性是根据具有恒定的物料厚度的筛分过程的原则而提出的。目前已有人提出了具有可变的椭圆轨迹的振动筛。人们已经根据所要求的结构运动特点建立了准确的力学模型。根据多学位的自由度振动理论，人们已经分析了振动筛的特点。运动轨迹为直线、盘状或椭圆形的振动筛的运动学参数也已被人们取得。通过计算机模拟人们得到了振动筛运动的稳定解法的动力学方程式。通过理论计算，人们得到了振动筛的技术参数包括振幅、运动速度和投掷指数以及沿着筛子表面的五个具体的点。结果表明新设计的振动筛的轨迹正好符合标准的筛分运动。从而提高振动筛的筛分效率和处理能力。关键词：变椭圆轨迹；恒定物料厚度的筛分过程；动态模型；运动特点；筛分特点 1 简介筛分作业是煤炭加工的一个重要组成部分。振动筛是被广泛地用于筛分作业的筛分工具之一。振动筛如直线振动筛、圆振动筛或椭圆振动筛都有一个简单的平移运动。这个运动会随着筛子上的一个相似的路线而运动。因此筛子就有恒定的运输速度和投掷指数，但这会降低筛子的筛分效率。而为了提高筛分速度而增加投掷指数就会损坏励磁电动机或降低工作强度。在本文中，我们展示了一种新的具有可变运动轨迹的振动筛的设计。它是基于恒定的物料厚度的筛分过程的原则而提出的。振动筛的不同部分遍布不同的椭圆轨迹，最后形成的运动就能很好的符合理想的运动。从而提高筛分作业的生产能力和生产效率。2 筛子表面理想运动和与可变椭圆轨迹振动筛有关的建议 2.1 常见振动筛的振动特性振动筛大部分都在一个恒定的振动强度下工作。筛子表面的物料一般都做抛掷、滚动和滑动运动。对于大多数筛子，物料的粒度广泛的分布在物料的结束段以上。与振动筛物料颗粒相等的能量将严重地被散失掉。通常情况下，大部分地颗粒分层，只有很少处于进料结束段之上。物料的透过率是在筛子首先透过的1/4到1/2，这会影响筛分和透筛作业的生产能力。细粒物料的减少会引起碎料的尺寸接近于筛孔尺寸或大于筛孔尺寸，从而引起筛孔尺寸增加。因此，筛分效率就会突然地降低。物料粒度会同时变得均匀，能量就会从振动传递到物料，但能量会产生一点亏损。因此，振幅和物料运行速度也会增加。这会引起物料层末端厚度的增加但排料段却会变薄。这种运动会引起沿着筛面的不对称的透筛从而影响筛分效率和透筛作业能力。常见振动特性如图1所示。图1 常见振动筛的振动特性2.2筛面理想运动和工艺结构根据常见厚度物料的筛分作业的原则，筛面理想运动描述如下。筛子的末端段有一个较大的投掷指数和较高的物料的排出速度，这会使得松散物料快速地透筛并引起物料快速的变厚。物料较快地变薄会增加细粒物料通过筛子的可能性。筛子在其中间部分会有一个适当地抛掷指数和一个较高的物料排放速度。这会沿着筛子长度有利于稳定细粒物料和物料的一致通过。在排料段附近一个较低的抛掷指数和物料排出速度会引起物料较长时间的呆在筛子上并使物料完全地透筛。有两种方法可用于提高筛子的效率。第一种方法是从多个进料口增加物料到筛子上。这种方法特别对于控制不同种类的多孔粒状物料在实际使用上会比较麻烦。因此，这种方法很少用于实际生产中。第二种方法是为了适应新型筛分机械的需要，如等厚筛。新的筛子表面的运动会使物料保持相同或持续增加的厚度。它实现了一个相对来说更理想的运动。等厚筛一个重要的问题是它的面积较大而且结构复杂不易保持。但是获得较高的筛分效率的简单结构的筛子也是必要的。我们已经设计出一种新型的筛子，其是基于未加工的煤分级中使用的一种理想运动的具有可变的椭圆轨迹的筛子。此种振动筛的尺寸为3.67.5m，筛分粒度范围是050m，分级粒度是6mm。椭圆振动筛是把直线振动筛和圆振动筛两者的基本特点结合而成的。确切的说，椭圆长轴代表物料排出，短轴影响物料的松散。3 可变椭圆轨迹振动筛的动力学模型分析我们使激振力偏离重力的中心来改变新型振动筛的运动模式。在这些环境下隔振弹簧的刚度并不是零，振动系统具有多元自由度。次要的横向摆动被忽视只作简化地研究。其运动被看作是在纵向对称面的刚性横梁的直线振动筛的运动。振动的每一点都是重心的偏移和筛子相对于其重心的偏移的合成。上述的研究忽视了弹性力在水平方向和垂直方向在摆动方向上的影响。一个确切的动力学模型包括三个差动的公式，这三个公式包括自由度在垂直方向、水平方向和摆动方向的运动的联合。图2 振动筛的数学模型振动筛的数学模型如图2所示。重心o是矩形坐标系在静态平衡中的原点，它与在筛面上的刚性运动相配合。在广义坐标中，联立的微分方程式用重心坐标(x, y)和摆动偏角来表示。它可以被写成 （1） 在这里M是振动筛的质量；J是M相对于重心o的惯量的力矩；和是在x 和y方向上的位移；和是x和y方向上的速度； 和是在x和y方向上的加速度；、是在x、y和方向上的阻尼系数；、是沿x 和 y方向的支承点的刚度系数；是激振力的振幅，其计算公式为，此处r为偏心块的半径，m为偏心块的质量，为激振角速度；和是每一个支承点与重心之间的距离；是和x方向的夹角。由于阻尼力相对来说很小，故可忽略不计。所以（1）式可简化为（2）式， （2）4可变椭圆轨迹振动筛的运动和筛分作用分析4.1运动参数