振动筛外文翻译---变椭圆轨迹振动筛的动力学和筛选特性
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变椭圆轨迹振动筛的动力学和筛选特性
何小梅，刘楚生
机械和电气工程学院，中国矿业大学科技，江苏省徐州市221116，中国
摘要：根据恒床厚度的筛选过程振动筛理想运动特征被提出，提出了一个新的振动筛变椭
圆跟踪。准确的力学模型建立，根据所需的结构构造运动特征。应用多种学位自由度振动理论、特点，分析振动筛的。振动筛运动参数获得，它的运动轨迹有线性的，圆的，椭圆的。振动筛的运动动态方程可通过计算机模拟得以有效的解决。屏幕表面五个特殊的点的技术参数，包括振幅，运动速度和引发指数，是通过理论计算获得。结果显示，新设计的振动筛的轨迹遵循理想的筛选运动。筛分效率及处理能力可能因此而有效改进。
关键字：变椭圆轨迹；筛选过程与常量床厚度；动态模型；运动特性；筛选特征
1介绍
筛分操作是一个重要的煤矿处理组成部分。振动筛是最广泛使用的筛选工具之一。振动筛，如直线振动筛、圆振动筛或椭圆振动筛，有一个简单的平移运动。在筛面上处处运动保持相同的运输速度和引发指数的，从而导致低效率的筛选。充实的抛掷指数提高加工能力打破了电机或降低了工作强度。
在本文中，我们报告的设计，一个新的振动筛变运动的痕迹，原则的基础上筛选过程固定床厚度不同的部分。振动筛穿越不同的椭圆轨迹和由此产生的议案，同意与理想的运动。因此，屏幕处理能力和效率均可以提高。
2振动表面的理想运动和变椭圆轨迹振动筛的建议
2.1振动筛常见的筛选特性
振动筛通常工作在固定振动筛上的物料表面强度。移动投掷，滚动或滑动运动”。为常见的安检，物料粒度广泛分布在进料端的能量传递。物质粒子的振动筛严重消退。因此，大量颗粒层只有很短的距离饲料结束。材料穿透屏幕在第一个1/ 4到1 /2的屏幕，它影响筛选和降低加工能力的。减少细粒物质导致比粒子的大小接近或大于网格。因此，筛分效率下降惊人。物料粒度同时统一的，从振动源给予物料的能量损失很小。因而物料粒子的振幅和速度增加。这导致了物料的垂直深度在送电端厚，而在放电结束端薄，进而影响了筛分效率和处理能力。常见的筛分特性如图1.
2.2屏幕表面的理想运动和实施方案
根据筛选过程恒床等厚的原则，理想的运动的屏幕表面的描述如下。
3 变椭圆轨迹振动筛的动力学模型分析
我们激振力偏离中心重力，要更改新的运动模式振动筛。刚度矩阵的振动隔离春天是根据这些不是零情况和振动系统有多重自由度。小横摇被忽视的简化研究。议案被认为是刚性梁的非线性振动纵向对称平面。在每个点振动是一个组合翻译的重心和屏幕投球重心。以前的研究被忽视水平弹性势力的影响垂直方向振动的秋千屏幕 [311] . 准确的动态模型组成包括耦合的三个微分方程自由度在垂直、水平和摆动方向建议。
振动筛的数学模型图中所示.2。重力澳中心，采取直角坐标系的原点在静态均衡，按照刚性运动平面 [12] . 微分方程组广义坐标使用重心坐标x、y和秋千赤纬角，θ，可以写成：
其中m是振动筛的质量；j# 转动惯量美元相对于中心重力，澳；x和y的x和y位移方向；x和y在x和y的速度方向；加速x和y在x和你们方向；θis摆动角位移；αthe安装角度；外汇、f横跨萨杨德河fθthe阻尼系数在x、y andθdirections；k和k ythe刚度系数的支持沿x 和y directions;a0汀春天激振力的振幅，提供的 2 0 =mrω，偏心其中r为半径，m的质量偏心块andωthe刺激角频率； 1 我和l2每个之间的距离支持春季和重心，我的距离偏心块的旋转中心之间重心；而βthe夹角我和x路之间。阻尼力相当小，可以忽略。
然后，式（1）可以简化式（2）。
4变椭圆轨迹振动筛的运动和筛选的效果分析
4.1个分析的运动参数多自由度振动理论用来寻找一个稳定解的强迫振动[ 13]，如下：
替代参数在式（3）到（2）式。允许一个稳定的解决方案被发现。
假设一个点的屏幕坐标为D(D x,D y).运动方程如下：
当222220
++=，D点的轨迹是一条直线。当E=S，C=HS时，D点的轨迹是圆。
E S C H ESCH
一般来说，（6）式表示方程的椭圆面直角坐标系。XOY坐标系以γ角速度逆时针旋转从而给定一个新的坐标系''
x oy。一个标准的椭圆公式在消除x D y D后可得公式（7）。
从这我们知道有些屏幕上的点移动或圆的行中，而其他移动椭圆。只要旋转的相对位置偏心块的中心和重心正确调整，变椭圆运动屏幕将获得的。这提供了一个合理的扔指数和材料传递速度和提高筛分效率。
4.2 运动轨迹和筛分效率分析
稳定振动系统解决方案，就振动筛而言的，可以给出
在振动筛上任一点的运动方程为
公式（8）表示重心的痕迹近似圆形，水平和垂直方向的振幅在3.5mm 和5mm之间。图 3表示如重心的移动存在三个自由度。图3水平和垂直方向的相位差和摆角的振幅一样。
5 结论
1）新振动筛变椭圆根据原则提出了运动轨迹常数床厚度的筛选过程。振动筛跟踪不同的不同点椭圆路径。运动规律也同意配合筛面的理想运动特性。因此，筛选能力和处理效率会增加。2）振动的理论运动学分析屏幕做是为了研究如何变不同参数会影响屏幕的议案。电影抽搐振动筛参数的议案线性跟踪，获得圆或椭圆。
3)总振动筛运动的痕迹通过计算机模拟获得。筛选技术参数，包括振幅，速度和引发指数，五个的特定点沿屏幕表面计算。这些参数是与筛分效率。结果显示模式设计的议案振动筛符合理想的筛选议案，设计能够有效提高筛分效率。
4)励磁机轴中心的地位，相对振动筛的重心，是筛选高效的极为重要的。因此，我们可以设计一个振动筛具有更高的处理的能力而又不会增加功耗调整轴中心的相对位置。这.。是一个点，需要进一步研究。
参考文献
[1]Wen B C,Liu F Q.振动的理论与应用机器.北京：中国机械出版,1982
[2]Gu Q B,Zhang E G.复杂轨迹振动筛研究.1998(1):42–46
[3]Hao F Y.煤制备手册：技术设备.北京：中国煤炭行业出版社,1993
[4]Yan F.筛分机械.北京：中国煤炭行业出版社.1995
[5]Liu C S,Zhao Y M..筛面上的非线性特性的研究. 矿物处理设备,1999(1):45–48
[6]Tao Y J,Luo Z F,Zhao Y M..在重力强力分离器使用方面的煤脱硫的实验研究.中国矿业与技术大学.2006,16(4):399–403
[7]Zhang E G.筛分，粉碎，脱水设备.北京:中国煤工业出版社，1991
[8]Khoury D L.煤清洁工艺.美国：诺易斯数据公司，1981
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[10]Ye H D.等厚圆筛分及其应用.烧结和码垛,1999,5(3):30–33
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[12]Wang F,Wang H.筛分机械. 北京：中国机械出版社，2001
[13]Ni Z H.振动力学.西安：西安交通大学出版社，1989
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Dynamics and screening characteristics of
a vibrating screen with variable elliptical trace
HE Xiao-mei,LIU Chu-sheng
School of Mechanical and Electrical Engineering,China University of Mining & Technology,Xuzhou,Jiangsu 221116,China
Abstract: 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 characteristics
1 Introduction
Screening 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 breaks the exciting motors processing capacity lowers the working.
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
[3–4].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 motion for a screen surface and the proposal of a vibrating screen with variable elliptical trace
2.1 Screening characteristics of common vibrating screens
Vibrating screens commonly work at a 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 [5].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 [6].Common screening characteristics are shown in Fig.1.
2.2 Ideal motion for screen surface and implementing scheme
The 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 [7–8].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 3.6 m×7.5 m,the feed granularity is 0 to 50 mm and the classification granularity is 6mm.Elliptically vibrating screens combine the basic advantages of both circular and linear vibrating screens [9–10].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 trace
We 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 [3,11].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, is taken as the origin of a rectangular coordinate system at static
equilibrium, in accordance with rigid motion on the plane [12].Simultaneous differential equations in generalized coordinates using center of gravity coordinates,(x,y),and the swing declination angle, θ,may be written as
where M is the mass of the vibrating screen’s the moment of inertia of M relative to the center of gravity,O;x and y the displacements in the x and y0directionas;x and y the velocities in the x and y directions’ and y the accelerations in the x and y directions; is the swing angular displacement; αthe installation angle;fx,f yond father damping coefficients in the x,y and directions;
x k and k the stiffness coefficients of the supporting spring along the x and y directions; A0 the amplitude of the exciting force, given by2 0 A =mrω, where r is the radius of eccentricity the mass
of the eccentric block and the exciting angular frequency; L1 and L2 the distances between each supporting spring and the center of gravity’s the distance between the rotating center of the eccentric block and the center of gravity; and,βthe 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 trace
4.1 Analysis of the motion parameters Multiple degree-of-freedom vibration theory was used to find
a stable solution for the forced vibration [13],as follows:
When E 2 S 2 +C 2 H 2 +2 ESCH=0, the trace of point D is a line. When E =Sand C =H, the trace of point D is a circle. In general. (6) expresses the equation of an ellipse.The xoy coordinate was rotated γ degrees anticlockwise to give a new set of x ′oy′coordinates. A standard elliptical equation was then obtained after eliminating D D x y in Eq.(7).
From 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 efficiency
The stable solution of a vibrating system, in terms of the vibrating screen, can be given by
The equations of motion for any point on the vibrating screen are
Eq.(8)shows that the center of gravity traces an approximate circle and that the amplitude in the horizontal and vertical directions is between 3.5 mm and 5 mm.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.
5 Conclusions
1)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 differentelliptical 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.Kinema- tics 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.
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