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本科生畢業(yè)設(shè)計(jì) (論文)
外 文 翻 譯
原 文 標(biāo) 題
Dynamics and screening characteristics of
a vibrating screen with variable elliptical trace
譯 文 標(biāo) 題
變橢圓軌跡振動(dòng)篩的動(dòng)力學(xué)和篩選特性
特性
作者所在系別
機(jī)電工程學(xué)院
作者所在專業(yè)
機(jī)械設(shè)計(jì)制造及其自動(dòng)化
作者所在班級(jí)
B13113
作 者 姓 名
魏許杰
作 者 學(xué) 號(hào)
20134011311
指導(dǎo)教師姓名
段新豪
指導(dǎo)教師職稱
教授
完 成 時(shí) 間
2017
年
3
月
北華航天工業(yè)學(xué)院教務(wù)處制
譯文標(biāo)題
變橢圓軌跡振動(dòng)篩的動(dòng)力學(xué)和篩選特性
原文標(biāo)題
Dynamics and screening characteristicsa vibrating screen with variable
作 者
HE Xiao-Mei，CS Liu
譯 名
何小梅，劉楚生
國(guó) 籍
中國(guó)
原文出處
《International Journal of Mining Science and Technology》
譯文：
摘要：根據(jù)恒床厚度的篩選過程振動(dòng)篩理想運(yùn)動(dòng)特征被提出， 提出了一個(gè)新的振動(dòng)篩變橢圓跟蹤。 準(zhǔn)確的力學(xué)模型建立，根據(jù)所需的結(jié)構(gòu)構(gòu)造運(yùn)動(dòng)特征。 應(yīng)用多種學(xué)位自由度振動(dòng)理論、特點(diǎn)，分析振動(dòng)篩的。 振動(dòng)篩運(yùn)動(dòng)參數(shù)獲得，它的運(yùn)動(dòng)軌跡有線性的，圓的，橢圓的。振動(dòng)篩的運(yùn)動(dòng)動(dòng)態(tài)方程可通過計(jì)算機(jī)模擬得以有效的解決。屏幕表面五個(gè)特殊的點(diǎn)的技術(shù)參數(shù)，包括振幅，運(yùn)動(dòng)速度和引發(fā)指數(shù)，是通過理論計(jì)算獲得。 結(jié)果顯示，新設(shè)計(jì)的振動(dòng)篩的軌跡遵循理想的篩選運(yùn)動(dòng)。篩分效率及處理能力可能因此而有效改進(jìn)。
關(guān)鍵字：變橢圓軌跡；篩選過程與常量床厚度；動(dòng)態(tài)模型；運(yùn)動(dòng)特性； 篩選特征
1介紹
篩分操作是一個(gè)重要的煤礦處理組成部分。振動(dòng)篩是最廣泛使用的篩選工具之一。 振動(dòng)篩，如直線振動(dòng)篩、圓振動(dòng)篩或橢圓振動(dòng)篩，有一個(gè)簡(jiǎn)單的平移運(yùn)動(dòng)。在篩面上處處運(yùn)動(dòng)保持相同的運(yùn)輸速度和引發(fā)指數(shù)的，從而導(dǎo)致低效率的篩選。充實(shí)的拋擲指數(shù)提高加工能力打破了電機(jī)或降低了工作強(qiáng)度。
在本文中，我們報(bào)告的設(shè)計(jì)，一個(gè)新的振動(dòng)篩變運(yùn)動(dòng)的痕跡，原則的基礎(chǔ)上篩選過程固定床厚度不同的部分。振動(dòng)篩穿越不同的橢圓軌跡和由此產(chǎn)生的議案，同意與理想的運(yùn)動(dòng)。因此，屏幕處理能力和效率均可以提高。
2振動(dòng)表面的理想運(yùn)動(dòng)和變橢圓軌跡振動(dòng)篩的建議
2.1振動(dòng)篩常見的篩選特性
振動(dòng)篩通常工作在固定振動(dòng)篩上的物料表面強(qiáng)度。移動(dòng)投擲，滾動(dòng)或滑動(dòng)運(yùn)動(dòng)”。 為常見的安檢，物料粒度廣泛分布在進(jìn)料端的能量傳遞。物質(zhì)粒子的振動(dòng)篩嚴(yán)重消退。因此，大量顆粒層只有很短的距離飼料結(jié)束。材料穿透屏幕在第一個(gè)1/ 4到1 /2的屏幕，它影響篩選和降低加工能力的。減少細(xì)粒物質(zhì)導(dǎo)致比粒子的大小接近或大于網(wǎng)格。因此，篩分效率下降驚人。物料粒度同時(shí)統(tǒng)一的，從振動(dòng)源給予物料的能量損失很小。因而物料粒子的振幅和速度增加。這導(dǎo)致了物料的垂直深度在送電端厚，而在放電結(jié)束端薄，進(jìn)而影響了篩分效率和處理能力。常見的篩分特性如圖1.
2.2屏幕表面的理想運(yùn)動(dòng)和實(shí)施方案
3 變橢圓軌跡振動(dòng)篩的動(dòng)力學(xué)模型分析
我們激振力偏離中心 重力，要更改新的運(yùn)動(dòng)模式 振動(dòng)篩。 剛度矩陣的振動(dòng) 隔離春天是根據(jù)這些不是零 情況和振動(dòng)系統(tǒng)有多重 自由度。 小橫搖 被忽視的簡(jiǎn)化研究。 議案 被認(rèn)為是剛性梁的非線性振動(dòng) 縱向?qū)ΨQ平面。 在每個(gè)點(diǎn) 振動(dòng)是一個(gè)組合翻譯 的重心和屏幕投球 重心。 以前的研究被忽視 水平彈性勢(shì)力的影響 垂直方向振動(dòng)的秋千 屏幕 [311] . 準(zhǔn)確的動(dòng)態(tài)模型組成 包括耦合的三個(gè)微分方程 自由度在垂直、水平和 擺動(dòng)方向建議。
振動(dòng)篩的數(shù)學(xué)模型 圖中所示.2。 重力澳中心，采取 直角坐標(biāo)系的原點(diǎn)在靜態(tài) 均衡，按照剛性運(yùn)動(dòng) 平面 [12] . 微分方程組 廣義坐標(biāo)使用重心 坐標(biāo)x、y和秋千赤緯角， θ，可以寫成：
其中m是振動(dòng)篩的質(zhì)量；j# 轉(zhuǎn)動(dòng)慣量美元相對(duì)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 你們方向；θis擺動(dòng)角位移； αthe安裝角度；外匯、f橫跨薩楊德河fθthe 阻尼系數(shù)在x、y andθdirections； k和k ythe剛度系數(shù)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為半徑，m的質(zhì)量 偏心塊andωthe刺激角頻率； 1 我和l2每個(gè)之間的距離支持 春季和重心，我的距離 偏心塊的旋轉(zhuǎn)中心之間 重心；而βthe夾角 我和x路之間。 阻尼力 相當(dāng)小，可以忽略。
然后，式（1）可以簡(jiǎn)化式（2）。
4變橢圓軌跡振動(dòng)篩的運(yùn)動(dòng)和篩選的效果分析
4.1個(gè)分析的運(yùn)動(dòng)參數(shù)多自由度振動(dòng)理論用來尋找一個(gè)穩(wěn)定解的強(qiáng)迫振動(dòng)
[ 13]，如下：
替代參數(shù)在式（3）到（2）式。允許一個(gè)穩(wěn)定的解決方案被發(fā)現(xiàn)。
假設(shè)一個(gè)點(diǎn)的屏幕坐標(biāo)為D(Dx,Dy).運(yùn)動(dòng)方程如下：
當(dāng)，D點(diǎn)的軌跡是一條直線。當(dāng)E=S，C=HS時(shí)，D點(diǎn)的軌跡是圓。
一般來說，（6）式表示方程的橢圓面直角坐標(biāo)系。XOY坐標(biāo)系以γ角速度逆時(shí)針旋轉(zhuǎn)從而給定一個(gè)新的坐標(biāo)系。一個(gè)標(biāo)準(zhǔn)的橢圓公式在消除xDyD后可得公式（7）。
從這我們知道有些屏幕上的點(diǎn) 移動(dòng)或圓的行中，而其他移動(dòng) 橢圓。 只要旋轉(zhuǎn)的相對(duì)位置 偏心塊的中心和重心 正確調(diào)整，變橢圓運(yùn)動(dòng) 屏幕將獲得的。 這提供了一個(gè)合理的 扔指數(shù)和材料傳遞速度和 提高篩分效率。
4.2 運(yùn)動(dòng)軌跡和篩分效率分析
穩(wěn)定振動(dòng)系統(tǒng)解決方案，就振動(dòng)篩而言的，可以給出
在振動(dòng)篩上任一點(diǎn)的運(yùn)動(dòng)方程為
公式（8）表示重心的痕跡近似圓形，水平和垂直方向的振幅在3.5mm 和5mm之間。圖 3表示如重心的移動(dòng)存在三個(gè)自由度。圖3水平和垂直方向的相位差和擺角的振幅一樣。
5 結(jié)論
1）新振動(dòng)篩變橢圓 根據(jù)原則提出了運(yùn)動(dòng)軌跡常數(shù)床厚度的篩選過程。振動(dòng)篩跟蹤不同的不同點(diǎn)橢圓路徑。運(yùn)動(dòng)規(guī)律也同意配合篩面的理想運(yùn)動(dòng)特性。因此，篩選能力和處理效率會(huì)增加。
2）振動(dòng)的理論運(yùn)動(dòng)學(xué)分析屏幕做是為了研究如何變不同 參數(shù)會(huì)影響屏幕的議案。振動(dòng)篩參數(shù)的議案線性跟蹤獲得圓或橢圓。
3) 總振動(dòng)篩運(yùn)動(dòng)的痕跡 通過計(jì)算機(jī)模擬獲得。篩選技術(shù)參數(shù)，包括振幅，速度和引發(fā)指數(shù)，五個(gè)的特定沿屏幕表面計(jì)算。這些參數(shù)是與篩分效率。結(jié)果顯示模式設(shè)計(jì)的議案 振動(dòng)篩符合理想的篩選議案，設(shè)計(jì)能夠有效 提高篩分效率。
4) 勵(lì)磁機(jī)軸中心的地位，相對(duì) 振動(dòng)篩的重心，是篩選高效的極為重要的。 因此，我們可以設(shè)計(jì)一個(gè)振動(dòng)篩具有更高的處理 的能力而又不會(huì)增加功耗 調(diào)整軸中心的相對(duì)位置。這是一個(gè)點(diǎn)，需要進(jìn)一步研究。
參考文獻(xiàn)
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原文：
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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