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混合振動(dòng)篩動(dòng)力學(xué)分析
摘要：一種新型的多自由度振動(dòng)篩和高效率的多自由度機(jī)械動(dòng)力學(xué)原理介紹。其突出的特點(diǎn)是有一個(gè)額外的高頻率和振幅振動(dòng)時(shí)間短。它能有效地增加物料破碎概率，消除致盲光圈，以及篩分效率高。一系列的力學(xué)方程的參數(shù)。建立了振動(dòng)波形圖進(jìn)行仿真計(jì)算。
關(guān)鍵詞：振動(dòng)篩；篩分效率；混沌動(dòng)力學(xué)分析
1 簡(jiǎn)介
精確篩選煤的過(guò)程是一種提高產(chǎn)品質(zhì)量結(jié)構(gòu)的煤炭生產(chǎn)和提高經(jīng)濟(jì)效益和社會(huì)節(jié)能效益的有效方法。目前，關(guān)鍵問(wèn)題是精確篩選過(guò)程抑制潮濕原煤的顆粒大小、表面積大小，水引起的孔徑和致盲。普通振動(dòng)篩完成篩選這個(gè)任務(wù)是困難的。現(xiàn)有的濕法篩選機(jī)很難使用粉煤干法篩分潮濕原煤。因此，在最近幾年的機(jī)械工程和礦物加工工程，重點(diǎn)是在研究了加工的難篩物料。因?yàn)楹Y選機(jī)是很容易被蒙蔽的篩選，這個(gè)話題在國(guó)內(nèi)和國(guó)外被廣泛而深入的研究。在本文中，我們打算開(kāi)發(fā)一個(gè)新型多自由度混合振動(dòng)篩。
2 混合振動(dòng)篩的工作原理及結(jié)構(gòu)
圖1是一個(gè)混合振動(dòng)篩的結(jié)構(gòu)，振動(dòng)器構(gòu)成部分1，2，3，4，和5。長(zhǎng)桿1和3導(dǎo)致加速度振動(dòng)周期長(zhǎng)，短桿2和4加速度振動(dòng)周期短，疊加的振動(dòng)使材料松散獲得較高的篩分效率。為了使物料篩容易，篩箱應(yīng)該傾斜，大角度（約30o）為粘性材料。振動(dòng)篩，組件1為主動(dòng)元件。驅(qū)動(dòng)轉(zhuǎn)矩，篩箱和材料形成一個(gè)動(dòng)態(tài)系統(tǒng)。當(dāng)電機(jī)驅(qū)動(dòng)系統(tǒng)運(yùn)動(dòng)時(shí)，篩箱將有一個(gè)混合運(yùn)動(dòng)。這一運(yùn)動(dòng)將有效地促進(jìn)篩選效率激勵(lì)頻率和設(shè)計(jì)。
1、 曲柄 2、短桿1 3、連桿 4、短桿2 5 支撐桿
圖1 混合振動(dòng)篩的動(dòng)力示意圖
圖1所示的混合振動(dòng)自由度是F=3×5－(2×6＋0)=3。根據(jù)經(jīng)典機(jī)構(gòu)的定義，充要條件是指定的運(yùn)動(dòng)是與原來(lái)的數(shù)目相等的運(yùn)動(dòng)的程度。如果一些自由運(yùn)動(dòng)是比原來(lái)的更大的數(shù)量，我們不能把它稱(chēng)為機(jī)制。然而，隨著機(jī)構(gòu)動(dòng)力學(xué)的發(fā)展，機(jī)制的概念已經(jīng)擴(kuò)展。如果我們認(rèn)為對(duì)于空間運(yùn)動(dòng)副或彈性元件在分析動(dòng)態(tài)的組成部分，一些自由運(yùn)動(dòng)數(shù)量遠(yuǎn)遠(yuǎn)大于原來(lái)的組件，然后機(jī)制是動(dòng)力機(jī)制。當(dāng)一些原有的元件數(shù)小于自由運(yùn)動(dòng)，位置跟隨功能的大規(guī)模的機(jī)制，慣性矩，和外部力量。適當(dāng)?shù)倪x擇尺寸時(shí)，輸出的運(yùn)動(dòng)機(jī)制可能是復(fù)合運(yùn)動(dòng)的長(zhǎng)周期振動(dòng)后，短周期振動(dòng)。該機(jī)構(gòu)有三個(gè)自由度的運(yùn)動(dòng)，一個(gè)產(chǎn)生長(zhǎng)期的幅度振動(dòng)篩網(wǎng)，其他兩個(gè)創(chuàng)造高頻率和混合振動(dòng)。目前，混合現(xiàn)象被認(rèn)為是一個(gè)最復(fù)雜的運(yùn)動(dòng)動(dòng)態(tài)系統(tǒng)，其中包括各種動(dòng)態(tài)系統(tǒng)?；旌鲜欠蔷€性動(dòng)態(tài)行為，產(chǎn)生固定點(diǎn)和周期點(diǎn)，達(dá)到特定形式的“障礙”通過(guò)乘法過(guò)程。對(duì)于非線性動(dòng)力學(xué)，人們用線性模型方法來(lái)進(jìn)行對(duì)真實(shí)系統(tǒng)簡(jiǎn)化的動(dòng)態(tài)分析與設(shè)計(jì)。然而，這種線性近似并不總是可行的，忽視非線性因素，往往造成不可接受的誤差分析與計(jì)算。近年來(lái)，人們認(rèn)識(shí)到，如果他們想設(shè)計(jì)和生產(chǎn)高品質(zhì)的系統(tǒng)，他們必須掌握非線性系統(tǒng)的動(dòng)態(tài)行為。
振動(dòng)篩取決于振動(dòng)的絲網(wǎng)材料投入、碰撞、分離、滾動(dòng)或滑動(dòng)，從而實(shí)現(xiàn)篩箱通過(guò)相對(duì)碰撞之間的材料和絲網(wǎng)。有另外一個(gè)長(zhǎng)周期振動(dòng)可以通過(guò)短時(shí)間的概率增加碰撞之間的材料、材料與材料之間的網(wǎng)格，然后可以很容易地分散和篩選。這個(gè)新的混合振動(dòng)篩的篩分效率可以達(dá)到目的。
3 動(dòng)態(tài)分析混合振動(dòng)篩
如圖1所示在建立的坐標(biāo)系的各部分，曲柄長(zhǎng)度是l1，角速度是δ1，A1點(diǎn)的轉(zhuǎn)動(dòng)慣量是JA；長(zhǎng)連桿是l2，角位移是δ2，C點(diǎn)的轉(zhuǎn)動(dòng)慣量是JC；短桿2和4的長(zhǎng)度是e1和e2，角位移是τ1和τ2，短桿4在D點(diǎn)的轉(zhuǎn)動(dòng)慣量是JD，E點(diǎn)在坐標(biāo)上水平和垂直方向的距離是x5和y5。
3.1 分解運(yùn)動(dòng)方程
從圖2中，我們可以得到分解的微分方程：
(1)
圖2 應(yīng)力分析 圖3 第一個(gè)偏心軸的應(yīng)力分析
3.2 第一個(gè)偏心軸的運(yùn)動(dòng)方程
從圖3中，我們可以得到第一偏心軸的微分方程：
(2)
(3)
(4)
3.3 導(dǎo)桿的運(yùn)動(dòng)方程
從圖4中，我們可以得到連桿的微分方程：
圖4 連桿的應(yīng)力分析 圖5 偏心軸的應(yīng)力分析
(5)
(6)
(7)
3.4 偏心軸的運(yùn)動(dòng)方程
從圖5中，我們可以得到偏心軸的微分方程：
(8)
(9)
(10)
3.5 篩箱的運(yùn)動(dòng)方程
(11)
(12)
圖6 模型盒的應(yīng)力分析
從約束條件，我們可以得到封閉機(jī)制的矢量方程：
(13)
(14)
(15)
(16)
(17)
(18)
(19)
一階導(dǎo)數(shù)的時(shí)間變量方程是從公式（14）到公式（19）
(20)
(21)
(22)
(23)
(24)
(25)
二階導(dǎo)數(shù)的時(shí)間變量方程是從公式（20）到公式（25）
(26)
(27)
(28)
(29)
(30)
(31)
根據(jù)消費(fèi)設(shè)備歐拉公式（13）
(32)
(33)
(34)
第一、二導(dǎo)數(shù)的時(shí)間變量方程的分別在（32）和（33）
(35)
(36)
(37)
(38)
加速篩箱框符合對(duì)角移動(dòng)
(39)
4 模擬曲線分析
根據(jù)上述公式，應(yīng)用程序，模擬運(yùn)動(dòng)的軌跡，我們可以得到曲線，并選擇一些進(jìn)行進(jìn)一步分析。
圖7 當(dāng)e1=e2=0mm時(shí)，篩箱的運(yùn)動(dòng)軌跡 圖8 當(dāng)e1=e2=1mm時(shí)，篩箱的運(yùn)動(dòng)軌跡
圖9 當(dāng)e1=e2=3mm時(shí)，篩箱的運(yùn)動(dòng)軌跡 圖10 當(dāng)e1=e2=6mm時(shí)，篩箱的運(yùn)動(dòng)軌跡
根據(jù)數(shù)字7，8，9，和10，水平方向（x）表示時(shí)間，垂直方（y）表示位移。為了在動(dòng)力學(xué)方法的基礎(chǔ)上測(cè)試出正確的解決方案，如圖7所示，我們假設(shè)的短桿長(zhǎng)度是e1=e2=0mm。在轉(zhuǎn)速恒定在這種情況下，本運(yùn)動(dòng)曲線的篩箱單和長(zhǎng)幅往復(fù)運(yùn)動(dòng)。其運(yùn)動(dòng)軌跡固定，不存在混合現(xiàn)象，表明從類(lèi)似于動(dòng)態(tài)方法中獲得動(dòng)力學(xué)結(jié)果。因此，無(wú)論是通過(guò)動(dòng)態(tài)方程和仿真都是準(zhǔn)確的。
如圖8所示，在短桿長(zhǎng)度是e1=e2=1mm，雖然可以看到高諧波運(yùn)動(dòng)，但不明顯；篩選粘性材料，材料之間崩潰的概率小。如圖9所示，在短桿長(zhǎng)度是e1=e2=3mm，高諧波運(yùn)動(dòng)是明顯的，原周期運(yùn)動(dòng)不會(huì)受損，混合運(yùn)動(dòng)是顯而易見(jiàn)的。因此，性質(zhì)的高諧波運(yùn)動(dòng)可以增加率崩潰，材料易分散。應(yīng)在增加粘性材料、提高粘度和致盲作出努力，。如圖9所示，在短桿長(zhǎng)度是e1=e2=6mm，高諧波運(yùn)動(dòng)是非常明顯的，但頻率和振幅開(kāi)始減少。平衡的運(yùn)動(dòng)被摧毀，它不再有積極努力提高粘度和盲目。
5 結(jié)論
一種新型的多自由度振動(dòng)篩及高效多自由度的提出，使長(zhǎng)期使用的振幅振動(dòng)頻率高、振幅疊加短振動(dòng)。理論上，它可以有效地增加的材料或材料絲網(wǎng)，分散的粘性材料，和單獨(dú)的材料網(wǎng)之間碰撞的概率。因此，它能有效的避免粘合材料之間的粘合和消除致盲孔徑。根據(jù)MATELAB運(yùn)動(dòng)曲線，在它有可能獲得高頻率和振幅的振動(dòng)的基礎(chǔ)上，長(zhǎng)期振幅要適當(dāng)?shù)倪x擇短桿長(zhǎng)度以達(dá)到更好的屏蔽作用的粘性材料。
參考文獻(xiàn)
[1] 劉C，設(shè)計(jì)和試驗(yàn)研究篩選機(jī)構(gòu)，煤炭學(xué)報(bào)，3（2004）364 - 366。
[2] 劉C，動(dòng)態(tài)特性的翻轉(zhuǎn)篩箱，其工藝參數(shù)的研究,中國(guó)礦業(yè)大學(xué)學(xué)報(bào)，29（2000）290-292。
[3] 趙Y和劉C，干法篩分的理論和應(yīng)用，科學(xué)出版社，1999。
單位代碼 0 2
學(xué) 號(hào) 100305001
分 類(lèi) 號(hào) TH6
密 級(jí) 秘密
畢業(yè)設(shè)計(jì)
文獻(xiàn)翻譯
院（系）名稱(chēng)
工學(xué)院機(jī)械系
專(zhuān)業(yè)名稱(chēng)
機(jī)械設(shè)計(jì)制造及其自動(dòng)化
學(xué)生姓名
馬春陽(yáng)
指導(dǎo)教師
楊漢嵩
2012年 03 月 10 日
The 6th International Conference on Mining Science & Technology
Dynamic analysis of a chaotic vibrating screen
Song Yan*, Jiang Xiao-hong, Song Juan, Zhang Jian-xun
China University of Mining & Technology, Xuzhou 221116, China
Abstract
A new type of multi-degree-of-freedom and highly efficient vibrating screen based on multi-degree of freedom mechanics principle of dynamics is presented. Its prominent character is to have an additionally high frequency and short amplitude vibration on long amplitude vibration. And it can efficiently increase probability of material crashing, eliminate blinding aperture,and get high screening efficiency. A series of mechanics Equ.s are set up and parameter vibrating wave charts are gained by emluator of Matlab.
Keywords: vibrating screen; dynamic analysis; screening efficiency; chaos
1. Introduction
The precisely screening process of coal is an effective way to improve the quality and structure of coal production and to increase economic efficiency and social energy saving benefit. At present, the key problem of restraining the precisely screening process of moist raw coal is the small size of particles, big specific surface area, and blinding aperture caused by water. It is difficult for ordinary vibrating screen to complete this screening task. Existing wet screening machines make it difficult to use fine-coal dry screening to screen the wet raw coal. Therefore, in recent years for the mechanical engineering and mineral process engineering, the focus is on the research into proscessing the difficult screening materials. As the screening machine is very easy to be blinded when screening, this topic has been extensively and deeply studied both at home and abroad. In this paper, we intend to develop a new type of multi-degree-of-freedom chaotic vibrating screen.
2. Structure and working principle of chaotic vibrating screen
Figure 1 is the structure of a chaotic vibrating screen. Vibrator is constituted of components 1, 2, 3, 4, and 5.Long bars 1 and 3 cause acceleration vibration of long period, short bars 2 and 4 cause acceleration vibration of short period, the superposition of the two vibrations make the material loose and get a high screening efficiency.In order to make the material screen easier, the box of screen should be tilted for a large angle (about 30o) for viscous material. The vibrating screen, component 1 is an initiative component. Driving torque, components, box of the screen and material form a dynamic system. When the motor drives the power system into motion, box of thescreen will have a chaotic motion. This motion will effectively promote screening efficiency if incentive frequency and bars are designed suitably.
1 winch; 2 short bar 1; 3 connecting rod 2; 4 short rod; 5 stander5
Fig. 1. Diagram of dynamics of the chaotic vibrating screen
The degree of freedom of the chaotic vibration shown in Fig. 1 is F＝3×5-(2×6＋0)=3. According to the definition of classic institutions, the necessary and sufficient condition of the specified movement is that the number of the original is equal to the number of the degree of motion. If the number of freedom of motion is greater than the number of the original, we can not call it mechanism. However, with the development of the mechanism dynamics,the concept of mechanism has become extended. If we think about the space of kinematic pair or elasticity of components when analyzing dynamic of components, the number of the freedom of motion is far greater than the number of the original components’, then the mechanism is dynamic mechanism. When the number of original components is less than the number freedom of motion, the location of the follower is the function of the mass of the mechanism, moment of inertia, and external force. When the size is suitably selected, the output movement of the mechanism may be the compound movement of long period vibration followed with short period vibration. This mechanism has three freedom degrees of motion, one generates long amplitude vibration on screen mesh, the other two create high frequency and chaotic vibration. At present, chaotic phenomenon is considered to be one of the most complex motions in dynamic system, which includes all kinds of dynamic system. Chaos is a nonlinear dynamic behavior, which generate fixed point and periodic point, and reach specific form of "disorder" through multiplicative process. As for nonlinear dynamics, people used to make the linear model to approach to true system, simplify dynamic analysis and design. However, this linear approximation is not always feasible, the nonlinear factors which
are overlooked often cause unacceptable error in analysis and calculation. In recent years, people realized that, ifthey want to design and produce high-quality system, they must command the nonlinear dynamic behavior of the system.
Vibrating screens depend on the vibrating of the screen mesh making materials to throw, collide, separate, and roll or slid so that it can implement screen through relative collision between materials and screen mesh. To have an additionally long period vibration on short period vibration can increase the probability of collision between materials and materials and between materials and screen meshs, then the materials can be easily decentralized and screened. This new chaotic vibrating screen can achieve the purpose of screening efficiency.
3. Dynamic analysis of chaotic vibrating screen
In building coordinate system of every component shown in figure 1, given that the length of crack 1 is l1, angular velocity is δ1, rotational inertia about point A1 is JA; the length of connecting bar is l2, angular displacement is δ2, rotational inertia about point C is JC; the lengths of short bars 2 and 4 is e1 and e2 , angular displacement is τ1 and τ2，rotational inertia of short bar 4 about point D is JD, horizontal and vertical distance between point E on the screen box and the origin of the coordinate is x5 and y5.
3.1. Motion equations of crack
From figure 2, we can get the rotational differential equation of the crack:
(1)
Fig. 2. Stress analysis model of the crack Fig. 3. Stress analysis model of the first eccentric shaft
3.2. Motion equations of the first eccentric shaft
From figure 3, we can get differential equations of the first eccentric shaft:
(2)
(3)
(4)
3.3. Motion equations of the guide bar
From figure 4, we can get differential equations of the connecting bar:
Fig. 4. Stress analysis model of the connecting bar
Fig. 5. Stress analysis model of the second eccentric shaft
(5)
(6)
(7)
3.4. Motion equations of the second eccentric shaft
From figure 5, we can get the differential equations of the second eccentric shaft:
(8)
(9)
(10)
3.5. Motion equations of the box
(11)
(12)
Fig. 6. Stress analysis model of the box
From constrain conditions, we can get vector closed equations of the mechanism:
(13)
(14)
(15)
(16)
(17)
(18)
(19)
The first derivative on time of every variable is got from Equ. (14) to Equ. (19)
(20)
(21)
(22)
(23)
(24)
(25)
The second derivative on time of every variable is got from Equ. (20) to Equ. (25)
(26)
(27)
(28)
(29)
(30)
(31)
Expend Equ. (13) according to Euler’s formula
(32)
(33)
(34)
The first and the second derivatives with respect to time are got respectively in Equ. (32) and Equ. (33)
(35)
(36)
(37)
(38)
The acceleration of the screen box moving diagonally satisfy
(39)
4. Simulating curves and analysis
According to the above formulas, using MATLAB to program, simulating the movement trajectory, we can get curves, and choose some of them for further analysis.
Fig. 7. When e1=e2=0mm,the movement trajectory of screen box
Fig. 8. When e1=e2=1mm,the movement trajectory of screen box
Fig. 9. When e1=e2=3mm,the movement trajectory of screen box
Fig. 10. When e1=e2=6mm,the movement trajectory of screen box
According to figures 7, 8, 9, and 10, the horizontal direction (x) represent time, the vertical direction (y) represent displacement. In order to test the correctness of the solutions based on dynamics method, we suppose that the length of short bars be e1=e2=0mm. Given that the rotational speed is a constant in this situation, as shown in figure 7, the movement curve of the screen box is single and long amplitude reciprocating motion. Its movement trajectory is fixed and there is no chaotic phenomena, indicating that the result obtained from dynamic method is similar to the
result obtained from kinetic method. Therefore, both the dynamic equations and simulation through MATLAB are accurate.
As shown in figure 8, when the length of the bars is e1=e2 =1mm, the character of the high harmonic movement can be seen but not obvious; for screening viscous material, the probability of crashing among materials is small. As shown in figure 9, when the length of the bars is e1=e2= 3mm, the character of the high harmonic movement is obvious, the original character of the periodic movement isn’t damaged, and the chaotic movement is obvious. Therefore, the character of the highly harmonic movement can increase the rate of the crashing and make the materials easy to be dispersed. For increasing viscous materials, an obvious effort should be made to improve the viscosity and blinding. As shown in figure 9, when the length of the bars is e1=e2=6mm, the character of the high harmonic movement is very obvious, but the frequency and the amplitude begin to reduce. The balance of the movement is destroyed, it no longer has the positive effort to improve the viscosity and blind.
5. Conclusion
A new type of multi-degree-of-freedom and high efficient vibrating screen based on multi-degree of freedom is presented, which makes use of long amplitude vibrating superimposing high frequency and short amplitude vibration. In theory, it can efficiently increase probability of crashing among materials or between materials and
screen mesh, scatter viscous materials, and separate materials from screen mesh. Therefore, it will effectively avoid bonding between materials and eliminate blinding aperture. According to movement curves got from MATELAB, it is possible to get a high frequency and short amplitude vibration on the basis of long amplitude as long as the length of bars is suitably chosen so as to achieve better screening effect for viscous material.
References
[1] C. Liu, Design and experimental research of screening machine of two degrees of freedom. Journal of Coal. 3 (2004) 364-366.
[2] C. Liu, Dynamic characteristics of the flip screen and researches of its process parameters. China University of Mining Journal. 29 (2000) 290-292.
[3] Y. Zhao and C. Liu, Theory and application of dry screening. The Science Press, 1999.