3090型直線振動篩結構設計含SW三維及5張CAD圖
3090型直線振動篩結構設計含SW三維及5張CAD圖,直線,振動篩,結構設計,sw,三維,cad
附錄
A virtual experiment showing single particle motion on a linearly vibrating screen-deck
ZHAO Lala , LIU Chusheng, YAN Junxia
School of Mechanical and Electrical Engineering, China University of Mining & Technology, Xuzhou 221008, China
1 Introduction
Vibration screening is a complicated process used in the mineral processing area that is affected by the vibration and other technical parameters of the screen and by the processed material's properties. The mo tion of the material on the screen deck has a direct relation to the quality of the screening process. Fac tors such as the penetration probability of the parti cles and the productivity of the apparatus are important. So investigating the theory of motion and the properties of the screened materials is of great sig nificance for choosing reasonable kinematic parame ters that ensure an effective screening process.
The sieving experiment forms the foundation of screening theory. The traditional experimental meth ods have the disadvantages of being complex to oper ate, being easily influenced by outside conditions and being difficult to carry out accurately in small scale. Virtual experimental technology, on the other hand, has the advantages of low cost, of having no limits in the field related to the available time and number of tests and of affording the simulation of complex processes. Virtual techniques have been widely ap plied in studies within military, medical and industrial fields.
We describe a virtual screening experimental sys tem built upon physical simulation principles. The motion of a single particle on a linearly vibrating screen deck was studied. The influences of kinematic parameters on the state of motion were discussed. These results could provide a reference for the con venient study of vibrating screen theory and sieving practice.
2 Theory of linear motion on a vibrating screen
Different kinematic parameters, such as the vibra tion frequency, f, the amplitude, λ, the inclination an gle of the screen plate, a0, or the direction angle of vibration, δ, may be changed to affect the motion of material on the screen deck. A motion that is static, positively sliding, negatively sliding or throwing can be obtained. The throwing motion provides good segregation performance, good screening and higher sieving efficiency and productivity. Hence, a throw ing motion is adopted for most vibrating screens.
Fig. 1 shows a kinematic model of a linear vibra tion screening process. The vibration motion is sinu soidal and linear. Its displacement is given by:
(1)
where λ is the amplitude of screen motion along the vibration direction, mm； ω the circular frequency of vibration, rad/s； t time, s； and φ the vibration phase angle, °.
Fig. 1 Kinematic model of a linear vibration screening process
We let the particle fall freely under the influence of gravity from its initial position until it hits the vibrat ing screen deck. The particle will then undergo a con tinuous throwing motion after elastic-plastic colli sions with the vibration deck. Let the time of the i'th collision between the particle and the screen be ti and ignore the time required for the collision process itself. Then, based on the law of conservation of en ergy, the particle velocity along the normal direction of the screen deck after the collision is given by:
(2)
where δ is the direction angle of vibration, °； the y-direction velocity of the particle before the i'th col lision, m/s； the screen deck velocity at the i'th collision, m/s； and e the elastic coefficient of restitu tion of the colliding particle.
Conservation of energy requires that the thrown height relative to the screen deck after the collision is:
(3)
where g is the gravitational acceleration constant, m/s2； and a0 the inclination angle of the screen deck, °. The theoretical average thrown height of the particle is then:
(4)
where n is the number of collisions of the particle. Because there is no collision along the screen deck direction (the x-direction) for the particle, the theo retical average throwing height of the particle is de termined by:
(5)
where iD is the throwing coefficient； and D the throwing index.
3 Simulation and discussion
The situation for simulation of a single particle on a cylindrical-bar type linear vibrating screen deck is shown in Fig. 2a. A global coordinate system (unit: cm) was adopted and the center of the scene at ground level was set as the origin of the coordinate system. The initial position of the screen and of the particle is (0, 0, 15) and (-25, 0, 30), respectively. The screen deck area is 60 cm×30 cm, the screen ap erture size (a) is 2 cm, the particle diameter (d) is 4 cm and the elastic coefficient of restitution (e) is 0.5. Fig. 2b shows the trajectory of the particle through space during the screening process.
Taking the trajectory in the z-direction as our re search object, the influence of vibration frequency and amplitude, inclination angle of the screen deck and vibration direction angle on the average particle velocity and average throwing height will be dis cussed.
Fig. 2 Virtual experiment of a single particle sieving process
3.1 Effect of vibration frequency, f
The influence of frequency on the particle trajec tory is shown in Fig. 3 for constant amplitude, incli nation angle and vibration direction. The average ve locity and throwing height are listed in Table 1 as a function of frequency.
Table 1 Influence of frequency on particle kinematics
f (Hz)
12
13
14
15
v (m/s)
0.2978
0.5458
0.2140
0.2056
Vd (m/s)
0.2849
0.3087
0.3324
0.3562
hz (cm)
26.4468
25.1961
26.4119
22.6399
Fig. 3 Influence of frequency on throwing trajectory
Note that the particle velocity initially increases as f decreases but then decreases for the final frequency increment. This is because increasing frequency of vibration causes the number of collisions between the particle and the screen deck to increase. The opportu nity for random collisions then also increases and a "back-throwing" phenomenon after collision even appears. This causes an increase in the number of particle bounces and in the time spent to complete the screening process. When f is 13 Hz, the number of particle bounces is 6, the time spent to complete screening is the minimum value of 1.15 s and the par ticle average velocity is the maximum value of 0.5458 m/s. But when f is 15 Hz the particle bounces 16 times and the time spent to complete screening is the maximum value of 2.267 s. At this frequency both the average velocity and the average throwing height are at their minimum values.
An analysis of the results in Table 1 shows that the correlation coefficient for the vibration frequency versus the average velocity is 0.494 and that the coef ficient is 0.725 for frequency versus the average throwing height. This indicates that frequency has a greater influence on the average throwing height and has no significant influence on the particle's average velocity. The highest average velocity and average throwing height is obtained when f is 13 Hz.
3.2 Effect of amplitude, λ
The influence of amplitude on the trajectory of a particle is shown in Fig. 4. The average velocity and average throwing height are listed in Table 2.
Fig. 4 Influence of amplitude on throwing trajectory
Fig. 4 and Table 2 show that an increase in X, which causes the relative velocity between the parti cle and the vibrating screen deck to increase, results in a gradual increase in the particle average velocity and height. The number of bounces decreases at the same time. These predictions are in reasonable agreement with related theories. When λ is 3.5 mm there are twenty bounces and the particle has low average velocity and height. The time needed to complete screening is the longest under this condition (2.417 s). As λ increases the incremental change in sieve time decreases as the time tends to about 1.6 s. And the particle average velocity and height increase rapidly when λ is 6.5 mm.
An analysis of the results in Table 2 gives a corre lation coefficient between amplitude and average ve locity of 0.793 and between amplitude and height of 0.924. This indicates that the amplitude has some influence on particle average velocity and a signifi cant influence on the average thrown height. Hence, amplitude should be selected according to the proper ties of the screened material. For materials difficult to screen relatively larger amplitude should be used to simultaneously obtain higher average velocities and throwing heights.
Table 2 Influence of amplitude on particle kinematics
X (mm)
3.5
4.5
5.5
6.5
v (m/s)
0.2107
0.2088
0.2140
0.2977
vd (m/s)
0.2116
0.2417
0.3324
0.3929
hZ (cm)
19.4694
21.5484
26.4119
40.9729
h (cm)
19.7285
19.8357
21.9001
24.2023
3.3 Effect of screen-deck inclination angle, a0
The influence of deck inclination angle on the par ticle trajectory is shown in Fig. 5. The average veloc ity and height are listed in Table 3.
Fig. 5 Influence of screen-deck inclination angle on throwing trajectory
Fig. 5 and Table 3 show that as a0 increases the av erage velocity also increases and the number of colli sions the particle undergoes decreases. The average height tends to decrease. When a0 is 0° the particle has twenty collisions with the screen and the average velocity is the minimum. The time needed to complete screening is then the longest (3 s). When a0 is 6° the average height of the particle is at its maximum value. For a0 equal to 9° the initial distance from the particle to the screen deck decreases and the relative velocity of the particle and screen deck is at a mini mum, which causes a decrease in the thrown height.
Table 3 Influence of screen-deck inclination angle on particle kinematics
00 (°)
0
3
6
9
v (m/s)
0.2477
0.29167
0.2509
0.3169
Vd (m/s)
0.2954
0.3139
0.3324
0.3512
hz (cm)
21.5082
22.6978
26.4119
15.1523
h (cm)
18.44713
16.7279
21.9001
15.3953
Correlation coefficients from data in Table 3 relat ing screening deck inclination angle to average veloc ity or to average height are 0.644 and 0.697, respec tively. Hence, the screen-deck inclination angle in fluences both particle average velocity and throwing height. When the screening deck inclination angle is 3°~6° high average velocity and high throw height can be obtained simultaneously.
3.4 Effect of vibration direction angle, δ
The effect of the angle of vibration the particle tra jectory was also studied. Fig. 6 shows the trajectories. The average velocity and average height are listed in Table 4.
Fig. 6 Influence of vibration angle on throwing trajectory
Table 4 Influence of vibrating-direction angle on particle kinematics
S (°)
30
40
50
60
v (m/s)
0.3672
0.5293
0.2509
0.1903
vd (m/s)
0.4222
0.3831
0.3324
0.2716
hz (cm)
19.8286
22.5425
26.4119
48.2712
Fig. 6 and Table 4 show that the average height in creases as δ increases but there is a decrease in the average velocity. When δ is 40°, the average particle suffers six collisions and the average velocity is the maximum. In this situation the time spent for com plete screening is the shortest (1.067 s). When δ is 60° the particle has minimum average velocity and suffers eleven collisions. The time spent for completion of screening is at the maximum (2.15 s). The increase in the normal component of the screen deck velocity causes the relative velocity of the particle after colli sion to increase. Thus, the average height increases in amplitude and reaches a maximum.
From the data in Table 4 correlation coefficients for vibration direction angle versus average velocity and average throw-height may be found. They are 0.70 and 0.889 respectively. This indicates that direc tion angle, δ, influences particle average velocity and height. So, higher average velocity and throwing height may be simultaneously obtained by using a vibration angle of about 40°.
4 Conclusions
1) A single particle on the vibrating screen deck has a complicated motion. The particle motion during the sieving process can be described well using elas tic-plastic collision theory.
2) The amplitude and the vibration direction angle have a great effect on the particle average velocity and the average throw height considered over the normal range of linear screen parameters. The vibra tion frequency and the inclination angle of the screen plate have a small influence. To obtain the ideal siev ing effect for materials that are difficult to sieve the frequency and amplitude of vibration, the inclination angle of the screen plate and the vibration direction angle should be chosen as 13 Hz, 6.6 mm, 6° and 40°, respectively.
3) A virtual screening experiment based on physi cal simulation principles reflects the objective laws of the sieving process and can provide a simple and re liable means to study screening theory.
一個展示直線振動篩篩板上單質點運動情況的仿真實驗
ZHAO Lala，LIU Chusheng，YAN Junxia
機電工程學院，中國礦業(yè)大學，徐州 221008，中國
1 簡介
振動篩分是礦物加工領域的一個復雜過程，它受振動情況、篩機的技術參數(shù)和物料的性質影響。篩分過程的效率直接影響物料在篩板上的運動狀態(tài)。物料穿透概率和篩機的效率是很重要的影響因素。因此，研究運動理論和物料的性質具有重要意義，是選擇合理的運動學參數(shù)，確保有效篩分的重要過程。
篩分實驗是篩分理論的基礎。傳統(tǒng)的實驗方法有難以比較結果、容易被外界因素影響和難以取得精確數(shù)值的缺點，而仿真實驗技術則有實驗費用低、沒有場地、時間以及實驗次數(shù)限制，能夠對復雜過程進行仿真等優(yōu)點。仿真技術現(xiàn)在被廣泛用于軍事、醫(yī)藥和工業(yè)領域的研究。
我們基于物理仿真理論建立了一個仿真篩分實驗系統(tǒng)，用于研究直線振動篩篩板上單質點的運動狀態(tài)， 質點運動的動力學參數(shù)的影響同樣被考慮了。本研究的結果可以為振動篩理論和篩分實踐的研究提供方便。
2 振動篩上物料的直線運動理論
不同的運動學參數(shù)，例如振動頻率，f，振幅，λ，篩面傾角，a0，振動方向角，δ，的改變可能影響篩面上物料的運動狀態(tài)。我們改變參數(shù)就能夠得到完全靜止、絕對滑行和絕對拋擲三種物料運動狀態(tài)。拋擲運動狀態(tài)能夠使物料有效地分離，為振動篩提供更高的篩分效率和生產率，所以大部分振動篩都采用了拋擲的方式。
圖1顯示了一個直線振動篩分過程的運動學模型，可以看出振動運動的軌跡是線性和正弦曲線的。其位移由下式給出：
(1)
式中λ振動方向的振幅，mm；ω振動的角頻率，rad/s；t 時間，s；φ振動相位角，°。
圖1 直線振動篩分過程的運動學模型
我們讓質點在重力的作用下做自由落體運動直到再次撞擊到篩面為止，在質點與篩面碰撞后將做連續(xù)的拋擲運動。我們設質點連續(xù)兩次碰撞之間的時間為ti同時忽略碰撞的時間。這樣，根據(jù)能量守恒定律，質點在篩面正向的正常速度為：
(2)
式中 δ 為振動的方向角，°；y方向的撞擊速度， m/s； 篩板在撞擊時的速度， m/s； e質點撞擊的回彈系數(shù)。
能量守恒定律指出質點的拋射高度與質點與篩面的撞擊有關：
(3)
式中g 重力加速度，m/s2；a0篩板的傾角， °。 則平均拋射高度為：
(4)
式中 n 質點的撞擊次數(shù)。因為質點沿x方向沒有撞擊，從理論上定義平均拋射高度為：
(5)
式中 iD 拋擲系數(shù)；D為拋擲指數(shù)。
3 仿真與討論
單質點在圓形棒條篩網的直線振動篩上的仿真條件見圖2a。我們采用將一個三維坐標（單位：cm）的原點定在原坐標系的水平軸上。篩板和質點的初始位置分別為(0， 0， 15) 、 (-25， 0， 30)。篩面尺寸為60 cm×30 cm，篩孔尺寸為 (a) 2 cm，質點的尺寸為(d) 4 cm回彈系數(shù)(e) 為0.5。圖2b顯示了質點在篩分過程中的運動軌跡。
我們以z軸方向的軌跡為研究對象，我們將討論在不同振動頻率、振幅、篩面傾角、振動方向角下質點的平均速度、平均拋射高度。
圖2 單質點的篩分實驗
3．1 振動頻率的影響， f
恒定振幅、傾角、振動方向角條件下下振動頻率對質點運動軌跡的影響見圖3。平均速度和平均拋射高度作為振動頻率的函數(shù)在表1中列出。
表1 振動頻率對質點的影響
f (Hz)
12
13
14
15
v (m/s)
0.2978
0.5458
0.2140
0.2056
Vd (m/s)
0.2849
0.3087
0.3324
0.3562
hz (cm)
26.4468
25.1961
26.4119
22.6399
圖3 振動頻率對拋射軌跡的影響
記錄顯示初始階段質點速度隨著頻率的增大而增大，但之后隨著頻率的增大而減小。這是因為頻率的提升引起質點與篩面的撞擊次數(shù)增加，同時隨機拋射現(xiàn)象增多，后拋現(xiàn)象出現(xiàn)。這導致了質點回彈現(xiàn)象的增多，增加了篩分過程的時間。 當 f 為13 Hz時，質點的回彈為6，完成篩分過程的時間為1.15s，質點的平均速度最大值為0.5458m/s。但是當 f 為15 Hz時回彈次數(shù)為16，完成篩分過程的最長時間為2.267 s。在這個頻率下，質點的平均速度和平均拋射高度均為最小值。
對表1的分析結果顯示振動頻率對平均速度的相關系數(shù)為0.494，對平均拋射高度的相關系數(shù)為0.725。這樣的結果指出振動頻率對拋射高度的影響較大，對質點的速度影響較小。最大平均速度和最大拋射高度是在振動頻率為13Hz時獲得的。
3.2 振幅的影響，λ
振幅對質點運動軌跡的影響見圖4。平均速度和平均拋射高度在表2中列出。
圖4 振幅對質點運動軌跡的影響
圖4和表2顯示振幅的提高導致質點和篩面之間的相對速度提高，從而提高了質點的速度和拋射高度，同時回彈現(xiàn)象減少。這個結果符合理論上的預判。 當 λ為3.5 mm 時回彈次數(shù)為20，質點的速度和拋射高度都比較小。這種情況下完成整個篩分過程所需的時間最長(2.417 s)。隨著λ的增加篩分時間逐漸縮短到1.6s左右。當λ為6.5mm時質點的速度和拋射高度明顯提升。
對表2的分析給出了振幅與速度的相關系數(shù)為0.793，與拋射高度的相關系數(shù)為0.924。這個結果指出振幅對速度有一定影響，對拋射高度的影響較大。因此振幅應該根據(jù)所篩分的物料進行選取。對于相對難以篩分的物料應該選取較大的振幅以提高質點的速度和平均拋射高度。
表2 振幅對質點運動的影響
X (mm)
3.5
4.5
5.5
6.5
v (m/s)
0.2107
0.2088
0.2140
0.2977
vd (m/s)
0.2116
0.2417
0.3324
0.3929
hZ (cm)
19.4694
21.5484
26.4119
40.9729
h (cm)
19.7285
19.8357
21.9001
24.2023
3.3 篩面傾角的影響， a0
篩面傾角對質點運動軌跡的影響見圖5。質點平均速度和平均拋射高度在表3中列出。
圖5 篩面傾角對質點運動軌跡的影響
圖5和表3顯示隨著a0的增加質點的平均速度增加而質點經歷的撞擊次數(shù)減少，拋射高度也有減少的趨勢。當a0為0°時質點與篩面有20次撞擊，平均速度為最小。完成篩分過程的時間為最長 (3 s)。 當a0為6°時拋射高度為最大值。當a0 為9° 時質點與篩板的最初距離和相對速度為最小值，同時引起拋射高度減小。
表3 篩面傾角對質點運動參數(shù)的影響
00 (°)
0
3
6
9
v (m/s)
0.2477
0.29167
0.2509
0.3169
Vd (m/s)
0.2954
0.3139
0.3324
0.3512
hz (cm)
21.5082
22.6978
26.4119
15.1523
h (cm)
18.44713
16.7279
21.9001
15.3953
根據(jù)表3篩面傾角與質點平均速度和平均拋射高度的相關系數(shù)分別為0.644和0.697。因此篩面傾角對質點平均速度和平均拋射高度的影響程度基本相同。當篩面傾角為3°~6°時能夠獲得較高的質點平均速度和平均拋射高度
3.4 振動方向角的影響, δ
振動方向角對質點運動軌跡的影響同樣被研究了。圖6顯示了軌跡，質點平均速度和平均拋射高度在表4中列出。
圖6 振動方向角對質點軌跡的影響
表4 振動方向角對質點運動參數(shù)的影響
S (°)
30
40
50
60
v (m/s)
0.3672
0.5293
0.2509
0.1903
vd (m/s)
0.4222
0.3831
0.3324
0.2716
hz (cm)
19.8286
22.5425
26.4119
48.2712
圖6和表4顯示，拋射高度隨著振動方向角的增大而增大，但是速度隨著振動方向角的增大而減小。 當δ為40°時，平均質點碰撞次數(shù)為6，平均速度這時取得最小值。在這種情況下完成篩分過程的時間最短 (1.067 s)。當 δ為 60° 時質點平均速度最小，撞擊次數(shù)為11，篩分實踐取得最大值 (2.15 s)。篩面垂直方向上速度的增加導致了質點與篩面相對速度的增加，因此，拋射高度迅速增加達到最大值。
通過表4的數(shù)據(jù)我們得到了振動方向角與質點平均速度和平均拋射高度的相關系數(shù)，分別是 0.70和0.889。這個結果指出，振動方向角δ同時影響質點平均速度和平均拋射高度。所以當振動方向角為40°左右時我們可以同時獲得較高的質點平均速度和平均拋射高度。
4 結論
1)振動篩面上的單質點運動比較復雜。質點在篩分過程中的運動可以較好的運用彈性碰撞理論進行描述。
2)在振動篩的參數(shù)中，振幅和振動方向角對質點平均速度和平均拋射高度的影響比較大，相對的振動頻率和篩面的傾角的影響就比較小。 對于難篩物料為了獲得較高的篩分效率比較理想的參數(shù)為頻率f 為13 Hz，振幅λ為6.6 mm，篩面傾角a0為6°，振動方向角δ為40°。
3)基于物理仿真原則和篩分過程客觀規(guī)律的振動篩仿真實驗是研究篩分理論的簡單而又可靠地辦法。
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