Procedia Earth and Planetary Science 1 (2009) 819–829
Procedia Earth and Planetary Science www.elsevier.com/locate/procedia
=
The 6th International Conference on Mining Science & Technology
Mathematic simulation of +13 mm particles motion in jig Kuang Ya-lia, ∗, Zhang Juna, Zhang Hai-yanga, Ge Junb ~
pÅÜççä=çÑ=`ÜÉãáÅ~ä=båÖáåÉÉêáåÖ=~åÇ=qÉÅÜåçäçÖóI=`Üáå~=råáîÉêëáíó=çÑ=jáåáåÖ=C=qÉÅÜåçäçÖóI=uìòÜçì=OONNNSI=`Üáå~= Ä gáååáì=båÉêÖó=oÉëçìêÅÉë=`çK=iqaI=uáåÖí~á=MRQMMMI=`Üáå~=
Abstract To meet the needs of the jigging process control, attempt to combine the studying on jigging mechanism with the operating and detecting parameters so as to use them in practical producing control. On the basis of studying the motion characteristic of water in jig, the motion of particles with different size and density was researched. A laboratorial model jig and a high-speed dynamic analysis meter were used and 60 group conditions were designed in experiment. The motion rule and curves were gained through analyzing the huge amount of data and pictures with the high-speed dynamic analysis meter. The conclusion is that the characteristic of the position curve of the particles is similar with the typical damped vibration. Then the motion differential equation of the particles was educed imitating the damped vibration and the solution equations were gained. In the equations the motion parameters of the particles in jig, such as velocity, acceleration, force etc. are in a direct proportion to the air pressure, and have a definite non-linear relationship with the jigging cycle, thickness, mobility of the jig bed, mass and size of the particles and so on. The equations might be used directly in control process of jig.
hÉóïçêÇë: jig process; particle motion; vibration equation; high-speed dynamic analysis
1. Intruduction In jigging process, the motion characteristic of particles affects the result of stratification of particles. The researches on motion characteristic of particle have been continued for many years. H.M. Welkhovsky[1], a Russia scholar, researched on the differential equation of a single particle without the horizontal flow in the jigging bed. ɗ.ɗ.lafalief-lamarka studied the differential equation of a single particle in interference moving when the elasticity collision occur with inertia force[1]. Japanese Kawashima claimed that the motion equation of particles in the jig bed is an differential equation which is related to the vertical displacement[2], terminal velocity, the water height in the chamber of jig, the speed of the water under the screen, mobility of the bed, etc. Zhang Rong-zeng[3] presented an equation of the force acted on the particles when he studied the mobility and stratification of the bed in jig. The tendency of most researches is that the motion differential equation is a second-order non-homogeneous one although the historical background, conditions, methods, and means are different in the researches. ∗
Corresponding author. Tel.: +86-516-83883530. bJã~áä=~ÇÇêÉëë:
[email protected].
1878-5220 © 2009 Published by Elsevier B.V. Open access under CC BY-NC-ND license. doi:10.1016/j.proeps.2009.09.129
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K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
In this paper, a series of +13 mm particles motion equations were developed based on a mass of experiment data and curves measured on line. The equations express the relationship between motion parameters, such as position, velocity, acceleration, force etc. and jigging parameters, i.e. air pressure, jigging cycle, thickness and mobility of jig bed. 2.
Experimental
OKNK=bñéÉêáãÉåí~ä=ÅçåÇáíáçåë= A set of experimental facility system is built in laboratory. The system consists of a U-shaped trough, an electromagnetic-air-valve controlled by digital controller, a compressor, and an air blower. The system used to simulate the jigging process of a BOM-jig. The U-shape though is made by transparent plastic so as to observe the bed moving. Digital controlling electromagnetic valve is used to control the model jig to adjust the jigging operation. Jigging cycle is a time in which liquid suffers a pulsation stroke and a suction stroke, and its range adjusted is 0.08-2.5 s. The durations of air entering, air exhaust, expand, and air addition are set as percentage of jigging cycle. Their adjustable ranges are 10%-40%, 10%-40%, 10%-65%, and 5%-20%, respectively. The total of the durations is 100%. Duration of air adding is a short time of air entering in the duration of expanded or ceasing, which is of benefit to make jig bed mobile. The material used in the test is rubber particles. The particles are regular cylinder. Their sizes are 25 mm (both diameter and height are the same) and 13 mm, and their specific gravities are 1.3 and 1.7 g/cm3 respectively. OKOK=bñéÉêáãÉåí=~å~äóëáë= Under the conditions mentioned above, jigging process was simulated in the experimental system, and the process was shot with high-speed dynamic camera at the same time. The photos were analyzed with the high-speed dynamic analysis meter [4] and the image analysis software NEW MOVIES in HSDAS (high-speed dynamic analyzing system). The analysis procedure is tedious. At first the photos were played in the high-speed dynamic analysis meter repeatedly so as to select the suitable particles easy to be analyzed, which should be representative and visible, i.e. not be covered by other particles during test and to conform the number of particles to be observed. Then with the image analysis software, the position marks were signed at each selected particle in the order of photos on the computer screen. At last the analysis software calculated the data of the distant moved by particles, velocity, and acceleration etc. and drawn curves of motion parameters based on the marks. 3.
Analysis of particle motion
PKNK ^å~äóëáë=çÑ=ÉñéÉêáãÉåí=ÅìêîÉë== Two groups of position curves of water and particles in jig are shown in Figure 1. They periodically changed their feature, i.e. shaking regularly round a static center. But at the very beginning, the situation was complex, and the shaking center rises up. After a short period, the vibrating stabilized. According to the theory of vibration [5], it is concluded that the feature of position curve of water and particles is the same as typical vibration curve, damped vibration by force. In practical, jigging water and particles do oscillate up and down periodically at a balance position. If condition changed, they will vibrate at a new balance position. According to the theory of vibration [5] the motion differential equation of water and particles in jig should be in form as following:
ã
d2ñ dñ + Å + âñ = m ( í ) 2 dí dí =
or
d 2 ñ Å dñ â 1 + + ñ = m (í ) ã d í 2 ã 2í ã
====ENF=
=
K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
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Fig. 1. Position curve of the water and particles in jig
2Ö â = =ω 2 ã ä The equation (1) expresses a linear non-homogeneous differential equation. Where is the natural
frequency of the un-damped vibration, c is the damped coefficient, and
ã is the mass of vibrating body.
PKOK qÜÉ=ãçîÉãÉåí=ÇáÑÑÉêÉåíá~ä=Éèì~íáçå=çÑ=íÜÉ=ï~íÉê=áå=àáÖ== The movement differential equation of the water in jig has been developed in the correlative research as follows[6]: Ç 2ñ Çñ 1 + 2 Üω + ω 2ñ = é 0 sin( ω í − ϕ ) Çí 2 Çí ã ==================================================================EOF============
The stabilized solution of equation (2) is: ñ (í ) = χ 0 +
m0 ⋅ â
1
[1 − (ω / ω ) ] + [2Ü(ω / ω )] 2 2
2
⋅ sin(ωí − ϕ )
======================================================================EPF=
2Ö â = ä ã is the natural frequency of water, ä is the equivalent length of vibrating liquid, m; ñ is the Where ξ ⋅µ ⋅Ç Çñ 2Üϖ = ã ⋅ θ is damped coefficient d is the Çí is the velocity of the water, position of the water in jig, m; thickness of the jigging bed, ȝ is the viscosity coefficient of water, ș is the mobility of the bed, ȟ is volume coefficient of the container of jig and particles in jig; m is the mass of vibrating water, kg;
ω2 =
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m ( í ) = é 0 sin( ω í − ϕ ) phase position of pulse air; í = 0.
is the pressure of pulse air changed periodically, ω
=
2 π T
q is jigging cycle, s;
χ
0
é0 is its maximal value, ϕ is initial
is the initial position of liquid level at the time
PKPK ^å~äóëáë=çÑ=íÜÉ=é~êíáÅäÉ=ãçîÉãÉåí= Comparing the position curves of water with that of the particles from Fig .1, it can be seen that the curves have the characteristics as follows: 1) There is a longer interregna at the falling end of the particles, because the screen plate prevents the continued movement of the particles, thus the shape of particle motion curve shows a section of flat straight line, which is out of the law of vibration curve. At this time liquid level continues to falling, then the curve of liquid is a complete vibration curve. 2) With the exception of the interregna, the shape of the position curve of the particle is the same basically as that of the water. This shows that the laws of its movement basically conform to that of the water. 3) The distance of the water motion is farther than that of particle; in spite of the initial position of the water is lower, but its vibration center higher than the particle. As analyzing above, the motion of the particle is forced vibration before the interregna, and its differential equation form is the same as the water’s, the basic form of differential (1). But the motion equation of particle should be different in the interregna, so the form of particle motion equation can be composed of sub-paragraph.
4.
Particle motion equation
From the deducing process[6] of the motion equation of the water in jig, it can be seen that the keys of solving Å â = 2Üω = ω 2 ã ã the differential equations (1) and (2) are solving the natural frequency , the drag coefficient , and the form of obtruding force. QKNK aÉíÉêãáåáåÖ=íÜÉ=å~íìê~ä=ÑêÉèìÉåÅó=çÑ=íÜÉ=é~êíáÅäÉ=ÑêÉÉäó=ìåJÇ~ãéÉÇ= In the liquid, the vibrating force of liquid drives the particle to vibrate. If the particle is regarded as a very small particle, its motion is the same as that of the water in the jig. The volume of particle is smaller than the liquid, so it can be similar to the form of the natural frequency of the liquid. However, its quality should be the quality of the particle.
ω2 =
2Ö âÇ 2Ö = âÇ = ãÇ ä ãÇ = , = ä =================================================================================EQF=
Where ä is the equivalent length of vibrating liquid. ãÇ= is quality of particle, and âÇ is vibration coefficient of vibrating liquid. QKOK qÜÉ=Ç~ãéáåÖ=ÅçÉÑÑáÅáÉåí= QKOKNK=qÜÉ=ãçÇÉä=çÑ=îáÄê~íáåÖ=ãÉÅÜ~åáÅë= The damping coefficient of liquid Fig.2 (a) as model.
Å in differential equation of freely damped vibration was derived by using
Å = 6πµÇ ( o / É) 3
ERF=
=
K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
823 =
Fig. 2. The model of vibrating mechanics
In the equation (5), o and É express volume in dimension m3, in which o represents the total volume of the 3 vibrating body, and É represents the total volume of the gap. Compare with the equation of the mobility of the bed jigging 3
θ =
3
3
total volume of the gap in the bed sÉ = total volume of the bed in jig síçí~ä
K==
The equation (5) can be changed as =====
Å ≈ µÇ (
o 3 1 ) ≈ µÇ É θ ================================================================================================ESF=
When the bed vibrates in the fluid, the damping coefficient is inversely proportion the mobility of bed when the bed is moving downward. Considering the different space patterns between container in Fig.1(a) and jigging bed, introduce a coefficient ȟ, so the damping coefficient based Fig.2 can be changed as =======
Å = ξ
µÇ θ =========================================================================================================ETF=
QKOKOK=qÜÉ=Ç~ãéáåÖ=ÅçÉÑÑáÅáÉåí=çÑ=é~êíáÅäÉ=ãçíáçå=áå=àáÖÖáåÖ=ÄÉÇ= Contrasting the model of vibrating mechanics, jigging bed has been abstracted as the form of Fig.2 (b). From the curve of the position of particles and velocity (Fig 3), it can be seen that the velocity that particles move in rising phase is different from decline phase, because of different resistance. The discussion on the different phases of the particle movement is as below. 1) The damping coefficient of particles motion in rising phase The velocity of the water in jig is larger than particles in rising phase, so the relative movement between water and particles produces driving force. At this time, the resistances that particles get are mechanical friction and gravity. The gravity is very small relative to the driving force of the water on rising phase, so it can be neglected. The mechanical friction is inversely proportional to the mobility of bed. Adding a coefficient, the damping coefficient can be identified as: Å =
where
ζ
ζ θ ==========================================================================================================EUF=
is related to the mobility of bed, and θ is mobility of bed.
Let 2 Üω =
Å ζ = ãÇ ã Ç θ ===========================================================================================EVF=
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K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
Fig. 3. The curve of the position of particles and velocity
2) The damping coefficient of particles motion in decline phase In decline phase, the gravity of particles is not resistance but driving force. Before the particles stop moving the velocity of water is lower than particles under the condition of experiment (Fig 3). So it can be considered that the resistance on the particles is only produced by water, and the expressing form of the damping coefficient c in the equation (7) is as follows:
Å =ξ
µ ⋅Ç θ =
Let
2 Üω =
ξµ ⋅ Ç Å = ãÇ ã Ç θ =========================================================================================================================ENMF=
3) Discussion on the interregna In the interregna, the resistance on the particles can be considered to be infinite and to result from the screen plate. So the displacement, velocity and acceleration of the particles are zero. QKPK qÜÉ=ÉñíÉêå~ä=ÑçêÅÉ=çÑ=é~êíáÅäÉë=mEíF= The external force on particles is driving force by water. Because the normal motion of the bed is in the stabilization period of the vibrating, the driving force of the particles by water is the force keeping simple harmonic
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825 =
moving. The external force on particles is direct proportion to water velocity. The water velocity equation had been derived through experiment:
Çñ = Çí
πm0q ã (
Öq 2 § ξµÇπq · − 2π 2 ) 2 + ¨ ¸ ä © θ ⋅ã ¹
2
cos(
2π í − ϕ) q =
Considering the damping coefficient of the particles is different in rising phase and decline phase, so the external force on the particles is: ζπ m0 q ° 2 Öq § ξµ Ç π q °θ ⋅ ã ⋅ ã ( − 2π 2 ) 2 + ¨ Ç ° ä © θ ⋅ã Çñ ° m = Å⋅ =® ξµ Ç πm0 q Çí ° ° 2 Öq § ξµ Ç π q °θ ⋅ ã Ç ⋅ ã ( − 2π 2 ) 2 + ¨ ä °¯ © θ ⋅ã 2π í −ϕ) = ® c ⋅ cos( q ¯
· ¸ ¹
2
· ¸ ¹
2
cos(
2π í − ϕ ), q
cos(
2π í −ϕ) q
===================================================ENN F=
Where c is the damping coefficient of particles; Çñ Çí is the velocity of liquid; F is the maximum amplitude when particles vibrate under external force. ζ ⋅ πm0q rising phase ° c1 = 2 Öq 2 § ξµÇπq · ° 2 2 − 2π ) + ¨ θ ⋅ ãÇ ⋅ ã ( ¸ ° ä © θ ⋅ã ¹ ° c =® ξµÇπm0q °c = ã Ö − decline phase Ç 2 ° 2 2 Öq ξµ Ç π q § · ° − 2π 2 ) 2 + ¨ θ ⋅ ãÇ ⋅ ã ( ¸ °¯ ä © θ ⋅ã ¹
========================================ENOF= QKQK m~êíáÅäÉ=ãçíáçå=Éèì~íáçå= Until now, the all the parameters in the differential equations of particle vibration have been fought out. The general differential equations are still used the form of equation (2). Noted that the mass ã should be changed as that of particles, ãÇ, and that P(t) is expressed as the equation (11). When the particle motion is stable, the solution of differential equations is:
ñ(í ) = ñ0 +
Take h, Ȧ,
ω , F,
c 1 2π ⋅ ⋅ cos( í − ϕ ) 2 2 âÇ 1 − (ω / ω ) 2 + [2Ü(ω / ω )] q =========================================================ENPF=
[
]
kd into the equation (13), then the displacement equation of particles motion can be shown as:
8= 26
K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829 ° ñ0 + ° 2ãÇ ° ° ° ° ñ ( í ) = ® ñ0 + ° 2ãÇ ° ° ° x(T ) 2 ° °¯
c1q 2 2
§ ζ ⋅ πq ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ © Ç
· ¸¸ ¹
2
⋅ cos(
c2 q 2 2
§ ξ ⋅ µ Ç πq ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ © Ç
· ¸¸ ¹
2π í − ϕ) q
⋅ cos(
2
0 ≤ í ≤ q1 ,
2π í − ϕ) q
q1 < í ≤ q 2
í > q2
==========================================ENQF=
Where ñEíF is the height of particles jumping at time t; ñM is the distance from the screen plate while particles are on the equilibrium position; F1 and F2 is the maximum external force that are determined by the equation (12); ãÇ is the mass of vibration particle; g is the gravity acceleration ; q is the cycle of jig;= ä is the equivalent length of
vibrating object; ȝ is the viscosity coefficient of liquid : ș is the mobility of bed; ζ is related to the mobility of bed in rising period; ȟ is the volume coefficient of the jigging chamber; ϕ is initial phase position of pulse air; Ç is thickness of jigging bed; í is time; T1 is air intake period; T2 is related to the interregna . Because it doesn’t create relationship between the cycle of the air valve and the motion cycle of water and particles in this experiment, so T1
and T2 is determined as this for a while. ζ and ȟ are coefficients that need to further study. Similarly, according to the position equation of particles, the equation of the velocity, acceleration, kinetic energy, force etc. can also be derived as follows: Velocity
=======
Acceleration
° ° ° ãÇ ° Çñ °° =® Çí ° ° ãÇ ° °0 ° °¯
− π c1q 2
§ ξπ q ªÖ 2 2º «¬ ä q − 2π »¼ + ¨¨ ã θ © Ç − π c2 q
· ¸¸ ¹
2
⋅ sin(
2
§ ξ ⋅ µÇπq ªÖ 2 2º «¬ ä q − 2π »¼ + ¨¨ ã θ Ç ©
° ° ° ãÇ ° 2 Ç ñ °° =® Çí 2 ° ° ãÇ ° °0 ° °¯
· ¸¸ ¹
2
2π í −ϕ) q
⋅ sin(
2π í −ϕ) q
0 ≤ í ≤ q1 ,
q1 < í ≤ q 2
í > q2 ========================ENRF= − 2π 2 c1 2
§ ζ ⋅ πq ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ © Ç − 2π 2 c2 2
§ξ ªÖ 2 2º « ä q − 2π » + ¨¨ ¬ ¼ ©
· ¸¸ ¹
2
⋅ cos(
2π í −ϕ) q
2π ⋅ cos( í −ϕ) 2 q ⋅ µ Çπ q · ¸ ã Ç θ ¸¹
0 ≤ í ≤ q1 , =ENSF=
q < í ≤ q2
í > q2
=
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K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
Kinetic energy
Force
1 ° ° 2ã Ç ° ° °° 1 b=® ° 2ã Ç ° ° °0 ° ¯°
° ° ° ° 2 Ç ñ °° =® ãÇ Çí 2 ° ° ° °0 ° °¯
(πc1q )2 2
§ ξπ q ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ © Ç
· ¸¸ ¹
2
sin 2 (
(πc2 q )2 2
§ ξ ⋅ µ Ç πq ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ Ç ©
· ¸¸ ¹
2
2π í − ϕ) q
⋅ sin 2 (
0 ≤ í ≤ q1 ,
2π í − ϕ) q
==ENTF= q1 < í ≤ q 2
í > q2 − 2π 2 c1 2
§ ξπ q ªÖ 2 2º « ä q − 2π » + ¨¨ ã θ ¬ ¼ © Ç − 2π 2 c2
· ¸¸ ¹
2
⋅ cos(
2π í −ϕ) q
2π ⋅ cos( í −ϕ) 2 2 q § · ⋅ ξ µ π Ö Ç q ª 2 2º « ä q − 2π » + ¨¨ ã θ ¸¸ ¬ ¼ Ç © ¹
0 ≤ í ≤ q1 ,
=ENUF q1 < í ≤ q 2
í > q2
QKRK ^å~äóëÉë=~Äçìí=íÜÉ=ãçíáçå=Éèì~íáçå= QKRKNK=qÜÉ=éçëáíáçå=Éèì~íáçå= From the equation (14), it can be seen that the jumping height of particles is related to initial position, is direct proportion to the jumping height of water, and is inversely proportional to the resistance on and the mass of particles. In rising phase, the bigger the mass of particles is, the lower the jumping height of particles is. In decline phase, the viscous resistance of water and the thickness of bed have much more relationship with ȟ, so the small particles may drop more for the more prominent effect of particle size. Comparing to the equation of water, the reason that particles jump lower is that F is less than 1, and the particle is much heavier than the water (m). Observing the curves given in section 3.4, it can be seen that these relations among the parameters are in line with the actual situation If revert the equation (14) to the original solution of (13), and solve the equations of velocity and acceleration, it can be found that each motion parameter only have relation to general frequency of the jigging system and vibrating frequency of pulse air. This should be noticed. From the process of formula deriving, it shows that the stratification of jigging is result from the pulse water in jig, which is closely related to the law of pulse air. . Although the motion law of the air is different as the structure and operating parameter of air-value is different, it’s replaced by the sin function in this paper. This will also help us to understand the motion law of water and particles, and derived the whole of formula. QKRKOK=cçêÅÉ=Éèì~íáçå= It can be considered that the equation (18) only shows calculation method of the compositive force on the particles, but no the express of the force analysis and decomposition, which is different from the study in the past. Previous researches on force on the particles in jig are different in theory, although which are very detailed, but they are difficult to measure and control in the actual production. While the parameters in the equation (18) are measurable or controllable, which are useful for actual control. QKRKPK=m~ê~ãÉíÉê=~å~äóëáë= Besides the maximum amplitude, every parameter in equations (14) to (18), such as cycle, quality, bed thickness
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K. Ya-li et al. / Procedia Earth and Planetary Science 1 (2009) 819–829
etc., is not standard linear relationship with the motion parameters, displacement, velocity, and acceleration. According to the power of T, the relationship between jigging cycle T and position should be the exponential relationship. As T increased, the displacement should be increased, but the rate of increase is non-linear. The effect of cycle T is gradually changing from the position equation to velocity and acceleration. According to the equation (15) and (16), it can be seen that T will reduce one power and the shape of the cure is more curving when solve differential coefficient to motion equation. The equivalent length ä of vibrating mass is directly proportional to the jumping height. It is easy to understand. The thickness of bed d is inversely proportional to the jumping height, so the driving force needed to drive the jigging bed to move will be increased while the thickness of bed is increased, if not, the jumping height will be reduced. The vibrating mass md is inversely proportional to the jumping height, so the height will be reduced with increasing ãÇ. Because ãZs√ȡ, the mass have relationship with density and particle size. According to the equation (14) and (15), the motion parameter is inversely proportional to the mass or density. In other words, when the other conditions keep stable, the jumping height of high-density particles is lower than that of the low-density. These are in line with the experimental curve. The second item in denominator of equations (14) to (18) includes the effects of resistance. When the mobility of the bed is increased, the motion parameters will increase with the resistance reducing. In practice, ș changes seasonally, but an optimum ș, the best mobility of the bed, can be specified at given time. Then take it into the equation to calculate. When check the equations, it is found that the value of the early phase ϕ is not fixed. If fix it, the phase relationship with the different motion parameters in the cures can not be achieved. The parameters ȟ and
5.
ζ
come from the resistance parameter derived, also need to be further studied.
Conclusions
Under the experimental conditions, the position curves of particles are cyclical changes, that is, the particles vibrate around a stable position. Comparing to the vibration characteristics described by vibration theory, the position curves of particles motion is in accord with the law of damped vibration by force. According to the damped model in vibration theory, the damped coefficient of particles in jig is derived. The coefficient is inversely proportional to the mobility of bed, directly proportional to the thickness of bed in decline phase, and is related to the shape of gap among particles and viscosity of liquid. The solution of vibrating differential equation of particles motion in jig is the position equation of the particles. The position equation is related with the jigging cycle, mobility of bed, air pressure, and thickness of bed. It can be seen that the jumping height of particles in jig is directly proportional to the maximal air pressure and the jigging cycle, and is inversely proportional to the damped coefficient and vibrating mass, which tallies with the actual situation. The equations of velocity, acceleration, force, and kinetic energy of water in jig can be derived based on the position equation, which have the specific relation with the air pressure, jigging cycle, damping etc. A complete series of motion parameter equation system of particle in jig is developed which can express completely the motion characteristic of bed in jig when consider the particles. Observing motion parameter equations of water, one can perceive that only the pressure of pulse air has linear relationship with the motion parameters. This needs to be noticed in industrial production because the air pressure to jig affects the separating perfection.
Acknowledgements Project 50474065 supported by the National Natural Science Foundation of China.
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