# Coal and Gangue Underground Pneumatic Separation Effect Evaluation Influenced by Different Airflow Directions

Authors: Kehong Zheng; Changlong Du; Jianping Li; Bingjing Qiu
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

Coal and gangue underground pneumatic separation is of key importance for green mining. Two kinds of arrangement schemes for high-pressure value used in pneumatic separation system are proposed in this study. Pneumatic separation effects are examined under different arrangement of high-pressure value. Here, theoretical pneumatic separation distance formulas of mineral particles affected by different airflow directions are derived and validated by a series of numerical simulations and orthogonal experiments. In the following analysis, the effects of gangue diameter (d), conveyor velocity (v0), and the height difference between conveyor belt and air nozzle (hp) are mainly considered. The numerical simulation and experimental results indicate that pneumatic separation effects under the condition of u and v0 being in the opposite direction will be better than that of u and v0 being in the same direction. The pneumatic separation distance ΔS shows a decreasing trend with the increasing of the three factors. The study also shows that gangue diameter has the most significant influence on separation distance, followed by conveyor velocity v0 and height difference hp.


---

## Body

## 1. Introduction

Coal has been regarded as the most widely used fuel in many countries because of the lack of oil and gas resources, which is expected to be prolonged over decades. Initial underground separation for coal and gangue is an indispensable process of mine production and has great significance for coal preparation. Gangue from underground separation can be used for filling mined-out areas, improving the quality of raw coal, decreasing the cost of preparation, saving transport capacity, and reducing the amount of waste polluting the environment above the ground [1, 2]. Currently, several technologies of underground separation coal and gangue are proposed, which include an automated hydraulic separation technology and a rotating impact method of coal gangue separation underground [3–6]. However, underground separation technologies mentioned above have the disadvantages of high cost, being time-consuming, and low automation.With the development of digital image processing technology, scholars mainly probed into a general machine vision approach for online identification of coal and gangue [7–10]. The influences of camera location, particle overlap, image blur degree, and conveyor velocity were investigated during the coal and gangue particles online transportation [11–14]. From the above discussion, machine vision process has the advantages of real-time processing, lower cost, and higher intelligence.Lots of researches have conducted the online identification of coal and gangue, which have proved the feasibility of image recognition of coal and gangue. Nevertheless, pneumatic separation of coal and gangue has not been discussed adequately and has not been applied in mineral separation.Currently, pneumatic separation has been widely used in agriculture field and rare metal recycling field. A cotton seed online separation system based on machine vision was designed to realize automatic separation of red-brown and black cotton seed by compressed airflow in the air [15]. Guo et al. proposed a series of methods to realize the recycling of printed circuit boards (PCBs); the whole process that involves crushing and electrostatic and pneumatic separation has formed a closed cycle that can return material and provide salable product [16]. Xu et al. described an effective mechanical process including impact crushing from printed circuit boards and investigated the pneumatic separation for metal recovery scraps [17]. Kumar et al. report a simple and eco-friendly physical pneumatic separation process for the recycling of metallic values from PCBs [18, 19]. The effect of orifices on spherical particles was clarified by Hayashi and Oki through numerical simulations of air-solid multiphase flow in a vertical single-column pneumatic separator to realize recycle important rare metals (such as tantalum) in the PCBs of waste electronic equipment [20]. Havlik et al. focused on studying mechanical-physical pretreatment of PCBs from used consumer equipment followed by extraction of copper and tin from residue fractions by leaching in hydrochloric acid solutions [21].Moreover, researchers also have done lots of research on pneumatic separation of coal particles (particle size, i.e., mainly less than 5 mm) in fluidized conveyor. Liu et al. investigated the pneumatic classification behavior in a laboratory CCMC reactor with such a configuration by removing the coal fraction below a given size (e.g., 3.0 mm) from 0 to 20.0 mm [22, 23]. Yang et al. attempted to carry out a systematic process analysis of fine coal preparation in a vibrated gas-fluidized bed (VGFB) [24].The research group has proved the feasibility of pneumatic separation technology for coal and gangue, yet pneumatic separation effects influenced by different arrangements of high-pressure value have not been presented. In this paper, theoretical models were established for the study of pneumatic separation process affected by different high-pressure airflow direction. Then, a series of numerical simulations and orthogonal experiments were conducted to evaluate the separation effect under different airflow direction. Finally, the theoretical models were corrected based on experiment data.


## 2. Principle

Underground coal and gangue pneumatic separation system, which is shown in Figure1, contains three parts: preliminary crush separation system, machine version system, and pneumatic separation system. Preliminary crush separation system mainly contains roll-type crusher, spiral size screen, and several conveyor belts, which aims to limit the granularity of coal and gangue sent into machine vision system within a range of 50 mm~100 mm. Machine vision system is a highly automated technology using digital image processing technology to identify the size and location of gangue based on identification algorithms; then the identified information will be sent to pneumatic separation system through image sensor. Pneumatic separation system is controlled by computer to realize coal and gangue pneumatic separation.Figure 1
Separation system of coal and gangue.(1) High-pressure gasholder; (2) air compressor; (3) separation equipment; (4) vibrating sieve; (5) sieve plate; (6) coal conveyor belt; (7) conveyer belt for coal and gangue recognition; (8) coal; (9) gangue; (10, 11) materials conveyor belt; (12) (a, b) high-pressure value array; (13) control equipment; (14) computer; (15) image acquisition equipment; (16) CCD camera; (17) camera box; (18) conveyor belt; (19) coal conveyor belt; (20) LED light array.Two kinds of arrangement schemes for high-pressure value used in pneumatic separation system are presented in Figure1. One is that particles’ motion direction is the same as that of high-pressure airflow; the other is that particles’ motion direction is opposite to that of high-pressure airflow. As shown in Figure 1, the high-pressure values 12(a) are arranged under the conveyor belt (7) in the first arrangement scheme, mixed mineral materials are thrown from conveyor belt (7), coal materials unaffected by high-pressure airflow will fall onto conveyor belt (10), and gangue materials affected by high-pressure airflow will fall onto conveyor belt (11). In the second arrangement scheme, high-pressure values 12(b) are arranged in front of conveyor belt (7), mixed mineral materials are thrown from conveyor belt (7), coal materials unaffected by high-pressure airflow will fall on conveyor belt (11), and gangue materials affected by high-pressure airflow will fall on conveyor belt (10).


## 3. Model Development

### 3.1. Theoretical Model

The movement of mineral materials affected by high-pressure airflow can be divided into three stages:(1) particle’s movement before falling into airflow domain; (2) movement of particle in airflow domain; (3) movement of particle after leaving the airflow domain. When the movement direction of mineral materials is the same as that of high-pressure airflow, coal particle trajectory unaffected by high-pressure airflow is shown in Figure 2(a) of curve 1 and gangue particle trajectory affected by high-pressure airflow is shown in Figure 2(a) of curve 2. When the movement direction of mineral materials is opposite to that of high-pressure airflow, coal particle trajectory unaffected by high-pressure airflow is shown in Figure 2(b) of curve 1 and gangue particle trajectory affected by high-pressure airflow is shown in Figure 2(b) of curve 2.Figure 2
Pneumatic separation model of coal and gangue.
(a)
x
˙ and u are in the same direction
(b)
x
˙ and u are in the opposite directionAs shown in Figure2, ΔS represents the pneumatic separation distance of coal and gangue, hp represents the height difference between gangue mass center on conveyor belt and upper boundary of the airflow domain, tp represents the motion time before gangue came into the airflow domain, vp1,2 is the velocity in direction y of gangue before falling into airflow domain, and hj represents the height of airflow domain. Si represents the displacement in x direction of gangue before entering airflow domain. tj1,2 represents the motion time of gangue in airflow domain, and Sj represents the motion displacement in x direction of gangue in airflow domain. vf1,2 represents the motion velocity in y direction of gangue in airflow domain, x˙(tj1,2) represents the motion velocity in x direction of gangue in airflow domain, tf1,2 represents the motion time of gangue after leaving airflow domain, and Sf1,2 represents the motion displacement in x direction of gangue after leaving airflow domain. In the following equations, subscript 1 is used to represent when airflow velocity and conveyor belt velocity are in the same direction, and subscript 2 is used to represent when airflow velocity and conveyor belt velocity are in the opposite direction.Coal and gangue materials will be recognized by machine vision system and the recognized image information will be sent to pneumatic separation system through image sensor. Coal particles will fall from the conveyor belt freely without the effect of high-pressure airflow. When the motion direction of mineral materials is the same as that of high-pressure airflow, gangue material will change its trajectory and will be thrown significantly farther than that of coal particle. When the motion direction of mineral materials is opposite to that of high-pressure airflow, gangue material will change its trajectory to an opposite direction compared with that of coal particle. The motions of coal and gangue particles are analyzed, respectively, in the following three sections.When coal materials are recognized by machine vision system, coal particles will fall from the conveyor belt freely unaffected by high-pressure airflow.t0 and S0 can be obtained through (1) and (2). Gangue motion law at this stage is the same as coal materials. Si and vp can be also shown by (3) and (4), where t0 represents the motion time of coal particle, and S0 represents the displacement of coal particle in x direction:(1)t0=2hp+hj+hfg,(2)S0=v02hp+hj+hfg,(3)Si=v02hpg,(4)vp=g2hpg.In order to calculate the acting force of high pressure on gangue particles, multiple rectangular polyline is used to approximate gangue particle’s physical shape if the dynamic pressure head of the airflow domain is known in special location. The acting force of high-pressure airflow on gangue can be presented by(5)F=∬APddA=∑i=1mPdiAi,where F represents the acting force of the high airflow on gangue, Pdi represents the high pressure in ring i, Ai represents the area of ring i, and m represents the total number of rings.As shown in Figure3, gangue is affected by airflow with different directions. In order to analyze the movement of gangue particle in high-pressure airflow domain, air resistance and horizontal momentum’s increment of airflow domain are ignored. The theoretical formula of gangue displacement in direction y can be expressed as s=∫0tj1,2(vp+gtj1,2)dt=h-d; then tj1,2 can be obtained as shown in(6)tj1,2=vp2+2gh-d-vpg.Figure 3
Schematic diagram of gangue’s motion in airflow domain.
(a)
x
˙ and u are in the same direction
(b)
x
˙ and u are in the opposite directionAs shown in (6), gangue affected by different airflow direction has the same motion time in airflow domain. Gangue will be affected by two forces after falling into high-pressure airflow domain. The two forces applied on gangue particle are gravity and high dynamic pressure. Airflow dynamic pressure will convert to static pressure on condition that the velocity of airflow u is larger than gangue’s horizontal velocity v0 and airflow must keep dynamic pressure pd=ρx˙2/2. The pressure difference can be expressed as Δpd=ρ(u2-x˙2)/2. According to (5), the formula of airflow force can be expressed by(7)F=∬pdA≈∑ipiAi=12ρ∑iui2-x˙2Ai.When the curvature of gangue surface is not too large, it can be approximately seen as a plane, so∀ui=u, (7) can be changed to(8)F=12ρu2-x˙2A.According to Newton’s second law, (8) can be changed to(9)mx¨=12ρAu2-x˙2,x˙anduare in same direction,mx¨=-12ρAu2+x˙2,x˙anduare in opposite direction.As shown in (9), the expressions are corresponding to different airflow directions. The general solution of displacement in x direction of gangue moving in the airflow can be obtained by taking Laplace transform to (9), and the result is shown in(10)xtj1=AρC2+mln⁡e2C1u-Atj1ρu/m+1-mC1+Atj1ρuAρ,x˙anduare in same direction,xtj2=AρC4+2mln⁡cos⁡Atj2uρ-2muC3/2mAρ,x˙anduare in opposite direction.The velocity of gangue inx direction in airflow domain can be obtained by taking derivation of (10). The general solution is shown in(11)x′tj1=ueAtj1uρ/me2C1u/m+eAtj1uρ/m,x˙anduare in same direction,x′tj2=-utan⁡Atj2ρu-2muC32m,x˙anduare in opposite direction.In order to calculate the constant coefficientsC1, C2, C3, and C4 in (10), the initial constraint conditions are as follows: the initial position of the gangue is x(0)=0 and the initial velocity of gangue is x′(0)=v0.Whenx˙ and u are in the same direction, the general solution of x(tj) and x′(tj) can be obtained by (10) and (11). C1 and C2 are shown in(12)C1=mln⁡u/v0-12u,C2=m2ln⁡u/v0-1-2muln⁡u/v02Auρ.The general solutions ofx(tj) and x′(tj) are shown in (13)xtj1=mln⁡emln⁡u/v0-1-Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu,x′tj1=ueAtj1uρ/meln⁡u/v0-1+eAtj1uρ/m.Whenx˙ and u are in the opposite direction, the general solution of x(tj) and x′(tj) can be obtained by (10) and (11). C3 and C4 are shown by (14)C3=arccos⁡u/v02+u2u,C4=-2mln⁡u/v02+u2Aρ.The general solutions ofx(tj) and x′(tj) are shown by (15) and (16), respectively,(15)xtj2=2mln⁡cos⁡Atj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ,(16)x′tj2=-utan⁡Atj2ρu-2marccos⁡u/v02+u22m.When gangue particles left the boundary of airflow domain, gangue particles would do flat parabolic motion. The formula of velocityvf in direction y is shown in(17)vf1,2=∫0tj1,2vp+gtdt.t
f
1,2 can be solved through (18) and the result is shown by (19):(18)hf=∫0tf1,2vf+gtdt=∫0tf1,2gtdt+∫0tf1,2∫0tjvp+gtd2t,(19)tf1,2=-gtj1,22-2tj1,2vp+8ghf+gtj1,22+2tj1,2vp22g.The displacementSf1,2 of gangue in direction x after leaving the airflow domain can be expressed by (20)Sf1,2=x′tj1,2tf1,2.To sum up, whenx˙ and u are in the same direction, the separation distance ΔS can be calculated by (21)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfueAtj1uρ/meln⁡u/v0-1+eAtj1uρ/mgtj1+2vptj1-v02hp+hj+hfg.Whenx˙ and u are in the opposite direction, the separation distance ΔS can be obtained by(22)ΔS=S0+Sj2+Sf2-Si=v02hp+hj+hfg+2mln⁡cosAtj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tan⁡Atj2ρu-2marccos⁡u/v02+u22m2uhftj2gtj2+2vp-v02hpg.The separation distanceΔS is shown by (21) and (22), which reflects the basic motion law of gangue when influenced by airflow field under different airflow directions. For the limitation of assumption, there exist big differences between theoretical model and practical model. In order to simplify the calculation and correct the difference between theoretical value and practical value, parameters kn (nonlinear correction factor) and kr (linear correction factor) are introduced. kn reflects the convergence rate of the fitting function, and kr reflects the convergent gain and is used to adjust the fitting effect of formula based on experimental value. Theoretical value will get close to experiment value by adjusting the value of kn and kr. The modified formulas with the correction factors are shown in(23)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-Akntj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfueAkntj1uρ/meln⁡u/v0-1+eAkntj1uρ/mgtj1+2vptj1-v02hp+hj+hfg-kr,(24)ΔS=S0+Sj+Sf-Si=v02hp+hj+hfg+2mln⁡cos⁡Akntjuρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tanAtjρu-2marccos⁡u/v02+u22m2uhftjgtj+2vp-v02hpg-kr.


### 3.2. Air-Solid Multiphase Pneumatic Separation Simulation

In order to evaluate the pneumatic separation effect under two kinds of arrangement schemes for high-pressure value, a “fixed coarse-grid” fluid scheme is applied in PFC3D for pneumatic separation simulations. In the fluid scheme, 550 (22 × 5 × 5:x, y, and z directions) fluid cells are created in a rectangular space (x = [0,  7000 mm], y = [−400 mm,  400 mm], and z = [300 mm,  400 mm]), which covers the rectangular space. A pneumatic boundary should be set for the fluid grid. Driving forces from the fluid flow are applied to the particles as body forces. These forces are also added to the fluid equations and cause change in momentum, as reflected by the change in the pressure gradient in the flow direction.As shown in Figures4(a) and 4(b), two available models are established to reduce the computation time without loss in accuracy. The gangue hopper, containing 300 balls, is built at the top right of conveying belt 1; it is aimed at reducing the computation time. The front view of the simulation models at an initial stage under different airflow directions is shown in Figures 4(a) and 4(b), respectively.Figure 4
Air-solid multiphase pneumatic separation.
(a)
v
0 and u in the opposite direction
(b)
v
0 and u in the same directionIn Figure4(a), the velocity v0 of conveyor belt 1 and airflow velocity u are in opposite directions. When gangue falls into the airflow domain, gangue particle will change its trajectory to an opposite direction and fall onto conveyor belt 2. The conveyor belt 2 has the same movement direction as airflow velocity; finally gangue particles will be transported to collecting box by conveyor belt 2. In Figure 4(b), conveyor belt v0 and airflow velocity u are in the same direction. When gangue falls into the airflow domain, gangue particle will throw much farther and fall on conveyor belt 2. The motion of conveyor belt 2 has the same motion direction as conveyor belt 1; finally the gangue particles are transported to collecting box by conveyor belt 2.In the fluid scheme, a pneumatic boundary is set for two available models. During the simulations, an approximation is made by specifying the velocity boundary at the right end of the model and a pressure boundary as 0.0 Pa at left end withx=0 mm. The slip boundary, in which the fluid velocity parallel to the wall surface is nonzero at the wall surface, is specified at the surrounding four walls. In simulation as shown by Figure 4(b), an approximation is made by specifying the velocity boundary at the left end of model and a pressure boundary as 0.0 Pa at the right end with x=7000 mm. The initial setup of the slip boundary in Figure 4(b) is the same as that shown in Figure 4(a) and material properties are shown in Table 1.Table 1
Materials properties.
Parameter
Value
Units
Ball
Diameter
50~100
mm
Number
300
—
Density
2700
kg/m3
Normal stiffness
1 × 106
N/m
Shear stiffness
1 × 106
N/m
Friction coefficient
0.7
—
Air
Density
1.205
kg/m3
Viscosity
1.8 × 10−6
Pa⋅s
Wall
Normal stiffness
1 × 106
N/m
Shear stiffness
1 × 106
N/m
Friction coefficient
0.3
—As shown in Figure4(a), airflow is injected with a velocity of 300 m/s from the negative direction of x at the starting point, while, in Figure 4(b), air is injected from the positive direction of x. When the pneumatic boundaries are applied at the initial stage, the two side walls applied to confine the assembly are removed simultaneously. Figure 5 shows the front view of simulation result from the initial stage to 1 sec.Figure 5
Front view (initial stage to 1 sec; apparent velocity, ±260 m/s).
(a)
v
0 and u are in the opposite direction
(b)
v
0 and u are in the same directionIt can be obtained from Figure5 that gangue particles have different motion trajectories under different airflow velocity. As shown in Figures 5(a) and 5(b), gangue particles will do horizontal projectile motion before entering airflow domain, as can be seen at t=0.2 s and t=0.4 s. As shown in Figure 5(a), velocities of conveyor belt 1 v0 and airflow u are in the opposite direction, and gangue particles will change their motion trajectories to an opposite direction compared with that of coal without the effect of airflow, which can be seen at t=0.6 s, t=0.8 s, and t=1.0 s. As shown in Figure 5(b), velocities of the conveyor belt 1 v0 and airflow u are in the same direction, and gangue particles will be blown much farther than that of coal without being affected by airflow, as can be seen at t=0.6 s, t=0.8 s, and t=1.0 s.As can be seen in Figures5(a) and 5(b), gangue particles will change their trajectories in area A and area C. Areas B and D, as shown in Figures 5(a) and 5(b), illustrated that gangue particles with smaller diameters can be blown much farther.In order to study the pneumatic separation distance influenced by different airflow directions, airflow velocities ±300 m/s are chosen for the research of separation effect. Conveyor velocityv0 and height difference hp between conveyor belt and air nozzle are kept constant. The relationships between separation distances and particle diameters under different airflow velocity directions are shown in Figure 6.Figure 6
The relationship between particle diameter and separation distance under different direction airflow velocity (u=±300 m/s, v0=+1 m/s).As can be seen in Figure6, separation distance decreases with the increase of particle diameter. It also can be concluded that the separation effect under airflow velocity −300 m/s is better than that under airflow velocity 300 m/s. The separation effect also can be analyzed from (9); dynamic pressure difference ΔPd can be expressed as ρ(u2-x˙2)/2 when u and v0 are in the same direction, while, when u and v0 are in the opposite direction, the dynamic pressure difference ΔPd can be expressed as ρ(u2+x˙2)/2. Thus, it can be obtained from the above analysis that separation effect under airflow velocity −300 m/s is significantly better than that of under airflow velocity 300 m/s.


### 3.3. Orthogonal Experiment of Pneumatic Separation

Digital image processing technology has been used to identify the target of various patterns of coal and gangue in underground pneumatic separation system. Before mineral materials are sent to machine vision system, coal and gangue have been crushed to 100 mm by impact crusher. The size of materials is ranging from 50 mm to 100 mm. These materials are sent by the conveyor belt for coal and gangue digital image information identification (as shown in Figure1).In this study, separation distanceΔS (m) is selected as the primary index to evaluate the pneumatic separation effect. Pneumatic separation influenced by different airflow direction can be achieved by changing the arrangement of high-pressure value. The pneumatic separation test system mainly consists of conveyor belt, queuing system, machine vision system, control system, and high-pressure air injection system. When coal and gangue materials fell down from the conveyor belt, gangue will be identified by machine vision system, and the information is transported to control system through image sensor to drive the electromagnetic value open. Thus, coal gangue pneumatic separation is realized. The air compressor used in pneumatic separation testing system is LG-6.5/10, its working pressure is 1.0 Mpa, and certified capacity is 6.5 m3/min.From the analysis shown in Section3, the conveyor velocity v0, height difference hp, and gangue diameter d are selected as the three factors. Factors and levels are listed in Table 2. According to the identified level of factors, orthogonal table L9 (34) is applied in the test. Orthogonal experiment arrangement and results are shown in Table 3.Table 2
Levels of factors.
Level
Factor
A gangue diameter d (mm)
B height difference hp (m)
C conveyor belt velocity v0 (m/s)
1
50
0.40
0.50
2
80
0.80
1.00
3
100
1.10
2.00Table 3
Experimental results of separation effect.
Experiment number
A
B
C
Separation distanceΔS (m)
u and v0 are in the opposite direction
u and v0 are in the same direction
1
50
0.4
0.5
3.05
2.21
2
50
0.8
1.0
2.2
1.14
3
50
1.1
2.0
2.05
0.78
4
80
0.4
1.0
2.15
1.08
5
80
0.8
2.0
1.48
0.65
6
80
1.1
0.5
1.25
0.42
7
100
0.4
2.0
1.85
0.98
8
100
0.8
0.5
1.55
0.37
9
100
1.1
1.0
1.40
0.28


## 3.1. Theoretical Model

The movement of mineral materials affected by high-pressure airflow can be divided into three stages:(1) particle’s movement before falling into airflow domain; (2) movement of particle in airflow domain; (3) movement of particle after leaving the airflow domain. When the movement direction of mineral materials is the same as that of high-pressure airflow, coal particle trajectory unaffected by high-pressure airflow is shown in Figure 2(a) of curve 1 and gangue particle trajectory affected by high-pressure airflow is shown in Figure 2(a) of curve 2. When the movement direction of mineral materials is opposite to that of high-pressure airflow, coal particle trajectory unaffected by high-pressure airflow is shown in Figure 2(b) of curve 1 and gangue particle trajectory affected by high-pressure airflow is shown in Figure 2(b) of curve 2.Figure 2
Pneumatic separation model of coal and gangue.
(a)
x
˙ and u are in the same direction
(b)
x
˙ and u are in the opposite directionAs shown in Figure2, ΔS represents the pneumatic separation distance of coal and gangue, hp represents the height difference between gangue mass center on conveyor belt and upper boundary of the airflow domain, tp represents the motion time before gangue came into the airflow domain, vp1,2 is the velocity in direction y of gangue before falling into airflow domain, and hj represents the height of airflow domain. Si represents the displacement in x direction of gangue before entering airflow domain. tj1,2 represents the motion time of gangue in airflow domain, and Sj represents the motion displacement in x direction of gangue in airflow domain. vf1,2 represents the motion velocity in y direction of gangue in airflow domain, x˙(tj1,2) represents the motion velocity in x direction of gangue in airflow domain, tf1,2 represents the motion time of gangue after leaving airflow domain, and Sf1,2 represents the motion displacement in x direction of gangue after leaving airflow domain. In the following equations, subscript 1 is used to represent when airflow velocity and conveyor belt velocity are in the same direction, and subscript 2 is used to represent when airflow velocity and conveyor belt velocity are in the opposite direction.Coal and gangue materials will be recognized by machine vision system and the recognized image information will be sent to pneumatic separation system through image sensor. Coal particles will fall from the conveyor belt freely without the effect of high-pressure airflow. When the motion direction of mineral materials is the same as that of high-pressure airflow, gangue material will change its trajectory and will be thrown significantly farther than that of coal particle. When the motion direction of mineral materials is opposite to that of high-pressure airflow, gangue material will change its trajectory to an opposite direction compared with that of coal particle. The motions of coal and gangue particles are analyzed, respectively, in the following three sections.When coal materials are recognized by machine vision system, coal particles will fall from the conveyor belt freely unaffected by high-pressure airflow.t0 and S0 can be obtained through (1) and (2). Gangue motion law at this stage is the same as coal materials. Si and vp can be also shown by (3) and (4), where t0 represents the motion time of coal particle, and S0 represents the displacement of coal particle in x direction:(1)t0=2hp+hj+hfg,(2)S0=v02hp+hj+hfg,(3)Si=v02hpg,(4)vp=g2hpg.In order to calculate the acting force of high pressure on gangue particles, multiple rectangular polyline is used to approximate gangue particle’s physical shape if the dynamic pressure head of the airflow domain is known in special location. The acting force of high-pressure airflow on gangue can be presented by(5)F=∬APddA=∑i=1mPdiAi,where F represents the acting force of the high airflow on gangue, Pdi represents the high pressure in ring i, Ai represents the area of ring i, and m represents the total number of rings.As shown in Figure3, gangue is affected by airflow with different directions. In order to analyze the movement of gangue particle in high-pressure airflow domain, air resistance and horizontal momentum’s increment of airflow domain are ignored. The theoretical formula of gangue displacement in direction y can be expressed as s=∫0tj1,2(vp+gtj1,2)dt=h-d; then tj1,2 can be obtained as shown in(6)tj1,2=vp2+2gh-d-vpg.Figure 3
Schematic diagram of gangue’s motion in airflow domain.
(a)
x
˙ and u are in the same direction
(b)
x
˙ and u are in the opposite directionAs shown in (6), gangue affected by different airflow direction has the same motion time in airflow domain. Gangue will be affected by two forces after falling into high-pressure airflow domain. The two forces applied on gangue particle are gravity and high dynamic pressure. Airflow dynamic pressure will convert to static pressure on condition that the velocity of airflow u is larger than gangue’s horizontal velocity v0 and airflow must keep dynamic pressure pd=ρx˙2/2. The pressure difference can be expressed as Δpd=ρ(u2-x˙2)/2. According to (5), the formula of airflow force can be expressed by(7)F=∬pdA≈∑ipiAi=12ρ∑iui2-x˙2Ai.When the curvature of gangue surface is not too large, it can be approximately seen as a plane, so∀ui=u, (7) can be changed to(8)F=12ρu2-x˙2A.According to Newton’s second law, (8) can be changed to(9)mx¨=12ρAu2-x˙2,x˙anduare in same direction,mx¨=-12ρAu2+x˙2,x˙anduare in opposite direction.As shown in (9), the expressions are corresponding to different airflow directions. The general solution of displacement in x direction of gangue moving in the airflow can be obtained by taking Laplace transform to (9), and the result is shown in(10)xtj1=AρC2+mln⁡e2C1u-Atj1ρu/m+1-mC1+Atj1ρuAρ,x˙anduare in same direction,xtj2=AρC4+2mln⁡cos⁡Atj2uρ-2muC3/2mAρ,x˙anduare in opposite direction.The velocity of gangue inx direction in airflow domain can be obtained by taking derivation of (10). The general solution is shown in(11)x′tj1=ueAtj1uρ/me2C1u/m+eAtj1uρ/m,x˙anduare in same direction,x′tj2=-utan⁡Atj2ρu-2muC32m,x˙anduare in opposite direction.In order to calculate the constant coefficientsC1, C2, C3, and C4 in (10), the initial constraint conditions are as follows: the initial position of the gangue is x(0)=0 and the initial velocity of gangue is x′(0)=v0.Whenx˙ and u are in the same direction, the general solution of x(tj) and x′(tj) can be obtained by (10) and (11). C1 and C2 are shown in(12)C1=mln⁡u/v0-12u,C2=m2ln⁡u/v0-1-2muln⁡u/v02Auρ.The general solutions ofx(tj) and x′(tj) are shown in (13)xtj1=mln⁡emln⁡u/v0-1-Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu,x′tj1=ueAtj1uρ/meln⁡u/v0-1+eAtj1uρ/m.Whenx˙ and u are in the opposite direction, the general solution of x(tj) and x′(tj) can be obtained by (10) and (11). C3 and C4 are shown by (14)C3=arccos⁡u/v02+u2u,C4=-2mln⁡u/v02+u2Aρ.The general solutions ofx(tj) and x′(tj) are shown by (15) and (16), respectively,(15)xtj2=2mln⁡cos⁡Atj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ,(16)x′tj2=-utan⁡Atj2ρu-2marccos⁡u/v02+u22m.When gangue particles left the boundary of airflow domain, gangue particles would do flat parabolic motion. The formula of velocityvf in direction y is shown in(17)vf1,2=∫0tj1,2vp+gtdt.t
f
1,2 can be solved through (18) and the result is shown by (19):(18)hf=∫0tf1,2vf+gtdt=∫0tf1,2gtdt+∫0tf1,2∫0tjvp+gtd2t,(19)tf1,2=-gtj1,22-2tj1,2vp+8ghf+gtj1,22+2tj1,2vp22g.The displacementSf1,2 of gangue in direction x after leaving the airflow domain can be expressed by (20)Sf1,2=x′tj1,2tf1,2.To sum up, whenx˙ and u are in the same direction, the separation distance ΔS can be calculated by (21)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfueAtj1uρ/meln⁡u/v0-1+eAtj1uρ/mgtj1+2vptj1-v02hp+hj+hfg.Whenx˙ and u are in the opposite direction, the separation distance ΔS can be obtained by(22)ΔS=S0+Sj2+Sf2-Si=v02hp+hj+hfg+2mln⁡cosAtj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tan⁡Atj2ρu-2marccos⁡u/v02+u22m2uhftj2gtj2+2vp-v02hpg.The separation distanceΔS is shown by (21) and (22), which reflects the basic motion law of gangue when influenced by airflow field under different airflow directions. For the limitation of assumption, there exist big differences between theoretical model and practical model. In order to simplify the calculation and correct the difference between theoretical value and practical value, parameters kn (nonlinear correction factor) and kr (linear correction factor) are introduced. kn reflects the convergence rate of the fitting function, and kr reflects the convergent gain and is used to adjust the fitting effect of formula based on experimental value. Theoretical value will get close to experiment value by adjusting the value of kn and kr. The modified formulas with the correction factors are shown in(23)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-Akntj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfueAkntj1uρ/meln⁡u/v0-1+eAkntj1uρ/mgtj1+2vptj1-v02hp+hj+hfg-kr,(24)ΔS=S0+Sj+Sf-Si=v02hp+hj+hfg+2mln⁡cos⁡Akntjuρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tanAtjρu-2marccos⁡u/v02+u22m2uhftjgtj+2vp-v02hpg-kr.


## 3.2. Air-Solid Multiphase Pneumatic Separation Simulation

In order to evaluate the pneumatic separation effect under two kinds of arrangement schemes for high-pressure value, a “fixed coarse-grid” fluid scheme is applied in PFC3D for pneumatic separation simulations. In the fluid scheme, 550 (22 × 5 × 5:x, y, and z directions) fluid cells are created in a rectangular space (x = [0,  7000 mm], y = [−400 mm,  400 mm], and z = [300 mm,  400 mm]), which covers the rectangular space. A pneumatic boundary should be set for the fluid grid. Driving forces from the fluid flow are applied to the particles as body forces. These forces are also added to the fluid equations and cause change in momentum, as reflected by the change in the pressure gradient in the flow direction.As shown in Figures4(a) and 4(b), two available models are established to reduce the computation time without loss in accuracy. The gangue hopper, containing 300 balls, is built at the top right of conveying belt 1; it is aimed at reducing the computation time. The front view of the simulation models at an initial stage under different airflow directions is shown in Figures 4(a) and 4(b), respectively.Figure 4
Air-solid multiphase pneumatic separation.
(a)
v
0 and u in the opposite direction
(b)
v
0 and u in the same directionIn Figure4(a), the velocity v0 of conveyor belt 1 and airflow velocity u are in opposite directions. When gangue falls into the airflow domain, gangue particle will change its trajectory to an opposite direction and fall onto conveyor belt 2. The conveyor belt 2 has the same movement direction as airflow velocity; finally gangue particles will be transported to collecting box by conveyor belt 2. In Figure 4(b), conveyor belt v0 and airflow velocity u are in the same direction. When gangue falls into the airflow domain, gangue particle will throw much farther and fall on conveyor belt 2. The motion of conveyor belt 2 has the same motion direction as conveyor belt 1; finally the gangue particles are transported to collecting box by conveyor belt 2.In the fluid scheme, a pneumatic boundary is set for two available models. During the simulations, an approximation is made by specifying the velocity boundary at the right end of the model and a pressure boundary as 0.0 Pa at left end withx=0 mm. The slip boundary, in which the fluid velocity parallel to the wall surface is nonzero at the wall surface, is specified at the surrounding four walls. In simulation as shown by Figure 4(b), an approximation is made by specifying the velocity boundary at the left end of model and a pressure boundary as 0.0 Pa at the right end with x=7000 mm. The initial setup of the slip boundary in Figure 4(b) is the same as that shown in Figure 4(a) and material properties are shown in Table 1.Table 1
Materials properties.
Parameter
Value
Units
Ball
Diameter
50~100
mm
Number
300
—
Density
2700
kg/m3
Normal stiffness
1 × 106
N/m
Shear stiffness
1 × 106
N/m
Friction coefficient
0.7
—
Air
Density
1.205
kg/m3
Viscosity
1.8 × 10−6
Pa⋅s
Wall
Normal stiffness
1 × 106
N/m
Shear stiffness
1 × 106
N/m
Friction coefficient
0.3
—As shown in Figure4(a), airflow is injected with a velocity of 300 m/s from the negative direction of x at the starting point, while, in Figure 4(b), air is injected from the positive direction of x. When the pneumatic boundaries are applied at the initial stage, the two side walls applied to confine the assembly are removed simultaneously. Figure 5 shows the front view of simulation result from the initial stage to 1 sec.Figure 5
Front view (initial stage to 1 sec; apparent velocity, ±260 m/s).
(a)
v
0 and u are in the opposite direction
(b)
v
0 and u are in the same directionIt can be obtained from Figure5 that gangue particles have different motion trajectories under different airflow velocity. As shown in Figures 5(a) and 5(b), gangue particles will do horizontal projectile motion before entering airflow domain, as can be seen at t=0.2 s and t=0.4 s. As shown in Figure 5(a), velocities of conveyor belt 1 v0 and airflow u are in the opposite direction, and gangue particles will change their motion trajectories to an opposite direction compared with that of coal without the effect of airflow, which can be seen at t=0.6 s, t=0.8 s, and t=1.0 s. As shown in Figure 5(b), velocities of the conveyor belt 1 v0 and airflow u are in the same direction, and gangue particles will be blown much farther than that of coal without being affected by airflow, as can be seen at t=0.6 s, t=0.8 s, and t=1.0 s.As can be seen in Figures5(a) and 5(b), gangue particles will change their trajectories in area A and area C. Areas B and D, as shown in Figures 5(a) and 5(b), illustrated that gangue particles with smaller diameters can be blown much farther.In order to study the pneumatic separation distance influenced by different airflow directions, airflow velocities ±300 m/s are chosen for the research of separation effect. Conveyor velocityv0 and height difference hp between conveyor belt and air nozzle are kept constant. The relationships between separation distances and particle diameters under different airflow velocity directions are shown in Figure 6.Figure 6
The relationship between particle diameter and separation distance under different direction airflow velocity (u=±300 m/s, v0=+1 m/s).As can be seen in Figure6, separation distance decreases with the increase of particle diameter. It also can be concluded that the separation effect under airflow velocity −300 m/s is better than that under airflow velocity 300 m/s. The separation effect also can be analyzed from (9); dynamic pressure difference ΔPd can be expressed as ρ(u2-x˙2)/2 when u and v0 are in the same direction, while, when u and v0 are in the opposite direction, the dynamic pressure difference ΔPd can be expressed as ρ(u2+x˙2)/2. Thus, it can be obtained from the above analysis that separation effect under airflow velocity −300 m/s is significantly better than that of under airflow velocity 300 m/s.


## 3.3. Orthogonal Experiment of Pneumatic Separation

Digital image processing technology has been used to identify the target of various patterns of coal and gangue in underground pneumatic separation system. Before mineral materials are sent to machine vision system, coal and gangue have been crushed to 100 mm by impact crusher. The size of materials is ranging from 50 mm to 100 mm. These materials are sent by the conveyor belt for coal and gangue digital image information identification (as shown in Figure1).In this study, separation distanceΔS (m) is selected as the primary index to evaluate the pneumatic separation effect. Pneumatic separation influenced by different airflow direction can be achieved by changing the arrangement of high-pressure value. The pneumatic separation test system mainly consists of conveyor belt, queuing system, machine vision system, control system, and high-pressure air injection system. When coal and gangue materials fell down from the conveyor belt, gangue will be identified by machine vision system, and the information is transported to control system through image sensor to drive the electromagnetic value open. Thus, coal gangue pneumatic separation is realized. The air compressor used in pneumatic separation testing system is LG-6.5/10, its working pressure is 1.0 Mpa, and certified capacity is 6.5 m3/min.From the analysis shown in Section3, the conveyor velocity v0, height difference hp, and gangue diameter d are selected as the three factors. Factors and levels are listed in Table 2. According to the identified level of factors, orthogonal table L9 (34) is applied in the test. Orthogonal experiment arrangement and results are shown in Table 3.Table 2
Levels of factors.
Level
Factor
A gangue diameter d (mm)
B height difference hp (m)
C conveyor belt velocity v0 (m/s)
1
50
0.40
0.50
2
80
0.80
1.00
3
100
1.10
2.00Table 3
Experimental results of separation effect.
Experiment number
A
B
C
Separation distanceΔS (m)
u and v0 are in the opposite direction
u and v0 are in the same direction
1
50
0.4
0.5
3.05
2.21
2
50
0.8
1.0
2.2
1.14
3
50
1.1
2.0
2.05
0.78
4
80
0.4
1.0
2.15
1.08
5
80
0.8
2.0
1.48
0.65
6
80
1.1
0.5
1.25
0.42
7
100
0.4
2.0
1.85
0.98
8
100
0.8
0.5
1.55
0.37
9
100
1.1
1.0
1.40
0.28


## 4. Result and Discussion

### 4.1. Variance Analysis and Range Analysis Based on Orthogonal Test

As can be seen from Table2, each factor at different levels is approximate linearity, so the method of regression analysis is to obtain the linear function relationship between them appropriately [25]. Thus, the regression equations of coal gangue separation distance under different airflow direction are derived. Equation (25) represents the regression equation when u and v0 are in the opposite direction, and (26) represents the regression equation when u and v0 are in the same direction, where y is the separation distance of coal and gangue, x1 represents the diameter of gangue, x2 is the height difference, and x3 is the velocity of conveyor belt:(25)y=4.67-0.019x1-1.773x2+0.092x3,(26)y=3.60-0.02x1-1.599x2-0.14x3.Variance analysis is carried out on the regression equation to make significance test, and the results are shown in Tables4 and 5. In order to determine the optimal pneumatic separation solutions, comparative analyses of the ranges between various levels of each factor are carried out. The range analysis is shown in Table 6.Table 4
Variance analysis (u and v0 are in opposite direction).
Factor
Squariance
DOF
Mean square
F value
A
1.346
2
0.673
Distinctively
B
1.013
2
0.506
Distinctively
C
0.041
2
0.020
Distinctively
Regression
2.163
3
0.721
11.752
Error
0.307
5
0.061
Sum
2.470
8Table 5
Variance analysis (u and v0 are in the same direction).
Factor
Squariance
DOF
Mean square
F value
A
1.160
2
0.58
Distinctively
B
1.411
2
0.705
Distinctively
C
0.067
2
0.034
Distinctively
Regression
2.509
3
0.836
15.397
Error
0.272
5
0.054
Sum
2.781
8Table 6
Range analysis.
A
B
C
A
1
A
2
B
1
B
2
C
1
C
2
K
j
1
7.30
4.13
7.05
4.17
5.85
3.00
K
j
2
4.88
2.15
5.23
2.16
5.75
2.49
K
j
3
4.8
1.63
4.7
1.48
5.38
2.43
R
j
0.83
0.83
0.78
0.90
0.16
0.19In Table6, subscripts 1 and 2 used in influence factors (A,B,C) represent the fact that u and v0 are in the opposite direction and the same direction, respectively. Kjm (m=1,2,…,n) is the sum of index values corresponding to factors in column j at level m. The value of Kjm determines the optimal level and combination of factors in column j. Rj reflects the ranges of the index with the variation of factors in column j, and the influence of the factor will be more significant if the value Rj is greater.According to Tables4 and 5, all the three factors mentioned above have significant influence on pneumatic separation distance. As shown in Table 6, the pneumatic separation distances ΔS are all decreasing with the increased value of the three factors. The analysis shows that gangue diameters have the most significant influence on separation distance.


### 4.2. Analysis of Experiment Results Based on Support Vector Machine (SVM)

From the above analysis shown in Section4.1, the significant degrees of different factors for separation distance are obtained by variance analysis. Besides, the primary and secondary relations of the influence factors with pneumatic separation distance could be obtained according to the range analysis. However, the optimal combination is a relative definition for the limited levels and has great one-sided characteristic. Most cases occurred in the experiment; the so-called “optimal combination of the factors” is a relative optimal, not the real optimal.For further analysis of the experiment result, SVM [26–30] is introduced. The detailed functional forms of SVM are given in the Appendix. Optimization settings for factors that have influences on coal gangue pneumatic separation could be divided into the following steps: (1) collect the necessary data using orthogonal experiment; (2) set SVM learning model parameters and determine SVM kernel function; (3) input learning samples, and obtain parameters; (4) establish the fitting model according to parameters obtained above; (5) determine the levels of parameters in a certain range, and then combine these levels to establish a large number of input vector samples; (6) input vector sample into the fitting model and then obtain the output sample.The relationship of separation distanceΔS and various influence factors is obtained through the above analysis. As shown in Figure 7, x- and y-axes represent two of the three influence parameters, respectively. 14 values equally spaced from the range of parameters of orthogonal experiment are taken, respectively. Thus, the comprehensive collection of the two parameters could form 196 samples, and the extreme value is selected in the third parameter in orthogonal experiment.Figure 7
Influence of three factors on gangue separation distance.
(a)
Influence of conveyor belt velocityv0 and height difference hp on gangue separation distance (u and v0 in opposite direction)
(b)
Influence of conveyor belt velocityv0 and gangue diameter d on gangue separation distance (u and v0 in opposite direction)
(c)
Influence of conveyor belt velocityv0 and height difference hp on gangue separation distance (u and v0 in the same direction)
(d)
Influence of conveyor belt velocityv0 and gangue diameter d on gangue separation distance (u and v0 in the same direction)Figures7(a) and 7(b) show the relationships of separation distance ΔS and the three factors when u and v0 are in the opposite direction. As can be seen from Figures 7(a) and 7(b), pneumatic separation distance ΔS decreases with the increase of conveyor velocity v0, the height difference hp, and gangue diameter d. It also can be concluded that gangue diameter d has the greatest influence on separation distance ΔS.Figures7(c) and 7(d) have shown the relationships of separation distance ΔS and factors when u and v0 are in the same direction. As can be seen from Figures 7(c) and 7(d), there is the same variation trend as that of Figures 7(a) and 7(b). Through the analysis of the two groups of figures, pneumatic separation effect will be better when u and v0 are in the opposite direction. It can be concluded that the SVM intelligent model has important guiding significance and practical value for coal gangue pneumatic separation.


### 4.3. Correction of the Theoretical Formula

Based on the least square method, (23) and (24) in Section 3.2 can be transformed into a function of kn and kr parameters through variable substitution; then set up equations based on the experiments data. The result of kn and kr can be calculated finally.Whenv0 and u are in the same direction, nonlinear correction term can be given as kn = 0.0205, and linear correction term kr=1.1. Thus, the formula can be expressed as(27)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-0.0205Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfue0.0205Atj1uρ/meln⁡u/v0-1+e0.0205Atj1uρ/mgtj1+2vptj1-v02hp+hj+hfg-1.1.Whenv0 and u are in the opposite directions, nonlinear correction term kn and linear correction term kr can be given as kn = 1.56 × 105 and kr=4.4. Thus, the formula is obtained as(28)ΔS=S0+Sj2+Sf2-Si=v02hp+hj+hfg+2mln⁡cos⁡1.56×105Atj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tan⁡Atj2ρu-2marccos⁡u/v02+u22m2uhftj2gtj2+2vp-v02hpg-4.4.In order to verify the effectiveness of theoretical formula, nine samples shown in Table3 are selected as verification samples. The comparison of experiment results and calculated results is shown in Table 7.Table 7
Experimental and calculated results of separation effect.
Experiment number
Experiment valueΔS (m)
Calculated valueΔ’S (m)
Error (%)
Experiment valueΔS (m)
Calculated valueΔ’S (m)
Error (%)
u and v0 are in the same direction
u and v0 are in opposite direction
1
2.21
2.33
5.15
3.05
3.16
3.48
2
1.14
1.21
5.78
2.2
2.37
7.17
3
0.78
0.92
15.2
2.05
2.21
7.23
4
1.08
1.23
12.2
2.15
2.36
8.89
5
0.65
0.71
8.45
1.48
1.69
12.42
6
0.42
0.49
14.3
1.25
1.43
12.58
7
0.98
1.14
14.03
1.85
2.07
10.62
8
0.37
0.44
15.9
1.55
1.74
10.92
9
0.28
0.33
15.2
1.40
1.56
10.26As can be seen from Table7, calculated value and experiment value of coal gangue pneumatic separation distance have high consistent degrees, the separation distance error between experiment value and calculated result is less for gangue with smaller diameter, and the separation distance error increases with the increase of gangue diameter. However, the separation distance error between experiment value and calculated result is still less than 16%. Thus, it can be concluded that (27) and (28) have important guiding significance and practical value for coal gangue pneumatic separation.


## 4.1. Variance Analysis and Range Analysis Based on Orthogonal Test

As can be seen from Table2, each factor at different levels is approximate linearity, so the method of regression analysis is to obtain the linear function relationship between them appropriately [25]. Thus, the regression equations of coal gangue separation distance under different airflow direction are derived. Equation (25) represents the regression equation when u and v0 are in the opposite direction, and (26) represents the regression equation when u and v0 are in the same direction, where y is the separation distance of coal and gangue, x1 represents the diameter of gangue, x2 is the height difference, and x3 is the velocity of conveyor belt:(25)y=4.67-0.019x1-1.773x2+0.092x3,(26)y=3.60-0.02x1-1.599x2-0.14x3.Variance analysis is carried out on the regression equation to make significance test, and the results are shown in Tables4 and 5. In order to determine the optimal pneumatic separation solutions, comparative analyses of the ranges between various levels of each factor are carried out. The range analysis is shown in Table 6.Table 4
Variance analysis (u and v0 are in opposite direction).
Factor
Squariance
DOF
Mean square
F value
A
1.346
2
0.673
Distinctively
B
1.013
2
0.506
Distinctively
C
0.041
2
0.020
Distinctively
Regression
2.163
3
0.721
11.752
Error
0.307
5
0.061
Sum
2.470
8Table 5
Variance analysis (u and v0 are in the same direction).
Factor
Squariance
DOF
Mean square
F value
A
1.160
2
0.58
Distinctively
B
1.411
2
0.705
Distinctively
C
0.067
2
0.034
Distinctively
Regression
2.509
3
0.836
15.397
Error
0.272
5
0.054
Sum
2.781
8Table 6
Range analysis.
A
B
C
A
1
A
2
B
1
B
2
C
1
C
2
K
j
1
7.30
4.13
7.05
4.17
5.85
3.00
K
j
2
4.88
2.15
5.23
2.16
5.75
2.49
K
j
3
4.8
1.63
4.7
1.48
5.38
2.43
R
j
0.83
0.83
0.78
0.90
0.16
0.19In Table6, subscripts 1 and 2 used in influence factors (A,B,C) represent the fact that u and v0 are in the opposite direction and the same direction, respectively. Kjm (m=1,2,…,n) is the sum of index values corresponding to factors in column j at level m. The value of Kjm determines the optimal level and combination of factors in column j. Rj reflects the ranges of the index with the variation of factors in column j, and the influence of the factor will be more significant if the value Rj is greater.According to Tables4 and 5, all the three factors mentioned above have significant influence on pneumatic separation distance. As shown in Table 6, the pneumatic separation distances ΔS are all decreasing with the increased value of the three factors. The analysis shows that gangue diameters have the most significant influence on separation distance.


## 4.2. Analysis of Experiment Results Based on Support Vector Machine (SVM)

From the above analysis shown in Section4.1, the significant degrees of different factors for separation distance are obtained by variance analysis. Besides, the primary and secondary relations of the influence factors with pneumatic separation distance could be obtained according to the range analysis. However, the optimal combination is a relative definition for the limited levels and has great one-sided characteristic. Most cases occurred in the experiment; the so-called “optimal combination of the factors” is a relative optimal, not the real optimal.For further analysis of the experiment result, SVM [26–30] is introduced. The detailed functional forms of SVM are given in the Appendix. Optimization settings for factors that have influences on coal gangue pneumatic separation could be divided into the following steps: (1) collect the necessary data using orthogonal experiment; (2) set SVM learning model parameters and determine SVM kernel function; (3) input learning samples, and obtain parameters; (4) establish the fitting model according to parameters obtained above; (5) determine the levels of parameters in a certain range, and then combine these levels to establish a large number of input vector samples; (6) input vector sample into the fitting model and then obtain the output sample.The relationship of separation distanceΔS and various influence factors is obtained through the above analysis. As shown in Figure 7, x- and y-axes represent two of the three influence parameters, respectively. 14 values equally spaced from the range of parameters of orthogonal experiment are taken, respectively. Thus, the comprehensive collection of the two parameters could form 196 samples, and the extreme value is selected in the third parameter in orthogonal experiment.Figure 7
Influence of three factors on gangue separation distance.
(a)
Influence of conveyor belt velocityv0 and height difference hp on gangue separation distance (u and v0 in opposite direction)
(b)
Influence of conveyor belt velocityv0 and gangue diameter d on gangue separation distance (u and v0 in opposite direction)
(c)
Influence of conveyor belt velocityv0 and height difference hp on gangue separation distance (u and v0 in the same direction)
(d)
Influence of conveyor belt velocityv0 and gangue diameter d on gangue separation distance (u and v0 in the same direction)Figures7(a) and 7(b) show the relationships of separation distance ΔS and the three factors when u and v0 are in the opposite direction. As can be seen from Figures 7(a) and 7(b), pneumatic separation distance ΔS decreases with the increase of conveyor velocity v0, the height difference hp, and gangue diameter d. It also can be concluded that gangue diameter d has the greatest influence on separation distance ΔS.Figures7(c) and 7(d) have shown the relationships of separation distance ΔS and factors when u and v0 are in the same direction. As can be seen from Figures 7(c) and 7(d), there is the same variation trend as that of Figures 7(a) and 7(b). Through the analysis of the two groups of figures, pneumatic separation effect will be better when u and v0 are in the opposite direction. It can be concluded that the SVM intelligent model has important guiding significance and practical value for coal gangue pneumatic separation.


## 4.3. Correction of the Theoretical Formula

Based on the least square method, (23) and (24) in Section 3.2 can be transformed into a function of kn and kr parameters through variable substitution; then set up equations based on the experiments data. The result of kn and kr can be calculated finally.Whenv0 and u are in the same direction, nonlinear correction term can be given as kn = 0.0205, and linear correction term kr=1.1. Thus, the formula can be expressed as(27)ΔS=Si+Sj1+Sf1-S0=v02hpg+mln⁡emln⁡u/v0-1-0.0205Atj1ρu/m+1-2muln⁡u/v0+Atj1ρu2Aρu+2hfue0.0205Atj1uρ/meln⁡u/v0-1+e0.0205Atj1uρ/mgtj1+2vptj1-v02hp+hj+hfg-1.1.Whenv0 and u are in the opposite directions, nonlinear correction term kn and linear correction term kr can be given as kn = 1.56 × 105 and kr=4.4. Thus, the formula is obtained as(28)ΔS=S0+Sj2+Sf2-Si=v02hp+hj+hfg+2mln⁡cos⁡1.56×105Atj2uρ-2marccos⁡u/v02+u2/2m-2mln⁡u/v02+u2Aρ+tan⁡Atj2ρu-2marccos⁡u/v02+u22m2uhftj2gtj2+2vp-v02hpg-4.4.In order to verify the effectiveness of theoretical formula, nine samples shown in Table3 are selected as verification samples. The comparison of experiment results and calculated results is shown in Table 7.Table 7
Experimental and calculated results of separation effect.
Experiment number
Experiment valueΔS (m)
Calculated valueΔ’S (m)
Error (%)
Experiment valueΔS (m)
Calculated valueΔ’S (m)
Error (%)
u and v0 are in the same direction
u and v0 are in opposite direction
1
2.21
2.33
5.15
3.05
3.16
3.48
2
1.14
1.21
5.78
2.2
2.37
7.17
3
0.78
0.92
15.2
2.05
2.21
7.23
4
1.08
1.23
12.2
2.15
2.36
8.89
5
0.65
0.71
8.45
1.48
1.69
12.42
6
0.42
0.49
14.3
1.25
1.43
12.58
7
0.98
1.14
14.03
1.85
2.07
10.62
8
0.37
0.44
15.9
1.55
1.74
10.92
9
0.28
0.33
15.2
1.40
1.56
10.26As can be seen from Table7, calculated value and experiment value of coal gangue pneumatic separation distance have high consistent degrees, the separation distance error between experiment value and calculated result is less for gangue with smaller diameter, and the separation distance error increases with the increase of gangue diameter. However, the separation distance error between experiment value and calculated result is still less than 16%. Thus, it can be concluded that (27) and (28) have important guiding significance and practical value for coal gangue pneumatic separation.


## 5. Conclusions

The established coal and gangue pneumatic separation model reflects the basis motion law of gangue affected by airflow and coal without being affected by airflow, which provides two feasible solutions for underground pneumatic separation under two kinds of arrangement scheme of high-pressure value. The analysis in theory is consistent with that obtained in the experiments, which validate the established theoretical model and present the following conclusions:(
1
) Different high-pressure value arrangement schemes have great influence on gangue pneumatic separation, the theoretical formulas of coal gangue pneumatic separation distance affected by different airflow direction are derived, and the expressions of the two formulas are different under different airflow direction.(
2
) A series of air-solid multiphase flow simulations and orthogonal experiments were conducted to clarify its effect under different airflow direction. Based on the analysis, pneumatic separation effect will be better under the condition of u and v0 being in the opposite direction. Pneumatic separation distance ΔS decreases with the increased values of the three factors (conveyor velocity v0, height difference hp, and gangue diameter d). These analyses also show that gangue diameters have the most significant influence on separation distance, followed by conveyor velocity v0 and height difference hp.(
3
) The relationship of pneumatic separation distance ΔS and influence factors was obtained by SVM intelligent model; the theoretical formulas of coal gangue pneumatic separation distance are corrected based on the analysis of orthogonal experiment data. The corrected formula is suitable to serve as the theory basis of coal gangue pneumatic separation.



---

*Source: 6465983-2016-03-17.xml*