Dynamics Behavior Research on Variable Linear Vibration Screen with Flexible Screen Face

Abstract

In order to enable the variable linear vibration screen with ideal movement behavior of screen surface and efficient screening capacity, five-freedom dynamic model and stability equations of the variable linear vibration screen were established based on power balance method and Hamilton principle. The motion behaviour of screen face was investigated, and − 0.10 m ≤ x _f ≤ − 0.04 m was confirmed as the best range of exciting position. With analysis of stability equations, the stable requirement of vibration screen was obtained: the direction angle of exciting force should be 0 ≤ θ ≤ 45°. Screening processes of variable linear vibration screen with flexible screen face, variable linear vibration screen with fixed screen face and linear vibration screen were investigated and compared by numerical simulation method, the results show that variable linear vibration screen with flexible screen face have such characteristics as higher intensity of projection and efficient screening. The correctness of theoretical research and simulation research were verified through experiment, and all of the work would provide some guidance for designing and studying variable linear vibration screen with flexible screen face.

1. Introduction

Vibration screen is often used for scattered materials in most areas of mining, metallurgy, building materials, food, medicine, chemical industry, energy, and environment [1]. General vibration screen should guarantee that exciting force crosses the mass center which makes the design of screen difficult and the material blocked phenomena occur often [2]. At present, most researchers focus on researches of general vibration screens, and very few pay their attention to the variable linear vibration screens [3].

Screen-penetrating schematic of a single material particle invested to screen surface was proposed by Gaudin [4] and Taggart [5]. Based on their researches, a more precise formula of screen-penetrating probability for a single particle was carried out by Mogensen [6], and a mathematical model of screening was set up by Brereton and Dymott [7]. The distribution equation of the materials under screen surface was derived by Schultz and Tppin [8]. Weibull model also was adopted for describing the screen-penetrating probability along the length of screen surface by Zhao [9]. Taking the effect of particles type by Mishra and Mehrotra into consideration [10], the screening process of material was simulated by discrete element method (DEM). Cleary et al. [11–13] researched the vibration screen working process using 3D DEM software and obtained the effects of particles’ type and accelerated velocity on materials movement and vibration screen screening effectiveness. Many Chinese scholars also took the discrete element method into the application of researching vibration screening performance and the materials movement on the screen surface and got a vast number of valuable results which had produced immeasurable benefits in manufacturing processes [13–20]. Considering the undesirability behaviors and low screening efficiencies of normal vibration screens, a new complex-locus vibration screen was designed by Gu and Zhang, and an ideal movement style of screen surface was also proposed [21]. Yang and Wang have built a dynamics model of the nonlinear resonance screen based on moving rigidity-body dynamics theory, and the effects of rotation speed and exciting angle on vibration screen trajectory and amplitude were analyzed in their work [22]. Zhang and Zhong have built a dynamics model of linear vibration screen using Lagrangian method; based on this work, the curves of vibration screen surface displacement, velocity, and accelerated velocity were given out, and the static analysis and fatigue analysis of vibration screen were also developed by finite element method [23]. The modal analysis of a large-scale linear vibration screen was conducted by Ma and Xiong with the methods of frequency domain decomposition and least squares complex exponent, and their work provided some guidance for the structural mechanics researches of vibration screen [24]. Liu and Yu have built a large-scaled linear vibration screen dynamic model, and pointed out the effects of vibrated quality, spring stiffness and eccentricity mass on vibration screen amplitude [25]. L. I. Slepyan and V. I. Slepyan have researched the dynamic model of a RR-based rectangular vibration screen, and a vibration screen machine was designed, built, and set up in LPMC [26, 27].

The researches mentioned above have promoted the vibration screening technology development in a large part, but the power distribution and movement of vibration surface are still not ideal, and more researches need to be developed. Therefore, a variable linear vibration screen with flexible screen face is proposed on the basis of predecessors’ research work, and the dynamic behavior and screening process of this vibration screen were researched which aim to get more appropriate screening approach and guide for the vibration design.

2. Dynamical Model of Variable Linear Vibration Screen

The simplified dynamic model of variable linear vibration screen with flexible surface was shown in Figure 1. The rectangular coordinates system is built with the mass center (O) of the screen box as origin; F is synthesis of exciting force caused by double vibration motor; θ is vibrating direction angle, the exciting force line, and horizontal line which crosses the mass center (O) intersect at x _f . As the rod's rotational inertia and damping of vibration screen are generally small, the influence of them on dynamic model could be ignored, and the relative motion between each screen rob and screen frame was assumed to be the same.

Figure 1:

Dynamic model of variable linear vibration screen with flexible screen face.

The kinetic equations are set up using the power balance method [27, 28]. The kinetic energy T and potential energy V of screen system can be expressed:

$\begin{array}{c}T=\frac{\mathrm{1}}{\mathrm{2}}[M({\dot{x}}_{\mathrm{1}}^{\mathrm{2}}+{\dot{y}}_{\mathrm{1}}^{\mathrm{2}})+{\displaystyle \sum }_{i=\mathrm{1}}^{n}m({\dot{x}}_{\mathrm{2}i}^{\mathrm{2}}+{\dot{y}}_{\mathrm{2}i}^{\mathrm{2}})+J{{\dot{\theta }}_s}^{\mathrm{2}}],\\ V=\frac{\mathrm{1}}{\mathrm{2}}[\phantom{{\displaystyle \sum }_{i=\mathrm{1}}^{n}m(k_{\mathrm{2}x}{x}_{\mathrm{2}i}^{\mathrm{2}}+k_{\mathrm{2}y}{y}_{\mathrm{2}i}^{\mathrm{2}})}(k_{\mathrm{1}x}{x}_{\mathrm{1}}^{\mathrm{2}}+k_{\mathrm{1}y}{y}_{\mathrm{1}}^{\mathrm{2}})+(l_y^{\mathrm{2}}{k}_{\mathrm{1}x}+l_x^{\mathrm{2}}{k}_{\mathrm{1}y}){\theta }_s^{\mathrm{2}}+{\displaystyle \sum }_{i=\mathrm{1}}^{n}m(k_{\mathrm{2}x}{x}_{\mathrm{2}i}^{\mathrm{2}}+k_{\mathrm{2}y}{y}_{\mathrm{2}i}^{\mathrm{2}})].\end{array}$

(1)

In generalized XY coordinate, the vibration equations of elastic screen surface variable linear vibration screen are established based on Lagrange method and it is shown as follows:

$\begin{array}{c}M{\ddot{x}}_{\mathrm{1}}+(k_{\mathrm{1}x}+k_{\mathrm{2}x})x_{\mathrm{1}}-k_{\mathrm{2}x}{x}_{\mathrm{2}}=F\sin \left(\omega t\right)\cos \theta ,\\ nm{\ddot{x}}_{\mathrm{2}}-k_{\mathrm{2}x}{x}_{\mathrm{1}}+k_{\mathrm{2}x}{x}_{\mathrm{2}}=\mathrm{0},\\ M{\ddot{y}}_{\mathrm{1}}+(k_{\mathrm{1}y}+k_{\mathrm{2}y})y_{\mathrm{1}}-k_{\mathrm{2}y}{y}_{\mathrm{2}}=F\sin \left(\omega t\right)\sin \theta ,\\ nm{\ddot{y}}_{\mathrm{2}}-k_{\mathrm{2}y}{y}_{\mathrm{1}}+k_{\mathrm{2}y}{y}_{\mathrm{2}}=\mathrm{0},\\ J{\ddot{\theta }}_s+\left(l_y^{\mathrm{2}}{k}_{\mathrm{1}x}+l_x^{\mathrm{2}}{k}_{\mathrm{1}y}\right){\theta }_s=x_{f}F\sin \left(\omega t\right)\sin \theta ,\end{array}$

(2)

where M is vibrating mass exclusion of screen rob, M = 155 kg; m is the mass of screen rob, m = 0.3 kg; n is the number of screen rods; J is the rotational inertia of vibrating mass, J = 15.5 kg·m²; F is the maximum exciting force, F = 3000 N; ω is the excitation angular frequency, ω = 16.2 rad/s; x _f is vibration force acting position, m; x₁ and y₁ are the displacements of the screen frame in X direction and Y direction, m; θ is vibration direction angle, rad; θ _s is swing angle of the screen frame, rad; k_1x, k_1y are the stiffness of supporting spring in X direction and Y direction, k_1x = 2e⁴ N/m, k_1y = 6e⁴ N/m; k_2x, k_2y are the stiffness of the elastic bodies in X direction and Y direction, k_2x = k_2y = 1040 N/m; l _x , l _y are the distance between supporting spring and mass center in X direction and Y direction, l _x = l_x1 = l_x2 = 0.5 m, l _y = 0.1 m; ${\ddot{x}}_{\mathrm{1}}$ , ${\ddot{y}}_{\mathrm{1}}$ are the accelerations of the screen frames in X direction and Y direction, m/s²; ${\ddot{x}}_{\mathrm{2}}$ , ${\ddot{y}}_{\mathrm{2}}$ are the accelerations of the screen rods in X direction and Y direction, m/s²; ${\ddot{\theta }}_s$ is swing angular acceleration of screen frame, rad/s².

3. Vibration Force Position and Stable Requirements of Variable Linear Vibration Screen

The power distribution form on surface of the vibration screen is determined by the acting position and direction angle of vibration force, so the determinations of optimal acting position and direction angle are the basis elements for the high efficient screen design. The research of screen surface movement way can be repalced by researching the motion behavior of different points on screen surface. The vibration equation of screen centre can be obtained by solving (2). As the motion trajectory of any point on screen surface is composed of motion and rotation which are relative to the centre, so it can be expressed by

$\begin{array}{c}x=(\phantom{\frac{F{x}_f}{\sqrt{{\left(J_{\mathrm{1}}{\omega }^{\mathrm{2}}-k_{\theta }\right)}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}}\frac{F\cos \theta }{\sqrt{{\left[\left(M+nm\right){\omega }^{\mathrm{2}}-k_{\mathrm{1}x}\right]}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}+y_p\frac{F{x}_f}{\sqrt{{\left(J_{\mathrm{1}}{\omega }^{\mathrm{2}}-k_{\theta }\right)}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}\phantom{\frac{F\cos \theta }{\sqrt{{\left[\left(M+nm\right){\omega }^{\mathrm{2}}-k_{\mathrm{1}x}\right]}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}})\sin \omega t,\\ y=(\phantom{\frac{F{x}_f}{\sqrt{{\left(J_{\mathrm{1}}{\omega }^{\mathrm{2}}-k_{\theta }\right)}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}}\frac{F\sin \theta }{\sqrt{{\left[\left(M+nm\right){\omega }^{\mathrm{2}}-k_{\mathrm{1}y}\right]}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}-x_p\frac{F{x}_f}{\sqrt{{\left(J_{\mathrm{1}}{\omega }^{\mathrm{2}}-k_{\theta }\right)}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}\phantom{\frac{F\sin \theta }{\sqrt{{\left[\left(M+nm\right){\omega }^{\mathrm{2}}-k_{\mathrm{1}y}\right]}^{\mathrm{2}}+{\omega }^{\mathrm{2}}}}})\sin \omega t,\end{array}$

(3)

where k_θ = (1/2)k_1y(l_x1² + l_x2²).

According to (3), the movement of material at any point on variable linear vibration screen is linear, and then the direction angle and vibration amplitude of projectile material can be obtained. The direction angle value of exciting force is set as 45° to analyze the movement of vibration screen surface. Then, the direction angle and vibration amplitude of projectile material change with x _f are shown in Figures 2 and 3.

Figure 2:

Direction angle of materials projection.

Figure 3:

Vibration amplitude of screen surface.

The efficiency, smooth discharge, and the usable area of the vibration screen need to be guaranteed at the same time. The movement of vibration screen should be conformed: the vibration amplitude of feeding side should be higher than the discharging side; the vibration amplitude decreases along the screen length from material inlet to material outlet; material movement direction should be pointed to outlet [29]. When x _f > 0, the projectile angle of the materials on the screen surface will be increased from the feeding side to the discharging side. If the exciting force position is too close to the discharging side, it will make the material at the inlet projectile to the opposite side. In general, the projectile angle at the feeding side should be large enough to make the material in this part layering; meanwhile, the vibration amplitude should be large enough to avoid the materials stack at the inlet, but, as x _f > 0, all of the unwished scene will happen. Therefore, x _f should not be greater than 0. When x _f = 0, variable linear vibration screen would change to linear vibration screen as the projectile direction angle and vibration amplitude irrelevant to material position. When x _f < 0, the projectile direction angle and the vibration amplitude decrease from feeding side to discharging side. When the value of vibration force acting position is too small (such as x _f = − 0.12 m), the materials would not discharge easily and it will be projected to opposite side. So, a suitable value range of x _f is very important for variable linear vibration screen design. Considering Figures 2 and 3 and the analysis above, in order to get better performance of feeding, layering, penetrating, and discharging, the numerical ranges of appropriate function area of vibration force can be set roughly: −0.10 m ≤ x _f ≤ −0.04 m.

The variable linear vibration screen should achieve the predefined function of screening materials, but also needs to satisfy the stable acquirement. The variable linear vibration screen, which is a complete nonconservation system, is subjected to the gravity, projectile force, and friction force at the same time in the processing of screening. The Hamilton action of this system in a complete period can be shown as [30, 31]

$H={{\displaystyle \int }}_{\mathrm{0}}^{\mathrm{2}\pi /\omega }(T-V)dt=\frac{\pi F^{\mathrm{2}}{\omega }^{\mathrm{2}}}{\mathrm{2}}\times (\frac{M{\cos }^{\mathrm{2}}\theta }{{\left(M{\omega }^{\mathrm{2}}-k_{\mathrm{1}x}\right)}^{\mathrm{2}}}+\frac{M{\sin }^{\mathrm{2}}\theta }{{\left(M{\omega }^{\mathrm{2}}-k_{\mathrm{1}y}\right)}^{\mathrm{2}}}+\frac{J{\sin }^{\mathrm{2}}\theta x_f^{\mathrm{2}}}{{\left(J{\omega }^{\mathrm{2}}-k_{\theta }\right)}^{\mathrm{2}}})+\frac{\mathrm{2}\pi T_{\mathrm{0}}}{\omega }.$

(4)

According to the principle of minimum potential energy and the variation theory, the Hamiltonian function H must take relative minimum to stabilize the vibration screen in an equilibrium state. The second functional variation is greater than or equal to zero which is a sufficient condition for functional minimum. Considering the influence of exciting force position x _f and the direction angle θ to the stability of the vibration screen, it can be obtained that

$\frac{{\delta }^{\mathrm{2}}H}{\delta x_f^{\mathrm{2}}}=\frac{J\pi {\omega }^{\mathrm{2}}{F}^{\mathrm{2}}{\sin }^{\mathrm{2}}\theta }{{\left({\omega }^{\mathrm{2}}J-k_{\theta }\right)}^{\mathrm{2}}}\ge \mathrm{0},$

(5)

$\frac{{\delta }^{\mathrm{2}}H}{\delta {\theta }^{\mathrm{2}}}\hspace{1em}=\pi F^{\mathrm{2}}{\omega }^{\mathrm{2}}(\text{si}{\text{n}}^{\mathrm{2}}\theta -{\cos }^{\mathrm{2}}\theta )\times (\frac{M}{{\left(M{\omega }^{\mathrm{2}}-k_{\mathrm{1}x}\right)}^{\mathrm{2}}}-\frac{M}{{\left(M{\omega }^{\mathrm{2}}-k_{\mathrm{1}y}\right)}^{\mathrm{2}}}-\frac{J{x}_f^{\mathrm{2}}}{{\left({\omega }^{\mathrm{2}}J-k_{\theta }\right)}^{\mathrm{2}}})\ge \mathrm{0}.$

(6)

From (5), we can see that the values of equations are greater than or equal to zero eternally. In other words, the stability of the vibration screen will not be affected by exciting force position. Due to the horizontal stiffness of the metal spring less than vertical stiffness, it can be obtained that

$\frac{M}{{\left(M{\omega }^{\mathrm{2}}-k_x\right)}^{\mathrm{2}}}-\frac{M}{{\left(M{\omega }^{\mathrm{2}}-k_y\right)}^{\mathrm{2}}}-\frac{J{x}_f^{\mathrm{2}}}{{\left({\omega }^{\mathrm{2}}J-k_{\theta }\right)}^{\mathrm{2}}}<\mathrm{0}.$

(7)

Taking into account (6) and (7), only under the condition of sin2θ − cos⁡2θ ≤ 0, (6) will be greater than zero. In other words, the stable requirement of the variable linear vibration screen should meet 0 ≤ θ ≤ 45°.

4. Dynamic Behavior Simulation of Variable Linear Vibration Screen

In order to improve the dynamics simulation efficiency of vibration screen and reduce the computer calculation complexity, the model of vibration screen was simplified as a whole except screen rods on the premise of almost not affecting the results. The establishment process of dynamics simulation model can be concluded as follows: firstly, establish vibration screen model using 3D entities modeling software, and obtain vibration screen's mass, center position, and inertia tensor; secondly, import the 3D model of vibration screen into mechanical dynamics analysis and simulation software, and define the model's mass, center position, inertia tensor, and constrains; thirdly, apply the driving force on the screen; finally, compute and get the simulation results. In constrains defining, constrains mainly include the supporting springs’ constrains and elastomers’ constrains, and the elastomers’ constrains are applied as flexible connection. As the vibration motor only provides exciting force and has no influence on the screen structure, the driving force applied on vibration screen is a resultant force composed of two vibration motor forces. The dynamics simulation model of variable linear vibration screen is shown in Figure 4.

Figure 4:

Simulation model of variable linear vibration screen.

According to the appropriate function area of vibrating force and suitable range of vibration direction angle, x _f and θ take the value of −0.1 m and 45°, respectively, in dynamic behavior simulation, and the five record points on screen box are shown in Figure 5. The vibrations of five different positions are recorded which is shown in Figure 6. We can see that the amplitude of the vibration screen decreases from the feeding side to the discharging side, and the points at different positions have the same movement period which indicates the materials can be well screened on screen surface. Comparing Figures 3 and 6, we find that the simulation results are consistent with theoretical results, which proves the correctness of dynamics model of variable linear vibration screen. In order to study the effects of elastomer on the movement of variable linear vibration screen, the vibrations of screen frame and rod at same position are measured, and the results are shown in Figure 7. From Figure 7, we find that the amplitude of the screen rod is greater than the screen frame at same position, which indicates that the amplitude of vibration screen surface could be improved by flexible screen surface, and it can make the vibration screen achieve better material screening without exciting force changing.

Figure 5:

Five record points on screen box.

Figure 6:

Amplitudes in Y direction with different positions of screen surface.

Figure 7:

Amplitudes in Y direction of screen frame and rod.

As mentioned above, three different vibration screens (variable linear vibration screen with flexible screen face, variable linear vibration screen with fixed screen face, and linear vibration screen) can be obtained by changing the former built simulation model exciting force position and the connection type of rod and frame. In order to research the material particles dynamics movement, the screening processes of a single material particle on the three vibration screens are simulated in the following research. The simulation model is shown in Figure 8.

Figure 8:

The screening simulation model of a single particle.

The displacements of particles in Y direction on the three different vibration screens are shown in Figure 9. From Figure 9, we can see the following: the projectile heights of the particle on variable linear vibration screen with flexible screen face and variable linear vibration screen with fixed screen face decrease from feeding side to discharging side. But the projectile height of the particle on linear vibration screen changes little, and it will be difficult to achieve the constant thick screening of the materials on this screen surface. In addition, since the flexible screen can increase the amplitude, so the times of projectile for screening process on flexible screen surface are less than that on the variable linear vibration screen surface, and also the screening percentage improved. Due to the effect of the elastomer, there are variable spaces between rods, and the blocking on the screen surface can be decreased. In summary, the power distribution of variable linear vibration screen is better than the general vibration screen, and its change law of the projectile strength meets the ideal requirements of the screen surface; the variable linear vibration screen with flexible screen face can increase the amplitude, which can prevent materials from lower vibration in discharging side and blocking phenomena between robs; under the same conditions of the exciting force's position and direction, variable linear vibration screen with flexible screen face has better screening performance than the variable linear vibration screen and general linear vibration screen.

Figure 9:

Y direction displacement-time curve of material.

5. Research Results of Verification by Experiment

In order to verify the correctness of dynamics model and simulation model of variable linear vibration screen, experimental prototype of vibration screen which takes the same parameters to 3D model is developed under the condition of x _f = − 0.1 m and θ = 45°. Besides the prototype of variable linear vibration screen with flexible screen face, signal amplifier and signal-processing software are included in the test, which is shown in Figure 10. The sampling frequency used in the test is 600 Hz, and sensitivity of sensor is 4.95 mV/g. Figure 10 shows the three in five record points which correspond to Figure 5, and the no-load test accelerations of five points are shown in Figure 11. The time domain data of vibration screen is shown in Table 1. From Table 1, we can see that the test results are well consistent with theoretical and simulation results. Figure 12 shows the following test points. The acceleration of vibration screen mass center, feeding side, and discharging side in X and Y direction are tested, which aim to obtain the trajectories of the three different positions. After test date double integrated and the recorded trajectories are shown in Figure 13. Comparing Figures 2, 3, 6, and 13, we can see that the recorded trajectories are well consistent with theoretical and simulation results. In addition, the correctness of dynamics model and simulation model of variable linear vibration screen established in this paper are confirmed. And all of the work can provide theoretical basis for the design of variable linear vibration screen.

Table 1:

Time domain data of vibration screen (in Y direction).

Point	Maximum (m/s2)	Minimum (m/s2)	Mean value (m/s2)	Virtual value of test (m/s2)	Virtual value of simulation (m/s2)
1	58.7146	−64.2139	34.9763	38.8801	41.0924
2	49.1461	−55.3129	28.5171	31.7847	33.4482
3	37.3046	−35.0156	19.5815	21.8088	24.5047
4	34.3959	−30.9942	15.3412	17.17	15.7387
5	29.1666	−27.6246	9.24355	10.7725	9.5161

Figure 10:

The two record points in no-load test.

Figure 11:

Acceleration of each measuring point in vertical direction to screen face.

Figure 12:

The three different test positions of vibration screen.

Figure 13:

The trajectories under different positions on screen surface.

6. Experiment of Screening

In the mining industry, screen method can be used to classify material, or isolate some specific material from the mixed material. In this paper, all the research work above is aimed at studying the effect of screen surface properties on the vibration screen screening efficiency and performance. In further research, screening efficiencies of flexible screen surface vibration screen and the fixed screen surface vibration screen are experimentally studied to verify the correctness of above conclusion. Figure 14 shows the particle size composition of screening material, where particles of 0~25 mm account for 40%, particles of 25~50 mm account for 40%, and particles of 50~100 mm account for 20%. In order to identify the different particles, gangue materials are used for particles of 0~50 mm, and coal materials are used for particles of 50~100 mm. For researching the distribution statistic of materials under screen surface after screening, the area below the screen surface is divided, and result is shown in Figure 15. Figure 16 is a screening test physical graph. Figure 17 shows the relationship between material mass and screen time. Table 2 shows the screening results of two style vibration screens. Figure 18 shows bar graph which is based on Table 2.

Table 2:

Screening results of two style vibration screens.

Screen type	Experiment number	Material	Input mass (kg)	Mass in Zone A (kg)	Mass in Zone B (kg)	Mass in Zone C (kg)	Mass in Zone D (kg)	Mass in Zone E (kg)	Total mass after screen (kg)
Fixed screen face	1	Gangue	40.45	14.83	22.21	2.96	0.57	0	40.57
		Coal	9.54	0.43	0.26	0.31	0.22	8.2	9.42
	2	Gangue	63.6	22.78	31.54	8.26	1.2	0	63.78
		Coal	16.43	0.83	1.72	0.93	0.61	12.16	16.25
	3	Gangue	88.25	29.63	40.86	13.1	4.27	0.75	88.61
		Coal	21.77	0.52	1.33	2.16	1.03	16.37	21.41
	4	Gangue	111.89	31.52	52.59	18.29	6.33	0.41	112.34
		Coal	28.03	0.73	2.85	3.22	1.37	19.41	27.58
Flexible screen face	5	Gangue	40.38	12.21	22.32	5.17	0.76	0	40.46
		Coal	9.66	0.33	0.23	0.13	0	8.89	9.58
	6	Gangue	63.77	19.59	22.42	14.68	6.74	0.42	63.85
		Coal	16.21	0.25	0.27	0.29	0.14	15.18	16.13
	7	Gangue	87.85	24.53	34.64	19.33	9.12	0.57	88.15
		Coal	22.1	0.41	0.25	0.37	0.23	20.54	21.8
	8	Gangue	112.07	29.96	37.37	27.53	15.48	2.53	112.87
		Coal	27.94	0.39	0.41	0.46	0.32	25.56	27.14

Figure 14:

Materiel for screening.

Figure 15:

Material partition under the screen.

Figure 16:

Screening experiment of coal and gangue.

Figure 17:

Relationship between material mass and screen time.

Figure 18:

Bar graphs of screening results of two style vibration screens.

From Figure 17, we can see that the screen time of fixed screen face style vibration screen is longer than flexible screen face style vibration screens, and the screen time of fixed screen face style vibration screen has a linear relationship with material mass. With the input material mass increase, the screen time ratio of two style vibration screens increases. From Figure 17 we also can get that the screen time ratio of two style vibration screens in this figure is much smaller than that in Figure 9, which is due to the fact that the interaction between particles is ignored in above research. In Table 2, the total mass of screened coal is a little lighter than input; it is just because some little debris of coal was rubbed off which was difficult to be noticed in counting, and it was counted as gangue. From Table 2 and Figure 18 we can conclude the following: the coal crush degree in flexible screen face screening process is smaller than in fixed screen face screening process which indicted the flexible screen can decrease the impact forces between gangue and coal or coal and screen rob or coal and coal; the screened material distribution under flexible screen face is more uniform than fixed screen face, and with the input material mass increase, the screened material distribution under flexible screen face is more and more uniform which indicates the flexible screen has a better screening ability. All of the experiment results verify the correctness of above work.

7. Conclusions

1. The dynamic model of variable linear vibration screen is built based on the power balance theory, and the dynamics equation of any point on the vibration screen is obtained, which provides a theoretical basis for the design and research of variable linear vibration screen; the appropriate function area of exciting force of variable linear vibration screen is confirmed with the aim of getting ideal movement of screen surface; in addition, the stable requirements of the variable linear vibration screen are defined based on the Hamilton theory, and the range of exciting force direction angle is determined under the stable requirements.

2. The simulation model of the variable linear vibration screen with flexible screen surface has been built based on the multibody dynamics theory, and the simulation results of screen surface movement were very consistent with theoretical results. By analyzing the screening process of three different vibration screens, it proves that the variable linear vibration screen has better power distribution and screen surface movement. In addition, the flexible screen surface can increase the amplitude of the screen surface and reduce the material blocking phenomenon.

3. The movement of variable linear vibration screen with flexible screen surface has been tested and analyzed. The recorded trajectories of five points at different positions in the test are consistent with the theoretical and simulation results, which illustrates the correctness of dynamic model we have built. All of these works can provide a scientific basis for the design and research of variable linear vibration screen.

4. The screen experiment results of the two style screen surface vibration screens show the huge advantage of flexible screen surface than fixed screen surface in screen efficiency and avoiding material crush, and it also provides a powerful proof to verify the correctness of the simulation work.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.