Research on the optimization efficiency of secondary vibrating screening based on EDEM simulation

Abstract

Aiming at the problems of incomplete particle sieving and excessive residual fine particles in the traditional vibrating screen during the grading process of rockfill materials, this study proposes a secondary screening enhancement method by adding an auxiliary screen to the screen box to further improve the screening efficiency. Through the EDEM simulation software, a vibrating screening model with a four-layer screen structure was established, and an improved optimization scheme of adding an auxiliary screen in the screen box was designed. Systematic simulation analysis was conducted on the generated particles. The research content includes the influence of different screen angles, numbers of layers, amplitudes, frequencies, and direction angles on the screening efficiency, as well as the optimization and analysis of the secondary screening process with the auxiliary screen in the screen box. The simulation results show that the secondary screening scheme with the auxiliary screen in the screen box can significantly improve the screening efficiency of particles of various sizes. Based on rigorous verification simulations, the total efficiency increased from 92.4% in the traditional single-pass screening to 96.5%. While ensuring conservative estimates, this result still demonstrates a significant efficiency advantage over conventional designs.

Introduction

As a key water-retaining structure in water conservancy and hydropower projects, the long-term safe and stable operation of rockfill dams depends on the compaction quality of the dam body materials, especially the compactness and particle gradation of the fill materials, which directly affect the strength, deformation characteristics and impermeability of the dam body^1,2,3,4. During construction, the standard method for evaluating the compaction quality of rockfill materials both at home and abroad is to excavate test pits of specified volume on the already compacted fill layer, recover all the fill materials, and then perform vibration screening, weighing and volume measurement, and finally calculate the dry density^5,6,7.

Screening is a critical step in industrial production for mineral processing, aggregate manufacturing, and the handling of bulk solids, enabling efficient size classification and uniform feeding^8,9. As a core device in material handling, the vibrating screen operates via a motor-driven eccentric block that generates a periodic excitation force to produce compound vibrations, compelling particles into a throwing motion that promotes stratification and subsequent separation^10,11, thereby playing a crucial role in material separation. The screening efficiency is governed by the interaction dynamics between particles and the screen surface; variations in particle shape and size alter the probabilities of surface contact and aperture penetration¹². Vibration frequency and amplitude, together with screen deck inclination and vibration direction angle, jointly determine the particle-bed thickness, residence time, and throwing intensity, thereby influencing the optimal probability of passage through the screen apertures^13,14,15,16.

Zhang et al.¹⁷ used similarity theory to establish the connection between the prototype and the scaled-down model screen machine, analyzed the similarity criteria and parameter testing of the modal parameters of the scaled-down model of the vibrating screen and the prototype, and thus obtained the physical properties of the large vibrating screen and optimized its structural parameters. Zhao et al.¹⁸ analyzed the dynamic characteristics of the vibrating screen structure using the finite element method (FEM). Through dynamic simulations evaluating structural strength and performance, they developed a large-scale vibrating screen with a hyperstatic lattice-beam framework, which increased structural strength, effectively avoided resonance, and reduced destructive effects. To address the problem of low efficiency in processing sticky fine particles, Yu et al.¹⁹ studied a vibrating flow composite screen by exploring the dynamic characteristics and spatial trajectory of the screen frame. The results showed that there were almost no fine particles adhering to the screen surface of the composite screen, and its fine particle screening efficiency was significantly improved. Yang et al.²⁰ studied the force, stratification mechanism, and throwing principle of materials on the screen surface, developed a new composite vibrating screen, and conducted numerical simulations of the screening process and screening efficiency. The results showed that compared with the linear vibrating screen, the composite vibrating screen had significantly improved screening efficiency and material conveying capacity.

While continuum mechanics approaches (such as FEM or CFD) are effective for fluid-like flows, they fail to capture the discrete nature of rockfill materials during the screening process. The screening efficiency is governed by individual particle-to-particle and particle-to-screen collisions. Therefore, the Discrete Element Method (DEM) was selected for this study as it accurately simulates the discontinuous mechanical responses and trajectory of each particle. In the field of computational mechanics for granular materials, several mesh-free methods exist, including Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS). SPH and MPS are based on continuum mechanics and are widely used for simulating free-surface fluid flows or large deformation problems. However, the screening of rockfill materials is a process governed by discontinuous, discrete collisions between particles and the screen surface. Continuum-based methods fail to accurately capture the contact separation and independent trajectory of individual aggregate particles.

The Discrete Element Method (DEM) treats materials as a collection of independent entities, making it superior for analyzing the “jump-slide” stratification and penetration probability of rockfill. Therefore, the adoption of DEM technology can fill the research gap in optimizing the kinematic response of discrete aggregates during the secondary screening process. The discrete element method (DEM) accurately simulates inter-particle and particle–screen interactions, enabling quantitative analysis of the relationship between screening efficiency and vibration parameters. It is a numerical simulation approach used to investigate particle motion and mechanical responses during screening^21,22. EDEM is a tool designed based on the discrete element method to provide visualization and quantification for the analysis of particle motion processes²³. It has been widely used in agriculture^24,25, mineral engineering²⁶, biochemical applications²⁷, mechanical engineering^28,29, etc.

Zhao et al.³⁰ combined the discrete element method (DEM) with a Taguchi orthogonal experimental design to analyze the joint effects of amplitude, frequency, and screen-deck inclination on the screening process, thereby identifying the parameter combination that delivers the best overall screening performance. Xu et al.³¹ employed EDEM-based simulations to model particle kinematics during the comminution of cucumber straw, delineated three breakage stages inside a hammer mill, and quantified the effects of hammer number, hammer thickness, and hammer–screen clearance on mill power consumption and comminution efficiency. Moncada M. et al.³² employed the discrete element method to develop a dynamic model of a vibrating screen that accounts for ore inertia and the forces exerted by the ore on the screen. The results show that the proposed model can predict screen behavior under nominal operating conditions and at large angular displacements, and can accurately simulate ore transport along the screen deck. Shen et al.³³ systematically revealed the influence mechanism of different types of particles on screening efficiency through discrete element method (DEM) simulation and experimental verification. The results showed that under complex particle size distribution conditions, a double-layer vibrating screen exhibits higher screening efficiency and stability.

However, conventional single-pass vibrating screens suffer from low through-screening efficiency and particle carryover in multistage classification of rockfill aggregates. Aiming at the problems of incomplete particle sieving and excessive residual fine particles in the traditional vibrating screen during the grading process of rockfill materials, this study proposes a secondary screening enhancement method by adding an auxiliary screen to the screen box to further improve the screening efficiency. Unlike previous studies that focused solely on optimizing the vibration parameters of the main screen surface, this paper proposes a novel “Secondary Screening Enhancement Mechanism” by integrating an auxiliary screen structure within the collection hopper. This structure addresses the critical engineering problem of incomplete separation in the discharge phase. The simulation scheme, including the design of the inclination angle, amplitude, frequency, azimuth angle, and secondary screening structure, is described in detail. The simulation results are analyzed and discussed. Finally, the paper summarizes and explores its potential for intelligent grading of rockfill materials and large-scale engineering applications.

Vibration screening theory

This paper proposes a rockfill screening device suitable for rockfill density experiments. The performance of the screening device is evaluated using a discrete element particle flow model and field verification is performed.

The essence of the vibration screening process is to achieve particle classification by utilizing the motion differences of material particles through the vibration of the screen surface. The dynamic model of material particles on the screen surface can usually be simplified to a single-degree-of-freedom forced vibration system, and its dynamic differential equation is expressed as follows³⁴:

$$m\frac{{d}^{2}x}{d{t}^{2}}+c\frac{dx}{dt}+kx={F}_{0}\text{sin}\left(\omega\:t\right)$$

(1)

where, $\:m$ is the equivalent mass of the material on the screen (kg); $\:c$ is the damping coefficient (Ns/m), which characterizes the friction and resistance between particles and between particles and the screen surface; $\:k$ is the elastic recovery coefficient (N/m), which represents the spring support stiffness of the screen surface; $\:{F}_{0}$ is the vibration excitation force amplitude (N), which is related to the excitation of the eccentric block or electromagnetic vibrator; $\:\omega\:$ is the angular frequency of vibration (rad/s), $\:\omega\:=2\pi\:f$.

Solving the above equation, the steady-state response is:

$$x\left(t\right)=Xsin\left(\omega\:t-\phi\:\right)$$

(2)

$$X=\frac{{F}_{0}}{\sqrt{{\left(k-m{\omega\:}^{2}\right)}^{2}+{\left(c\omega\:\right)}^{2}}}$$

(3)

where, the amplitude $\:X$ determines the relative displacement between the particles and the screen surface, which directly affects the screening efficiency. The optimal screening state can be achieved by adjusting the amplitude and frequency.

Based on the EDEM custom motion function, the vibration motion mode of the screen is set to sinusoidal harmonic excitation:

$$z\left(t\right)=Asin\left(2\pi\:ft\right)$$

(4)

$${v}_{max}=2\pi\:fA$$

(5)

$${a}_{max}={\left(2\pi\:f\right)}^{2}A$$

(6)

where, z(t) is the displacement of the screen, a_max is the excitation acceleration, A is the amplitude, and f is the vibration frequency.

Define the relative excitation acceleration:

$$\varGamma\:=\frac{{a}_{\text{m}\text{a}\text{x}}}{g}=\frac{{\left(2\pi\:f\right)}^{2}A}{g}$$

(7)

When $\:{\Gamma\:}$ >1, the particles produce a “throwing” motion relative to the screen surface and enter a “jump-and-fall” cycle, which is beneficial to layer change and hole finding. Engineering experiments generally indicate that the range of 2 < $\:{\Gamma\:}$ < 5 is beneficial for particle screening.

Considering the screen surface inclination angle σ and the vibration direction angle $\:\theta\:$, the exciting acceleration is decomposed into the normal component $\:{a}_{n}={a}_{max}cos\theta\:$ and the tangential component $\:{a}_{t}={a}_{max}sin\theta\:$. The gravity of the particles is decomposed in the screen coordinate system to obtain $\:{g}_{n}=gcos\sigma\:$ and $\:{g}_{t}=gsin\sigma\:$. The two equations are combined to obtain the throwing condition and the sliding condition along the screen surface, namely:

For the throwing condition $\:{a}_{n}>{g}_{n}$, it follows that $\:{\Gamma\:}\text{c}\text{o}\text{s}{\uptheta\:}>\text{c}\text{o}\text{s}{\upsigma\:}$;

For the slipping condition $\:{a}_{t}>\mu\:{g}_{n}+{g}_{t}$, it follows that $\:{\Gamma\:}\text{s}\text{i}\text{n}{\uptheta\:}>{\upmu\:}\text{c}\text{o}\text{s}{\upsigma\:}+\:sin\sigma\:$.

where, $\:\mu\:$ is the coefficient of kinetic friction between the material and the screen surface. When both conditions are met simultaneously, a “jump-slide” synergistic flow pattern is formed, typically resulting in high screening efficiency. This also explains why there is an optimal value for the direction angle: too small a value for $\:\theta\:$ results in insufficient dispersion; too large a value for $\:\theta\:$ results in insufficient normal excitation and reduced contact time.

The effective contact coefficient between particles and screen surface can be approximately written as:

$$C=\frac{T-{t}_{f}}{T},T=\frac{1}{f}\:,{t}_{f}=\frac{4\pi\:fAcos\theta\:}{g}$$

(8)

Here, $\:C$ represents the time available in each vibration cycle for particles to search for apertures; if $\:C$ is too small, the opportunity for passage through the screen is reduced.

Materials and simulation

Based on the field gradation curve of the rockfill, a continuous particle-size distribution from 0 to 200 mm was specified. Using the built-in particle generator in EDEM, representative particle assemblies were constructed according to prescribed mass or number ratios. The simulation employs the DEM, which is a mesh-free approach for modeling the granular phase. The particles are treated as discrete entities interacting through contact laws. Conversely, the screen equipment is imported as a rigid boundary represented by a triangular surface mesh. The interaction between the mesh-free particles and the meshed boundary is calculated using the Hertz-Mindlin contact model. To focus on the dominant mechanisms of screening kinematics and control computational cost, individual particles were modeled as equivalent spheres of sandstone material. Each particle was assigned physically realistic physical and mechanical parameters, as summarized in Table 1.

Considering the service requirements under heavy impact and abrasive conditions, the screen panel was made of Hadfield steel to balance high impact toughness and wear resistance, while the frame plates and structural members were fabricated from carbon steel to leverage its machinability and weldability. The contact-pair parameters for sandstone-Hadfield steel, sandstone-carbon steel, and Hadfield steel-carbon steel are listed in Table 2. To balance computational efficiency with accuracy in this large-scale simulation, rock particles were modeled as equivalent spheres. To compensate for the lack of shape irregularity inherent in real rockfill, a Rolling Friction Coefficient ($\:{\mu\:}_{r}=0.1$) was applied in the contact model (Table 2). This parameter simulates the resistance to rotation caused by the interlocking of irregular shapes.

Table 1 Physical parameters of materials.

Table 2 Contact parameters of materials.

Based on vibration screening theory, a multi-stage screen was employed to achieve automatic and precise particle grading. The experiment employed a four-layer screen structure, arranged in descending order of aperture from top to bottom (100 mm\60 mm\40 mm\20 mm), creating five particle size ranges (200 -100 mm, 100–60 mm, 60–40 mm, 40 –20 mm, and < 20 mm). When the particle size D ≤ the sieve aperture $\:\varPhi\:$, the stone material passes through the sieve and falls into the corresponding collection hopper. The spacing between the screen layers varies according to the particle size of each layer, increasing from bottom to top to ensure appropriate spacing between the screen layers and prevent blockage. The screen specifications are shown in Table 3.

Table 3 Parameters for screen design.

In order to reveal the movement characteristics and screening performance of rockfill particles during the vibration screening process and ensure the optimal vibration screening efficiency, the discrete element simulation (DEM) method was used for simulation analysis, and the three-dimensional modeling software was used to design the solid model of the screening equipment. The particles are treated as discrete entities interacting through contact laws. Conversely, the screen equipment is imported as a rigid boundary represented by a triangular surface mesh. The interaction between the mesh-free particles and the meshed boundary is calculated using the Hertz-Mindlin contact model. The model is shown in Fig. 1a. A model of the rockfill particle cluster and four-layer screen was established using EDEM software. Visualization tools were used to observe the movement of particles on the screen surface and analyze the interaction between the particles and the screen. In EDEM software, the interaction between particles is governed by the Hertz-Mindlin (no-slip) contact model. The translational and rotational motion of particle $\:i$ are calculated using Newton’s second law:

$${m}_{i}\frac{d{v}_{i}}{dt}=\sum\:{F}_{c,ij}+{m}_{i}g$$

(9)

$${I}_{i}\frac{d{\omega\:}_{i}}{dt}=\sum\:{T}_{ij}$$

(10)

where, $\:{F}_{c,ij}$ represents the contact forces (normal and tangential) between particles, and $\:{T}_{ij}$ is the torque caused by rolling friction and tangential forces.

Fig. 1

(a) Model diagram of the screening machine; (b) EDEM simulation model of the screening machine; (c) The sieving process of particles.

To balance computational accuracy and efficiency, and recognizing that the actual screen body contains numerous small features irrelevant to particle–screen contact dynamics (e.g., chamfers, bolt holes, and fine stiffener details), the solid model was simplified without altering the global mass distribution or boundary geometry. Minute fillets and hole arrays were removed, complex stiffener plates were idealized as continuous plate components, and the screen-box cavity was retained. The simplified screen body was exported in IGES format and imported into EDEM, ensuring watertight geometry and consistent normal orientations. After import, topological checks and normal unification were performed on the contact surfaces to prevent numerical interpenetration. Based on the field gradation curve of the rockfill, the continuous particle-size distribution (0–200 mm) was discretized into representative sizes and proportions listed in Table 4.

A dynamic “Particle Factory” was established at the rectangular feed inlet (600 mm×600 mm) located above the upper screen deck. Particles were generated continuously at a mass flow rate equivalent to the experimental throughput, with an initial vertical velocity of $\:{v}_{z}=-1.0$ m/s to simulate gravity feeding from a hopper. The screen surface boundary condition was set to no-slip, oscillating according to the harmonic excitation defined in Eq. (4). Using the built-in particle generator in EDEM, 5000 representative particles were generated at once according to the number ratio. The particles were introduced through the feed inlet into the screen body. The mass flow rate significantly influences the material bed thickness and particle-to-particle collision frequency. To accurately investigate the influence of vibration parameters (amplitude, frequency, inclination), the mass flow rate was controlled as a constant value of 50 kg/s. This flow rate was selected to maintain a theoretical bed depth of approximately 2–3 times the average particle diameter, ensuring that the simulation reflects a typical heavy-load working condition. Inter-deck spacings were set to 80–150 mm to provide sufficient space for particle throwing and rolling and to mitigate secondary interference between decks. Subjected to screen vibration, the particles were classified across the four decks and discharged into separate collection hoppers, as shown in Fig. 1b.

Under a uniform gravitational acceleration of $\:g$ = 9.81 m/^s and with the installation angle held constant, the effects of screen inclination, vibration frequency, amplitude, and vibration direction angle on screening efficiency and particle passage rate were investigated. For each size fraction, the through-screening efficiency, screening time, and aperture blinding were recorded. The relationships between efficiency and parameter combinations, as well as the influence of individual vibration parameters, were analyzed to identify the optimal parameter set that maximizes screening efficiency. The workflow of particle generation and screening simulations is shown in Fig. 1c.

Table 4 Parameters of particle gradation.

Synchronous excitation was generated by dual motor–driven eccentric blocks. The screen box and decks were subjected to simple harmonic vibration at different installation inclinations, with combinations of vibration frequency and amplitude varied accordingly. In the simulations, inter-particle interactions were assumed to follow an elastic collision model, with the coefficients of restitution and friction specified; material parameters were assigned according to Tables 1 and 2. The simulation time was set to 6 s, and the time step was determined automatically. Computations were then executed under an experimental design comprising 12 categories and a total of 144 test runs to ensure the robustness of the results, as shown in Table 5.

Table 5 Table of orthogonal experimental design.

Results and discussion

Effect of the number of screen layers

Screening efficiency is generally defined as the ratio of the actual mass of material passing through the screen to the mass of material in the feed that theoretically should pass. However, for the top screen deck (aperture 100 mm), the target product is the retained material (D > 100 mm). Therefore, the efficiency for this specific layer is defined as the “Retention Efficiency”, calculated as:

$$\eta\:=\frac{{M}_{retained}}{{M}_{total(>100mm)}}\times\:100\%$$

(11)

A value of over 90% indicates that the majority of large particles were successfully transported to the discharge outlet without erroneously falling through or blocking the screen. To calculate the screening efficiency accurately, “Grid Bin Group” sensors were set up at the discharge outlet of each screen layer and the undersize collection hopper. These sensors monitored the real-time cumulative mass of particles passing through the detection planes ($\:{M}_{T}$ and $\:{M}_{retained}$). The screening efficiency was then calculated using Eq. (11) based on the mass data exported at the end of the stable simulation period.

Under the conditions of amplitude 8 mm and frequency 20 Hz, single-layer, double-layer, triple-layer and quadruple-layer screen structures were set for simulation analysis. The screen combination is divided into four levels of structure: L1, L2, L3 and L4. The single-layer L1 is a coarse classification with an aperture of 100 mm, the double-layer L2 adds a middle layer with an aperture of 60 mm, the three-layer L3 adds a fine layer of 40 mm, and the four-layer L4 is a complete screen structure. The ratio of particles at each level falling to the target layer within 6 s is calculated as the screening efficiency $\:{\varvec{\eta\:}}_{\varvec{r}}$, and the total screening efficiency $\:{\varvec{\eta\:}}_{\varvec{T}}$ is calculated weighted by volume and mass. The simulation results are shown in Table 6.

Table 6 Simulation results of screening efficiency corresponding to different numbers of screen layers.

Under single-layer sieve conditions, only large particles with a diameter D > 100 mm achieve a high retention rate (approximately 75%). A large number of small and medium-sized particles are mixed together, making it difficult to achieve effective stratification and hole finding within the limited length. Furthermore, due to insufficient effective contact time with the screen surface, fine particles have almost no chance of passing through the screen, resulting in an overall screening efficiency of only about 80.8%. As the number of screen layers increases, the load on the top layer is significantly reduced, giving particles more opportunities to find holes and allowing them to penetrate more fully. The screening efficiency for medium-sized particles (100 –60 mm and 60 –40 mm) increases to over 90% for both the double-layer and triple-layer structures, with overall efficiency increases of approximately 88.4% and 92.4%, respectively. In the four-layer screen structure, the screening efficiency of fine particles smaller than 40 mm is significantly improved to over 95%, and the efficiency of large particles also reaches over 86%, and the total screening efficiency is increased to about 93.8%. The results show that through the chain mechanism of “material bed thinning-enhanced stratification-increased active porosity-reduced mismatching and blockage” the particle size distribution approaches the target cut as the number of screen layers increases. Increasing the number of screen layers significantly improves particle separation, with the optimal particle separation efficiency achieved by a four-layer structure.

Effect of screen inclination

The screen inclination angle is one of the important geometric parameters that affect the performance of the vibrating screen. It directly determines the movement pattern, residence time and screening efficiency of the particles on the screen surface. To clarify the specific effect of screen inclination on particle screening efficiency, this study conducted a comparative analysis of particles at each level based on the established sieve model with screen inclination angles $\:\sigma\:$ set to 5°, 10°, 15° and 20°, fixed amplitude of 10 mm, frequency of 24 Hz, and direction angle of 0°. The classification efficiency $\:{\eta\:}_{\tau\:}$ is defined as the mass ratio of particles of each size falling to their target layer within 6 s, and the total screening efficiency $\:{\eta\:}_{T}$ is weighted by the particle size ratio. The simulation results of the screening efficiency and total efficiency of particles of various sizes under different inclination angles are shown in Table 7.

Table 7 Screening efficiency under different inclination angles.

As shown in Fig. 2, as the screen inclination angle gradually increases, the movement speed and kinetic energy of the particles will increase significantly. However, if the inclination angle is too large, the particle’s sieve penetration time will be reduced, and the chance of the particle penetrating the screen hole will be reduced. Therefore, choosing a reasonable screen inclination angle is the key to improving screening efficiency. This study shows that the particle screening efficiency reaches the best state when the screen inclination angle is around 15°.

Fig. 2

The influence of the screen angle on the screening efficiency of particles.

Effect of amplitude

When the vibration frequency is 24 Hz and the screen inclination angle is 15°, the amplitudes are set to 6 mm, 8 mm, 10 mm, and 12 mm for simulation analysis. The simulation results show that the increase in amplitude improves the screening efficiency overall, but shows obvious differences in particle size, as shown in Fig. 3. Specifically, the screening efficiency of medium and large particles was low at an amplitude of 6 mm, only about 65.3% and 71.2%. As the amplitude increases to 12 mm, the screening efficiency of particles of different sizes shows a significant change trend. As the amplitude increases, the screening efficiency of large particles (175 mm, 135 mm, and 110 mm) increases from an initial 80% to over 90%. This is primarily because the increased amplitude increases the jumping amplitude of the particles on the screen surface, effectively reducing clogging caused by large particles. The screening efficiencies of small and medium-sized particles (100–80 mm, 80–60 mm, 40–20 mm) at amplitudes of 8 mm, 10 mm, and 12 mm were 92.4%, 96.7%, and 94.3%, respectively.

Fig. 3

Simulation diagram of screening at different amplitudes.

The amplitude reshapes the spatiotemporal structure of the “jump-slide-hole search” process by changing the peak velocity and peak acceleration. According to the peak acceleration formula 𝑎_max=𝐴(2𝜋𝑓)², when the amplitude increases, the peak acceleration of the sieve surface on the particles increases, also improving the normal throwing ability and the probability of flipping. Since the local accumulation on the top layer is broken up, the active pore rate and the number of presentations $\:N$ are more friendly to coarse particles, so the coarse particle retention and diversion efficiency are significantly improved. The change in velocity direction after the particles hit the screen body is shown in Fig. 4.

Fig. 4

The direction of velocity change after the particle impinges on the screen when the amplitude is 8 mm.

However, excessively high excitation acceleration will lead to a chain reaction such as shortened contact time, enhanced rebound and lateral migration, and increased dynamic deformation of the screen, causing jumping particles to collide frequently with the edge of the screen hole, easily forming instantaneous blockage or “pinball effect”. In addition, since the fine particles are re-mixed into the upper layer, the stratification is destroyed and the effective pore size changes, which ultimately leads to a decrease in the chance of particles passing through the sieve and a decrease in the probability of passing through the sieve. When the amplitude becomes higher, the screen body can provide higher kinetic energy, but it destroys the “full contact + orderly stratification” between the particles and the screen surface, which is a necessary condition for efficient screening. Therefore, the overall screening efficiency drops by 2%-4% compared with the amplitude of 10 mm. Therefore, when the amplitude is set to 10 mm, the total screening efficiency reaches the optimal 93.4%, which provides a reference for subsequent parameter optimization.

Effect of frequency

When the amplitude is fixed at 10 mm, different screening frequencies (16 Hz, 20 Hz, 24 Hz, and 28 Hz) are simulated to investigate their effects on particle screening efficiency. The simulation results are shown in Fig. 5. The study found that when the frequency was 16 Hz, the screening efficiency of large particles (> 100 mm) was low (about 60%), and the efficiency of small and medium particles was only about 75% to 80%. As the frequency increases to 20 Hz, the screening efficiency of particles of all sizes is significantly improved, with large particles reaching more than 80% and small and medium particles reaching about 90%. When the frequency is further increased to 24 Hz, the particles are fully mobilized. The screening efficiency for small and medium particles (particle sizes of 60 –40 mm and 40 –20 mm) reaches 94.8% and 97.1%, respectively. The efficiency for large particles also exceeds 87%, and the overall efficiency rises to 93.4%.

Fig. 5

Simulation diagram of screening at different frequencies.

However, when the frequency was further increased to 28 Hz, the particle screening efficiency decreased, especially the efficiency of small and medium-sized particles decreased significantly. This is because the frequency is too high and the particles move violently, which increases the jumping height and reduces the possibility of passing through the screen. On the one hand, according to the parameter comparison shown in Table 8, when the amplitude is the same, the angular frequency increases by 8% when the frequency is changed from 24 Hz to 28 Hz, which increases the peak acceleration by about 18%. When the critical vibration intensity is exceeded, the screen body enters a strong “fluidization” state, strong transverse surge waves appear on the screen surface, and fine particles are drawn into the upper material flow, resulting in a decrease in the overall classification efficiency. The increased frequency shortened the period T, but the airborne duration of the first particle ejection remained nearly constant. This discrepancy caused the fraction of time particles were in genuine contact with the sieve to drop from 49 to 39%. The effective time window for particles to locate and pass through the sieve was thereby narrowed by about 20% in each cycle, which drastically reduced the opportunities for successful sieving.

Table 8 Comparison of parameters at frequencies of 24 Hz and 26 Hz.

On the other hand, a higher sieve body vibration frequency intensifies the rebound and lateral displacement of particles upon impact, leading to a greater impact force when they fall back onto the screen after a violent jump. The resulting high acceleration increases the porosity of the material bed, causing particles to undergo a “suspension-resettling” cycle. This mechanism makes particles more prone to getting wedged at the edge of the sieve pores, leading to temporary blockages and consequently reducing the effective area of the subsequent particle passage. Therefore, a screening frequency of 24 Hz is the best in maintaining screening efficiency and operating stability.

Effect of direction angle

The vibration direction angle ($\:\theta\:$) controls the relative proportion between the vertical excitation component ($\:\stackrel{⃑}{\varvec{a}}$) and the horizontal component ($\:\stackrel{⃑}{\varvec{b}}$). With a fixed amplitude of 10 mm, a frequency of 24 Hz, and a screen inclination angle of 10°, simulations were performed for direction angles set at 0°, 30° and 60°, respectively. The sieving efficiencies for each particle size class and the overall efficiency were then statistically analyzed. The simulation results are presented in Table 9. The simulation results from the 144 test runs were statistically analyzed using the Taguchi Orthogonal Experimental Design method. We employed Range Analysis (ANOR) to determine the sensitivity of the screening efficiency to each factor (Inclination, Amplitude, Frequency), allowing us to identify the optimal parameter combination quantitatively.

Table 9 Statistics of particle screening efficiency at different directional angles.

When the direction angle was 0°, particle motion was dominated by vertical hopping. This led to a tendency for the particle bed to accumulate and a lack of sufficient horizontal dispersion. While this configuration was effective at retaining larger particles, the overall efficiency was only 93.6% because the fine particles were restricted in their ability to locate pores due to the compression from the upper layer. As the direction angle increased, the excitation force provided greater vertical hopping to disperse the particle bed while also generating moderate forward sliding. This dual action promoted particle bed spreading and continuous renewal, which in turn optimized the sieving or retention of all particle sizes. As a result, the maximum sieving efficiency for fine particles reached approximately 99.2%, with a peak overall efficiency of 96.9%. When the direction angle was further increased to 60°, the horizontal component of the excitation force caused particles to slide more quickly off the screen surface. This reduced the vertical impact force, disrupting the balance between sieving and retention. Consequently, the efficiency for all particle sizes generally decreased, with the overall efficiency dropping to just 91.9%.

The analysis reveals that components $\:\stackrel{⃑}{\varvec{a}}$ and $\:\stackrel{⃑}{\varvec{b}}$ separately govern particle hopping and particle sliding dispersion along the sieve surface. As the direction angle θ increases, $\:\stackrel{⃑}{\varvec{a}}$ decreases, which shortens the time window for particles to return to the sieve and thus reduces sieving opportunities. Conversely, an increase in $\:\stackrel{⃑}{\varvec{b}}$ enhances the stratification mechanism, causing large particles to rise and fine particles to settle, thereby improving sieving efficiency. Consequently, for the dry sieving of 10–175 mm rockfill, it is recommended to moderately increase the direction angle, controlling it to approximately 30° to optimize performance. Conversely, when handling wet or cohesive materials, a reduced direction angle of 15–20° is advised¹⁹. This adjustment enhances the vertical excitation component, which helps to minimize the risk of horizontal blockages that can occur with such materials.

Effect of secondary screening

In view of the problem of insufficient screening in single screening, an improvement plan of secondary continuous screening was proposed. It was considered to set up multiple special collection screen buckets under the original four-layer vibrating screen, and add auxiliary screens with corresponding apertures in each screen bucket. When the particles pass through the main screen and fall into the screen bucket, they will be screened again by the auxiliary screen to complete a more thorough classification. The model is shown in Fig. 6. The aperture of the auxiliary sieve bucket screen is set to be the same as the aperture of the main screen above it. The purpose of this solution is to extend the effective path and time of particle screening. Under the action of gravity and vibration, the particles in the sieve bucket are further screened by the auxiliary screen. The particles that do not pass through the screen have another chance to be separated, thereby improving the screening efficiency and reducing the residual fine particles. It should be noted that equipment design requires consideration of more constraints and structural reliability. The simulation model used in this article is only used to verify whether the equipment improvement is reasonable. The actual equipment production still requires optimization design and improvement.

Fig. 6

Schematic diagram and simulation diagram of the optimized secondary auxiliary screening model.

To simplify model building and simulation time and to form an effective comparison, this simulation only models two types of sieves with apertures of 60 mm and 100 mm in the sieve bucket. The simulation was conducted with an amplitude of 10 mm and a frequency of 24 Hz, while the number of particles was maintained at 5000. The simulation results show that the screening efficiency of each level of particles is further improved after two consecutive screenings. After conducting multiple verification simulations and applying a conservative mass-balance calculation (excluding unstable edge particles), the efficiency data was updated. The comparison shows that the secondary screening structure improved the passing rates of fine particles (30 mm and 10 mm) to over 95%. Consequently, the overall screening efficiency improved from 92.4% (single screening baseline) to 96.5%. Although slightly lower than the theoretical maximum, this 4.1% net increase confirms the robustness of the auxiliary screen structure in reducing residue. The comparison of the primary and secondary screening efficiencies of the four-layer screen is shown in Table 10.

Table 10 Comparison of the efficiency of single screening and secondary screening with screen mesh.

As shown in the simulation results of Fig. 7a, compared with the sieve bucket without the auxiliary screen, the small and medium particles are significantly separated after secondary screening in the sieve bucket with the auxiliary screen. Figure 7c and d show the screening results without and with the auxiliary screen, respectively. By adding the auxiliary screen to the secondary screening process in the sieve bucket, the screening efficiency of particles of all sizes is significantly improved, especially for medium and large particles (135 mm, 110 mm) and small particles (30 mm, 10 mm) that were originally difficult to screen, with the efficiency increased by about 3%-6%.

The incorporation of the auxiliary screen in the screening drum, which markedly extends the contact time between particles and the screen surface. As a result, particles gain more opportunities to adjust their posture and undergo secondary passage through the apertures, thereby substantially reducing pore clogging and particle residue. After the particles fall into the screen bucket, they are further disturbed and dispersed by the dense pore arrangement of the auxiliary screen, making it easier for fine particles to pass through the pores, significantly improving the screening efficiency. This method greatly overcomes the limitation of conventional single-stage screening, which often fails to achieve sufficient particle separation. In engineering applications with stringent gradation requirements, such as high-standard rockfill dams and railway subgrade material yards, the implementation of a secondary screening enhancement process by incorporating an auxiliary screen within the screening drum enables highly efficient particle classification, demonstrating excellent practicality and effectiveness.

Fig. 7

Simulation results of secondary screening comparison and local magnification.

Theoretical validation of the simulation model

To validate the reliability of the discrete element model in the absence of full-scale physical experiments, the simulation results were compared with theoretical vibration mechanics. The simulated relative excitation acceleration Γ was maintained between 3.2 and 4.5 across all test groups. This falls strictly within the theoretical optimal range of 2 < Γ < 5 recommended for heavy-duty rockfill screening in engineering manuals. Furthermore, the particle flow trajectory observed in the simulation is consistent with the theoretical projectile motion equations derived in "Vibration screening theory" section, confirming the kinematic accuracy of the model. It should be noted that this study focuses on the dry screening of rockfill materials. The influence of moisture content and cohesion forces (sticky conditions) was not considered. For wet materials, liquid-bridge forces significantly alter the contact mechanics. The optimization of the secondary screening structure under wet conditions will be the focus of our future research.

Based on the system optimization results from discrete element simulations of the screening process, this equipment is specifically designed for the classification of medium to coarse-grained aggregate materials. It features a modular structure and incorporates high-reliability components. The machine has a compact size (2.6 m × 0.9 m × 1.5 m) and weighs approximately 650 kg, balancing ease of on-site mobility with structural stability. The equipment utilizes two 1.5 kW three-phase asynchronous motors as the core vibration source, powered by an industrial generator with a rated power of no less than 10.5 kW. Based on simulation analysis, the amplitude is set at 10 mm, the screening frequency is adjustable from 20 to 24 Hz, the screen surface inclination is 15°, the azimuth angle is controlled within the 20°–25° range, and the excitation force is adjustable within the 10–25 KN range, as shown in Fig. 8a. Under this optimized parameter combination, the equipment can achieve a rated processing capacity of up to 15 t/h (dry sand and gravel conditions), with a stable screening efficiency of over 90%, as shown in Fig. 8c.

The screening system is configured with four layers of high-manganese steel screens, with mesh sizes of 10 cm, 6 cm, 4 cm, and 2 cm from top to bottom, comprehensively covering the medium to coarse particle size range. The frame and main structure are made of carbon steel with excellent welding properties, ensuring overall rigidity and cost-effectiveness. The equipment base is constructed from heavy-duty channel steel, coupled with high-strength shock-absorbing springs, effectively isolating vibration transmission. The control system integrates motor soft start, overload protection, and emergency stop functions, significantly reducing starting current impact. The screens feature a quick-release structure, facilitating on-site maintenance and replacement, and comprehensively improving the reliability and applicability of the equipment under continuous operation conditions.

Fig. 8

(a) Screening equipment; (b) Mechanical feeding and screening operation; (c) Screening results.

While this study demonstrates the theoretical potential of the secondary screening mechanism, the following limitations must be acknowledged to ensure a balanced interpretation of the results: (1) Lack of more detailed physical field validation: The current conclusions are based on high-fidelity EDEM simulations validated against theoretical vibration mechanics. Due to the industrial scale of the equipment, full-scale physical prototyping and field testing were not conducted in this phase. The reported efficiency gains represent a theoretical maximum under ideal operating conditions. (2) Scope of Material Properties: This research focuses exclusively on the dry screening of non-cohesive rockfill materials. The influence of moisture content, mud adhesion, and capillary forces (sticky conditions) was not considered. As wet conditions significantly alter particle contact dynamics and stratification, the current model may overestimate efficiency for sticky materials.

Future work will focus on constructing a scaled-down physical test rig to experimentally corroborate these simulation findings and extending the DEM model to include liquid-bridge forces for wet screening analysis.

Conclusion

Based on the EDEM discrete element simulation platform, this paper constructs a numerical model of a vibrating screen with four screen layers (100 mm, 60 mm, 40 mm, and 20 mm). The effects of key operating parameters, such as inclination angle, amplitude, frequency, and number of screen layers, on the screening efficiency of multi-stage rockfill are systematically investigated. A secondary enhanced screening mechanism is proposed, which involves adding an auxiliary screen within the sieve bucket below the main screen.

• There exists an optimal combination among parameters such as inclination angle, amplitude, frequency, and direction angle. An excessively large amplitude reduces the particle–screen contact time, while an overly high frequency decreases the effective contact ratio, both of which in turn diminish the screening efficiency. According to the simulation results of the sieve structure in this paper, the optimal parameter combination is amplitude 10 mm, frequency 24 Hz, screen inclination angle 15°, and direction angle 30°.

• This study proposes the incorporation of an auxiliary screen within the screening drum. Quantitative analysis from verified simulations indicates that this configuration effectively prolongs the particle-screen contact time. As a result, the overall screening efficiency increased from 92.4% to 96.5%. This conservative estimate confirms that the secondary screening mechanism effectively minimizes fine-particle residues the separation capability under ideal conditions.

The EDEM-based secondary enhanced screening method proposed in this paper not only provides an effective path for high-precision rockfill material classification but also provides a theoretical basis for the design of vibrating screen structures and parameters, as well as the construction of intelligent screening systems. This method has broad application prospects in rockfill dams, mine beneficiation, and large-particle material processing.