A Method for Optimizing Screening Characteristics of a Double-Layer Vibrating Screen in a Slurry Shield Tunnel Based on CFD-DEM-FEM Coupling

Abstract

This invention relates to the field of vibrating screen optimization technology, and discloses a method for optimizing the screening characteristics of a double-layer vibrating screen for slurry shield tunneling based on CFD-DEM-FEM coupling. The method includes establishing a coupled simulation framework of CFD, DEM, and FEM; evaluating the impact of vibrating screen operating parameters, screen inclination angle, and initial particle velocity on the screening performance of the double-layer vibrating screen for slurry shield tunneling, and obtaining an initial optimization scheme for the vibrating screen; aiming at balancing the screening efficiency and screen wear of the vibrating screen, and based on a Latin hypercube sampling modeling surrogate model, combined with discrete element model simulation technology and the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, optimizing the initial optimization scheme of the vibrating screen, and outputting recommended values ​​for optimized screening characteristics. This invention can more accurately and precisely present particle behavior, slurry flow, and screen dynamics; and achieve a quantitative trade-off between screening efficiency and screen wear of a double-layer vibrating screen.

Description

Technical Field

[0001] This invention relates to the field of vibrating screen optimization technology, and specifically to a method for optimizing the screening characteristics of a double-layer vibrating screen for slurry shield tunneling based on CFD-DEM-FEM coupling. Background Technology

[0002] The in-depth development of underground space is of great significance for promoting urbanization and sustainable economic development. In recent years, large-scale underground engineering projects have continued to advance globally. As a fully mechanized tunneling method, slurry balance TBMs have been widely used in the construction of subway tunnels, railway tunnels, and highway tunnels. In hard rock or gravel strata, slurry balance TBMs generate a large amount of rock debris or slag during construction, which is then transported to the surface through slurry discharge pipelines for screening and filtration.

[0003] Screening, as a key unit operation for separating materials of different particle sizes, plays an irreplaceable role in many industrial fields. Vibrating screens are core screening equipment in slurry balance TBM construction, widely used for the grading, dewatering, and desliming of rock debris particles. With the increasing excavation diameter of slurry balance TBMs, the amount of rock debris transported increases significantly, placing higher demands on the efficient and stable operation of vibrating screen equipment. Therefore, it is necessary to conduct optimization research on the screening performance and effect of vibrating screens in slurry balance TBMs. Furthermore, the development of vibrating screen equipment that combines high performance, large processing capacity, and high reliability remains a current research hotspot.

[0004] The screening process involves simultaneous coupling effects between particles, between particles and slurry, and between particles and the screen body. The combined influence of various operating parameters on particle motion makes the screening mechanism quite complex. Existing studies have investigated the screening performance and screen dynamics of vibrating screens through indoor experiments. Specifically, they analyzed the impact of screen operating parameters on the kinematics of individual particles and proposed corresponding optimization schemes. However, due to constraints such as complex load conditions and high experimental costs, direct research on the screening performance and dynamic response of vibrating screens using measuring devices is difficult to achieve intuitive observation and is not economically viable.

[0005] With the development of computer science, numerical simulation has provided an effective means to overcome the above limitations and reveal the intrinsic mechanism and screening performance of vibrating screens. For example, discrete element method (DEM) numerical simulation has been widely used in screening process research. Recent studies have shown that DEM can be used to evaluate the influence of various factors on screening performance, thus providing a basis for formulating effective optimization strategies. For instance, based on DEM, the influence of amplitude, frequency, tilt angle, and vibration direction angle on the evaluation indicators of small-diameter particle materials was studied under low-frequency conditions of 14-22Hz, and optimization schemes for each indicator were given. Based on DEM, the optimal ratio of adjacent holes in a rectangular mesh screen was proposed, effectively improving screening performance and processing capacity. Compared with the CFD-DEM method, the CFD-DEM-Finite Element Method (FEM) can not only reveal the fluid domain flow field distribution and particle phase transport characteristics, but also further analyze the stress and deformation distribution at solid boundaries.

[0006] In complex slurry conditions, a significant contradiction exists between screening efficiency and screen wear in double-layer vibrating screens used in slurry shield tunneling machines. Improving screening efficiency often requires stronger vibration intensity, higher material movement speed, or more unfavorable operating conditions, thus exacerbating screen wear, shortening replacement cycles, and causing downtime. Conversely, reducing wear may lead to insufficient fine particle penetration, increased backflow, and decreased processing capacity. Existing methods largely rely on empirical parameter tuning or single-objective optimization, making it difficult to quantitatively predict steady-state screening efficiency and screen wear depth rate under the coupled effects of multiple variables such as operating parameters, inclination angle, and feed rate, and to obtain the optimal setpoint that balances efficiency and lifespan within a feasible range.

[0007] No effective solutions have yet been proposed to address the problems in the relevant technologies. Summary of the Invention

[0008] To address the problems in related technologies, this invention proposes a method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, in order to overcome the aforementioned technical problems existing in the current related technologies.

[0009] Therefore, the specific technical solution adopted by the present invention is as follows:

[0010] A method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling includes:

[0011] A coupled simulation framework of CFD, DEM, and FEM was established. Within this framework, the effects of vibrating screen operating parameters, tilt angle, and initial particle velocity on the screening performance of the double-layer vibrating screen in a slurry shield tunnel were evaluated, resulting in an initial optimization scheme for the vibrating screen. With the goal of balancing screening efficiency and screen wear, a surrogate model based on Latin hypercube sampling was used. This model, combined with discrete element method (DEM) simulation technology and the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, was used to optimize the initial scheme and output recommended values ​​for the screen screening characteristics.

[0012] The beneficial effects of this invention are as follows:

[0013] 1. This invention employs a multi-method combined simulation technique, integrating CFD-DEM-FEM, which, compared to traditional single-method simulations, can more accurately and precisely represent particle behavior, slurry flow, and screen dynamics. This integrated model not only captures the transport characteristics of particles but also delves into the stress and deformation experienced by the screen surface. It not only expands upon existing findings, such as the influence of operating parameters like frequency and amplitude on screening efficiency, but also reveals a more complex interaction mechanism between particles, slurry, and the screen surface.

[0014] 2. This invention calculates screening efficiency within a steady-state statistical time window using discrete element simulation (DEM), and extracts particle-screen contact load and tangential slip from the same simulation trajectory. Combined with the Archard wear model, it obtains the screen wear depth rate. Then, it utilizes Latin hypercube sampling to construct a sample dataset covering the decision space, establishes and cross-validates surrogate models for the decision variables to screening efficiency and wear depth rate, performs multi-objective optimization on the surrogate model to obtain a non-dominated optimal solution set, and selects the final recommended operating condition through weighted comprehensive objective selection. This allows for a parameter optimization process while meeting equipment constraints, achieving a quantitative trade-off between screening efficiency and screen wear in a double-layer vibrating screen, and outputting optimized recommended values ​​for operating parameters, inclination angle, and feed rate. This improves screening performance while reducing screen wear and downtime for replacement. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a CFD-DEM coupling flowchart according to an embodiment of the present invention;

[0017] Figure 2This is a simplified geometric model schematic diagram of a double-layer vibrating screen according to an embodiment of the present invention;

[0018] Figure 3 This is an irregular particle model diagram established in the discrete element model according to an embodiment of the present invention;

[0019] Figure 4 This is a 3D multiphase flow model diagram of a double-layer vibrating screen according to an embodiment of the present invention;

[0020] Figure 5 This is a CFD mesh sensitivity analysis diagram according to an embodiment of the present invention;

[0021] Figure 6 This is a schematic diagram of the coarse screening process of a double-layer vibrating screen obtained based on DEM according to an embodiment of the present invention;

[0022] Figure 7 This is a schematic diagram of the fine screening process of a double-layer vibrating screen obtained based on DEM according to an embodiment of the present invention;

[0023] Figure 8 This is a particle velocity distribution diagram along the longitudinal direction of the sieve body obtained by DEM simulation according to an embodiment of the present invention;

[0024] Figure 9 This is a particle velocity distribution diagram at different positions along the Z direction according to an embodiment of the present invention;

[0025] Figure 10 These are box plots of particle velocities of different sizes according to embodiments of the present invention;

[0026] Figure 11 This is a volume fraction distribution diagram of the local mud distribution along the length of the screen body obtained by CFD simulation according to an embodiment of the present invention.

[0027] Figure 12 This is a velocity distribution diagram of the local mud distribution along the length of the screen body obtained by CFD simulation according to an embodiment of the present invention;

[0028] Figure 13 This is a graph showing the change in screening efficiency according to an embodiment of the present invention;

[0029] Figure 14 This is a graph showing the variation of the total impact force on the screen surface according to an embodiment of the present invention;

[0030] Figure 15 This is a schematic diagram of a coarse sieve with different Z-coordinates according to an embodiment of the present invention, showing the number of collisions between particles and the sieve surface.

[0031] Figure 16 This is a schematic diagram of a fine sieve showing the number of collisions between particles and the sieve surface at different Z coordinates according to an embodiment of the present invention;

[0032] Figure 17 This is a schematic diagram showing the wear distribution of the coarse screen surface at 3.0 seconds according to an embodiment of the present invention;

[0033] Figure 18 This is a schematic diagram showing the wear distribution of the fine sieve surface at 3.0 seconds according to an embodiment of the present invention;

[0034] Figure 19 This is a schematic diagram of the equivalent stress of the static structure analysis of the coarse screen surface obtained by FEM simulation according to an embodiment of the present invention.

[0035] Figure 20 This is a schematic diagram of the total deformation of the coarse screen surface obtained by FEM simulation according to an embodiment of the present invention.

[0036] Figure 21 This is a schematic diagram illustrating the effect of vibration frequency on screening characteristics according to an embodiment of the present invention;

[0037] Figure 22 This is a schematic diagram illustrating the effect of vibration amplitude on screening characteristics according to an embodiment of the present invention;

[0038] Figure 23 This is a schematic diagram illustrating the influence of the vibration direction angle on the screening characteristics according to an embodiment of the present invention;

[0039] Figure 24 This is a schematic diagram illustrating the effect of the tilt angle of the vibrating screen on the screening characteristics according to an embodiment of the present invention;

[0040] Figure 25 This is a schematic diagram illustrating the effect of the initial particle velocity on the screening characteristics according to an embodiment of the present invention;

[0041] Figure 26 This is a schematic diagram illustrating the screening efficiency of coarse and fine screens before and after optimization according to an embodiment of the present invention.

[0042] Figure 27 This is a schematic diagram of the impact force of the coarse screen in the screening characteristics before and after optimization according to an embodiment of the present invention;

[0043] Figure 28 This is a flowchart of a method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, according to an embodiment of the present invention.

[0044] In the picture:

[0045] Ⅰ. Pelletizing plant; Ⅱ. Coarse screen; Ⅲ. Fine screen; Ⅳ. Discharge end; Ⅴ. Velocity inlet; Ⅵ. Non-slip wall; Ⅶ. Pressure outlet. Detailed Implementation

[0046] To further illustrate the various embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. These drawings are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these drawings, those skilled in the art should be able to understand other possible implementation methods and the advantages of the present invention. The components in the drawings are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0047] According to an embodiment of the present invention, a method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling is provided.

[0048] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments, such as... Figure 28 As shown, according to an embodiment of the present invention, a method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling is provided, comprising:

[0049] S1. Establish a coupled simulation framework for CFD, DEM and FEM.

[0050] S2. In the coupled simulation framework, evaluate the impact of vibrating screen operating parameters, vibrating screen tilt angle and initial particle velocity on the screening performance of the double-layer vibrating screen of the slurry shield tunnel, and obtain the initial optimization scheme of the vibrating screen.

[0051] S3. With the goal of balancing and optimizing the screening efficiency and screen wear of the vibrating screen, and based on the Latin hypercube sampling modeling proxy model, combined with the discrete element model simulation technology and the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, the initial optimization scheme of the vibrating screen is optimized, and the recommended value of the screening characteristics of the vibrating screen is output.

[0052] In one embodiment, establishing a coupled simulation framework of CFD, DEM, and FEM includes: constructing the contact behavior between particles and a vibrating screen; constructing the interaction force between particles and slurry based on fluid phase density, particle density, fluid phase velocity vector, particle phase velocity vector, diameter of an equal-volume sphere, fluid viscosity, particle Reynolds number, and drag coefficient; modeling the slurry fluid phase using CFD simulation technology and performing mesh sensitivity analysis to ensure that the computational accuracy and time consumption meet preset requirements; simultaneously modeling the particle phase within the screen using DEM simulation technology and establishing a digital geometric model of the particles through 3D scanning; coupling CFD simulation and DEM simulation by configuring the relationship between the fluid phase time step and the particle phase time step; and using the transient results at preset times in the CFD and DEM simulations as the load input for the FEM simulation to observe the screen surface stress and deformation.

[0053] In one embodiment, the interaction force between particles and mud is constructed based on fluid phase density, particle density, fluid phase velocity vector, particle phase velocity vector, diameter of an isovolumic sphere, fluid viscosity, particle Reynolds number, and drag coefficient. This includes: multiplying the ratio of fluid phase density to particle density by gravitational acceleration to obtain the buoyancy between particles and mud; establishing a first value based on particle density, fluid viscosity, and diameter of an isovolumic sphere; establishing a second value based on particle Reynolds number and drag coefficient; obtaining a third value through the difference between fluid phase velocity vector and particle phase velocity vector; multiplying the first, second, and third values ​​to obtain the drag force between particles and mud; and calculating the pressure gradient force between particles and mud based on fluid phase density and particle density.

[0054] In one embodiment, modeling the mud fluid phase using CFD simulation technology includes: treating the mud as a continuous and homogeneous fluid phase in the CFD simulation, and ensuring that the flow process of the fluid phase satisfies the mass conservation and momentum conservation equations; describing the rheological properties of the mud using the Herschel-Balkley model, and simulating the turbulent behavior of the mud flow using the k-ε turbulence model.

[0055] In one embodiment, modeling the particulate phase within the screen using DEM simulation technology includes:

[0056] Establish the governing equations for each particle:

[0057] ;

[0058] ;

[0059] In the formula, m i U p,i I i and ω i These represent the mass, velocity, moment of inertia, and angular velocity of particle i, respectively; F c,ij F d,ij With T ij These represent the contact force, viscous damping force, and torque between particles i and j, respectively; F c,iw F d,iw With T iw These represent the contact force, viscous damping force, and torque between particle i and the sieve surface, respectively; F f,i t represents the force exerted by the fluid phase on particle i; t represents time. This represents the total number of particles.

[0060] In one embodiment, evaluating the impact of vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity on the screening performance of a double-layer vibrating screen in a slurry shield tunneling machine, and obtaining an initial optimization scheme for the vibrating screen, includes: configuring the adjustment range of vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity; within the adjustment range, obtaining an initial optimization scheme for the vibrating screen by gradually adjusting the vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity, combined with feedback from the characteristics of the vibrating screen; wherein, the initial optimization scheme for the vibrating screen includes the initial optimized frequency, the initial optimized amplitude, the initial optimized vibration direction angle, the initial optimized tilt angle, and the initial optimized initial particle velocity.

[0061] In one embodiment, the goal is to balance and optimize the screening efficiency and screen wear of a vibrating screen. Based on a Latin hypercube sampling modeling surrogate model, combined with discrete element modeling simulation technology and the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, the initial optimization scheme of the vibrating screen is optimized. The recommended values ​​for the optimized screening characteristics of the vibrating screen include: within the steady-state statistical time window, the ratio of the mass of particles smaller than the characteristic size of the screen aperture in the statistical region of the screen surface to the total mass of all particles in that statistical region is used as the screening efficiency, i.e., the screening efficiency algorithm; the screen wear depth rate calculated based on the Hertz-Minderlin-Achad wear model is used as the screen wear; the operating parameters of the vibrating screen, the tilt angle of the vibrating screen, and the initial particle velocity are used as optimization decision variables; based on the initial optimization scheme of the vibrating screen and the adjustable constraints of the equipment, the allowable range of the optimization decision variables is determined; a discrete element model simulation example is configured to evaluate the screening efficiency and screen wear; the discrete element model simulation is executed, and the screen surface wear statistics are statistically analyzed within the steady-state statistical time window. The particle set of the simulation area is used to calculate the screening efficiency. The normal contact force and relative tangential slip distance between the particles and the screen are extracted from the same simulation trajectory and substituted into the Hertz-Minderlin-Achad wear model to output the screen wear depth rate. The optimization decision variables are sampled using Latin hypercube sampling within allowable ranges to cover the optimization decision variable space, and screening efficiency and screen wear depth rate data are generated for each sampling point, forming a sample dataset for optimization. Based on the sample dataset, a surrogate model is established from the optimization decision variables to the screening efficiency and screen wear depth rate, and cross-validation is used to ensure that the prediction error of the surrogate model meets the optimization requirements. Based on the surrogate model, the balance between screening efficiency and screen wear is optimized as the objective, and an optimization search is performed, outputting a set of non-dominated optimal solutions for screening efficiency and screen wear depth rate. The optimal solution is obtained by weighted comprehensive objective calculation in the non-dominated solution set. The optimal solution is mapped to recommended set values ​​for the vibrating screen operating parameters, the vibrating screen tilt angle, and the initial particle velocity, serving as recommended values ​​for optimizing the screening characteristics of the vibrating screen.

[0062] In one embodiment, the discrete element model simulation example configured to evaluate screening efficiency and screen wear includes: calculating the normal contact force between particles and the screen, and between particles themselves, based on the Hertz-Mundling contact model; establishing the vibration boundary conditions of the screen box using the simple harmonic motion kinematic equations, and determining the vibration characteristics using operating parameters; determining the geometric orientation of the screen surface and the direction of gravity based on the tilt angle, and determining the feed inlet boundary conditions based on the initial particle velocity; and calculating the wear depth rate of the particle-screen contact using the Achard wear model based on the normal contact force between particles and the screen and the relative tangential slip distance.

[0063] In one embodiment, based on a sample dataset, a surrogate model is established from the optimization decision variables to screening efficiency and screen wear depth rate. Cross-validation is used to ensure that the prediction error of the surrogate model meets the optimization requirements. This includes: splitting the sample dataset into vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity, and performing preprocessing and standardized dimensionless processing. K-fold cross-validation is selected to construct training and validation sets. A surrogate model is selected, and the training and validation sets are used to train and iteratively improve the surrogate model, and the surrogate model is then solidified.

[0064] In one embodiment, based on a surrogate model, the balance between screening efficiency and screen wear is optimized as the objective, and an optimization search is performed to output a set of non-dominated optimal solutions for screening efficiency and screen wear depth rate. The optimal solution is obtained by applying a weighted comprehensive objective function to the set of non-dominated solutions, including: within the feasible region defined by the allowable range of the optimization decision variables, calling the surrogate model to obtain predicted values ​​for screening efficiency and screen wear depth rate respectively, with the optimization objective being to maximize the predicted value of screening efficiency and minimize the predicted value of screen wear depth rate; iteratively searching a multi-objective optimization problem, using the output of the surrogate model as the fitness evaluation basis, until the termination condition is met; non-dominated sorting of the candidate solutions obtained from the iterative search to obtain a set of non-dominated optimal solutions for screening efficiency and screen wear depth rate; normalizing the predicted values ​​of screening efficiency and screen wear depth rate in the set of non-dominated optimal solutions; constructing a weighted comprehensive objective function based on the normalized screening efficiency and screen wear depth rate, and selecting the optimal solution from the set of non-dominated optimal solutions.

[0065] According to another embodiment of the present invention, a system for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling is also provided, comprising:

[0066] The Coupled Framework module is used to establish a coupled simulation framework for CFD, DEM, and FEM.

[0067] The evaluation module is used to evaluate the impact of vibrating screen operating parameters, vibrating screen tilt angle and initial particle velocity on the screening performance of the double-layer vibrating screen in the slurry shield tunnel within a coupled simulation framework, and to obtain the initial optimization scheme for the vibrating screen.

[0068] The optimization module aims to balance the screening efficiency and screen wear of the vibrating screen. Based on the Latin hypercube sampling model, it combines discrete element model simulation technology with the screen wear depth rate and screening efficiency output by the screening efficiency algorithm to optimize the initial optimization scheme of the vibrating screen and output the recommended values ​​for the optimized screening characteristics of the vibrating screen.

[0069] To facilitate understanding of the above technical solutions of the present invention, the working principle of the present invention in actual process will be described in detail below.

[0070] To evaluate and optimize the screening characteristics of a double-layer vibrating screen in slurry balance TBM tunnel construction, this invention establishes a three-dimensional (3D) coupled model of the vibrating screen based on an integrated CFD–DEM–FEM method. This model reveals particle transport characteristics and slurry flowability, and provides a comprehensive analysis of the screen surface dynamics. Results show that particles are relatively uniformly distributed on the screen surface, and the particle velocity along the screen length generally increases steadily from 0 m / s to 5 m / s. Influenced by bed formation and collision dynamics, the peak impact force on the coarse screen surface can reach 90 times that of the fine screen surface, indicating that the bed effect weakens the direct load of particles on the screen surface to some extent. The screening efficiencies of the coarse and fine screens are stable at approximately 61% and 73%, respectively, with the coarse screen efficiency fluctuating more significantly, mainly related to particle size distribution and the collision process. Stress and deformation are mainly concentrated in the middle of the screen surface and in areas near the feed and discharge ends, requiring structural reinforcement to improve the strength and stiffness of the screen body. Finally, this invention proposes optimization schemes for each parameter and applies them to the slurry balance TBM construction of a second undersea tunnel in a certain location. The research results can provide reference and suggestions for the efficient operation of the slurry-water balance TBM double-layer vibrating screen.

[0071] This invention establishes a three-dimensional coupled model of a vibrating screen. The main advantage of this research lies in the use of a multi-method integrated framework (CFD-DEM-FEM). Compared to the single-method simulations commonly found in existing studies, the coupled vibrating screen model can more meticulously and accurately characterize particle behavior, slurry flow, and the dynamic response of the screen body. Based on revealing the characteristics of particle transport and the laws of slurry fluid dynamics, this invention further analyzes the dynamic response of the screen surface and systematically explores the influence of vibrating screen operating parameters and initial particle velocity on the screening process. The research conclusions can provide a reference for the efficient operation of a slurry-water balance TBM double-layer vibrating screen.

[0072] I. CFD-DEM Coupled Modeling:

[0073] 1. CFD-DEM Coupled Algorithm:

[0074] The CFD-DEM coupled calculations for the research content were performed using two software programs: for example, FLUENT was used to simulate the mud fluid phase, and EDEM was used to simulate the rock debris particle phase. Figure 1 As shown, the CFD-DEM coupling algorithm flow is presented.

[0075] 2. CFD fluid phase modeling:

[0076] In CFD simulations, the mud is treated as a continuous and homogeneous fluid phase, and its flow process satisfies the mass conservation and momentum conservation equations.

[0077] (1)

[0078] (2)

[0079] In the formula, α f ρ f U f With p f These represent the fluid phase volume fraction, density, velocity vector, and pressure, respectively; τ is the viscous stress tensor; F pf This represents the total force exerted by the particles on the fluid. The rheological properties of mud can be better characterized by the Herschel-Bulkley (HB) model. This invention uses the HB model to describe the rheological properties of mud, and its constitutive relations are as follows:

[0080] (3)

[0081] (4)

[0082] In the formula, Let τ be the shear rate, τ0 be the yield stress, k be the viscosity coefficient, and n be the power-law exponent. The shear stress-shear rate relationship can be determined using a rheometer with a CCT-40 coaxial cylindrical measuring system. The bentonite slurry used in this invention was taken from a slurry-water balance TBM engineering site, and its main components include bentonite and carboxymethyl cellulose (CMC). To avoid sample settling, the sample was stirred at 200 rpm for 1 min before the rheological test. Due to the presence of large, irregularly sized particles, the slurry flow during the sieving process exhibited typical turbulent characteristics; a k-ε turbulence model was used to simulate the turbulent behavior.

[0083] 3. DEM particle phase modeling:

[0084] Rock fragments within the screen, acting as the particulate phase, are subjected to the combined effects of the slurry, the screen wall, and other particles during the screening process. Particle transport and collision can be solved using Newton's second law. The governing equations for each particle are as follows:

[0085] (5)

[0086] (6)

[0087] In the formula, m i U p,i I i and ω i These represent the mass, velocity, moment of inertia, and angular velocity of particle i, respectively; F c,ij F d,ij With T ij These represent the contact force, viscous damping force, and torque between particles i and j, respectively; F c,iw F d,iw With T iw These represent the contact force, viscous damping force, and torque between particle i and the sieve surface, respectively; F f,i t represents the force exerted by the fluid phase on particle i; t represents time. This represents the total number of particles.

[0088] like Figure 2 As shown, a simplified geometric model of a double-layer vibrating screen is presented. The screen width is 1500 mm, the length is 4200 mm, and the installation inclination angle α is 17°. To reduce model complexity and improve computational efficiency, this invention only models the side plates, the coarse screen surface, and the fine screen surface, as these components have the most significant impact on particle transport. The coarse screen surface consists of grids with a width of 6 mm and a length of 30 mm, allowing particles smaller than 6 mm to pass through; the fine screen surface consists of grids with a width of 3 mm and a length of 30 mm, allowing particles smaller than 3 mm to pass through; the distance between the two screen surfaces is 250 mm. Furthermore, a particle plant is set up at the feed end to generate particles.

[0089] The shape and size of particles larger than 20 mm are key factors affecting the accuracy of screening simulation. To realistically represent the characteristics of rock particles in a DEM, this invention performed three-dimensional scanning on randomly selected typical rock blocks and established corresponding digital geometric models, such as... Figure 3 As shown, "Particle size" represents the particle size, and "Scale" represents the proportion. Rock debris particles with a diameter less than 20 mm can be simplified to spherical particles in the DEM. Based on the tunnel boring machine's (TBM) advance speed and the slurry discharge rate, the mass flow rates of spherical and irregular particles are set to 5.52 kg / s and 30.21 kg / s, respectively. Commonly used contact models in existing studies include the Hertz–Mindlin no-slip model, the Hertz–Mindlin–JKR model, the Hertz–Mindlin–Archard wear model, and the Hertz–Mindlin bonding model. This invention uses the Hertz–Mindlin–Archard wear model to describe the contact behavior between rock debris particles and the vibrating screen, as well as among the particles themselves. This model assumes that the wear on the geometric surface is positively correlated with the applied normal force, thereby allowing for the estimation of wear loss on the vibrating screen.

[0090] 4. Fluid-solid interaction:

[0091] The interaction forces between rock particles and mud mainly include buoyancy F. b Resistance F d and pressure gradient force F p Its expression is as follows:

[0092] (7) (8) (9)

[0093] In the formula, ρ p U is the particle density, g is the acceleration due to gravity, and U is the acceleration due to gravity. p Let d be the particle phase velocity vector. V Let μ be the diameter of a sphere of equal volume, μ be the fluid viscosity, and Re be the viscosity. p C is the particle Reynolds number. D The drag coefficient can be calculated using the following formula:

[0094] (10)

[0095] In the formula, Re is the fluid Reynolds number; a1, a2, and a3 are different constants, and their values ​​are as follows:

[0096] (11)

[0097] 4. Boundary conditions:

[0098] like Figure 4 As shown, Ⅰ represents the pellet mill, Ⅱ the coarse screen, Ⅲ the fine screen, Ⅳ the discharge end, Ⅴ the velocity inlet, Ⅵ the non-slip wall, and Ⅶ the pressure outlet. This invention establishes a three-dimensional multiphase flow model of a vibrating screen based on CFD-DEM coupling. In the CFD model, the fluid domain includes two media: bentonite slurry and air. The slurry inlet is set as a velocity inlet, and the outlet is set as a 0Pa pressure outlet, equivalent to a default outlet connected to the atmosphere. The number of nodes and elements in the fluid mesh are 269,568 and 163,570, respectively. To ensure the accuracy and validity of the numerical results, a CFD mesh sensitivity analysis was conducted (see...). Figure 5The results show that as the number of grid cells increases, the mass flow rate at the bottom outlet first decreases and then tends to stabilize, while the computation time increases with the number of grid cells. Considering both computational accuracy and time consumption, the grid scale and quality of the CFD model established in this invention can meet the requirements of accuracy and efficiency. A no-slip wall is used as the wall boundary condition. On the other hand, field engineering shows that most of the slurry has already passed through the screen surface near the feed end; to save computational resources and improve efficiency, this invention shortens the screen surface length in the Z direction. In the DEM model, the geometric model of the double-layer vibrating screen is constructed using rigid wall elements, and the screen surface motion is set as a displacement-controlled sinusoidal vibration, consistent with the settings of the CFD region.

[0099] The time step for the fluid phase can be 10-100 times the time step for the particle phase. In this invention, the fluid time step is set to 0.001 s, and the particle time step is set to 1 × 10⁻⁶. -5 During the 3-second simulation, DEM and CFD data were automatically saved every 0.01 seconds, ultimately generating 300 DEM data files and 300 CFD data files respectively; a single CFD-DEM coupling calculation took approximately 22 hours. Table 1 shows the other CFD-DEM simulation parameter settings for the control group. Furthermore, this numerical method has been widely applied and validated in the field of vibrating screens, demonstrating its suitability for describing the screening process of a double-layer vibrating screen. Therefore, CFD-DEM coupling can be used to study the screening characteristics of a slurry-water balance TBM double-layer vibrating screen.

[0100] Table 1. Parameter settings for the control group of CFD–DEM coupled simulation

[0101] II. Results and Analysis:

[0102] 1. Particle transport characteristics and mud fluidity during screening:

[0103] The transport characteristics of rock debris particles and the fluidity of the slurry near the screen surface can well reflect the screening characteristics of the mud-water balance TBM double-layer vibrating screen. Figures 6-7 This demonstrates the complete screening process of a double-layer vibrating screen. Diameter represents the diameter, coarse screen represents the coarse screen, and fine screen represents the fine screen. (Example:) Figure 6As shown, in the initial stage of the simulation, the coarse screen surface was almost not covered by particulate material, and particles with smaller diameters (less than 6 mm) had not yet fully passed through the screen openings. As screening continued, the periodic motion of the vibrating screen caused small-diameter particles to gradually pass through, while larger-diameter particles (greater than 6 mm) and some small-diameter particles that had not passed through migrated towards the discharge end. As the screening process progressed further (after approximately 2 seconds), under the action of high-frequency vibration, the particle distribution on the screen surface tended to stabilize, and the particles were generally uniformly dispersed without significant agglomeration, but a small number of small-diameter particles still failed to pass through. (See fine screen surface...) Figure 7 It also exhibits a particle sieving process similar to that of the coarse sieve.

[0104] The particle velocity on the screen surface has a significant impact on the screening process. While excessively high particle velocities can shorten residence time and increase equipment processing capacity, they will reduce screening efficiency; conversely, excessively low particle velocities may lead to material accumulation and blockage. Figure 8 The particle velocity distribution along the longitudinal (Z-direction) of the screen body obtained from DEM simulation is presented. It can be seen that the velocities of most particles tend to stabilize, mainly distributed in the range of 2–3 m / s; only a few particles exceed 3.5 m / s after colliding with the screen surface or other particles. Furthermore, the initial particle motion direction is relatively disordered and the velocity is low upon first contact with the screen surface; as the vibrating screen continues to move, the particle motion direction on the screen surface gradually changes from disordered to ordered, and the particles move as a whole towards the discharge end.

[0105] Figure 9 The particle velocity distribution at different positions along the Z-axis (from the feed end to the discharge end) is presented. It can be seen that the velocity distribution patterns of particles of different sizes are highly consistent: as the distance along the Z-axis increases from 0–4000 mm, the particle velocity generally shows a steady increase from 0 m / s to 5 m / s. Furthermore, the smaller the particle size, the more pronounced the polarization of the velocity distribution. Figure 10 It is evident that small particles with a diameter of 0–6 mm exhibit numerous velocity outliers, with the maximum velocity exceeding 6 m / s and the minimum velocity approaching 0 m / s. This is primarily due to two factors: firstly, small-diameter particles are more susceptible to the resistance of bentonite slurry; secondly, small particles have lower inertia, making their velocity more easily altered by external disturbances, and they are more prone to sudden velocity increases when colliding with the screen surface or larger particles.

[0106] Velocity distribution and volume fraction distribution can comprehensively reflect the flow field distribution characteristics of the fluid phase during vibration desliming. Figure 11 and Figure 12 The volume fraction and velocity distribution of slurry passing through the screen surface along the longitudinal direction of the screen body, obtained from CFD simulation, are presented. For example... Figure 11As shown, the volume fraction distribution of the air-slurry mixture characterizes the flow process of the slurry from the feed end to the screen surface: the slurry forms a relatively stable flow on the screen surface and eventually passes through the screen holes; simultaneously, a small amount of slurry flows along the rear wall of the vibrating screen towards the outlet. Figure 12 As shown, when the slurry comes into contact with the coarse screen surface, the local turbulence is enhanced, and an acceleration zone is formed at the coarse and fine screen surfaces near the feed end.

[0107] 2. Screening efficiency of the screen surface:

[0108] To quantitatively analyze the screening performance of a vibrating screen, this invention designs three mass monitors to monitor the mass of fine and coarse particles on the two screen surfaces. A screening efficiency factor η is also introduced, defined as follows:

[0109] (12)

[0110] In the formula: m1 is the mass of particles passing through the screen surface, and m2 is the mass of particles smaller than the screen surface size. Figure 13 The sieving efficiency curves for the two types of screen surfaces are shown. Both sieving efficiencies exhibit roughly similar trends: initially increasing gradually, then stabilizing. The stable sieving efficiency of the coarse screen is approximately 61%, slightly lower than that of the fine screen (approximately 73%). Furthermore, the sieving efficiency fluctuations of the coarse screen are more pronounced than those of the fine screen. These phenomena are due to the wider and greater particle size distribution on the coarse screen mesh, as well as the increased number of collisions between fine and coarse particles, preventing fine particles from passing through the coarse screen mesh quickly.

[0111] 3. Dynamic response of the screen surface:

[0112] The dynamic response of the screen surface is also of great significance to the screening process of the vibrating screen. Figure 14 The curves showing the variation of the total impact force on the screen surface are presented. Clearly, the impact force curves for both screen surfaces exhibit significant time-varying characteristics, which is related to the sinusoidal vibration mode of the screen surface. The positive peak value represents the maximum impact force, while the negative peak value corresponds to the force experienced when the particles completely leave the screen surface. The maximum impact force for both the coarse and fine screen surfaces occurs at 2.91 s. The maximum impact force of the coarse screen is approximately 90 times that of the fine screen, at 3616.1 N and 39.9 N, respectively.

[0113] Further research was conducted to better understand the contact behavior between particles and the screen surface. Figures 15-16 This shows the statistical distribution of particle-screen collision information at different Z coordinates, directly exported from DEM software. For example... Figure 15As shown, the collision results between particles and the coarse screen surface indicate that the collision frequency distribution varies for particles of different sizes; the smaller the particle size, the more collisions occur. Particles with a diameter of 50mm-100mm rarely collide with the coarse screen surface. This is attributed to the relatively small number of large-diameter particles and the relatively large number of small-diameter particles, forming a particle bed-like transport pattern on the coarse screen surface. This arrangement results in more collisions between large-diameter particles and the particle bed, effectively reducing the direct impact load on the screen surface. Furthermore, the collision frequency of small-diameter particles (0-6mm) with the coarse screen surface is generally high and fluctuates significantly. This is one of the direct reasons for the slightly lower and unstable screening efficiency of the coarse screen. Figure 16 As shown, the fine screen also exhibits the pattern that the smaller the particle size, the higher the collision frequency. Furthermore, as the distance in the Z-coordinate increases, the number of collisions between small particles (0-3mm) and the fine screen surface gradually decreases and stabilizes at a low level. This phenomenon also confirms the high stability of the sieving efficiency of the fine screen surface.

[0114] Figures 17-18 This shows the wear distribution on the coarse and fine screen surfaces at 3.0 seconds. Archard Wear indicates Archard wear. Figure 17 As shown, the wear distribution on the coarse screen surface is uneven. Wear is more concentrated in the central area of ​​the screen surface near the feed end, gradually becoming more uniform towards the discharge end. This is closely related to the particle movement trajectory, with the maximum wear depth occurring directly below the feed end. Figure 18 As shown, the wear on the surface of the fine screen is also concentrated in the central area, and its maximum wear depth also appears directly below the feed end, but it is only about 1 / 100th of the wear depth of the coarse screen. In practical applications, special attention should be paid to the wear damage on the surface of the coarse screen near the feed end to avoid the problem of reduced screening efficiency due to excessive wear of the coarse screen.

[0115] Furthermore, the screen surface should possess sufficient stiffness and strength reserves. For structural analysis, information on the loads acting on the screen surface is an indispensable prerequisite. However, analyzing the load distribution on the screen surface is a challenging task. Fortunately, DEM simulation can acquire the actual interactions and real-time loads on the screen surface. However, the geometry in the DEM simulation is treated as a rigid body. FEM, on the other hand, can acquire stress and deformation information of the screen surface under load during the screening process. Therefore, this invention employs a unidirectional DEM-FEM data coupling analysis method to observe the stress and deformation of the screen surface. The 2.91-second transient result from the CFD-DEM simulation is used as the load input for the FEM simulation because... Figure 14 The impact force on the surface of the coarse screen reaches its maximum at 2.91 seconds. Figure 19 and Figure 20The equivalent stress and total deformation information of the screen surface are displayed respectively. Equivalent (von-Mises) Stress represents the equivalent stress, and Total Deformation represents the total deformation. The equivalent stress σ... e The relationship with the principal stresses (σ1, σ2, and σ3) can be expressed as:

[0116] (13)

[0117] According to the deformation energy density theory, when the equivalent stress σ e When the material's ultimate stress [σ] is exceeded, yield failure will occur. For example... Figure 19 As shown, the entire screen is essentially under stress, with the equivalent stress mainly concentrated in the middle of the screen near the feed end. Furthermore, due to the fixed constraint boundaries at both ends of the screen, localized stress concentration occurs at these ends. The peak equivalent stress on the screen surface is 36.84 MPa, far below the material's ultimate stress value of 490 MPa. Figures 19-20 As shown, the total deformation is mainly concentrated in the central area of ​​the screen surface, especially at the feed and discharge ends, with a maximum total deformation of approximately 0.79 mm. This is because the ends of the screen are fixed, while the central area lacks fixed constraints, making it prone to large deformation and damage under variable loads. Therefore, it is of great significance to rationally set up a reinforcement structure in the central part of the screen to reduce stress and deformation, thereby improving the strength and stiffness of the screen. It should be noted that in the static simulation of the finite element method, the material is assumed to be linearly elastic, neglecting the influence of dynamic response and nonlinear material behavior, while particle loads usually have dynamic and nonlinear characteristics. At the same time, this method ignores the reaction force of particles on the structure, which may lead to errors in the stress and deformation calculation results.

[0118] 4. Parameter Analysis:

[0119] To evaluate the impact of vibrating screen parameters (frequency, amplitude, vibration direction angle), screen inclination angle, and initial particle velocity on screening performance, this invention simulates the process by varying these parameters. Particle velocity, screening efficiency of the coarse and fine screen surfaces, and impact force of the coarse screen surface are selected as evaluation indicators. Simulation examples of parameter analysis are shown in Table 2.

[0120] Table 2 Simulation Cases for Parameter Analysis

[0121] 4.1 The Influence of Operating Parameters on Vibrating Screens:

[0122] Figure 21The effect of vibration frequency on screening characteristics was demonstrated. It can be observed that when the frequency increases from 35Hz to 55Hz, the screening efficiency of both the coarse and fine screen surfaces, as well as the maximum impact force of the coarse screen surface, exhibit similar trends: they first gradually increase and then gradually decrease, with the inflection point occurring at a vibration frequency of 40Hz. The screening efficiency of the coarse screen surface increases from 57% to 71% and then decreases to 51%, while the screening efficiency of the fine screen surface increases from 75% to 85% and then decreases to 64%. The maximum impact force of the coarse screen surface increases from 3337.2N to 3922.1N and then decreases to 3028.4N. Furthermore, it can be observed that when the vibration frequency increases from 35Hz to 55Hz, the particle velocity increases linearly from 2.4m / s to 3.9m / s. The principle behind this is that when the vibration frequency is below 40Hz, increasing the frequency leads to an increase in the particle impact frequency, resulting in more sufficient contact with the screen surface and thus improving screening efficiency. However, when the vibration frequency exceeds 40Hz, further increases in frequency will lead to excessively high particle velocity. Therefore, insufficient residence time of the material on the screen surface prevents it from passing through the screen holes before reaching the discharge end, resulting in reduced screening efficiency. Accordingly, the vibration frequency should not be too high or too low; it is recommended to maintain the vibration frequency between 40Hz and 45Hz during slurry shield tunneling.

[0123] Figure 22 This illustrates the effect of vibration amplitude on screening characteristics. It can be seen that when the vibration amplitude increases from 5.5 mm to 7.5 mm, the particle velocity increases linearly from 2.3 m / s to 3.3 m / s, and the maximum impact force increases quadratically from 2281.3 N to 4538.6 N. The screening efficiencies of the coarse and fine screens decrease linearly from 76% and 85% to 54% and 69%, respectively. This indicates that as the vibration amplitude increases, particles are thrown higher and farther, generating greater kinetic energy and velocity. Higher particle velocity results in less contact between particles and the screen surface, thus reducing screening efficiency. The high kinetic energy is converted into high gravitational potential energy, leading to a higher impact force acting on the screen surface. Therefore, the vibration amplitude should not be set too high; it is recommended to keep it between 6 and 7 mm.

[0124] Figure 23 The effect of vibration direction angle on screening characteristics is demonstrated. When the vibration direction angle increases from 25º to 65º, the particle velocity decreases from 3.3 m / s to 2.3 m / s (a quadratic function), while the maximum impact force increases from 3081.7 N to 4492.3 N (a quadratic function), and the screening efficiencies of the coarse and fine screens increase linearly from 53% and 68% to 69% and 80%, respectively. This shows that as the vibration direction angle increases, the excitation force component along the screen surface decreases, leading to a decrease in particle velocity. Simultaneously, the excitation force component along the screen surface normal increases, causing the particle height to rise, which promotes particle stratification and improves screening efficiency. However, the impact force on the screen surface also increases accordingly. Therefore, it is recommended to control the vibration direction angle between 45º and 55º.

[0125] 4.2 Influence of the inclination angle of the vibrating screen:

[0126] Figure 24 The effect of the vibrating screen's tilt angle on screening performance is demonstrated. It is evident that as the tilt angle increases from 10º to 24º, the particle velocity increases quadratically from 2.2 m / s to 4.8 m / s, while the maximum impact force decreases quadratically from 3907.2 N to 2788.1 N. The screening efficiencies of the coarse and fine screen surfaces linearly decrease from 76% and 83% to 52% and 64%, respectively. With increasing tilt angle, the gravitational component of the particles along the screen surface increases, resulting in greater velocities and accelerations parallel to the screen surface. This leads to a shorter residence time on the screen surface, thus reducing screening efficiency. Furthermore, the gravitational component of the particles along the normal direction of the screen surface decreases, consequently reducing the impact force acting on the screen surface. Therefore, it is recommended to control the vibrating screen's tilt angle between 13.5º and 17º.

[0127] 4.3 Influence of initial particle velocity:

[0128] Figure 25 The effect of initial particle velocity on screening characteristics was demonstrated. It was observed that as the initial particle velocity increased from 0.4 m / s to 1.6 m / s, the particle velocity exhibited a quadratic increase, rising from 1.8 m / s to 5.2 m / s; the maximum impact force decreased quadratically, from 2267.3 N to 4338.6 N; and the screening efficiencies of the coarse and fine screens linearly decreased from 75% and 82% to 50% and 63%, respectively. With increasing initial particle velocity, the initial kinetic energy of the particles increases, leading to a shorter movement time on the screen surface and thus reducing screening efficiency. Furthermore, excessively high initial kinetic energy can cause the screen surface to withstand enormous impact forces. However, excessively low initial velocity reduces the processing capacity per unit time of the vibrating screen. Therefore, the initial particle velocity should not be too high or too low, and should be controlled between 0.8 m / s and 1 m / s.

[0129] 4.4 Quantitative trade-off between screening efficiency and screen wear:

[0130] With the goal of synergistically optimizing the screening efficiency and screen wear depth rate of a vibrating screen, the operating parameters of the vibrating screen (frequency, amplitude, vibration direction angle, etc.), the tilt angle of the screen box / screen surface, and the initial particle velocity are used as optimization decision variables. Based on the initial optimization scheme and equipment adjustable constraints, the feasible region is determined. Its physical meaning is to limit the allowable vibration and feeding states of the vibrating screen under the conditions of structural strength, driving capacity, and process requirements. Subsequently, by constructing a calculable mapping from the optimization decision variables to the screening efficiency and screen wear depth rate, the particle movement, screening behavior, and screen contact wear during the screening process can be quantitatively predicted. This transforms the problem, which originally relied on experience-based adjustments, into an executable multi-objective optimization problem: maximizing the predicted screening efficiency and minimizing the predicted screen wear depth rate within the feasible region.

[0131] Under each set of candidate decision variables, discrete element simulation examples were configured and run. The Hertz–Mindlin contact model was used to solve for the normal and tangential contact forces between particles and between particles and the screen. The vibration boundary of the screen box was applied using the simple harmonic motion kinematic equations. The screen surface attitude and gravity decomposition were determined by combining the tilt angle, and the feed inlet conditions were determined by combining the initial particle velocity. After the simulation entered steady state, within the preset steady-state statistical time window and the statistical region of the screen surface, the screening efficiency was defined as the ratio of the mass of particles smaller than the characteristic size of the screen aperture to the total mass of all particles in that region. At the same time, the normal contact force and the relative tangential slip distance increment were extracted from the particle-screen contact pairs of the same simulation trajectory. These were substituted into the Archard wear relation (with wear accumulation driven by contact load and slip) to obtain the screen wear depth rate. Since both the screening efficiency and the screen wear depth rate come from the same set of dynamic trajectories and steady-state statistical windows, their sensitivity to vibration parameters, tilt angle, and feed velocity has a consistent physical basis, which can truly reflect the coupling contradiction between improving screening and aggravating wear.

[0132] The Hertz-Mundling-Achad wear model integrates contact mechanics, friction slip, and empirical wear laws, using contact loads and slippage in the DEM trajectory to accumulate the volumetric loss of the screen material and further convert it into wear depth. Adjustable constraints refer to the parameter boundaries that a vibrating screen can achieve in actual equipment and allows for long-term stable operation. These constraints typically stem from structural, drive, electrical control, process, and safety limitations. Decision variables include operating parameters (frequency / amplitude / direction angle, etc.), tilt angle, and initial particle velocity. Therefore, the allowable range is determined centered on the initial optimization scheme, the upper / lower limits of the equipment, and the process boundaries.

[0133] To avoid high-cost global search on discrete element simulations, Latin hypercube sampling is first performed on the decision variables within the feasible region to obtain a well-covered set of sample points. Discrete element simulations are then run on each sample point to calculate the training dataset. Based on this dataset, surrogate models are established separately or jointly, and their prediction errors are constrained through cross-validation to meet the accuracy requirements of subsequent optimization. Subsequently, a multi-objective optimization search is performed on the surrogate models to obtain the non-dominated optimal solution set (Pareto solution set) for screening efficiency and wear depth rate. This solution set characterizes the optimal trade-off boundary between efficiency and lifespan under different preferences. Finally, a weighted comprehensive objective (weighted after normalization of the two objectives) is introduced into the non-dominated solution set, and the solution with the optimal comprehensive index is selected. The optimal solution is mapped to recommended settings for frequency, amplitude, vibration direction angle, tilt angle, and initial particle velocity, thus outputting recommended optimized values ​​for the screening characteristics of the vibrating screen that can be directly used for engineering tuning.

[0134] Gaussian process regression was chosen as the surrogate model, and two surrogate models were established: one predicting screening efficiency and the other predicting screen wear depth rate. The model structure consists of a deterministic trend term and a stochastic correlation term. Inputs are a set of optimization decision variables, such as vibration frequency, amplitude, vibration direction angle, screen inclination angle, and initial particle velocity; the output is the corresponding screening efficiency or wear depth rate. Gaussian process regression assumes that two sets of similar input parameters should also have similar outputs. In Gaussian process regression, a kernel function is used to represent the similarity between the two sets of input parameters.

[0135] (14)

[0136] In the formula, A vector consisting of a set of decision variables With another set of decision variable vectors Relevance For vectors The One portion, For vectors The d is the number of decision variables. For the first The length scale of each decision variable The signal variance controls the overall fluctuation range of the output function. Noise variance is used to characterize unexplained disturbances such as statistical fluctuations and numerical errors in the DEM. This is an indicator function.

[0137] Once the kernel function is determined, the similarity is calculated for any two samples in the training set using the kernel function: the closer the decision variables of the two samples are, the greater the similarity; the farther apart they are, the smaller the similarity. The similarity scores of all samples are arranged into a square matrix to obtain the correlation matrix. To reflect the unavoidable errors caused by fluctuations in the statistical window and random initial placement in discrete element simulation, an additional noise intensity term is added to the diagonal of the correlation matrix. This prevents the model from being forced to fit every training point identically, thus making it more robust. Hyperparameters are automatically learned using marginal likelihood maximization. The kernel function contains hyperparameters such as length scale, signal strength, and noise intensity, which determine how tortuous the function can be, how sensitive different variables are to the output, and whether data fluctuations should be treated as noise or regularity, respectively. During training, the algorithm finds a set of hyperparameters such that, under this set, the model can both explain existing samples (small prediction error) and not excessively follow noise (good generalization ability). During prediction, similar samples are weighted and averaged, with the weights determined by similarity. For a new combination of decision variables, the model first calculates its similarity to each training sample: the more similar the training sample, the higher the weight; the less similar the training sample, the lower the weight. Then, the outputs of the training samples are fused according to these weights to obtain the predicted value of the new point. GPR also provides uncertainty: when the new point is in a dense region of training samples, there are many similar samples, and the uncertainty is small; when the new point is far from all training samples, the overall similarity is low, and the uncertainty increases. This is very useful in optimization because it can be used to determine whether the surrogate model is extrapolating and whether new simulation sample points need to be added. Cross-validation is used to verify whether it can be used for optimization and to close the loop for improvement. After training, cross-validation is usually used to divide the samples into several parts: one part is used for training each time, and the other part is used for testing, and the prediction error index is statistically analyzed. If the error does not meet the optimization requirements, improvement is returned: either increase the number of Latin hypercube sampling points, increase sampling density in regions with large errors, adjust the steady-state statistical time window to reduce output noise, or make a more suitable transformation to the output or change the kernel type. The surrogate model is fixed only after the cross-validation error meets the requirements, and can then be used for subsequent non-dominated solution search and weighted selection.

[0138] 4.5. Simulation Examples of Discrete Element Models:

[0139] (1) The Hertz-Mundling contact model is used to calculate the contact force. The discrete element method treats the material as a large number of independent particles, and the interaction between particles and between particles and the screen is reflected through contact. The Hertz part describes the contact law of two elastic bodies under pressure: the greater the contact compression, the greater the normal reaction force, and the relationship is non-linear, which is consistent with the characteristics of elastic contact between real particles / metal surfaces. The Mindling part describes the elastic shear and friction constraints in the tangential direction: the contact point will generate elastic shear force in the tangential direction, but its magnitude is limited by the friction limit. If the limit is exceeded, slippage will occur. In this way, the normal force, tangential state and energy dissipation of each contact can be obtained at each time step, providing a mechanical basis for subsequent motion, stratification, screening and wear calculations.

[0140] (2) Apply the simple harmonic motion kinematic equation to the screen box to apply vibration boundary conditions. The core drive of the vibrating screen is the periodic motion of the screen box (or screen surface) according to a certain pattern. The discrete element method does not directly build the details of the motor and exciter, but applies the screen box motion as a known boundary condition to the screen geometry. The principle of the simple harmonic equation is that the steady-state vibration formed by the actual exciter can be approximated as a periodic motion of a single frequency under many working conditions. Its displacement, velocity, and acceleration change with time according to a sine / cosine law. The operating parameters determine the speed, amplitude, and direction of the vibration, thereby determining the strength of the periodic inertial excitation of the particles: the stronger the excitation, the easier it is for the particles to be thrown up, loosened, rolled, and migrated, thus affecting the probability of passing through the screen and the degree of impact on the screen surface.

[0141] (3) The tilt angle determines the screen surface attitude and gravity direction projection; the initial velocity determines the feed inlet conditions. The tilt angle of the screen surface determines the spatial relationship between the screen surface and gravity: gravity is decomposed into a component along the screen surface and a component perpendicular to the screen surface in the screen surface coordinate system. The component along the screen surface dominates the forward conveying of materials, residence time and material layer thickness; the component perpendicular to the screen surface affects the degree of compaction between particles and the screen surface and the driving force for passing through the screen. The initial velocity at the feed inlet reflects the momentum input brought by the upstream conveying, which determines the velocity of particles entering the screen surface, impact position, initial material layer distribution and diffusion mode; these inlet conditions will significantly affect the upstream stockpiling, jumping, redistribution and overall screening efficiency and local wear hot spots.

[0142] (4) The normal force and tangential slip are converted into the screen wear depth rate using the Achard wear model. The physical essence of screen wear is that particles undergo micro-cutting, plowing, or fatigue spalling under contact pressure, and the amount of wear is strongly correlated with the pressure and the distance of slip. The Achard model is a classic engineering wear law: the amount of wear per unit time (or unit slip distance) is proportional to the normal load and inversely proportional to the material hardness, and the wear coefficient reflects the material pairing and working conditions, such as dry friction, slurry, lubrication, etc. In the discrete element method, the normal force of each particle-screen contact has been calculated in the previous step, and the relative tangential slip distance of the contact point can be obtained from the Mindlin friction process; substituting both into the Achard law and accumulating them for all contacts and all time steps, the cumulative wear volume of the screen in a certain area is obtained, which is further converted into wear depth according to the wear area, and then divided by the simulation time to obtain the wear depth rate. In this way, the mapping from particle motion and contact behavior to quantifiable screen wear indicators is realized.

[0143] 4.6 Multi-objective optimization:

[0144] For a certain nondominated solution, its normalized screening efficiency is E, and its normalized wear depth rate is W, both of which are scaled to 0 to 1.

[0145] (15)

[0146] In the formula, For the weighted comprehensive objective function value, This is a normalized value for screening efficiency, ranging from 0 to 1. A higher value indicates higher screening efficiency. This is the normalized value of the screen wear depth rate, ranging from 0 to 1. A larger value indicates greater wear. This is a weighting coefficient, ranging from 0 to 1, used to reflect the preference between prioritizing efficiency and prioritizing lifespan / wear. The larger the value, the more likely it is to improve screening efficiency. The smaller the value, the more it tends to reduce wear.

[0147] 5. Optimization Plan:

[0148] Based on parameter analysis, an optimized scheme for the double-layer vibrating screen in slurry shield tunnel construction can be obtained, as shown in Table 3. To verify the effectiveness of the optimized scheme, corresponding numerical simulations are required.

[0149] Table 3 Optimization scheme for double-layer vibrating screen in slurry shield tunnel construction

[0150] Figures 26-27The screening characteristics before and after optimization were compared. After optimization, the screening efficiency of both the coarse and fine screens was improved. The efficiency of the coarse screen increased from 61% to 66%, and the efficiency of the fine screen increased from 73% to 81%, with the increase in the fine screen efficiency being more significant. In addition, the maximum impact force that the coarse screen could withstand decreased from 3616.1N to 3028.8N. Therefore, the optimization effect is significant, achieving a satisfactory improvement in efficiency.

[0151] This invention evaluates and optimizes the screening performance of a double-layer vibrating screen in slurry shield tunnel construction. Its core advantage lies in employing a multi-method combined simulation technique, integrating CFD-DEM-FEM, which, compared to traditional single-method simulations, can more accurately and precisely represent particle behavior, slurry flow, and screen dynamics. This integrated model not only captures the particle transport characteristics but also delves into the stress and deformation experienced by the screen surface—a aspect often overlooked in previous studies. The research results not only expand upon existing findings, such as the influence of operating parameters like frequency and amplitude on screening efficiency, but also reveal a more complex interaction mechanism between particles, slurry, and the screen surface. Furthermore, the research provides new insights into the causes of fluctuations in coarse screening efficiency due to particle size distribution and collisions. Observed time-varying impact forces show that the coarse screen can withstand impact forces up to 90 times that of the fine screen, revealing how the formation of the particle bed effectively reduces the direct impact load on the screen surface. Future research can also investigate the clogging mechanism between particles and the screen surface.

[0152] This invention establishes a three-dimensional coupled model of a vibrating screen. Its main advantage lies in employing a multi-method approach combining CFD, DEM, and FEM, providing a more detailed and accurate characterization of particle behavior, slurry flow, and screen dynamics compared to existing single-method simulations. Furthermore, the influence of the vibrating screen's operating parameters and the initial particle velocity on screening performance was investigated. The main conclusions are as follows:

[0153] (1) When the screening process is stable, the particles are evenly distributed on the screen surface, and their velocity shows a steady increasing trend from 0-5 m / s. In addition, when the slurry comes into contact with the coarse screen, local turbulence will be generated, and then the slurry will form a stable flow on the screen surface and eventually be discharged through the screen holes.

[0154] (2) The screening efficiency of the two sets of screens showed a roughly similar trend, that is, it gradually increased first and then tended to stabilize. The screening efficiency of the coarse screen and the fine screen stabilized at about 61% and 73%, respectively. It is worth noting that the screening efficiency of the coarse screen fluctuated significantly more than that of the fine screen.

[0155] (3) The impact forces on both screens have obvious time-varying characteristics. The maximum impact force of the coarse screen is about 90 times that of the fine screen. A large number of small-diameter particles form a transport pattern similar to a particle bed on the surface of the coarse screen, which helps to reduce the direct impact load on the screen surface.

[0156] (4) The equivalent stress and total deformation are mainly concentrated in the middle of the screen surface near the feed end and the discharge end. Therefore, it is of great significance to reasonably set up a reinforcement structure in the middle of the screen surface to reduce stress and deformation, thereby improving the strength and rigidity of the screen surface.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, characterized in that, include: Establish a coupled simulation framework for CFD, DEM, and FEM; In a coupled simulation framework, the effects of vibrating screen operating parameters, vibrating screen tilt angle and initial particle velocity on the screening performance of the double-layer vibrating screen in a slurry shield tunnel are evaluated, and the initial optimization scheme of the vibrating screen is obtained. With the goal of balancing and optimizing the screening efficiency and screen wear of a vibrating screen, and based on a Latin hypercube sampling modeling surrogate model, combined with discrete element modeling simulation technology and the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, the initial optimization scheme of the vibrating screen is optimized, and recommended values ​​for the optimized screening characteristics of the vibrating screen are output.

2. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 1, is characterized in that... The establishment of the coupled simulation framework of CFD, DEM and FEM includes: The contact behavior between particles and vibrating screens, as well as between particles, is constructed; the interaction force between particles and mud is constructed based on fluid phase density, particle density, fluid phase velocity vector, particle phase velocity vector, diameter of an equal-volume sphere, fluid viscosity, particle Reynolds number, and drag coefficient. CFD simulation technology is used to model the fluid phase of the mud and perform mesh sensitivity analysis to ensure that the calculation accuracy and time consumption meet the preset requirements. At the same time, DEM simulation technology is used to model the particle phase inside the screen and establish a digital geometric model of the particles through three-dimensional scanning. By configuring the relationship between the fluid phase time step and the particle phase time step, CFD simulation and DEM simulation are coupled. The transient results at preset times in CFD and DEM simulations are used as load inputs for FEM simulation to observe the stress and deformation of the screen surface.

3. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 2, is characterized in that... The interaction force between particles and mud is constructed based on fluid phase density, particle density, fluid phase velocity vector, particle phase velocity vector, diameter of an equal-volume sphere, fluid viscosity, particle Reynolds number, and drag coefficient, including: The buoyancy between the particles and the mud is obtained by multiplying the ratio of the fluid phase density to the particle density by the gravitational acceleration. The first value is established based on particle density, fluid viscosity, and the diameter of an equal-volume sphere; the second value is established based on particle Reynolds number and drag coefficient; the third value is obtained by the difference between the fluid phase velocity vector and the particle phase velocity vector; the drag between the particles and the mud is obtained by multiplying the first, second, and third values. The pressure gradient force between particles and mud is calculated based on the fluid phase density and particle density.

4. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 2, is characterized in that... The modeling of the mud fluid phase using CFD simulation technology includes: In CFD simulations, mud is treated as a continuous and homogeneous fluid phase, and the flow process of the fluid phase is made to satisfy the mass conservation and momentum conservation equations. The rheological properties of mud were described using the Herschel-Balkley model, and the turbulent behavior of mud flow was simulated using the k-ε turbulence model.

5. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 2, is characterized in that... The process of modeling the particulate phase within the screen using DEM simulation technology includes: Establish the governing equations for each particle: ； ； In the formula, m i U p,i I i and ω i Let be the mass, velocity, moment of inertia, and angular velocity of particle i, respectively; F c,ij F d,ij With T ij These represent the contact force, viscous damping force, and torque between particles i and j, respectively. F c,iw F d,iw With T iw These represent the contact force, viscous damping force, and torque between particle i and the sieve surface, respectively. F f,i The force exerted by the fluid phase on particle i; t is time, This represents the total number of particles.

6. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling as described in claim 1, characterized in that, The evaluation of the impact of vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity on the screening performance of the double-layer vibrating screen in the slurry shield tunneling machine yielded the following initial optimization schemes for the vibrating screen: Configure the operating parameters of the vibrating screen, the adjustment range of the vibrating screen tilt angle and the initial velocity of the particles; Within the adjustment range, by gradually adjusting the operating parameters of the vibrating screen, the tilt angle of the vibrating screen, and the initial velocity of the particles, and combining the characteristic feedback of the vibrating screen, the initial optimization scheme of the vibrating screen is obtained. The initial optimization scheme for the vibrating screen includes the initial optimized frequency, initial optimized amplitude, initial optimized vibration direction angle, initial optimized tilt angle, and initial optimized particle velocity.

7. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling as described in claim 1, characterized in that, The method aims to optimize the balance between screening efficiency and screen wear of a vibrating screen. Based on a Latin hypercube sampling modeling surrogate model, and combining discrete element method (DEM) simulation technology with the screen wear depth rate and screening efficiency output by the screening efficiency algorithm, the initial optimization scheme of the vibrating screen is optimized. The recommended optimized values ​​for the screening characteristics of the vibrating screen include: Within the steady-state statistical time window, the ratio of the mass of particles smaller than the characteristic size of the sieve aperture in the statistical region of the sieve surface to the total mass of all particles in the statistical region is taken as the screening efficiency; the sieve wear depth rate calculated based on the Hertz-Mundling-Achad wear model is taken as the sieve wear. The operating parameters of the vibrating screen, the tilt angle of the vibrating screen, and the initial velocity of the particles are used as optimization decision variables; based on the initial optimization scheme of the vibrating screen and the adjustable constraints of the equipment, the allowable range of the optimization decision variables is determined. Configure a discrete element model simulation example to evaluate screening efficiency and screen wear; The discrete element model simulation is performed, and the particle set of the statistical region on the screen surface is statistically analyzed within the steady-state statistical time window to calculate the screening efficiency. The normal contact force and relative tangential slip distance between the particles and the screen are extracted from the same simulation trajectory and substituted into the Hertz-Mundling-Achad wear model to output the screen wear depth rate. The optimization decision variables are sampled using Latin hypercube within the allowable range to cover the optimization decision variable space, and screening efficiency and screen wear depth rate data are generated for each sampling point to form a sample dataset for optimization. Based on the sample dataset, a surrogate model was established from the optimization decision variables to screening efficiency and screen wear depth rate. Cross-validation was then used to ensure that the prediction error of the surrogate model met the optimization requirements. Based on the surrogate model, the balance between screening efficiency and screen wear is optimized as the objective, and an optimization search is performed to output the non-dominated optimal solution set of screening efficiency and screen wear depth rate. The optimal solution is obtained by weighted comprehensive objective in the non-dominated solution set. The optimal solution is mapped to recommended settings for the operating parameters of the vibrating screen, the tilt angle of the vibrating screen, and the initial velocity of the particles, and these settings are used as recommended values ​​for optimizing the screening characteristics of the vibrating screen.

8. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 7, is characterized in that... The configuration used to evaluate the discrete element model simulation examples for screening efficiency and screen wear includes: Based on the Hertz-Mundling contact model, the normal contact forces between particles and the screen, as well as between particles, are calculated. The vibration boundary conditions of the screen box are established using the kinematic equation of simple harmonic motion, and the vibration characteristics are determined by the operating parameters; the geometric orientation of the screen surface and the direction of gravity are determined based on the tilt angle, and the feed inlet boundary conditions are determined based on the initial velocity of the particles. Based on the normal contact force and relative tangential slip distance between the particles and the screen, the Achard wear model is used to calculate the wear depth rate of the particle-screen contact.

9. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling, as described in claim 7, is characterized in that... The process of establishing a surrogate model based on the sample dataset, from the optimization decision variables to screening efficiency and screen wear depth rate, and ensuring that the prediction error of the surrogate model meets the optimization requirements through cross-validation includes: The sample dataset was split into vibrating screen operating parameters, vibrating screen tilt angle, and initial particle velocity. Preprocessing and standardization were performed to achieve dimensionless processing. K-fold cross-validation was selected to construct training and validation sets. Select a proxy model, train and iteratively improve the proxy model using the training and validation sets, and then solidify the proxy model.

10. The method for optimizing the screening characteristics of a double-layer vibrating screen in a slurry shield tunnel based on CFD-DEM-FEM coupling as described in claim 7, characterized in that, The surrogate model-based approach takes the balance between screening efficiency and screen wear as its objective, performs an optimization search, and outputs a set of non-dominated optimal solutions for screening efficiency and screen wear depth rate. The optimal solution obtained by weighted summing of the objective from the non-dominated solution set includes: Within the feasible domain formed by the allowable range of the optimization decision variables, the surrogate model is invoked to obtain the predicted values ​​of screening efficiency and screen wear depth rate, respectively, and the optimization objectives are to maximize the predicted value of screening efficiency and minimize the predicted value of screen wear depth rate. The algorithm iteratively searches a multi-objective optimization problem and uses the output of the surrogate model as the fitness evaluation criterion until the termination condition is met. The candidate solutions obtained by iterative search are sorted by non-dominated order to obtain the set of non-dominated optimal solutions for screening efficiency and screen wear depth rate; the predicted values ​​of screening efficiency and screen wear depth rate in the set of non-dominated optimal solutions are normalized. Based on the normalized screening efficiency and screen wear depth rate, a weighted comprehensive objective function is constructed, and the optimal solution is selected from the set of non-dominated optimal solutions.

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