Simulation analysis method for flexible particles based on bonding combination hyper-ellipsoid model

Abstract

The invention discloses a simulation analysis method of flexible particles based on a bonding combination hyper-ellipsoid model. The simulation analysis method comprises the following steps: determining shapes, sizes, positions, numbers and material attributes of first-level sub-particles forming the flexible particles according to real flexible particles; determining the shape, the size, the position and the number of second-level sub-particles forming each first-level sub-particle, and constructing the first-level sub-particles through a hyper-ellipsoid model; according to the determined position and material attribute of the first-level sub-particle, setting a bonding bond model for the contact model of the material attribute of the adjacent first-level sub-particle; corresponding coordinate positions, rotation angles and material attributes are given to the first-level sub-particles, and the first-level sub-particles are combined to form a bonding combination hyper-ellipsoid model of the flexible particles; and applying the bonded combined hyper-ellipsoid model to a flexible particle system in a discrete unit analogue simulation industrial process to obtain a simulation result. According to the simulation method, accurate modeling of the flexible particles is achieved, the motion law of the flexible particles is obtained, and the authenticity of the simulation result of the flexible particle system is improved.

Description

Technical Field

[0001] The present invention relates to the field of particle systems, and in particular to a simulation analysis method for flexible particles based on a bonded combined superellipsoid model. Background Art

[0002] There are a large number of flexible particle materials in nature. Obtaining the motion law of flexible particles is of great significance for improving many industrial processes. The discrete element method is the main simulation means for studying particle systems. However, the traditional discrete element method is mostly applied to rigid particles that do not deform, and it is not convenient to simulate the deformation process of flexible particles. In recent years, a large number of scholars have developed computational simulation methods for studying flexible particles. The main methods include the data-based stem bending modeling method (Leblicq T, Smeets B, Ramon H, et al. A discrete element approach for modelling the compression of crop stems [J]. Computers and Electronics in Agriculture, 2016, 123(C): 80-88.), the bonded sphere model (Guo Y, Wassgren C, Hancock B, et al. Validation and timestep determination of discrete element modeling of flexible fibers [J]. Powder Technology, 2013, 249(Complete): 386-395.), and the bonded sphere-cylinder model (Guo Y, Wassgren C, Curtis J S, et al. A bonded sphero-cylinder model for the discrete element simulation of elasto-plastic fibers [J]. Chemical Engineering Science, 2017, 175.).

[0003] However, for the above flexible particle models, there are certain disadvantages and deficiencies. The data-based stem bending modeling method utilizes a large amount of crop stem experimental data and has no explicit mathematical expression, making it difficult to adapt to other materials. The bonded sphere model represents an uneven surface of flexible particles, affecting the calculation accuracy of the contact force direction and magnitude in simulation. When the aspect ratio of flexible particles is relatively large, too many sub-particles are required for simulation, significantly reducing the calculation efficiency. In the bonded sphere-cylinder model, the establishment of the contact model is relatively complex, and three contact forms, namely sphere-sphere, sphere-cylinder, and cylinder-cylinder, need to be considered. During simulation, considering these three contact forms will significantly increase the workload of contact detection and mechanical calculation. Especially when the number of particles is large, it may lead to a decrease in calculation efficiency. Summary of the Invention

[0004] The object of the present invention is to provide a simulation analysis method for flexible particles based on the bonded combined super-ellipsoid model. This simulation method realizes the accurate modeling of flexible particles and obtains the motion laws of flexible particles, improving the authenticity of the simulation results for flexible particle systems.

[0005] The simulation analysis method for flexible particles based on the bonded combined super-ellipsoid model. The flexible particles based on the bonded combined super-ellipsoid model include two levels of sub-particles: primary sub-particles and secondary sub-particles. The primary sub-particles are combined super-ellipsoids, and the secondary sub-particles are super-ellipsoids. The secondary sub-particles combine to form the primary sub-particles.

[0006] The simulation analysis method includes the following steps:

[0007] (1) According to the size, shape, and material properties of real flexible particles, determine the shape, size, position, number, and material properties of the primary sub-particles that make up the flexible particles.

[0008] (2) According to the shape and size of the primary sub-particles determined in step (1), determine the shape, size, position, and number of the secondary sub-particles that make up each primary sub-particle, and construct the primary sub-particles through the super-ellipsoid model.

[0009] (3) According to the position and material properties of the primary sub-particles determined in step (1), set the bonding key model for the contact model of the material properties of adjacent primary sub-particles in the flexible particles.

[0010] (4) Assign the corresponding coordinate positions, rotation angles, and material properties to the primary sub-particles according to the shape, size, and material properties of the real flexible particles, and combine the primary sub-particles to form the bonded combined super-ellipsoid model of the flexible particles.

[0011] (5) Apply the bonded combined super-ellipsoid model obtained in step (4) to discrete element simulation to simulate the flexible particle system in the industrial process and obtain the simulation results.

[0012] In step (1), the shapes, sizes, and material properties of the first-level sub-particles may be different.

[0013] In step (2), the super-ellipsoid model is as follows:

[0014]

[0015] where a, b, and c are the lengths of the three semi-major axes of the particle, and s1, s2 are shape indices that determine the curvature of the particle edge.

[0016] In step (2), the second-level sub-particles that form the two ends of the first-level sub-particle are spherical particles.

[0017] In step (2), the second-level sub-particles in the first-level sub-particle do not completely overlap.

[0018] In step (3), the bonding bond model includes a serial bond model and a parallel bond model.

[0019] In the serial bond model, there is no sliding friction and rolling friction between two bonded particles. Therefore, the contact model used in the serial bond model is a four-equation spring-damping bond model:

[0020] F b,n =-k t,n δ n -η t,n v n

[0021] F b,t =-k t,t δ t -η t,t ν t

[0022] T b,r,n =-k r,n α n -η r,n ω n

[0023] T b,r,t =-k r,t α t -η r,t ω t

[0024] where F b,n is the normal bonding force between particles, k t,n is the translational normal spring stiffness, η t,n is the translational normal damping coefficient, δ n is the displacement of the particle in the normal direction, v n is the relative velocity of the particle in the normal direction, Fb,t is the tangential bonding force between particles, k t,t is the translational tangential spring stiffness, η t,t is the translational tangential damping coefficient, δ t is the displacement of the particle in the tangential direction, v t is the relative velocity of the particle in the tangential direction, T b,r,n is the torsional moment between particles, k r,n is the rotational normal spring stiffness, η r,n is the rotational normal damping coefficient, α n is the rotational normal displacement between particles, ω n is the relative angular velocity of the particle in the normal direction, T b,r,t is the bending moment between particles, k r,t is the rotational tangential spring stiffness, η r,t is the rotational tangential damping coefficient, α t is the rotational tangential displacement between particles, ω t is the relative angular velocity of the particle in the tangential direction.

[0025] In the parallel bond model, the bonding force (moment) between particles and the base contact force (moment) are parallel and act on the particles simultaneously. The base contact force (moment) is calculated according to the base contact model, and the bonding force (moment) is calculated according to the parallel bond model:

[0026] F b,n = -k b,t,n δ b,n - η b,t,n v n

[0027] F b,t = -k b,t,t δ b,t - η b,t,t ν t

[0028] T b,r,n = -k b,r,n α b,n - η b,r,n ω n

[0029] T b,r,t = -k b,r,t α b,t - η b,r,t ω t

[0030] Among them, F b,n is the normal bonding force between particles, k b,t,n is the translational normal spring stiffness of the bond, η b,t,n is the translational normal damping coefficient of the bond, δb,n is the displacement of the particle in the normal direction of the bond, v n is the relative velocity of the particle in the normal direction, F b,t is the tangential bond force between particles, k b,t,t is the translational tangential spring stiffness of the bond, η b,t,t is the translational tangential damping coefficient of the bond, δ b,t is the displacement of the particle in the tangential direction of the bond, v t is the relative velocity of the particle in the tangential direction, T b,r,n is the torsional moment between particles, k b,r,n is the rotational normal spring stiffness of the bond, η b,r,n is the rotational normal damping coefficient of the bond, α b,n is the rotational normal displacement of the bond between particles, ω n is the relative angular velocity of the particle in the normal direction, T b,r,t is the tangential bond force moment generated by rolling between particles, i.e., the bending moment, k b,r,t is the rotational tangential spring stiffness of the bond, η b,r,t is the rotational tangential damping coefficient of the bond, α b,t is the rotational tangential displacement of the bond between particles, ω t is the relative angular velocity of the particle in the tangential direction.

[0031] In step (3), the bonded bond model includes two fracture models, namely minimum diameter fracture and fracture strength fracture.

[0032] In the minimum diameter fracture model, the bond will break when the distance between the first-level sub-particles exceeds the minimum diameter allowed for particle bonding in the current project, that is, during the simulation, the bond is not easily broken. In the fracture strength fracture model, the bond will break when the interaction between the first-level sub-particles reaches the fracture strength (including tensile strength and shear strength).

[0033] In step (4), between adjacent first-level sub-particles, the second-level sub-particles of the two will not completely overlap.

[0034] Based on the simulation results obtained in step (5), the corresponding real industrial process can be controlled.

[0035] In step (5), during the discrete element simulation process, there will be cases where particles come into contact with each other. In the discrete element method, the contact between first-level sub-particles is judged by detecting whether each second-level sub-particle contacts other particles.

[0036] The discrete element method takes each particle as the calculation object, and the simulation of the particle system requires iterative calculations of the particle displacement increment and the contact force increment. By solving the contact forces between a certain particle and other particles or boundaries, the motion velocity and displacement of the particle are calculated using Newton's second law. Before calculating the contact forces between this particle and other particles, the particles or boundaries in contact with this particle should be determined first. This process is called contact judgment.

[0037] In step (5), in the discrete element simulation, the interaction between the secondary sub-particles in the primary sub-particles is not considered, and the primary sub-particles will not deform.

[0038] The simulation analysis method provided by the present invention constructs a flexible particle model through a bonded combined super-ellipsoid model, which is closer to real flexible particles, thus more accurately simulating the actual physical properties and motion behaviors of the particles. Applying this model to the simulation analysis of processes such as the dispersion, packing, fracture, and flow of flexible particles can obtain more accurate simulation results. Accordingly, the processing and operation processes of the particles can be optimized and regulated.

[0039] In step (5), the flexible particle system in the industrial process is for the production of biomass energy, the processing of fiber-reinforced composite materials, the design of high-performance structural fabrics, the polymer macromolecule reaction engineering, the harvesting of straw-like crops, and the fibrous and slender flexible particle materials in agricultural production engineering.

[0040] The discrete element simulation described in the present invention is also called the discrete element method.

[0041] Compared with the prior art, the beneficial effects of the present invention are reflected in:

[0042] The present invention combines multiple primary sub-particles by assigning corresponding coordinate positions, rotation angles, and material properties to the primary sub-particles to form a flexible particle with a relatively smooth surface and a high-precision particle model, thus realizing the accurate modeling of flexible particles, and solving the problems that the data-based stem bending modeling method is not applicable to other materials, the surface of the bonded sphere model is not smooth, and the establishment of the contact model of the bonded sphere column model is complex; applying the obtained bonded combined super-ellipsoid model to the discrete element simulation improves the authenticity of the simulation results of the flexible particle system, has more guiding significance for the actual industrial production process containing flexible particles, and is conducive to improving production efficiency. Description of the Drawings

[0043] Figure 1 is a flowchart of the simulation analysis method for flexible particles based on the bonded combined super-ellipsoid model;

[0044] Figure 2 is the sub-super-ellipsoid model under different parameters;

[0045] Figure 3 Schematic diagram of the sub - super - ellipsoid of the combined super - ellipsoid model in Example 1;

[0046] Figure 4 Schematic diagram of the bonded combined super - ellipsoid model in Example 1;

[0047] Figure 5 Schematic diagram of the axial tensile process of the bonded combined super - ellipsoid model in Example 2;

[0048] Figure 6 Comparison diagram of the axial tensile simulation results and theoretical results of the bonded combined super - ellipsoid model in Example 2;

[0049] Figure 7 Schematic diagram of the cantilever bending process of the bonded combined super - ellipsoid model in Example 3;

[0050] Figure 8 Comparison diagram of the cantilever bending simulation results and theoretical results of the bonded combined super - ellipsoid model in Example 3;

[0051] Figure 9 Schematic diagram of the axial torsion process of the bonded combined super - ellipsoid model in Example 4;

[0052] Figure 10 Comparison diagram of the axial torsion simulation results and theoretical results of the bonded combined super - ellipsoid model in Example 4;

[0053] Figure 11 Schematic diagram of the mowing process simulation in Example 5;

[0054] Figure 12 Schematic diagram of the deformation and fracture of the bonded combined super - ellipsoid model in Example 5. Specific implementation manners

[0055] The following further elaborates on the content of the present invention in conjunction with the accompanying drawings and examples.

[0056] As Figure 1 shown, the simulation analysis method of flexible particles based on the bonded combined super - ellipsoid model. The flexible particles based on the bonded combined super - ellipsoid model include two - level sub - particles: primary sub - particles and secondary sub - particles. The primary sub - particles are combined super - ellipsoids, and the secondary sub - particles are super - ellipsoids. The secondary sub - particles combine to form the primary sub - particles;

[0057] The simulation analysis method includes the following steps:

[0058] (1) According to the size, shape, and material properties of the real flexible particles, determine the shape, size, position, number, and material properties of the primary sub - particles that make up the flexible particles;

[0059] (2) Determine the shape, size, position, and number of secondary sub-particles that make up each primary sub-particle based on the shape and size of the primary sub-particles determined in step (1), and construct the primary sub-particles through a super-ellipsoid model;

[0060] The super-ellipsoid model is:

[0061]

[0062] where a, b, and c are the lengths of the three semi-major axes of the particle, and s1 and s2 are shape indices that determine the curvature of the particle edge. As the shape indices s1 and s2 increase, the sharpness of the particle edge also continuously increases. As Figure 2 shown, by changing the parameters, various non-spherical particles with high precision can be obtained, such as spherical particles, columnar particles, ellipsoidal particles, etc.

[0063] (3) Set the bonding bond model for the contact model of the material properties of adjacent primary sub-particles in the flexible particle according to the position and material properties of the primary sub-particles determined in step (1).

[0064] (4) Assign the corresponding coordinate positions, rotation angles, and material properties to the primary sub-particles according to the shape, size, and material properties of the real flexible particle, and combine the primary sub-particles to form the bonded combined super-ellipsoid model of the flexible particle;

[0065] (5) Apply the bonded combined super-ellipsoid model obtained in step (4) to the discrete element simulation, simulate the flexible particle system in the industrial process, and obtain the simulation results.

[0066] Example 1

[0067] As Figure 1 shown, the above simulation analysis method of flexible particles based on the bonded combined super-ellipsoid model is described below in combination with the actual process. The flexible particles in the particle system involved in this example are grass particles, and the shape is rod-shaped flexible particles.

[0068] (1) Determine the shape, size, position, number, and material properties of the primary sub-particles that make up the flexible particle according to the size, shape, and material properties of the real flexible particle;

[0069] For real rod-shaped particles, by measuring the size of the real flexible particle, the size data of the real flexible particle can be obtained, with a total length of 140 mm and a diameter of 5 mm; according to the measured data, construct the shape, size, position, number, and material properties of the required primary sub-particles. The secondary sub-particles required for the primary sub-particles are two spheres and one cylindrical particle. The diameter of the sphere is 5 mm, the diameter of the cylindrical particle is 5 mm, and the height is 20 mm. The number of primary sub-particles is 6, and the material properties are the same.

[0070] (2) Determine the shape, size, position, and number of secondary sub-particles that make up each primary sub-particle according to the shape and size of the primary sub-particles determined in step (1), and construct the primary sub-particles through a super-ellipsoid model.

[0071] The construction process is as Figure 3 shown. According to the super-ellipsoid model particle formula, for spherical particles, a = b = c = 2.5, s1 = s2 = 2; for cylindrical particles, a = b = 2.5, c = 10, s1 = 20, s2 = 2. A secondary sub-particle model is constructed.

[0072] The center coordinates of the cylindrical particle are (0, 0, 0), and the coordinates of the two spherical particles are (0, 0, 10) and (0, 0, -10) respectively. Through the combination of three secondary sub-particle models, the primary sub-particles required for flexible grass modeling are formed.

[0073] (3) Set the bonding bond model for the contact model of the material properties of adjacent primary sub-particles in the flexible particles according to the position and material properties of the primary sub-particles determined in step (1).

[0074] In this embodiment, the serial bond model is selected for the bonding model, and the fracture strength is used for the fracture model.

[0075] (4) Assign the corresponding coordinate positions, rotation angles, and material properties to the primary sub-particles according to the shape, size, and material properties of the real flexible particles, and combine the primary sub-particles to form a bonded combined super-ellipsoid model of the flexible particles.

[0076] The construction process is as Figure 4 shown. The coordinates of the first primary sub-particle are (0, 0, 0), and the rotation angle is (0, 1.57, 0); the coordinates of the second primary sub-particle are (0, 23, 0), and the rotation angle is (0, 1.57, 0); the coordinates of the third primary sub-particle are (0, 46, 0), and the rotation angle is (0, 1.57, 0); the coordinates of the fourth primary sub-particle are (0, -23, 0), and the rotation angle is (0, 1.57, 0); the coordinates of the fifth primary sub-particle are (0, -46, 0), and the rotation angle is (0, 1.57, 0); the coordinates of the sixth primary sub-particle are (0, -69, 0), and the rotation angle is (0, 1.57, 0). The six primary sub-particles have the same material properties. Through the combination of the six primary sub-particles, a rod-shaped flexible particle along the y-axis direction is formed.

[0077] Example 2

[0078] To verify the correctness of the model, a static simulation of the tensile characteristics of the model is carried out, and the simulation results are compared with the theoretical calculation values. As Figure 5As shown, one end of the bonded combined super-ellipsoid model of flexible particles is fixed, and an axial tensile load is applied to the center of the first-level sub-particle at the other end of the model. The comparison between the simulation results and the theoretical calculation values is as Figure 6 shown, and the maximum relative error is 0.03%.

[0079] Example 3

[0080] To verify the correctness of the model, a static simulation of the bending characteristics of the model is carried out, and the simulation results are compared with the theoretical calculation values. As Figure 7 shown, one end of the bonded combined super-ellipsoid model of flexible particles is fixed, and a point load perpendicular to the model is applied to the center of the first-level sub-particle at the other end of the model. The comparison between the simulation results and the theoretical calculation values is as Figure 8 shown, and the maximum relative error is 1.8%.

[0081] Example 4

[0082] To verify the correctness of the model, a static simulation of the torsional characteristics of the model is carried out, and the simulation results are compared with the theoretical calculation values. As Figure 9 shown, one end of the bonded combined super-ellipsoid model of flexible particles is fixed, and an axial torsional load is applied to the center of the first-level sub-particle at the other end of the model. The comparison between the simulation results and the theoretical calculation values is as Figure 10 shown, and the maximum relative error is 0.2%.

[0083] Example 5

[0084] The above simulation analysis method of flexible particles based on the bonded combined super-ellipsoid model will be described below in combination with dynamic simulation. As Figure 11 shown, the process involved in this embodiment is the mowing process, and the equipment used is a small mower blade. The simulation process is as follows: 1) Import the equipment model and set its motion parameters; 2) Establish a flexible particle model using the flexible particle modeling method based on the bonded combined super-ellipsoid model (Example 1); 3) Establish a contact model between the flexible particles and the equipment; 4) Perform contact detection on the discrete elements; 5) Update the force and motion information of the equipment and the flexible particles; 6) Determine whether the set simulation time is reached. If so, the simulation ends. If not, repeat steps 4)-6) until the set simulation time is reached.

[0085] In this embodiment, the fracture strength between rod-shaped flexible particles is 0.1 MPa, the traveling speed of the mower blade is 1 m / s, the rotational speed is 954 rpm, and the number of simulated rod-shaped flexible particles is 1500. As Figure 12 shown, during the simulation process, when the mower blade contacts the flexible particles, the flexible particles first deform, and when the tensile strength and shear strength acting on the serial bond are greater than the fracture strength, the flexible particles break.

Claims

1. A simulation analysis method for flexible particles based on a bonded composite superellipsoid model, characterized in that The flexible particles based on the bonded composite super-ellipsoid model contain two levels of sub-particles: primary sub-particles and secondary sub-particles. The primary sub-particles are composite super-ellipsoids, and the secondary sub-particles are super-ellipsoids. The secondary sub-particles combine to form the primary sub-particles. The simulation analysis method includes the following steps: (1) Determine the shape, size, position, number, and material properties of the primary sub-particles that make up the flexible particles according to the size, shape, and material properties of the real flexible particles. (2) Determine the shape, size, position, and number of the secondary sub-particles that make up each primary sub-particle according to the shape and size of the primary sub-particles determined in step (1), and construct the primary sub-particles through the super-ellipsoid model. (3) Set the bonding bond model for the contact model of the material properties of adjacent primary sub-particles in the flexible particles according to the position and material properties of the primary sub-particles determined in step (1). (4) Assign the corresponding coordinate positions, rotation angles, and material properties to the primary sub-particles according to the shape, size, and material properties of the real flexible particles, and combine the primary sub-particles to form the bonded composite super-ellipsoid model of the flexible particles. (5) Apply the bonded composite super-ellipsoid model obtained in step (4) to the discrete element simulation, simulate the flexible particle system in the industrial process, and obtain the simulation results.

2. The simulation analysis method of the flexible particles based on the bonded composite superellipsoid model according to claim 1, wherein The secondary sub-particles at both ends of the combined primary sub-particles are spherical particles.

3. The simulation analysis method of flexible particles based on the bonded combined superellipsoid model according to claim 1, wherein In step (2), the super-ellipsoid model is: where a, b, and c are the lengths of the three semi-major axes of the particle, and s1 and s2 are shape indices that determine the curvature of the particle edge.

4. The simulation analysis method of the flexible particles based on the bonded composite superellipsoid model according to claim 1, wherein In step (2), the secondary sub-particles in the primary sub-particles do not completely overlap.

5. The simulation analysis method of flexible particles based on the bonded combined superellipsoid model according to claim 1, characterized in that In step (3), the bonding bond model includes a serial bond model and a parallel bond model; the bonding bond model includes two fracture models, namely minimum diameter fracture and fracture strength fracture.

6. The simulation analysis method of the flexible particles based on the bonded combined superellipsoid model according to claim 1, characterized in that In step (4), between adjacent primary sub-particles, the secondary sub-particles of the two do not completely overlap.

7. The simulation analysis method of flexible particles based on the bonded composite superellipsoid model according to claim 1, wherein In step (5), in the discrete element simulation, it is judged whether the primary sub-particles are in contact by detecting whether each secondary sub-particle is in contact with other primary sub-particles.

8. The simulation analysis method of flexible particles based on the bonded composite superellipsoid model according to claim 1, wherein In step (5), in the discrete element simulation, the interaction between the secondary sub-particles in the primary sub-particles is not considered, and the primary sub-particles do not deform.

9. The simulation analysis method of flexible particles based on the bonded composite superellipsoid model according to claim 1, wherein, In step (5), the industrial process is the dispersion, packing, fracture, or flow process of flexible particles.

10. The simulation analysis method of flexible particles based on the bonded combined superellipsoid model according to claim 9, characterized in that, In step (5), the flexible particle system in the industrial process is the production of biomass energy, the processing of fiber-reinforced composites, the design of high-performance structural fabrics, the reaction engineering of polymer macromolecules, the harvesting of straw-like crops, and the fibrous and slender flexible particle materials in agricultural production engineering.

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