Simulation and prediction method for the densest packing density of multi-size particle packing systems

Abstract

The present invention discloses a method for simulating and predicting the maximum packing density of a multi-size particle filling system, comprising: S1, determining characteristic parameters of the filling particles of the filling system; S2, establishing a simulation box and setting an initial packing density; S3, inserting the filling particles into the simulation box to complete initial modeling; S4, reducing the simulation box according to a predetermined ratio to increase the packing density; S5, performing relaxation under the conditions of a microcanonical ensemble; S6, calculating the packing density and the relative overlap change rate of the filling particles; S7, determining whether the relative overlap change rate is greater than a threshold: if so, proceeding to step S8; if not, executing steps S4 to S6 again; S8, calculating the maximum packing density of the system based on the packing density and relative overlap change rate calculated in step S6. The present invention can simulate and predict the maximum packing density of a multi-size particle filling system, provide effective guidance for the filler gradation scheme of the filling system, shorten the product design and development cycle, and reduce costs.

Description

Technical Field

[0001] The present invention relates to the technical field of computational materials science, and in particular to a simulation prediction method for the densest packing density of a multi-size particle packing system, a computer device, and a computer-readable storage medium. Background Art

[0002] In recent years, the packaging of electronic components has gradually evolved towards miniaturization and higher power. However, while this increased packaging integration has also led to excessive heat generation and insufficient heat dissipation within the electronic components, seriously affecting device performance and lifespan. An effective solution to this problem is to fill a layer of thermal interface material with high thermal conductivity and good compressibility between the chip and the heat sink. This composite material is generally based on a polymer matrix and filled with a highly thermally conductive filler to form a particle-to-particle thermal path to improve thermal conductivity.

[0003] Experiments have shown that the proper gradation of fillers of varying particle sizes can improve the thermal conductivity and particle distribution uniformity of thermal interface materials and underfills, reduce material viscosity, and ultimately enhance device performance. For systems using fillers of varying particle sizes, determining the optimal packing density to determine the optimal gradation is a challenge that needs to be addressed, particularly during the product design and development phase. While a relatively accurate estimate of the optimal packing density can be achieved through extensive experimentation, this approach can significantly increase product design and development cycles and incur significant costs. Summary of the Invention

[0004] In view of this, the present invention provides a simulation prediction method, computer equipment and computer-readable storage medium for the densest packing density of a multi-particle filling system to solve the problem of how to simulate and predict the densest packing density of a multi-particle filling system, and can provide effective guidance for the reasonable grading of a multi-particle filling system.

[0005] In order to solve the above technical problems, one aspect of the present invention is to provide a method for simulating and predicting the closest packing density of a multi-size particle packing system, which comprises:

[0006] S1. Determine the characteristic parameters of the filling particles of the filling system;

[0007] S2, establish a simulation box and set the initial filling density;

[0008] S3, inserting the filling particles into the simulation box according to the requirements of the initial filling density to complete the initial modeling of the filling system;

[0009] S4, reducing the simulation box according to a predetermined ratio to increase the packing density of the system;

[0010] S5. Relaxing the filling system under microcanonical ensemble conditions;

[0011] S6. Calculating the packing density of the packing system after relaxation and the rate of change of the relative overlap of the packing particles in the simulation box;

[0012] S7, determining whether the relative overlap change rate is greater than a set threshold: if so, proceed to the following step S8; if not, perform the above steps S4 to S6 again;

[0013] S8. Calculate the closest packing density of the packing system according to the packing density and relative overlap change rate calculated in step S6.

[0014] Specifically, steps S1 to S3 are performed in discrete element analysis software, the contact model is set to a Hertz model, and the parameter units adopt the International System of Units; wherein, the filling particles are inserted into the simulation box through the Monte Carlo algorithm.

[0015] Specifically, in step S1, the filling particles include filling particles of at least two different particle sizes, and the characteristic parameters of the filling particles include the particle size and volume ratio of the filling particles; in step S2, the initial filling density is set to 0.10-0.20.

[0016] Specifically, steps S4 to S7 are performed in molecular dynamics analysis software, the normal contact model is set to the Hertz model, the tangential contact model is set to the Mindlin model, the damping coefficient model is set to the Tsuji-Station model, and the parameter units adopt the International System of Units.

[0017] Specifically, in step S4, the predetermined ratio is γ, and the value range of the predetermined ratio γ meets the following requirements: by reducing the simulation box by the ratio of γ each time, after 40 to 60 reductions, the filling density of the filling system can be increased from the initial filling density to 1.

[0018] Specifically, in step S7, the set threshold value α is set to α=0.05-0.06, preferably α=0.0572.

[0019] Specifically, if the relative overlap change rate calculated after shrinking the simulation box for the Nth time is greater than the set threshold α, the calculation method of the densest packing density in step S8 is as follows:

[0020] Take the filling density Φ calculated after shrinking the simulation box for the N-1th time N-1 and the relative overlap rate of change Vs N-1 , take the filling density Φ calculated after shrinking the simulation box for the Nth time Nand the relative overlap rate of change Vs N ;

[0021] With the filling density Ф as the horizontal coordinate and the relative overlap rate Vs as the vertical coordinate, the numerical point (Ф N-1 , Vs N-1 ) and numerical points (Ф N , Vs N )

[0022] Substituting the set threshold value α as the overlap change rate parameter into the linear equation to calculate the densest packing density Φ0 of the packing system;

[0023] Here, N is an integer greater than or equal to 2.

[0024] In order to solve the above technical problems, the present invention also provides a computer device, which includes a memory, a processor and a computer program stored in the memory and runnable on the processor, wherein when the processor executes the program, the steps of the simulation prediction method described above are implemented.

[0025] In order to solve the above technical problems, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the simulation prediction method described above are implemented.

[0026] Based on the above technical solutions, the beneficial effects of the present invention are:

[0027] The embodiment of the present invention provides a method for simulating and predicting the densest packing density of a multi-size particle filling system. A model is established based on the characteristic parameters of the filling particles of the filling system. The densest packing density of the filling system is calculated through model simulation and prediction, providing effective and reasonable guidance for the filler grading scheme of the filling system, which can shorten the product design and development cycle and reduce costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 1 is a flowchart of a method for simulating and predicting the densest packing density according to an embodiment of the present invention;

[0029] Figure 2 illustrative diagrams of three situations in which particles overlap with each other in an embodiment of the present invention;

[0030] Figure 3 is an exemplary diagram of simulation prediction of a single particle size filling system in an embodiment of the present invention;

[0031] Figure 4 is a graph showing the change rate of overlap relative to the packing density for a single particle size packing system according to an embodiment of the present invention;

[0032] Figure 5 is an exemplary diagram of simulation prediction of a three-particle-size filling system in an embodiment of the present invention;

[0033] Figure 6 is an exemplary diagram of simulation prediction of a filling system with more particle sizes in an embodiment of the present invention;

[0034] Figure 7 is a triangular coordinate diagram of the simulation prediction results of the three-particle size filling system in the embodiment of the present invention;

[0035] Figure 8 It is a structural block diagram of a computer device in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of the present invention more apparent, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. Examples of these preferred embodiments are illustrated in the accompanying drawings. The embodiments of the present invention shown in and described with reference to the accompanying drawings are merely exemplary, and the present invention is not limited to these embodiments.

[0037] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show structures and / or processing steps closely related to the solutions according to the present invention, while other details that are not closely related to the present invention are omitted.

[0038] The embodiment of the present invention first provides a method for simulating and predicting the closest packing density of a multi-size particle packing system. Figure 1 The simulation prediction method mainly includes the work of initial modeling, compression measurement and final calculation of the densest filling density.

[0039] In an embodiment of the present invention, the initial modeling work is performed in discrete element analysis software (LIGGGHTS software), and the compression measurement work is performed in molecular dynamics analysis software (LAMMPS software).

[0040] In the embodiment of the present invention, Figure 1 As shown, the initial modeling work includes the following steps:

[0041] Step S1: determining characteristic parameters of filling particles of the filling system.

[0042] The filling particles include at least two types of filling particles with different particle sizes, and the characteristic parameters of the filling particles include the particle size and volume ratio of the filling particles.

[0043] Step S2: Create a simulation box and set the initial filling density.

[0044] The initial packing density can be set to 0.10 to 0.20. In a preferred embodiment, the initial packing density is set to 0.15.

[0045] Step S3: inserting the filling particles into the simulation box according to the requirements of the initial filling density to complete the initial modeling of the filling system.

[0046] In a specific embodiment of the present invention, the contact model for initial modeling is the Hertz model, the parameter units are in the International System of Units, and the time step is 1×10 -5 , the time step is 1×10 3 The filling particles are sequentially inserted into the simulation box using the Monte Carlo algorithm, and the initial filling density is set to 0.15.

[0047] After completing the initial modeling in the discrete element analysis software, the model data file is imported into the molecular dynamics analysis software for subsequent compression measurement.

[0048] In the embodiment of the present invention, Figure 1 As shown, the compression calculation work includes the following steps:

[0049] Step S4: reducing the simulation box according to a predetermined ratio to increase the filling density of the system.

[0050] Specifically, the side length of the box is proportionally reduced to increase the packing density of the system. In a preferred embodiment, the predetermined ratio is set to γ, and the range of values of the predetermined ratio γ meets the following requirements: by reducing the simulation box by the ratio γ each time, after 40 to 60 reductions, the packing density of the packing system can be increased from the initial packing density to 1. For example, if the initial packing density is 0.15 and the number of reductions is selected as 50, then based on theoretical calculations of the model, the compression ratio that can increase the packing density of the packing system from 0.15 to 1 after 50 reductions is γ0, and γ0 is set as the predetermined ratio for each reduction of the simulation box.

[0051] Step S5: Relaxing the filling system under the conditions of a microcanonical ensemble.

[0052] In step S4, the simulation box is reduced in size, and the filling system is relaxed under the conditions of a microcanonical ensemble to release the potential energy generated by the unreasonable configuration.

[0053] Step S6: Calculate the packing density of the packing system after relaxation and the rate of change of the relative overlap of the packing particles in the simulation box.

[0054] Specifically, the calculation methods for the packing density and the relative overlap amount change rate of the packing system are as follows:

[0055] (1) Calculation of the packing density: Calculate the total volume V of all the packing particles inserted into the simulation box in step S3 T , calculate the volume V of the simulation box reduced according to a predetermined ratio in step S4 H , the packing density Ф = V T / V H .

[0056] (2) Calculation of the relative overlap amount change rate: Traverse and calculate the overlap amount of every two packing particles and sum them up to obtain the total overlap amount V Z , compare the total overlap amount V Z with the total volume V T to obtain the relative overlap amount V X , and take the derivative of the relative overlap amount V X with respect to the packing density Ф to obtain the relative overlap amount change rate.

[0057] Among them, in the calculation process of the overlap amount of every two packing particles, first obtain the radius R1 of the first particle, the radius R2 of the second particle, and the center distance d between the two particles, and then calculate the overlap amount of the two packing particles in the following three cases:

[0058] The first case: As Figure 2 in (a), d ≥ R2 + R1, that is, the two packing particles do not overlap at all, then the overlap amount between them is V(R1, R2, d) = 0;

[0059] The second case: As Figure 2 in (b), d ≤ R2 - R2, that is, the smaller packing particle is inside the larger packing particle, then the overlap amount between them is

[0060] The third case: As Figure 2 in (c), R2 - R1 < d < R2 + R1, that is, the two packing particles partially overlap each other. At this time, let h1 = R1(1 - cosβ), h2 = R2(1 - cosα), then the overlap amount between them is

[0061] S7. Judge whether the relative overlap amount change rate is greater than the set threshold: If so, perform the following step S8; if not, execute the above steps S4 to S6 again.

[0062] Specifically, the value of the set threshold α is α = 0.05 - 0.06. In a preferred solution, the value of the set threshold α is 0.0572.

[0063] In the specific embodiment of the present invention, in the above work of the cyclic compression model, the normal contact model is set to the Hertz model, the tangential contact model is set to the Mindlin model, the damping coefficient model is set to the Tsuji Static model, and the parameter units are in the International System of Units. In the model, the Young's modulus is 4×10 12 , Poisson's ratio is 0.3, normal restitution coefficient is 0.2, tangential damping coefficient is 1.0, sliding friction coefficient is 0.5, and time step is 1×10 -7 It should be noted that the specific parameters of these models can be selected and set according to actual conditions.

[0064] When the packing system reaches the densest packing state, the rate of change of the relative overlap is linearly related to the packing density, and the corresponding rate of change is constant when the system reaches the densest packing state. Therefore, the value of the threshold value α needs to be set reasonably.

[0065] In the embodiment of the present invention, Figure 1 As shown, the final calculation of the densest packing density includes the following steps:

[0066] Step S8: Calculate the densest packing density of the packing system based on the packing density and relative overlap change rate calculated in step S6.

[0067] Specifically, if the relative overlap change rate calculated after shrinking the simulation box for the Nth time is greater than the set threshold α, the calculation method of the densest packing density in step S8 is as follows:

[0068] (1) Take the filling density Φ calculated after shrinking the simulation box for the N-1th time N-1 and the relative overlap rate of change Vs N-1 , take the filling density Φ calculated after shrinking the simulation box for the Nth time N and the relative overlap rate of change Vs N ; Wherein, N is an integer greater than 2.

[0069] (2) With the filling density Ф as the horizontal coordinate and the relative overlap rate Vs as the vertical coordinate, the numerical point (Ф N-1 , Vs N-1 ) and numerical points (Ф N , Vs N ) is the equation of the line.

[0070] (3) Substituting the set threshold value α as the overlap change rate parameter into the linear equation, the densest filling density Φ0 of the filling system is calculated.

[0071] As previously mentioned, in the simulation prediction method provided by the present invention, the value of the threshold value α needs to be reasonably set. In an embodiment of the present invention, based on the process of the above steps S1 to S6, a simulation test is performed on a single-particle packing system to generate a curve of the overlap change rate Vs relative to the packing density φ. The linear portion of the curve is obtained from the change curve to determine the tightest packing density of the single-particle packing system and its corresponding overlap change rate. The overlap change rate of the single-particle packing system at the tightest packing density is used as the threshold value α for the multi-particle packing system.

[0072] Figure 3 This is an exemplary diagram of the simulation prediction of a single-particle packing system, where (a) is the diagram of the initial modeling state and (b) is the diagram of the most densely packed state.

[0073] In the embodiment of the present invention, simulation tests were conducted on single particle size filling systems with particle sizes of 1 unit, 5 units, 10 units and 20 units, and the following results were obtained: Figure 4 The overlap rate of change Vs is plotted against the packing density Φ. Figure 4 The small figure in the upper left corner is an enlarged view of the curve portion near the filling density Φ of 0.65.

[0074] according to Figure 4 The curve shows a linear change from point A to point B. Based on the average packing density at points A and B, the closest packing density for the single-size particle system is 0.64, corresponding to an overlap change rate Vs of 0.0572. Therefore, in subsequent simulations and predictions of multi-size particle packing systems, it is preferable to set the overlap change rate threshold α to 0.0572. Based on this, in other specific embodiments, setting the threshold α within the range of 0.05 to 0.06 is more reasonable.

[0075] Figure 5 The following diagrams illustrate simulation predictions for a three-particle packing system in an embodiment of the present invention. (a) shows the initial modeling state, and (b) shows the most densely packed state. The particle size ratio of the three particle sizes is 1:5:20, and the packing volume ratio is 0.2:0.1:0.7.

[0076] Figure 6 The following are exemplary diagrams of simulation predictions using a system with multiple particle sizes, as described in an embodiment of the present invention. (a) shows the initial modeling state, and (b) shows the most densely packed state. The multiple particle sizes mentioned specifically refer to the addition of several particle sizes to the aforementioned three-particle-size system.

[0077] Based on the simulation and prediction method of the densest packing density described above, by changing parameters such as the particle size or volume ratio in the initial modeling, the densest packing density corresponding to multi-particle size systems with different large particle size ratios can be calculated. The densest packing density of particle systems with specific particle size distributions can also be calculated to form a corresponding database.

[0078] For example, in this embodiment, Figure 5 Taking the simulation prediction of the three-particle filling system as an example, the particle size ratio of the three particle sizes is limited to 1:5:20, the filling volume ratio in the initial modeling is changed, the most compact filling density under each filling volume ratio is obtained, the corresponding database is established, and the following is drawn: Figure 7 The triangular coordinate diagram shown in Figure 7 In the figure, the three sides of the triangular coordinate diagram represent the filling volume ratio of the three particle sizes changing from 0 to 1.

[0079] based on Figure 7 From the triangular coordinate diagram, when the filling volume ratio of a three-particle-size filling system with a particle size ratio of 1:5:20 is determined, the densest packing density of the system can be obtained from the diagram; or, when a three-particle-size filling system with a particle size ratio of 1:5:20 is required and the densest packing density of the filling system is to be made to reach a certain value, the filling volume ratio of the three particle sizes can be inferred from the diagram.

[0080] It is easy to understand that if the filling volume ratio of the three particle sizes is limited to a specific ratio, the particle size ratio in the initial modeling is changed to obtain the most dense packing density under each particle size ratio, a corresponding database can also be established to draw a similar Figure 7 Triangular coordinate diagram of .

[0081] The simulation prediction method for the densest packing density provided in the above embodiment can simultaneously meet the requirements for size control of large-scale filling systems with large particle size ratios and multi-particle size mixed filling particles, adapt to conditions of different particle size ratios, volume ratios and particle size distributions, and the simulation calculation results are accurate and stable. It can better match the production conditions of composite materials such as thermal interface materials and bottom filling glue in actual applications, provide effective and reasonable guidance for the development and optimization of filler grading schemes for filling systems, shorten the product design and development cycle and reduce costs.

[0082] The embodiment of the present invention also provides a computer device, such as Figure 8 As shown, the computer device includes: a processor 10, a memory 20, an input device 30 and an output device 40. The processor 10 is provided with a GPU. The number of the processors 10 can be one or more. Figure 8 In the figure, a processor 10 is used as an example. The processor 10, memory 20, input device 30 and output device 40 in the computer device can be connected via a bus or other means.

[0083] Memory 20, as a computer-readable storage medium, can be used to store software programs, computer executable programs, and modules. Processor 10 executes the various functional applications and data processing of the device by running the software programs, instructions, and modules stored in memory 20, thereby implementing the steps of the method for simulating and predicting the maximum packing density described in the aforementioned embodiment of the present invention. Input device 30 is used to receive image data, input digital or character information, and generate key signal input related to user settings and function control of the device. Output device 40 may include a display device such as a display screen, for example, for displaying images.

[0084] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program implements the steps of the method for simulating and predicting the maximum packing density described in the aforementioned embodiment of the present invention. The computer storage medium can be any available medium or data storage device accessible by a computer, including but not limited to magnetic memory, optical memory, and semiconductor memory.

[0085] It should be noted that the above embodiments are merely illustrative of the technical concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. They are not intended to limit the scope of protection of the present invention. Any equivalent variations or modifications made in accordance with the spirit and substance of the present invention are intended to be encompassed within the scope of protection of the present invention.

Claims

1. A method for simulating and predicting the densest packing density of a multi-size particle packing system, characterized in that: include: S1. Determine the characteristic parameters of the filling particles of the filling system; S2, establish a simulation box and set the initial filling density; S3, inserting the filling particles into the simulation box according to the requirements of the initial filling density to complete the initial modeling of the filling system; S4, reducing the simulation box according to a predetermined ratio to increase the packing density of the system; S5. Relaxing the filling system under microcanonical ensemble conditions; S6. Calculating the packing density of the packing system after relaxation and the rate of change of the relative overlap of the packing particles in the simulation box; S7, determining whether the relative overlap change rate is greater than a set threshold value α: if so, proceed to the following step S8; if not, perform the above steps S4 to S6 again; S8. Calculate the closest packing density of the packing system based on the packing density and relative overlap change rate calculated in step S6; If the relative overlap change rate calculated after the Nth shrinkage of the simulation box is greater than the set threshold α, the calculation method of the densest packing density in step S8 is as follows: Take the filling density Φ calculated after shrinking the simulation box for the N-1th time N-1 and the relative overlap rate of change Vs N-1 , take the filling density Φ calculated after shrinking the simulation box for the Nth time N and the relative overlap rate of change Vs N ; With the filling density Ф as the horizontal coordinate and the relative overlap rate Vs as the vertical coordinate, the numerical point (Ф N-1 , Vs N-1 ) and numerical points (Ф N , Vs N ) of the straight line; Substituting the set threshold value α as the overlap change rate parameter into the linear equation to calculate the densest packing density Φ0 of the packing system; Here, N is an integer greater than or equal to 2.

2. The simulation prediction method according to claim 1, characterized in that: Steps S1 to S3 are performed in discrete element analysis software, the contact model is set to the Hertz model, and the parameter units are in the International System of Units; wherein the filling particles are inserted into the simulation box by using the Monte Carlo algorithm.

3. The simulation prediction method according to claim 2, characterized in that: In step S1, the filling particles include filling particles of at least two different particle sizes, and the characteristic parameters of the filling particles include the particle size and volume ratio of the filling particles; in step S2, the initial filling density is set to 0.10-0.

20.

4. The simulation prediction method according to any one of claims 1 to 3, characterized in that: Steps S4 to S7 are performed in molecular dynamics analysis software, the normal contact model is set to the Hertz model, the tangential contact model is set to the Mindlin model, the damping coefficient model is set to the Tsuji-Station model, and the parameter units adopt the International System of Units.

5. The simulation prediction method according to claim 4, characterized in that: In step S4, the predetermined ratio is γ, and the value range of the predetermined ratio γ meets the following requirements: by reducing the simulation box by the ratio of γ each time, after 40 to 60 reductions, the filling density of the filling system can be increased from the initial filling density to 1.

6. The simulation prediction method according to claim 4, characterized in that: In step S7, the set threshold α is set to a value of α=0.05~0.

06.

7. The simulation prediction method according to claim 6, characterized in that: The set threshold α is set to α=0.0572.

8. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the simulation prediction method according to any one of claims 1 to 7 are implemented.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the simulation prediction method as described in any one of items 1-7 are implemented.

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