A numerical simulation method for 3D printing process based on near-field dynamic method

Abstract

The application relates to the technical field of 3D printing process simulation, in particular to a 3D printing process numerical simulation method based on a near-field dynamic method, which comprises the following steps: step one, establishing a near-field dynamic transient heat transfer model; step two, establishing a near-field dynamic living and dead material point model; step three, introducing a near-field dynamic key breaking mechanism; step four, establishing a 3D printing process simulation model based on the near-field dynamic method; step five, defining basic parameters, boundary conditions and initial conditions according to 3D printing process conditions; and step six, simulating calculation and exporting results. In the application, the accumulation of materials in the 3D printing process is regarded as a change process of a scalar field, and 0-1 is used to describe the life and death states of material points in the scalar field, so that the 3D printing process can be described physically in a quite intuitive way; in combination with an explicit calculation method, the calculation amount of each time step in the numerical simulation process is greatly simplified.

Description

Technical Field

[0001] This invention relates to the field of 3D printing process simulation technology, specifically to a numerical simulation method for 3D printing process based on near-field dynamics. Background Technology

[0002] 3D printing technology is a manufacturing method that uses design data as a basis to automatically accumulate raw materials (including liquids, powders, filaments, or blocks) into a solid structure. 3D printing technology overcomes the limitations of traditional casting technology, effectively solving the problem of manufacturing complex structures; and it greatly reduces the product design and development cycle. This makes 3D printing technology one of the fastest-growing, most actively researched, and most closely watched disciplines in the world's advanced manufacturing field.

[0003] Over the past decade, with the rapid advancement of intelligent manufacturing and revolutionary changes in product concepts, the research and application of 3D printing technology have received widespread attention from researchers. Domestic and international researchers have conducted extensive experimental studies on 3D printing technology. However, experimental research is costly and time-consuming; therefore, appropriate numerical simulation techniques can effectively help researchers study the 3D printing process and the mechanical properties of the products. The 3D printing process involves the accumulation of a large number of tiny materials, which not only involves changes in structural boundaries but also heat conduction. The 3D printing process includes material melting-solidification and elastoplastic deformation, which can lead to residual deformation and defects in the structure. Simultaneously, temperature distribution, residual deformation, and defects during the 3D printing process are important factors affecting the functional integrity and mechanical properties of the 3D printed structure.

[0004] Currently, the finite element method (FEM) is generally used for numerical simulation of the 3D printing process. However, the FEM suffers from low computational efficiency and difficulty in analyzing complex defects and discontinuous issues such as fractures that occur during 3D printing. Therefore, to analyze the processes of material accumulation, heat conduction, and defect generation during 3D printing, and to facilitate subsequent research on the fracture behavior of 3D printed materials and structures, it is necessary to introduce a near-field dynamics method that incorporates a point-birth model and a bond fracture mechanism to numerically simulate the 3D printing process.

[0005] Therefore, it is necessary to design a numerical simulation method for 3D printing process based on near-field dynamics to solve the technical problems of low computational efficiency and difficulty in analyzing complex defects and discontinuous problems such as fractures generated during 3D printing when using the finite element method for numerical simulation of the 3D printing process in the above-mentioned existing technologies. Summary of the Invention

[0006] The technical solution of the present invention:

[0007] A numerical simulation method for 3D printing process based on near-field dynamics includes the following steps:

[0008] Step 1: Establish a near-field dynamic transient heat transfer model;

[0009] Step 2: Establish a near-field dynamics model of life and death matter points;

[0010] Step 3: Introduce a near-field dynamic bond breaking mechanism;

[0011] Step 4: Establish a simulation model of the 3D printing process based on near-field dynamics;

[0012] Step 5: Define the basic parameters, boundary conditions, and initial conditions according to the 3D printing process conditions;

[0013] Step 6: Perform simulation calculations and export the results.

[0014] Step 1 establishes a near-field dynamic transient heat transfer model, including:

[0015] The transient heat transfer equation for near-field dynamics is given by the following equation (1):

[0016]

[0017] Where ρ is density, kg·m -3 c θ Specific heat capacity, J·(kg·℃) -1 K[δ] is the microscopic thermal conductivity coefficient, W·m -5 ·℃ -1 δ is the neighborhood radius of the material point, in meters; Q(x) i ,t) represents the heat source, J·m -3 ;T(x i ,t) and T(x j ,t) represent the material point x and t respectively. i and x j Temperature at time t, °C; H xi Represents the material point x i The neighborhood of V xj Represents the material point x j Volume;

[0018] ω(ξ) is the weighting coefficient, representing the distribution of the microscopic thermal conductivity along the radial direction in the neighborhood. In this model, the microscopic thermal conductivity is linearly related to the bond length.

[0019]

[0020] δ is the near-field radius, and K[δ] has a corresponding relationship with the thermal conductivity coefficient k in the classical differential equation. (One-dimensional) Two-dimensional 3D

[0021] Step 2: Establish a near-field dynamics model of life and death matter points, including:

[0022] In the 3D printing process, the geometric dimensions of the 3D printing area are a function of time; in the numerical simulation process, when the material points of the 3D printing area are covered by the influence area of ​​the moving heat source, it is necessary to activate the state of the corresponding material points.

[0023] Within the framework of near-field dynamics, by introducing a scalar field To describe the inactive / active state of material points in the 3D printing area; any material point x i The life or death status is represented by the following formula (2):

[0024]

[0025] in: Represents the material point x i The critical time for activation is determined by the moving speed of the heat source. Represents the material point x i Not activated Represents the material point x i Activated; based on the near-field dynamics life and death matter point model, any matter point x i and x j They interact at time t

[0026] The penalty function used is expressed by the following formula (3):

[0027]

[0028] Step 3: Introduce a near-field dynamic bond breaking mechanism, including:

[0029] During the 3D printing process, uncertainties in the process and environmental factors can lead to defects such as cracks and holes in the 3D printed structure. These defects can affect the heat transfer and mechanical deformation of the 3D printed structure.

[0030] In the model, the interaction between defective material points is characterized by introducing a near-field dynamic bond breaking mechanism, as shown in Equation (4):

[0031]

[0032] Step 4: Establishing a simulation model of the 3D printing process based on near-field dynamics includes:

[0033] Based on the near-field dynamics life-and-death point model and bond fracture mechanism, the simulation equation for 3D printing process is as follows (5):

[0034]

[0035] In formula (5) μ ij =μ(x) i ,x j ,t);

[0036] In this model, the moving heat source in the 3D printing process adopts an ellipsoidal heat source model, and its distribution function is as follows (6):

[0037]

[0038] P is the heat input power, W; η is the absorption coefficient; a, b, and c are the major semi-axis, minor semi-axis, and depth of the ellipsoidal heat source model, respectively, in m;

[0039] For programming calculations, the equation is discretized into the following equation (7):

[0040]

[0041] Δt is the time step; Represents the material point x i The number of matter points in the neighborhood.

[0042] Step five, defining basic parameters, boundary conditions, and initial conditions based on 3D printing process conditions, includes:

[0043] Set basic parameters based on process conditions, such as heat source power, heat source moving speed, material accumulation sequence, and assumed defects;

[0044] Set appropriate initial and boundary conditions; consider the thermal radiation dissipation phenomenon of the free outer surface of the 3D printed structure. According to the Stefan-Boltzmann law, the heat dissipation per unit area on the outer surface is expressed by the following formula (8):

[0045]

[0046] ε is the emissivity of the object's outer surface; σ is the Stefan-Boltzmann constant; T s and T ∞ These represent the external surface temperature of the structure and the ambient temperature, respectively.

[0047] Step Six: Simulate and calculate and export the results, including: writing a Fortran program, inputting the necessary parameters (from the process), and running the calculation in the program software to obtain the results such as the shape evolution of the structure, the influence domain of the heat source, and the temperature distribution during the 3D printing process.

[0048] The beneficial effects of this invention are:

[0049] (1) The present invention designs a numerical simulation method for 3D printing process based on near-field dynamics, which regards the accumulation of material in the 3D printing process as a change process of scalar field, and uses 0-1 to characterize the life and death state of material points in scalar field. This can describe the 3D printing process in a fairly intuitive way from a physical perspective. Combined with explicit calculation method, it greatly simplifies the calculation amount of each time step in the numerical simulation process.

[0050] (2) This invention regards the defects such as cracks and holes generated during the 3D printing process as discontinuous characteristics between material points, and uses the bond breaking mechanism to describe these defects. This can successfully simulate the generation of defects during the 3D printing process and study their effects on temperature distribution, residual deformation and mechanical properties. It can better help researchers study 3D printing technology, and the cycle is shorter and the cost is lower.

[0051] In numerical simulation of 3D printing, the calculation results obtained by this method can provide important guidance for the design and optimization of 3D printing processes, as well as the mechanical analysis and evaluation of 3D printing materials and structures. Attached Figure Description

[0052] Figure 1 This is a flowchart of a numerical simulation method for 3D printing process based on near-field dynamics, according to the present invention.

[0053] Figure 2 This is a schematic diagram of an example of a 3D printed titanium alloy (Ti-6Al-4V) rib plate in an embodiment of the present invention;

[0054] Figure 3 This is a cloud map showing the structural shape and temperature distribution at 28.6 seconds during the 3D printing of a titanium alloy (Ti-6Al-4V) rib in an embodiment of the present invention.

[0055] Figure 4 This is a cloud map showing the structural shape and temperature distribution at 88 seconds during the 3D printing of a titanium alloy (Ti-6Al-4V) rib in an embodiment of the present invention.

[0056] Figure 5 This is a temperature change curve of different measuring points over time during the 3D printing of a titanium alloy (Ti-6Al-4V) rib plate in an embodiment of the present invention. Detailed Implementation

[0057] The following detailed description of a numerical simulation method for 3D printing process based on near-field dynamics, in conjunction with the accompanying drawings and embodiments, illustrates the present invention.

[0058] A numerical simulation method for 3D printing process based on near-field dynamics includes the following steps:

[0059] Step 1: Establish a near-field dynamic transient heat transfer model;

[0060] Step 2: Establish a near-field dynamics model of life and death matter points;

[0061] Step 3: Introduce a near-field dynamic bond breaking mechanism;

[0062] Step 4: Establish a simulation model of the 3D printing process based on near-field dynamics;

[0063] Step 5: Define the basic parameters, boundary conditions, and initial conditions according to the 3D printing process conditions;

[0064] Step 6: Perform simulation calculations and export the results.

[0065] Step 1 establishes a near-field dynamic transient heat transfer model, including:

[0066] The transient heat transfer equation for near-field dynamics is given by the following equation (1):

[0067]

[0068] Where ρ is density, kg·m -3 c θ Specific heat capacity, J·(kg·℃) -1 K[δ] is the microscopic thermal conductivity coefficient, W·m -5 ·℃ -1 δ is the neighborhood radius of the material point, in meters; Q(x) i ,t) represents the heat source, J·m -3 ;T(x i ,t) and T(x j ,t) represent the material point x and t respectively. i and x j The temperature at time t, in °C; Represents the material point x i The neighborhood of V xj Represents the material point x j Volume;

[0069] ω(||ξ||) is a weighting coefficient representing the distribution of the microscopic thermal conductivity along the radial direction in the neighborhood. In this model, the microscopic thermal conductivity is linearly related to the bond length.

[0070]

[0071] δ is the near-field radius, and K[δ] has a corresponding relationship with the thermal conductivity coefficient k in the classical differential equation. (One-dimensional) Two-dimensional 3D

[0072] Step 2: Establish a near-field dynamics model of life and death matter points, including:

[0073] In the 3D printing process, the geometric dimensions of the 3D printing area are a function of time; in the numerical simulation process, when the material points of the 3D printing area are covered by the influence area of ​​the moving heat source, it is necessary to activate the state of the corresponding material points.

[0074] Within the framework of near-field dynamics, by introducing a scalar field To describe the inactive / active state of material points in the 3D printing area; any material point x i The life or death status is represented by the following formula (2):

[0075]

[0076] in: Represents the material point x i The critical time for activation is determined by the moving speed of the heat source. Represents the material point x i Not activated Represents the material point x i Activated; based on the near-field dynamics life and death matter point model, any matter point x i and x j They interact at time t

[0077] The penalty function used is expressed by the following formula (3):

[0078]

[0079] Step 3: Introduce a near-field dynamic bond breaking mechanism, including:

[0080] During the 3D printing process, uncertainties in the process and environmental factors can lead to defects such as cracks and holes in the 3D printed structure. These defects can affect the heat transfer and mechanical deformation of the 3D printed structure.

[0081] In the model, the interaction between defective material points is characterized by introducing a near-field dynamic bond breaking mechanism, as shown in Equation (4):

[0082]

[0083] Step 4: Establishing a simulation model of the 3D printing process based on near-field dynamics includes:

[0084] Based on the near-field dynamics life-and-death point model and bond fracture mechanism, the simulation equation for 3D printing process is as follows (5):

[0085]

[0086] In formula (5) μ ij =μ(x) i ,x j ,t);

[0087] In this model, the moving heat source in the 3D printing process adopts an ellipsoidal heat source model, and its distribution function is as follows (6):

[0088]

[0089] P is the heat input power, W; η is the absorption coefficient; a, b, and c are the major semi-axis, minor semi-axis, and depth of the ellipsoidal heat source model, respectively, in m;

[0090] For programming calculations, the equation is discretized into the following equation (7):

[0091]

[0092] Δt is the time step; N xi Represents the material point x i The number of matter points in the neighborhood.

[0093] Step five, defining basic parameters, boundary conditions, and initial conditions based on 3D printing process conditions, includes:

[0094] Set basic parameters based on process conditions, such as heat source power, heat source moving speed, material accumulation sequence, and assumed defects;

[0095] Set appropriate initial and boundary conditions; consider the thermal radiation dissipation phenomenon of the free outer surface of the 3D printed structure. According to the Stefan-Boltzmann law, the heat dissipation per unit area on the outer surface is expressed by the following formula (8):

[0096]

[0097] ε is the emissivity of the object's outer surface; σ is the Stefan-Boltzmann constant; T s and T ∞ These represent the external surface temperature of the structure and the ambient temperature, respectively.

[0098] Step Six: Simulate and calculate and export the results, including: writing a Fortran program, inputting the necessary parameters (from the process), and running the calculation in the program software to obtain the results such as the shape evolution of the structure, the influence domain of the heat source, and the temperature distribution during the 3D printing process.

[0099] The following describes the 3D printing of titanium alloy (Ti-6Al-4V) ribs based on the method provided in this invention, such as... Figure 2 As shown, taking process simulation as an example, the specific implementation scheme of the present invention is explained in conjunction with the technical solution and accompanying drawings.

[0100] Step 1: Establish a near-field dynamic transient heat transfer model:

[0101] The transient heat conduction equation based on near-field dynamics is:

[0102]

[0103] Wherein, density ρ = 4430 kg·m -3 Microscopic thermal conductivity in three-dimensional problems Weight coefficients are taken The neighborhood radius δ = 0.9 mm; the thermal conductivity and specific heat capacity of Ti-6Al-4V at different temperatures are shown in Table 1;

[0104] Table 1 Physical properties of Ti-6Al-4V at different temperatures

[0105]

[0106] Step 2: Establish a near-field dynamics model of life and death matter points:

[0107] Step 2.1 During the 3D printing process, the geometric dimensions of the 3D printing area are a function of time; during the numerical simulation, when the material points of the 3D printing area are covered by the influence area of ​​the moving heat source, it is necessary to activate the state of the corresponding material points.

[0108] Within the framework of near-field dynamics, by introducing a scalar field To describe the inactive / active state of material points in the 3D printing area; any material point x i The state of life and death is represented as:

[0109]

[0110] Represents the material point x i The critical time for activation is determined by the moving speed of the heat source. Represents the material point x i Not activated Represents the material point x iIt has been activated;

[0111] Step 2.2 Based on the near-field dynamics birth and death matter point model, any matter point x i and x j The penalty function for the interaction at time t is expressed as:

[0112]

[0113] Step 3: Introducing a near-field dynamic bond breaking mechanism:

[0114] Step 3.1 During the 3D printing process, uncertainties in the process and environmental factors may lead to defects such as cracks and holes in the 3D printed structure. These defects will affect the heat transfer and mechanical deformation of the 3D printed structure.

[0115] In step 3.2 of the model, the interaction between defective material points is characterized by introducing a near-field dynamic bond breaking mechanism:

[0116]

[0117] Step 4: Establish a simulation model of the 3D printing process based on near-field dynamics, and write the equations in discretized form:

[0118] Step 4.1 Simulation equations for 3D printing process based on near-field dynamics:

[0119]

[0120] In the formula, μ ij =μ(x) i ,x j ,t);

[0121] Step 4.2 In this model, the moving heat source during the 3D printing process adopts an ellipsoidal heat source model, and its distribution function is:

[0122]

[0123] Wherein, the heat input power P = 400W; the absorption coefficient η = 0.45; the semi-major axis, semi-minor axis and depth of the ellipsoidal heat source model are a = b = 1.5mm and c = 0.9mm, respectively;

[0124] Step 4.3 Discretize the equations:

[0125] To simplify the computation of the numerical simulation, half of the symmetric model is used for calculation. The computational model is uniformly discretized in space, such that the size of the material point is Δx = Δy = Δz = 0.3 mm, and the neighborhood radius of the material point is δ = 3.015Δx. The discretized expression is:

[0126]

[0127] Wherein, the time step Δt = 0.001s;

[0128] Step 5: Define the basic parameters, boundary conditions, and initial conditions based on the 3D printing process:

[0129] Step 5.1 Set basic parameters, such as heat source power of 400W, heat source moving speed v = 8.5mm / s, material accumulation order, assumed defects, etc. Figure 2 To analyze the impact of different 3D printing processes on temperature field changes, the 3D printing processes are analyzed as follows:

[0130] A single print height of 0.3mm, printing 40 layers, with a total print height of 12mm;

[0131] A single print height of 0.6mm, printing 20 layers, with a total print height of 12mm;

[0132] Step 5.2 Set initial and boundary conditions; Considering the thermal radiation dissipation phenomenon of the free outer surface of the 3D printed structure, according to the Stefan-Boltzmann law, the radiative heat dissipation per unit area on the outer surface is:

[0133]

[0134] Among them, the emissivity of the object's outer surface ε = 0.54; the Stefan-Boltzmann constant σ = 5.67e⁻⁸; and the ambient temperature T ∞ =20℃;

[0135] Step 6: Simulate and calculate, and export the results:

[0136] Based on the above steps, a Fortran program was written, the necessary parameters (derived from the process) were input, and the calculations were run in the software to obtain results such as the shape evolution of the structure, the influence domain of the heat source, and the temperature distribution during the 3D printing process. Figure 3 , 4 By comparing the calculation results with those in the references, it can be seen that the method based on the near-field dynamics life-and-death point model provided by this invention can effectively simulate the 3D printing process and accurately obtain results such as the shape evolution of the structure, the influence domain of the heat source, and the temperature distribution during the 3D printing process.

[0137] The embodiments described above in this patent are for illustrative purposes only and are not intended to limit the scope of the invention.

[0138] The embodiments of the present invention have been described in detail above. The present invention is not limited to the above examples. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A numerical simulation method for 3D printing process based on near-field dynamics, characterized in that, Includes the following steps: Step 1: Establish a near-field dynamic transient heat transfer model; including: The transient heat transfer equation for near-field dynamics is as follows (1): ……………（1） in, For density, ; For specific heat capacity, ; The microscopic thermal conductivity coefficient, ; The near-field radius, ; Indicates the heat source. ; and Representing material points respectively and exist Temperature at any moment ; Representing a point of matter The neighborhood, Representing a point of matter Volume; The weighting coefficients represent the distribution of the microscopic thermal conductivity coefficient along the radial direction in the neighborhood. In this model, the microscopic thermal conductivity coefficient is linearly related to the bond length. The near-field radius, The thermal conductivity coefficient in classical differential equations There is a correspondence, one-dimensional Two-dimensional 3D ; Step 2: Establish a near-field dynamics model of life and death matter points, including: In the 3D printing process, the geometric dimensions of the 3D printing area are a function of time; in the numerical simulation process, when the material points of the 3D printing area are covered by the influence area of ​​the moving heat source, it is necessary to activate the state of the corresponding material points. Within the framework of near-field dynamics, by introducing a scalar field To describe the inactive / activated state of material points in the 3D printing area; arbitrary material points. The life or death status is represented by the following formula (2): …………（2） in: Representing a point of matter The critical time for activation is determined by the moving speed of the heat source. Representing a point of matter Not activated Representing a point of matter Activated; based on the near-field dynamics life and death matter point model, any matter point and exist The penalty function for the interaction at any given time is expressed by the following equation (3): …………（3）; Step 3: Introduce a near-field dynamic bond breaking mechanism; including: During the 3D printing process, uncertainties in the process and environmental factors can lead to cracks and holes in the 3D printed structure. These defects can affect the heat transfer and mechanical deformation of the 3D printed structure. In the model, the interaction between defective material points is characterized by introducing a near-field dynamic bond breaking mechanism, as shown in the following equation (4): …………（4）; Step 4: Establish a simulation model of the 3D printing process based on near-field dynamics; including: Based on the near-field dynamics life-and-death point model and bond fracture mechanism, the simulation equation for 3D printing process is as follows (5): …………（5） In formula (5) , ; In this model, the moving heat source in the 3D printing process adopts an ellipsoidal heat source model, and its distribution function is as follows (6): …………（6） For heat input power, ; The absorption coefficient; , and These represent the major semi-axis, minor semi-axis, and depth of the ellipsoidal heat source model. ; For programming calculations, the equation is discretized into the following equation (7): ………………（7） For time step; Representing a point of matter The number of matter points in the neighborhood; Step 5: Define the basic parameters, boundary conditions, and initial conditions according to the 3D printing process conditions, including: The basic parameters set according to the process conditions include: heat source power, heat source moving speed, material accumulation sequence, and assumed defects; Set appropriate initial and boundary conditions; consider the thermal radiation dissipation phenomenon of the free outer surface of the 3D printed structure. According to the Stefan-Boltzmann law, the heat dissipation per unit area on the outer surface is expressed by the following formula (8): ………………（8） The emissivity of the object's outer surface; It is the Stefan-Boltzmann constant; and These represent the external surface temperature of the structure and the ambient temperature, respectively. Step 6: Perform simulation calculations and export the results.

2. The numerical simulation method for 3D printing process based on near-field dynamics as described in claim 1, characterized in that: Step 6: Simulate and calculate and export the results, including: writing a Fortran program, inputting the necessary parameters and running the calculation in the program software to obtain the shape evolution of the structure, the influence domain of the heat source and the temperature distribution results during the 3D printing process.

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