A multi-scale machining simulation method for fused deposition modeling

Abstract

The present invention discloses a multi-scale processing simulation method for fused deposition technology. The method comprises: obtaining a crystal growth model based on the Lyapunov energy function; obtaining a conduction heat transfer model based on the movement speed and temperature of the nozzle; coupling the crystal growth model and the conduction heat transfer model using temperature to obtain a macro-scale model, solving to obtain macro-scale phase field variables and transient temperature; obtaining a micro-scale model based on the macro-scale phase field variables, transient temperature, crystal anisotropy function, and crystal growth variables, solving to obtain micro-scale phase field variables, performing visualization, and achieving simulation. The method utilizes a physical model to project the real additive manufacturing process into virtual space, establishing a connection between digital space and physical space. The method has high numerical simulation performance and uses appropriate parameters to simulate the state of materials at both macro and micro scales, while also capturing a variety of physical phenomena.

Description

Technical Field

[0001] The present invention belongs to the field of modeling of fused deposition processes in additive manufacturing, and in particular relates to a multi-scale machining simulation method for fused deposition processes. Background Art

[0002] Additive manufacturing (AM), also known as 3D printing, integrates computer-aided design, material processing and molding technologies. Based on digital model files, it uses software and numerical control systems to stack specialized metal materials, non-metallic materials, and medical biomaterials layer by layer through extrusion, sintering, melting, photocuring, spraying, and other methods to produce physical objects. The additive manufacturing process is usually accompanied by high temperature, high pressure, large demand for consumables, and high cost, but lacks the ability to predict characteristics such as track unevenness, material spheroidization effect, and gaps between tracks. Fused deposition technology is a process that extrudes a filament of material such as thermoplastic, wax, or metal from a heated nozzle and deposits the melt at a fixed rate according to the predetermined trajectory of each layer of the part. After each layer is completed, the workbench descends by one layer thickness to deposit a new layer, and this process is repeated until the deposition molding of the part is achieved.

[0003] There are currently models based on Monte Carlo simulation that can account for the characteristics of materials and electron beams; particle-based AM selective laser melting methods that combine the finite volume method and discrete element method to overcome the challenges of discontinuous physics; numerical modeling methods for different powder bed melting processes at multiple length scales and time scales; simulation of the evolution of the melt pool in additive manufacturing through a quantitative model that links different scales through physical parameters such as temperature gradient and solidification rate; multiphase flow models established by bidirectionally coupling discrete element method and finite volume method to study the evolution of the melt pool; and models established by fluid volume method to track free surfaces. However, there is no suitable multiscale model for the simulation and calculation of fused deposition (FD) technology and the recommendation of AM process feedback.

[0004] Fused deposition modeling (FDM) is a high-temperature, melt-extrusion AM process. A nozzle moves at a given speed along a path defined by the G-code, depositing filament onto solidified material. This technology is widely used in many fields due to its simplicity, low cost, and compatibility with a wide range of materials (metals, ceramics, PLA, etc.).

[0005] However, physical modeling using FD technology still faces challenges, such as multiple processing parameters that affect mechanical properties, dimensional accuracy, part quality, and processing time. The main challenges of physical modeling using FD technology can be summarized as follows: (1) During the AM process, temperature changes dramatically and changes much more slowly in space and time than in phase field. (2) The established model is used to balance the relationship between multiple scales, which leads to a large amount of calculation. (3) The efficiency and relationship between model parameters and manufacturing parameters determine whether the model can accurately predict and feedback the AM process.

[0006] Establishing multi-scale modeling of the additive manufacturing process involves complex physical and chemical phase changes and thermodynamic behaviors. In the additive manufacturing process driven by a rapidly evolving temperature field, problems such as trajectory inhomogeneity, material spheroidization effect, and gaps between trajectories will arise, posing a major challenge to prediction. In addition, few studies have currently used physical models to project the real additive manufacturing process into virtual space, which is not conducive to the actual manufacturing of additive materials. Projecting the additive manufacturing process into digital space can numerically predict trajectory inhomogeneity, material spheroidization effect, and gaps between trajectories, thereby reducing losses. Summary of the Invention

[0007] In response to the above problems, the purpose of the present invention is to provide a multi-scale processing simulation method for fused deposition technology. This method can not only enable the multi-scale system to simulate the material state with appropriate parameters at the macro and micro levels, but also, within the multi-scale framework, can numerically predict the trajectory unevenness, material spheroidization effect and gaps between trajectories in the additive manufacturing process.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A multi-scale processing simulation method for a fused deposition modeling process includes the following steps:

[0010] 1) Obtain the crystal growth model based on the Lyapunov energy function;

[0011] According to the movement speed and temperature of the nozzle, the conduction heat transfer model is obtained;

[0012] The crystal growth model and the conduction heat transfer model are coupled using temperature to obtain a macroscopic model.

[0013] Solve the model at the macro scale to obtain the phase field variables and transient temperature at the macro scale;

[0014] 2) Obtain a microscopic model based on macroscopic phase field variables, transient temperature, crystal anisotropy functions, and crystal growth variables;

[0015] Substitute the temperature field into the microscopic model and solve for the microscopic phase field variables.

[0016] Visualize phase field variables at the microscopic scale and enable simulations.

[0017] Preferably, in step 1), the crystal growth model is as follows:

[0018]

[0019] in, is the gradient operator, Δ is the Laplace operator, λ is a dimensionless parameter, and U is the dimensionless temperature.

[0020] Preferably, in step 1), the conduction heat transfer model is:

[0021]

[0022] Where T is the transient temperature, is the temperature gradient, ρ is the density, c is the specific heat coefficient, S is the emission of the nozzle per unit time, v p is the moving speed of the nozzle, and q is the heat source.

[0023] Preferably, in step 1), the model at the macro scale is:

[0024]

[0025]

[0026] Where, is the gradient operator, Δ Laplace operator, λ is the dimensionless parameter, U is the dimensionless temperature; T is the transient temperature, ρ is the density, c is the specific heat coefficient, S is the emission of the nozzle per unit time, v p is the moving speed of the nozzle, and q is the heat source.

[0027] Preferably, the dimensionless temperature U is calculated by the following formula:

[0028] U=c(TT M ) / L

[0029] Where, T M is the ambient temperature and L is the latent heat of fusion.

[0030] Preferably, in step (2), the variable of crystal growth is Calculated by the following formula:

[0031]

[0032] Where S is the spray volume of the nozzle per unit time, and D is the diameter of the sphere.

[0033] Preferably, in step (2), the diameter D of the sphere is calculated by the following formula:

[0034]

[0035] Where Q is the speed of feeding material into the nozzle, v S It is the speed at which the molten material leaves the nozzle.

[0036] Preferably, the model at the microscopic scale is:

[0037]

[0038] Where, is the phase field variable at the microscopic scale, is the intensity parameter of crystal anisotropy, They are Partial derivatives in the x, y, and z directions.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] (1) This method is based on fused deposition technology and couples multiple scales (macro and micro) and multiple physical fields (crystal growth model and conduction heat transfer model), making up for the deficiency of single scale in being unable to predict trajectory gaps, trajectory inhomogeneity and material spheroidization effect. It also numerically simulates the entire process of high-temperature fused deposition, which is very consistent with the actual additive manufacturing results. Through numerical simulation, trajectory gaps, inhomogeneity and material spheroidization effect are predicted in time to prevent greater losses. The present invention uses a modeling technology that simulates the state of materials with appropriate parameters from the macro and micro scales, and the technology can also capture a variety of physical phenomena.

[0041] Furthermore, within the framework of multi-physics coupling, this invention comprehensively considers factors such as transient temperature and crystal anisotropy functions to propose a multi-scale machining simulation method for fused deposition modeling. This method projects the actual additive manufacturing process into virtual space, establishing a connection between digital and physical space and achieving high numerical simulation performance. Furthermore, this invention pushes additive manufacturing technology towards a new direction of multi-scale, multi-physics coupled simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the manufacturing process involving multi-scale and multi-physics coupling;

[0043] Figure 2 It is a schematic diagram of the multi-scale model, which highlights the correlation between multi-scale spaces.

[0044] Figure 3The figure is a comparison of the numerical simulation and additive manufacturing results at different stages. Among them, Figures (a)-(f) are the figures generated by simulation, and Figures (g)-(l) are the figures actually printed; (a) is Figure (e) in the horizontal direction. The cross-sectional view at (b) is the vertical direction of (f). The cross-sectional view at (c) is the horizontal direction of (e). The cross-sectional view at (d) is the vertical direction of (f). (e) is the horizontal placement diagram, (f) is the vertical placement diagram; (g) is the horizontal placement diagram of (k) The cross-sectional view at (h) is the vertical direction of (l). The cross-sectional view at (i) is the horizontal direction of (k). The cross-sectional view at (j) is the vertical direction of (l). Cross-sectional view at , (k) is the horizontal placement view, and (l) is the vertical placement view. DETAILED DESCRIPTION

[0045] The present invention will be described in detail below with reference to the accompanying drawings.

[0046] The present invention addresses the modeling problem of the molten deposition process and provides a multi-scale processing simulation method for the molten deposition process. The method describes the molten deposition process in the additive manufacturing process at macroscale and microscale. The system couples the conduction heat transfer model and the dendrite solidification model, and can simulate the material state with appropriate parameters at the macroscale and microscale, and can capture a variety of physical phenomena.

[0047] First, the main symbols of the present invention are defined as shown in Table 1:

[0048] Table 1 Meaning of main symbols in the present invention

[0049]

[0050]

[0051] 1) At the macroscale, φ is used to represent the phase field variable, where φ = 1 represents the solid state and φ = -1 represents the molten state. The time evolution of φ is obtained through the Lyapunov energy function ε(φ), which is the crystal growth model. In the additive manufacturing process, the printer's nozzle is a mobile heat source, continuously ejecting molten filaments. The transformation of the filaments from the molten state to the solid state involves temperature changes and thermal diffusion effects. This process is described by the heat conduction equation. Considering that heat is mainly released by the filaments during solidification, the heat conduction term, which couples the nozzle's movement speed with the temperature, is added to the heat conduction equation to obtain a conduction heat transfer model. The crystal growth model and the conduction heat transfer model are then coupled using temperature to obtain a macroscale model.

[0052] The Lyapunov energy function ε(φ) is:

[0053]

[0054] Perform variational differentiation on the Lyapunov energy function and introduce gradient flow to obtain the evolution of φ over time:

[0055]

[0056] in, is the gradient operator, Δ Laplace operator, λ is a dimensionless parameter with a value of 0.1, and U is the dimensionless temperature. The crystal growth model can describe the crystallization phenomenon.

[0057] The conduction heat transfer model is:

[0058]

[0059] Where T is the transient temperature, ρ is the density, c is the specific heat coefficient, S is the emission of the nozzle per unit time, v p is the movement speed of the nozzle, and q is the heat source. The heat source is mainly released when the nozzle ejects the filament, and is described by the following formula:

[0060] q(x,y,t)=ρcT inj Sδ(xx S ),

[0061] Among them, T inj is the injection temperature, x S is the injection position, injection temperature T inj The relationship between and injection velocity is as follows:

[0062]

[0063] A S ,B S ,C Sis a coefficient determined by the manufacturing mode. During the simulation, the values of these three process parameters are A S =113,B S =3440,C S =203.

[0064] The final coupled model, i.e. the model at the macro scale, is:

[0065]

[0066]

[0067] The crystal growth model and the heat transfer model are coupled through temperature, where U = c(TT M ) / L,T M Is the ambient temperature. During the simulation, the ambient temperature T M The value of is 293.15K, L is the latent heat of fusion, and k is the thermal conductivity. Solving the coupled model requires discrete time and space. The calculation of the coupled model is based on the pressure correction method. The superscript is the discrete time, and the subscript is the discrete space, such as φ n+1 Represents the value of φ in the nth step, and the macro-scale model is discretized into a uniform grid. The computational domain is Total Grids:

[0068]

[0069]

[0070] in,

[0071]

[0072] U n+1 =c(T n+1 -T M ) / L,

[0073]

[0074] G(φ n+1 )=-(4λU n+1 (φ n ) 3 +3(φ n ) 2 -4λU n+1 φ n )φ n+1

[0075] +3λU n+1 (φ n ) 4 +2(φn ) 3 -2λU n+1 (φ n ) 2

[0076] Considering the computational complexity and efficiency, the discrete macro model is solved by parallel fast Fourier transform and the discrete macro model is reformulated as follows:

[0077]

[0078] UP=3λU n+1 (φ n ) 4 +2(φ n ) 3 -2λU n+1 (φ n ) 2 -λU n+1 +S

[0079] Rearranging the above formula, we can get the following linear decoupling format:

[0080] T n+1 =(Ι-ΔtM0L) -1 (ΔtUT+T n ),

[0081]

[0082] Where Ι and L are the unit matrix and Laplace matrix respectively. The discrete system derives the decoupled elliptic equations for calculation, so that the temperature field and phase field can be solved separately at each time step. The solution algorithm has a large-scale parallel computing algorithm framework, with the formula T n+1 =(Ι-ΔtM0L) -1 (ΔtUT+T n ) as an example to illustrate the algorithm:

[0083] Step 1: Initialize the ambient temperature field T of the AM process 0 ;

[0084] Step 2: Perform FFT algorithm in the x direction on the right side of the equation;

[0085] Step 3: The 3D data obtained in step 2 is transposed between the computational cores, thereby distributing the generated data in the X direction and maintaining continuity with the Y and Z directions.

[0086] Step 4: Alternate step 2 and step 3 in three directions to obtain T in Fourier space n+1 ;

[0087] Step 5: Perform inverse FFT algorithm in the X direction on the 3D data obtained in step 4;

[0088] Step 6: The 3D data obtained in step 4 is transposed between the computational cores, thereby distributing the generated data in the X direction and maintaining continuity with the Y and Z directions.

[0089] Step 7: Alternate step 5 and step 6 in three directions, so that T n+1 ;

[0090] right The above algorithm is also applicable to the solution of and transient temperature T.

[0091] The heat conduction equation also involves the material density ρ, specific heat capacity c, and thermal conductivity k. These three variables are defined as functions of φ:

[0092] ρ(φ)=0.5(ρ1(1+φ)+ρ2(1-φ))

[0093] c(φ)=0.5(c1(1+φ)+c2(1-φ))

[0094] k(φ)=0.5(k1(1+φ)+k2(1-φ))

[0095] Among them, ρ1 and ρ2 are the densities of polymer and air respectively, c1 and c2 are the specific heat coefficients, k1 and k2 are the thermal conductivity. The values of the following process parameters in the simulation process are ρ1 = 1240 kg / m 3 ,ρ2=0.9kg / m 3 , c1 = 2000 J / kgK, c2 = 1000 J / kgK, k1 = 0.195 W / mK, k2 = 0.034 W / mK, and solve the above equations for the material density ρ, specific heat c, and thermal conductivity k discretely:

[0096] ρ n+1 =0.5(ρ1(1+φ n+1 )+ρ2(1-φ n+1 ))

[0097] c n+1 =0.5(c1(1+φ n+1 )+c2(1-φ n+1 ))

[0098] k n+1 =0.5(k1(1+φ n+1 )+k2(1-φ n+1 ))

[0099] Get the density ρ of the n+1th step n+1 , the specific heat capacity c of the n+1th step n+1 , the thermal conductivity k of the n+1th step n+1 .

[0100] 2) At the mesoscopic scale, since the temperature of the filament ejected from the nozzle is higher than the temperature of the surrounding environment, heat transfer will occur. This part of the convective heat transfer can be compensated by modifying the thermal conductivity. At the same time, the change of thermal conductivity will directly affect the preparation of the filament, so the thermal conductivity k meso The changes of the phase field variables were studied by macroscopic calculation. and transient temperature T, the thermal conductivity k at the mesoscopic scale can be calculated meso :

[0101]

[0102] Among them, H flux is the total heat flux, T grad is the temperature gradient, D is the diameter of the deposited filament, Q is the feed rate. During the simulation, the feed rate Q is 9.62×10 -9 m 3 / s. Calculate the thermal conductivity k for the above mes The equation of o is discretized to obtain the thermal conductivity of the n+1th step

[0103]

[0104] 3) At the microscopic scale, using Represents the phase field variables at the microscopic scale, and uses represents the crystal anisotropy function, and the mobility ε in the growth model is replaced by At the same time, the variable S (the amount of spray from the nozzle per unit time) in the growth model is converted into a variable representing crystal growth at the microscopic scale through the corresponding formula Thus, a model at the microscopic scale is obtained. The specific process is as follows:

[0105] Step 1: Use The variable representing crystal growth at the microscopic scale is represented by S (the amount of spray from the nozzle per unit time):

[0106]

[0107] The speed and position of the filament ejected by the nozzle are controlled by G-code. The volume source can be regarded as a sphere at the ejection position. is the diameter of the sphere, Q is the speed of supplying material to the nozzle, v S It is the speed at which the molten material leaves the nozzle.

[0108] Step 2: After replacing ε and S, the microscopic model is:

[0109]

[0110]

[0111]

[0112] in, is the phase field variable at the microscopic scale, is the intensity parameter of crystal anisotropy, They are Partial derivatives in the x, y, and z directions.

[0113] When calculating the model at the micro scale, an auxiliary variable is introduced The original microscopic model is transformed into:

[0114]

[0115]

[0116]

[0117] in,

[0118]

[0119]

[0120]

[0121] use The variable representing crystal growth at the microscopic scale is represented by S (the amount of spray from the nozzle per unit time): The rate and position of the filament ejected by the nozzle are controlled by G-code. The volume source can be regarded as a sphere at the ejection position. is the diameter of the sphere, Q is the speed of supplying material to the nozzle, v S is the speed at which the molten material leaves the nozzle. Discretizing the above model with the introduction of auxiliary variables, we obtain:

[0122]

[0123] It should be noted that the time in the macro model and the micro model is not consistent. The temperature fluctuation of the system is mainly caused by the temperature change of the filaments at the macro scale, so the temperature disturbance effect caused by crystallization at the micro scale is masked. Therefore, as long as the temperature field distribution is obtained by calculating the macro model, the temperature field can be substituted into the micro model to solve the phase field variables at the micro scale.

[0124] The invention introduces auxiliary variables mainly to facilitate calculation. The introduction of auxiliary variables can transform the control equation into a linear, decoupled form. At the same time, the discrete system is unconditionally energy stable, allowing calculation with a large time step.

[0125] The phase field variables at the microscopic scale Perform visualization to achieve the purpose of simulation.

[0126] In the solution of the model in the present invention, the discrete system derives the decoupled elliptic equations, which can solve the temperature field and phase field separately at each time step. The solution process has an algorithm framework for large-scale parallel computing, and at the same time converts the nonlinear, coupled system into a linear, decoupled format, which can eliminate the oscillation caused by crystal anisotropy. In addition, the format is unconditionally energy stable, can converge quickly, is simple and easy to implement, and has the characteristics of real-time repair.

[0127] Figure 1 It is a diagram of the manufacturing process involving multi-scale and multi-physics coupling. Figure 1 As can be seen, during the additive manufacturing process, the nozzle moves at a given speed along the path defined by the G-code, depositing a filament onto the solidified material. Macroscopically, this displays a filament, while microscopically, it displays a crystal. The temperature distribution varies depending on the distance of the filament from the nozzle, and the direction of crystal growth varies depending on whether the crystal grows on the surface or within the filament. The upper left image shows a crystal growing in a single direction, while the bottom image shows crystal growth with a center distribution.

[0128] Figure 2 is a schematic diagram of the multi-scale model. Figure 2 It can be seen that the figure highlights the correlation between multi-scale spaces. From left to right, the 3D effects that can be obtained by the model of the present invention at the macro scale, the model at the meso scale and the model at the micro scale are shown. At the beginning of this figure, the multi-scale simulation process with texture is introduced, which simulates the manufacturing of molten filaments under the guidance of G code. For detailed detection at a small scale, the present invention selects the middle slice of the numerical model. At the mesoscale, the present invention has demonstrated the evolution of the intermediate layer path and the temperature field. In order to study the performance of the microstructure during the spraying process, the behavior of the phase change is compared by simulating the extrusion of the filament from the nozzle, and the process of material melting is explored from a microscopic perspective.

[0129] Figure 3 This is a comparison chart of the numerical simulation and additive manufacturing results at different stages. Figure 3 (a)-(l), Figure 3 The first row shows the multi-scale simulation of surface temperature distribution, while the second row shows the results of additive manufacturing using PLA. It can be seen that the proposed digital model closely matches the results of additive manufacturing using PLA. Furthermore, the digital model shows that heat is concentrated at the junction or inflection point, as the inflection point is the intersection of the nozzle trajectory and the heat released by the filament. This indicates that heat distribution is closely related to the nozzle trajectory, and that the temperature simulation of the current layer is affected not only by the moving heat source but also by the heat diffusion of the underlying layer.

[0130] Through the simulation in the present invention, the numerical simulation and the actual additive manufacturing results are highly matched, indicating that the numerical simulation can be used to timely predict the trajectory gap, trajectory non-uniformity and material spheroidization effect to prevent greater losses.

[0131] This invention uses a physical model to map the additive manufacturing process into a virtual space. This model involves coupling multiple physical fields and can capture a variety of physical phenomena, such as the cooling and solidification of filaments. It effectively describes the molten deposition process and simulates the state of the material at both the macro and micro scales. Within this multi-scale framework, numerical predictions are made for the trajectory non-uniformity, material spheroidization, and gaps between the trajectories of the additive manufacturing process. This invention is the first to project the additive manufacturing process into a digital space. This invention establishes models at both the macro and micro scales. The macro model considers the effects of high nozzle temperature, simulating the temperature distribution and shape changes of the prepared parts. The physical model is used to project the AM process into a virtual space. At the mesoscale, attention is paid to temperature-induced changes in thermal conductivity, with the goal of compensating for lost convective heat exchange by modifying thermal conductivity. At the microscale, the anisotropic properties of crystal growth are primarily described, and the thermal strain between the material and the crystal is studied. The macroscopic and microscopic models are discretized separately, and the decoupled elliptic equations are derived from the discrete system. The temperature field and phase field can be solved separately at each time step. The solution process has an algorithm framework for large-scale parallel computing. At the same time, the original nonlinear, coupled system is converted into a linear, decoupled format. This format is unconditionally energy stable, can converge quickly, is simple to implement, and has the characteristics of real-time repair.

Claims

1. A multi-scale processing simulation method for fused deposition process, characterized in that: The following steps are involved: 1) Obtain the crystal growth model based on the Lyapunov energy function; According to the movement speed and temperature of the nozzle, the conduction heat transfer model is obtained; The crystal growth model and the conduction heat transfer model are coupled using temperature to obtain a macroscopic model. Solve the model at the macro scale to obtain the phase field variables and transient temperature at the macro scale; 2) Based on the macroscopic phase field variables, transient temperature, crystal anisotropy function, and crystal growth variables, a microscopic model is obtained; Substitute the temperature field into the microscopic model and solve for the microscopic phase field variables. Visualize phase field variables at the microscopic scale to achieve simulation; In step 1), the macroscopic model is: Where, is the gradient operator, Laplace operator, is a dimensionless parameter, U is the dimensionless temperature; T is the transient temperature, is the density, is the specific heat coefficient, S is the emission amount of the nozzle per unit time, is the moving speed of the nozzle, It is a heat source; The model at the microscopic scale is: Where, is the phase field variable at the microscopic scale, is the variable of crystal growth, They are the phase field variables at the microscopic scale Partial derivatives in the x, y, and z directions.

2. The multi-scale processing simulation method for fused deposition process according to claim 1, characterized in that: In step 1), the crystal growth model is as follows: in, Laplace operator, is a dimensionless parameter and U is the dimensionless temperature.

3. The multi-scale processing simulation method for fused deposition process according to claim 1, characterized in that: In step 1), the conduction heat transfer model is: Where T is the transient temperature, is the temperature gradient, is the density, is the specific heat coefficient, is the moving speed of the nozzle, It is a heat source.

4. The multi-scale processing simulation method for fused deposition process according to claim 1, characterized in that: The dimensionless temperature U is calculated by the following formula: Where, is the ambient temperature and L is the latent heat of fusion.

5. The multi-scale processing simulation method for fused deposition process according to claim 1, characterized in that: In step 2), the variables of crystal growth Calculated by the following formula: Where, is the diameter of the sphere.

6. The multi-scale processing simulation method for fused deposition process according to claim 5, characterized in that: In step 2), the diameter of the sphere Calculated by the following formula: Where, is the speed of feeding material into the nozzle, It is the speed at which the molten material leaves the nozzle.

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