CN115221719A - Multi-scale processing simulation method for fused deposition process - Google Patents

Multi-scale processing simulation method for fused deposition process Download PDF

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CN115221719A
CN115221719A CN202210886970.0A CN202210886970A CN115221719A CN 115221719 A CN115221719 A CN 115221719A CN 202210886970 A CN202210886970 A CN 202210886970A CN 115221719 A CN115221719 A CN 115221719A
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temperature
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fused deposition
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李义宝
蒋小玉
夏青
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Xian Jiaotong University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/10—Additive manufacturing, e.g. 3D printing
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Abstract

The invention discloses a multi-scale processing simulation method facing a fused deposition process, which obtains a crystal growth model according to a Lyapunov energy function; obtaining a conduction heat transfer model according to the moving speed and the temperature of the spray head; coupling the crystal growth model and the conduction heat transfer model by using temperature to obtain a model under a macro scale, and solving to obtain a phase field variable and a transient temperature under the macro scale; and obtaining a model under the micro scale according to the phase field variable, the transient temperature, the crystal anisotropy function and the crystal growth variable under the macro scale, solving to obtain the phase field variable under the micro scale, visualizing and realizing simulation. The invention utilizes the physical model to project the real additive manufacturing process to the virtual space, establishes the relation between the digital space and the physical space, has higher numerical simulation performance, sends a modeling technology for simulating the state of the material by using proper parameters from the macro scale and the micro scale, and can capture various physical phenomena at the same time.

Description

Multi-scale processing simulation method for fused deposition process
Technical Field
The invention belongs to the field of modeling of a fused deposition process in additive manufacturing, and particularly relates to a fused deposition process-oriented multi-scale machining simulation method.
Background
Additive Manufacturing (AM), also known as 3D printing, incorporates computer aided design, material processing and molding techniques, and a manufacturing technique for manufacturing solid articles by stacking dedicated metallic, non-metallic, and medical biomaterials layer by software and numerical control systems based on digital model files in manners of extrusion, sintering, melting, photocuring, jetting, and the like. Additive manufacturing processes are typically associated with high temperature, high pressure, high consumable requirements, and costly characteristics, but lack the ability to predict characteristics such as rail non-uniformity, material balling effects, and inter-rail voids. The fused deposition technique is to carry out the fused deposition at a fixed speed by extruding a fusing wire of filamentary material such as thermoplastic, wax or metal from a heated nozzle according to a predetermined track of each layer of the part, and each time one layer is finished, the worktable descends one layer thickness to carry out the superposed deposition of a new layer, thus repeating the steps to finally realize the deposition forming of the part.
There are models based on monte carlo simulations that can interpret the properties of materials and electron beams; a particle-based AM selective laser melting method that combines a finite volume method and a discrete element method to overcome the challenges of discontinuous physics; numerical modeling methods performed on multiple length scales and time scales for different powder bed melting processes; simulating the evolution of a molten pool in the additive manufacturing process through a quantitative model, wherein the model relates different scales through physical parameters such as temperature gradient and solidification rate; establishing a multiphase flow model by a bidirectional coupling discrete unit method and a finite volume method, and researching the change of a molten pool by using the model; modeling by a fluid volume method to track a free surface; there is no suitable multi-scale model for simulation and calculation of Fused Deposition (FD) techniques and suggestion of AM process feedback.
The fused deposition technique is a melt extrusion AM process driven by high temperatures. The nozzle moves at a given speed along the path set by the G code and deposits the filament on the material that has solidified. This technology is widely used in many fields due to its simple process, low cost, and multiple materials (metals, ceramics, PLA plastics, etc.).
FD techniques, however, still present challenges for physical modeling, such as a number of process parameters that can affect mechanical properties, dimensional accuracy, part quality, and processing time. The main challenges of physical modeling with FD techniques can be summarized as follows: (1) During AM, temperature changes dramatically and much more slowly in space and time than the phase field; (2) The established model is used to balance the relationships between multiple scales, resulting in a large number of calculations; (3) The efficiency and relationship between the model parameters and the manufacturing parameters determine whether the model can accurately predict and feed back the AM process.
Establishing multi-scale modeling for the additive manufacturing process relates to complex physical-chemical phase change and thermodynamic behaviors, problems of track nonuniformity, material spheroidization effect, track gaps and the like can occur in the additive manufacturing process driven by a rapidly-evolving temperature field, and a great challenge is brought to prediction.
Disclosure of Invention
In view of the above problems, an object of the present invention is to provide a multi-scale machining simulation method for a fused deposition process, which can not only realize that a multi-scale system simulates a material state with appropriate parameters in a macro-scale and a micro-scale, but also numerically predict trajectory non-uniformity, a material spheroidization effect and gaps between trajectories in an additive manufacturing process under a multi-scale framework.
In order to realize the purpose, the technical scheme adopted by the invention is as follows:
a multi-scale processing simulation method for a fused deposition process comprises the following steps:
1) Obtaining a crystal growth model according to a Lyapunov energy function;
obtaining a conduction heat transfer model according to the moving speed and the temperature of the spray head;
coupling the crystal growth model and the conduction heat transfer model by using temperature to obtain a model under a macro scale;
solving the model under the macro scale to obtain a phase field variable and a transient temperature under the macro scale;
2) Obtaining a model under the micro scale according to the phase field variable, the transient temperature, the crystal anisotropy function and the crystal growth variable under the macro scale;
substituting the temperature field into the model under the microscale, and solving to obtain a phase field variable under the microscale;
and visualizing the phase field variable at the microscopic scale to realize simulation.
Preferably, in step 1), the crystal growth model is as follows:
Figure BDA0003766186050000031
wherein the content of the first and second substances,
Figure BDA0003766186050000032
is the gradient operator, Δ laplace operator, λ is a dimensionless parameter, and U is a dimensionless temperature.
Preferably, in step 1), the conduction heat transfer model is:
Figure BDA0003766186050000033
wherein, T is the transient temperature,
Figure BDA0003766186050000034
is the temperature gradient, rho is the density, c is the specific heat coefficient, S is the shot size of the nozzle in unit time, v p Is the moving speed of the nozzle, and q is the heat source.
Preferably, in step 1), the model at the macro scale is:
Figure BDA0003766186050000035
Figure BDA0003766186050000036
in the formula (I), the compound is shown in the specification,
Figure BDA0003766186050000037
is a gradient operator, Δ laplace operator, λ is a dimensionless parameter, U is a dimensionless temperature; t is the transient temperature, ρ is the density, c is the specific heat coefficient, S is the shot size per unit time, v p Is the moving speed of the nozzle, and q is the heat source.
Preferably, the dimensionless temperature U is calculated by the following formula:
U＝c(T-TM)/L
in the formula, T M Is ambient temperature and L is fusion latent heat.
Preferably, in step (2), the variation of crystal growth
Figure BDA0003766186050000038
Calculated by the following formula:
Figure BDA0003766186050000041
wherein S is the jet quantity of the nozzle in unit time, and D is the diameter of the sphere.
Preferably, in step (2), the diameter D of the sphere is calculated by the following formula:
Figure BDA0003766186050000042
wherein Q is the speed of the material supplied to the head, v S The velocity of the material in the molten state as it leaves the nozzle.
Preferably, the model at the microscopic scale is:
Figure BDA0003766186050000043
in the formula (I), the compound is shown in the specification,
Figure BDA0003766186050000044
is a phase field variable at the microscopic scale,
Figure BDA0003766186050000045
is a strength parameter of the crystal anisotropy,
Figure BDA0003766186050000046
are respectively
Figure BDA0003766186050000047
Partial derivatives in the x, y, z directions.
Compared with the prior art, the invention has the following beneficial effects:
(1) The method is based on the fused deposition technology, multi-scale (macro and micro) multi-physical field (a crystal growth model and a conduction heat transfer model) coupling is carried out, the defects that track gaps cannot be predicted in a single scale, track nonuniformity and a material spheroidizing effect are overcome, numerical simulation is carried out on the whole process of high-temperature fused deposition, the simulation is matched with the actual additive manufacturing result, the track gaps, the nonuniformity and the material spheroidizing effect are predicted in time through the numerical simulation, and larger loss is prevented. The invention develops a modeling technology for simulating the state of a material by using proper parameters from a macro scale and a micro scale, and simultaneously, the technology can capture various physical phenomena.
Furthermore, the invention provides a multi-scale processing simulation method facing the fused deposition process under the framework of multi-physical-field coupling and by comprehensively considering factors such as transient temperature, crystal anisotropy function and the like. The real additive manufacturing process is projected to the virtual space, and the relation is established between the digital space and the physical space, so that the numerical simulation performance is high. Meanwhile, the invention pushes the additive manufacturing technology to a new direction of multi-scale and multi-physical field coupling simulation.
Drawings
FIG. 1 is a schematic diagram of a manufacturing process involving multi-scale multi-physical field coupling;
FIG. 2 is a schematic diagram of a multi-scale model in which the correlation between multi-scale spaces is highlighted.
Fig. 3 is a graph comparing results of different stages of numerical simulation and additive manufacturing. Wherein, graphs (a) - (f) are graphs generated by simulation, and graphs (g) - (l) are graphs actually printed; (a) Is shown in the horizontal direction in the figure (e)
Figure BDA0003766186050000051
A cross-sectional view of (a), (b) is a view of (f) in the vertical direction
Figure BDA0003766186050000052
Is a cross-sectional view of (c) is a view of (e) in the horizontal direction
Figure BDA0003766186050000053
(d) is a cross-sectional view of (f) in the vertical direction
Figure BDA0003766186050000054
(e) is a horizontally placed view, and (f) is a vertically placed view; (g) Is shown in the horizontal direction of the drawing (k)
Figure BDA0003766186050000055
(h) is a vertical section of the drawing (l)
Figure BDA0003766186050000056
(ii) is a cross-sectional view of (k) in the horizontal direction
Figure BDA0003766186050000057
(j) is a cross-sectional view of the drawing (l) in the vertical direction
Figure BDA0003766186050000058
The sectional view of (a), (k) is a horizontally disposed view, and (l) is a vertically disposed view.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The invention provides a multi-scale processing simulation method for a fused deposition process, which aims at the modeling problem of the fused deposition process, describes the fused deposition process in the additive manufacturing process through a macro scale and a micro scale, couples a conduction heat transfer model and a dendritic crystal solidification model, can simulate the material state by using proper parameters on the macro scale and the micro scale, and can capture various physical phenomena.
First, the main symbol definitions of the present invention are shown in table 1:
TABLE 1 meanings of main symbols in the present invention
Figure BDA0003766186050000059
Figure BDA0003766186050000061
1) On a macroscopic scale, the phase field variables are represented by phi, phi =1 represents the solid state, and phi = -1 represents the molten state. The evolution process of phi along with time is obtained through a Lyapunov energy function epsilon (phi), and the evolution function is a crystal growth model. In the additive manufacturing process, a nozzle of a printer is a moving heat source, molten filaments are continuously sprayed outwards through the nozzle, the temperature change and the heat diffusion effect are involved when the filaments are changed from a molten state to a solid state, the process is described through a heat conduction equation, and meanwhile, the heat is mainly released by the filaments in the solidification process, so that a heat convection term of the coupling of the moving speed and the temperature of the nozzle is added into the heat conduction equation to obtain a conduction heat transfer model, and the crystal growth model and the conduction heat transfer model are coupled through the temperature, so that the model under the macroscopic scale is obtained.
The Lyapunov energy function ε (φ) is:
Figure BDA0003766186050000071
carrying out variational derivation on the Lyapunov energy function, and introducing gradient flow to obtain a process that phi evolves along with time:
Figure BDA0003766186050000072
wherein the content of the first and second substances,
Figure BDA0003766186050000073
is a gradient operator, a delta laplace operator, lambda is a dimensionless parameter value of 0.1, and U is a dimensionless temperature. The crystal growth model may describe the crystallization phenomenon.
The conduction heat transfer model is as follows:
Figure BDA0003766186050000074
wherein T is the transient temperature, ρ is the density, c is the specific heat coefficient, S is the emission amount per unit time of the nozzle, v p Is the moving speed of the spray head, q is the heat source, which is mainly released when the spray head sprays the filaments, and is described by the following formula:
q(x,y,t)＝ρcT inj Sδ(x-x S )，
wherein, T inj Is the injection temperature, x S Is the injection position, the injection temperature T inj And the injection speed are as follows:
Figure BDA0003766186050000075
A S ,B S ,C S is a coefficient determined by a manufacturing mode, and the values of the three process parameters are respectively A in the simulation process S ＝113,B S ＝3440,C S ＝203。
The coupling model obtained finally, i.e. the model on the macro scale, is:
Figure BDA0003766186050000081
Figure BDA0003766186050000082
coupling the crystal growth model and the heat transfer model by temperature, wherein U = c (T-T) M )/L，T M Is the ambient temperature, T, of the environment during the simulation M The value of (A) is 293.15K, L is fusion latent heat, and k is thermal conductivity. Solving the coupling model is carried out in discrete time and space, the calculation of the coupling model is based on a pressure correction method, the superscript is discrete time, and the subscript is discrete space, such as phi n+1 Expressing the value of phi in the nth step, performing uniform grid dispersion on the macro scale model, and calculating the domain as
Figure BDA0003766186050000083
In common with
Figure BDA0003766186050000084
Each grid is as follows:
Figure BDA0003766186050000085
Figure BDA0003766186050000086
wherein the content of the first and second substances,
Figure BDA0003766186050000087
U n+1 ＝c(T n+1 -T M )/L，
Figure BDA0003766186050000088
G(φ n+1 )＝-(4λU n+1 (φ n ) 3 +3(φ n ) 2 -4λU n+1 φ n )φ n+1
+3λU n+1 (φ n ) 4 +2(φ n ) 3 -2λU n+1 (φ n ) 2
considering the calculation amount and the calculation efficiency, the discrete macroscopic model is subjected to parallel fast Fourier solution, and is represented again as follows:
Figure BDA0003766186050000089
UP＝3λU n+1 (φ n ) 4 +2(φ n ) 3 -2λU n+1 (φ n ) 2 -λU n+1 +S
rearranging the above formula, the following linear decoupling format can be obtained:
T n+1 ＝(Ι-ΔtM 0 L) -1 (ΔtUT+T n ),
Figure BDA00037661860500000810
and I and L are a unit matrix and a Laplace matrix respectively, and a discrete system derives a decoupling elliptic equation for calculation, so that the temperature field and the phase field can be solved at each time step respectively. The solving algorithm has an algorithm framework of large-scale parallel computing, and is represented by a formula T n+1 ＝(Ι-ΔtM 0 L) -1 (ΔtUT+T n ) For example, the algorithm is illustrated:
step1: ambient temperature field T for initializing AM Process 0 ；
Step2: performing an FFT algorithm in the x direction on the right side of the equation;
step3: 3D data obtained by step2 is transposed between the computation cores so that the generated data is distributed in the X direction and is kept continuous with the Y, Z direction;
step4: cross in three directionsStep2 and step3 are performed alternately, thereby obtaining T of Fourier space n+1 ；
Step5: performing an inverse FFT algorithm in the X direction on the three-dimensional data obtained in step 4;
step6: 3D data obtained by step4 is transposed between the computation cores so that the generated data is distributed in the X direction and is kept continuous with the Y, Z direction;
step7: step5 and step6 are alternately performed in three directions so that T is n+1 ；
For is to
Figure BDA0003766186050000091
The above algorithm is also applicable, and the phase field variables can be obtained by the above solution
Figure BDA0003766186050000092
And a transient temperature T.
In the heat conduction equation, the density ρ, the specific heat capacity c, and the thermal conductivity k of the material are also referred to, and these three variables are defined as a function of:
ρ(φ)＝0.5(ρ 1 (1+φ)+ρ 2 (1-φ))
c(φ)＝0.5(c 1 (1+φ)+c 2 (1-φ))
k(φ)＝0.5(k 1 (1+φ)+k 2 (1-φ))
where ρ is 1 And ρ 2 Density of polymer and air, respectively, c 1 And c 2 Is the specific heat coefficient, k 1 And k 2 Is the thermal conductivity, and the values of the following process parameters are rho respectively in the simulation process 1 ＝1240kg/m 3 ,ρ 2 ＝0.9kg/m 3 ，c 1 ＝2000J/kgK,c 2 ＝1000J/kgK，k 1 ＝0.195W/mK,k 2 =0.034W/mK, the above equation for the density ρ, specific heat capacity c, and thermal conductivity k of the material is solved discretely:
ρ n+1 ＝0.5(ρ 1 (1+φ n+1 )+ρ 2 (1-φ n+1 ))
c n+1 ＝0.5(c 1 (1+φ n+1 )+c 2 (1-φ n+1 ))
k n+1 ＝0.5(k 1 (1+φ n+1 )+k 2 (1-φ n+1 ))
obtaining the density rho of the n +1 step n+1 Specific heat capacity c of step n +1 n+1 Heat conductivity k at step n +1 n+1 。
2) In a mesoscopic scale, as the temperature of the filaments sprayed by the spray head is higher than that of the ambient environment, a heat transfer phenomenon occurs, and the part of convective heat transfer can be compensated by modifying the thermal conductivity. While the change in thermal conductivity directly affects the preparation of the filament, so the thermal conductivity k is a function of meso Is studied, and the phase field variable is calculated by macroscopic scale
Figure BDA0003766186050000101
And transient temperature T, the thermal conductivity k at mesoscopic scale can be calculated meso ：
Figure BDA0003766186050000102
Wherein H flux Is the total heat flux of the heat exchanger,
Figure BDA0003766186050000103
T grad is the temperature gradient, D is the diameter of the deposited filament,
Figure BDA0003766186050000104
q is the feed rate, and the value of the feed rate Q in the simulation process is 9.62 multiplied by 10 -9 m 3 And s. For the above-mentioned heat conduction rate k mes The equation of o is dispersed to obtain the thermal conductivity of the step (n + 1)
Figure BDA0003766186050000105
Figure BDA0003766186050000106
3) At the microscopic scale, using
Figure BDA0003766186050000107
Representing phase field variations at microscopic scale by
Figure BDA0003766186050000108
Expressing the crystal anisotropy function, replacing the mobility epsilon in the growth model by
Figure BDA0003766186050000109
Meanwhile, the variable S (the injection quantity of the spray head in unit time) in the growth model is converted into the variable expressing crystal growth under the changed microscale through a corresponding formula
Figure BDA00037661860500001010
Thus obtaining a model under the micro scale, and the specific process is as follows:
step1: by using
Figure BDA00037661860500001011
A variable representing crystal growth at a microscopic scale is represented by S (ejection volume of the head per unit time):
Figure BDA00037661860500001012
the speed and position of the spray head to spray out the filament are controlled by G-code, and the volume source can be regarded as a sphere at the spray position
Figure BDA00037661860500001013
Is the diameter of the sphere, Q is the speed of the material supplied to the nozzle, v S Is the speed at which the molten material exits the spray head.
Step 2. The microscopic model obtained after the replacement of epsilon and S is:
Figure BDA0003766186050000111
Figure BDA0003766186050000112
Figure BDA0003766186050000113
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003766186050000114
is a phase field variable at the microscopic scale,
Figure BDA0003766186050000115
is a strength parameter of the crystal anisotropy,
Figure BDA0003766186050000116
are respectively
Figure BDA0003766186050000117
Partial derivatives in the x, y, z directions.
Introducing an auxiliary variable when calculating the model under the micro scale
Figure BDA0003766186050000118
The original micro model is changed into:
Figure BDA0003766186050000119
Figure BDA00037661860500001110
Figure BDA00037661860500001111
wherein the content of the first and second substances,
Figure BDA00037661860500001112
Figure BDA00037661860500001113
Figure BDA00037661860500001114
by using
Figure BDA00037661860500001115
A variable representing crystal growth at a microscopic scale is represented by S (ejection volume of the head per unit time):
Figure BDA00037661860500001116
the speed and position of the spray head to spray out the filament are controlled by G-code, and the volume source can be regarded as a sphere at the spray position
Figure BDA00037661860500001117
Is the diameter of the sphere, Q is the speed of the material supplied to the nozzle, v S Is the speed at which the molten material exits the spray head. Dispersing the model with the introduced auxiliary variables to obtain:
Figure BDA0003766186050000121
it should be noted that, the time under 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 filament on the macro scale, so the temperature disturbance effect caused by crystallization on the micro scale is covered, therefore, as long as the distribution of the temperature field is obtained by calculating the macro model, the temperature field can be substituted into the micro model, and the phase field variable under the micro scale is solved
Figure BDA0003766186050000122
The auxiliary variable is introduced to facilitate calculation, the control equation can be converted into a linear and decoupling form by introducing the auxiliary variable, and meanwhile, the discrete system is unconditionally energy-stable and allows calculation of large time step.
Varying the phase field at the microscopic scale
Figure BDA0003766186050000123
Visualization is carried out, and the purpose of simulation is achieved.
In the invention, in the solution of the model, a discrete system derives a decoupling elliptic equation, the temperature field and the phase field can be respectively solved in each time step, the solution process has an algorithm framework of large-scale parallel calculation, simultaneously, a nonlinear and coupled system is converted into a linear and decoupled format, the oscillation caused by the anisotropy of the crystal can be eliminated, and the format is unconditionally energy-stable, can be quickly converged, is simple and easy to realize, and has the characteristic of real-time repair.
FIG. 1 is a diagram of a manufacturing process involving multi-scale multi-physical field coupling. As can be seen from fig. 1, during the additive manufacturing process, the spray head moves at a given speed along a path set by the G-code and deposits a filament on the already solidified material. Macroscopically, a filament is shown, and microscopically, a crystal is shown, and the temperature distribution is different due to the difference of the distance of the filament from the spray head, and the direction of the crystal growth is different due to the difference of the crystal in the surface of the filament or in the interior of the filament. The upper left panel is a single side growth crystal and the bottom panel is a center distribution crystal growth.
Fig. 2 is a schematic diagram of a multi-scale model, and as can be seen from fig. 2, the correlation between the multi-scale spaces is highlighted. From left to right, the 3D effect that the model under the macro scale, the model under the meso scale and the model under the micro scale of the present invention can obtain is shown. At the beginning of the figure, a textured multi-scale simulation process is presented, which simulates the manufacture of a molten filament under the guidance of the G-code. For detailed probing at a small scale, the invention selects a middle slice of the numerical model. At the mesoscopic scale, the present invention has demonstrated the evolution of the interlayer path and the temperature field. In order to research the performance of the microstructure in the spraying process, the phase change behavior was compared by simulating the extrusion of a filament from a nozzle, and the process of melting the material was studied from a microscopic perspective.
Fig. 3 is a graph comparing results of different stages of numerical simulation and additive manufacturing. Referring to fig. 3 (a) - (l), the first row in fig. 3 is a multi-scale simulation process of the surface temperature distribution, and the second row is the result of additive manufacturing with PLA material. It can be seen that the proposed digital model of the invention matches closely the results of additive manufacturing with PLA material. Furthermore, it can be seen from the digital model that the heat is concentrated at the junction or inflection point, since the inflection point is the intersection of the trajectory of the spray head and the heat released by the filament, indicating that the heat distribution is closely related to the trajectory of the spray head, and that the temperature simulation of the current layer is affected not only by the moving heat source but also by the thermal diffusion of the lower layer.
Through simulation in the invention, the numerical simulation is highly matched with the actual additive manufacturing result, which shows that the track gap, the track nonuniformity and the material spheroidizing effect can be predicted in time through the numerical simulation, and the larger loss is prevented.
The invention utilizes a physical model to map the additive manufacturing process to a virtual space, relates to the coupling of a plurality of physical fields, can capture a plurality of physical phenomena such as cooling, solidification and the like of filaments, well describes the fused deposition process, and simulates the state of a material on a macro scale and a micro scale. Numerical prediction of the track non-uniformity, material spheroidizing effect and inter-track gaps of the additive manufacturing process under a multi-scale framework is the first invention to project the additive manufacturing process to a digital space. According to the invention, models are respectively established on a macro scale and a micro scale, the influence caused by high temperature of a spray head is considered in the macro model, the temperature distribution and the shape change of a prepared part can be simulated, and the AM process is projected to a virtual space by utilizing a physical model; at the mesoscopic scale, the change in thermal conductivity due to temperature is of concern in order to compensate for the lost convective heat exchange by modifying the thermal conductivity; at the microscopic scale, mainly the anisotropic nature of crystal growth is described, and the thermal strain between the material and the crystal is studied. The method is characterized in that the macroscopic model and the microscopic model are respectively dispersed, a discrete system derives a decoupling elliptic equation, a temperature field and a phase field can be respectively solved in each time step, the solving process has an algorithm framework of large-scale parallel calculation, meanwhile, the original nonlinear and coupled system is converted into a linear and decoupling format, and the format is unconditionally energy-stable, can be quickly converged, is simple and easy to realize, and has the characteristic of real-time restoration.

Claims (8)

1. A multi-scale processing simulation method for a fused deposition process is characterized by comprising the following steps:
1) Obtaining a crystal growth model according to a Lyapunov energy function;
obtaining a conduction heat transfer model according to the moving speed and the temperature of the spray head;
coupling the crystal growth model and the conduction heat transfer model by using temperature to obtain a model under a macro scale;
solving the model under the macro scale to obtain a phase field variable and a transient temperature under the macro scale;
2) Obtaining a model under the micro scale according to the phase field variable, the transient temperature, the crystal anisotropy function and the crystal growth variable under the macro scale;
substituting the temperature field into the model under the microscale, and solving to obtain a phase field variable under the microscale;
and visualizing the phase field variable under the microscale to realize simulation.
2. The fused deposition process oriented multi-scale machining simulation method as claimed in claim 1, wherein in the step 1), the crystal growth model is as follows:
Figure FDA0003766186040000011
wherein the content of the first and second substances,
Figure FDA0003766186040000012
is the gradient operator, Δ laplace operator, λ is a dimensionless parameter, and U is a dimensionless temperature.
3. The method for simulating the multi-scale processing of the fused deposition process as claimed in claim 1, wherein in the step 1), the conduction heat transfer model is as follows:
Figure FDA0003766186040000013
wherein, T is the transient temperature,
Figure FDA0003766186040000014
is the temperature gradient, rho is the density, c is the specific heat coefficient, S is the shot size of the nozzle in unit time, v p Is the moving speed of the nozzle, and q is the heat source.
4. The fused deposition process-oriented multi-scale machining simulation method as claimed in claim 1, wherein in the step 1), the model under the macro scale is as follows:
Figure FDA0003766186040000021
Figure FDA0003766186040000022
in the formula (I), the compound is shown in the specification,
Figure FDA0003766186040000023
is a gradient operator, Δ laplace operator, λ is a dimensionless parameter, U is a dimensionless temperature; t is the transient temperature, ρ is the density, c is the specific heat coefficient, and S is the unit timeShot size of nozzle touch, v p Is the moving speed of the head, and q is the heat source.
5. The method of claim 4, wherein the dimensionless temperature U is calculated by the following equation:
U＝c(T-TM)/L
in the formula, T M Is ambient temperature and L is fusion latent heat.
6. The fused deposition modeling method of claim 1, wherein in step (2), the variation of crystal growth
Figure FDA0003766186040000024
Calculated by the following formula:
Figure FDA0003766186040000025
wherein S is the jet quantity of the nozzle in unit time, and D is the diameter of the sphere.
7. The fused deposition process oriented multi-scale machining simulation method of claim 6, wherein in the step (2), the diameter D of the sphere is calculated by the following formula:
Figure FDA0003766186040000026
wherein Q is the speed of the material supplied to the head, v S Is the velocity at which the molten material exits the nozzle.
8. The fused deposition process oriented multi-scale machining simulation method of claim 6, wherein the model at the micro-scale is as follows:
Figure FDA0003766186040000027
in the formula (I), the compound is shown in the specification,
Figure FDA0003766186040000031
is a phase field variation at the microscopic scale,
Figure FDA0003766186040000032
is a strength parameter of the crystal anisotropy,
Figure FDA0003766186040000033
are respectively
Figure FDA0003766186040000034
Partial derivatives in the x, y, z directions.
CN202210886970.0A 2022-07-26 2022-07-26 Multi-scale processing simulation method for fused deposition process Pending CN115221719A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116702524A (en) * 2023-08-09 2023-09-05 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116702524A (en) * 2023-08-09 2023-09-05 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer
CN116702524B (en) * 2023-08-09 2023-10-20 华芯程(杭州)科技有限公司 Etching simulation method, device and equipment using diffusion boundary layer

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