CN114953439B - Prediction method of deposited corner outline in direct-write 3D printing - Google Patents

Prediction method of deposited corner outline in direct-write 3D printing Download PDF

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CN114953439B
CN114953439B CN202210706897.4A CN202210706897A CN114953439B CN 114953439 B CN114953439 B CN 114953439B CN 202210706897 A CN202210706897 A CN 202210706897A CN 114953439 B CN114953439 B CN 114953439B
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corner
nozzle
deposition
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陈张伟
涂勇强
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Shenzhen University
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    • B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
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Abstract

The invention discloses a prediction method of a deposited corner outline in direct-writing 3D printing, which comprises the following steps: s1, constructing a three-dimensional geometric model of a direct-writing 3D printing process, S2, carrying out grid division on the three-dimensional geometric model of the direct-writing 3D printing process constructed in the step S1, S3, setting ink material characteristics, phase fraction initial conditions, boundary conditions of each surface in the model and boundary initial conditions, S4, solving by using a fluid volume numerical method to obtain a three-dimensional image of a deposition corner, S5, adjusting the three-dimensional image of the deposition corner to overlook the deposition corner, and further obtaining the outline of the deposition corner; the prediction method achieves the purpose of predicting the outer contour of the deposition corner at any angle including an acute angle, a right angle and an obtuse angle by using a simulation method, and compared with a direct-writing 3D printing experiment, the maximum deviation of a prediction result is only 0.4mm, so that the method has better effectiveness, accuracy and practicability in the prediction of the deposition corner outer contour in direct-writing 3D printing.

Description

Prediction method of deposited corner outline in direct-write 3D printing
Technical Field
The invention relates to the technical field of numerical simulation of direct-writing 3D printing processes, in particular to a method for predicting the outline of a deposited corner in direct-writing 3D printing.
Background
Direct-writing 3D printing belongs to extrusion type additive manufacturing technology, is an advanced manufacturing technology with great development prospect, has the greatest advantages of universality of materials and flexibility of manufacturing processes, and can manufacture various metal or nonmetal materials into complex three-dimensional parts with lower cost and higher precision. The working principle of direct-writing 3D printing is as follows: firstly, preparing a material into pasty or pasty ink with shear thinning property and viscoelastic property; then, extruding the prepared ink into continuous filaments through a nozzle by using a direct-writing 3D printer; finally, the extruded filaments are stacked layer by layer to form a three-dimensional solid part.
In direct-write 3D printing, the quality of the formation of the deposited corners greatly affects the geometric dimensional accuracy of the part. In order to better control the geometric dimensional accuracy of parts manufactured by direct-write 3D printing, a numerical simulation modeling method is widely applied to analysis of direct-write 3D printing processes. For example, tu et al provide a method for predicting the topography of extruded filaments in air in direct-write 3D printing using numerical simulation (Y.Tu, A.Hassan, J.A.Arrieta-Escobar, et al Modeling and evaluation of freeform extruded filament based on numerical simulation method for direct ink writing, the International Journal of Advanced Manufacturing Technology 120 (5) (2022) 3821-3829); the invention patent with the application number of CN2022104982687 discloses a cross section prediction method of deposited filaments in direct-writing printing based on numerical simulation; comminal et al constructed a model of the deposited corners in extruded 3D printing using numerical simulations (R.Comminal, M.P.Serdeczny, D.B.Pedersen, et al motion planning and numerical simulation of material deposition at corners in extrusion additive manufacturing, additive Manufacturing 29 (2019) 100753.).
However, the above-mentioned existing numerical simulation modeling and prediction method for a deposition corner in direct-writing 3D printing can only construct a model of a deposition corner with a small angle smaller than 90 °, and has a defect that the deposition corner with any angle cannot be predicted. Accordingly, to overcome the deficiencies of the prior art, there is a need to provide an improved numerical simulation method that predicts the deposited corner outer contours in write-through 3D printing at arbitrary angles.
Disclosure of Invention
The invention aims to provide a prediction method for accurately predicting the deposition corner outline in direct-write 3D printing, which has any angle in the direct-write 3D printing.
For this purpose, the technical scheme of the invention is as follows:
a prediction method of deposited corner outline in direct-writing 3D printing comprises the following steps:
1. a prediction method of deposited corner outline in direct-writing 3D printing is characterized by comprising the following steps:
s1, constructing a three-dimensional geometric model of a direct-writing printing process, wherein the three-dimensional geometric model consists of a first calculation area and a second calculation area; the outer contour of the first calculation area is a three-dimensional cuboid, the top surface, the back surface, the left side surface and the right side surface of the first calculation area are air boundary surfaces, the front surface of the first calculation area is a first bonding surface, and the bottom surface of the first calculation area is a first deposition substrate surface; a cylindrical blind hole is vertically and downwards formed in the top surface of one side of the three-dimensional cuboid, the diameter of the cylindrical blind hole is equal to the outer diameter of a nozzle in the direct-writing 3D printer, and the inner side surface of the cylindrical blind hole is the outer surface of the nozzle; a cylindrical boss is arranged in the center of the cylindrical blind hole, the diameter of the cylindrical boss is equal to the inner diameter of the nozzle, the top surface of the cylindrical boss is flush with the top surface of the three-dimensional cuboid, the bottom surface of the cylindrical boss is flush with the bottom surface of the blind hole, the top surface of the cylindrical boss is a nozzle inlet surface, and the outer side surface of the cylindrical boss is a nozzle inner surface; the annular bottom surface of the cylindrical blind hole between the inner side surface of the cylindrical blind hole and the outer side surface of the cylindrical boss is the bottom surface of the nozzle; the second calculation area is a three-dimensional cuboid consistent with the outer contour of the first calculation area, the front surface, the top surface, the left side surface and the right side surface of the second calculation area are air boundary surfaces, the back surface of the second calculation area is a second combination surface, and the bottom surface of the second calculation area is a second deposition substrate surface; the second bonding surface is completely overlapped with the first bonding surface;
s2, meshing the three-dimensional geometric model of the direct-writing printing process constructed in the step S1, wherein the principle is as follows: 1) The density maximum grid is divided from the inner surface of the nozzle to the cylindrical area formed in the nozzle and consistent with the inner diameter of the nozzle, and from the bottom surface of the nozzle to the cylindrical area formed between the projection surfaces of the first deposition substrate surface and consistent with the outer diameter of the nozzle; 2) The horizontal section of the bottom surface of the nozzle is taken as an interface, and the grids divided by the lower area of the nozzle are denser than the grids divided by the upper area of the nozzle;
s3, setting ink material characteristics, phase fraction initial conditions, boundary conditions of each surface and boundary initial conditions in simulation; wherein, the liquid crystal display device comprises a liquid crystal display device,
(1) Ink material properties include density ρ, surface tension coefficient σ, and viscosity μ;
(2) The initial conditions of the phase fraction are: the phase fraction from the inner surface of the nozzle to the inner region of the nozzle (i.e. the region where the cylindrical boss is located) is 1, and the phase fraction of the other regions is 0;
(3) The boundary conditions and boundary initial conditions of the respective surfaces are:
(1) setting the boundary type of the inlet face of the nozzle as an inlet boundary, wherein the boundary conditions comprise: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is the ink speed of the nozzle inlet;
(2) setting the boundary types of the inner surface, the outer surface and the bottom surface of the nozzle as non-slip boundaries, and corresponding to non-slip conditions; the boundary condition is a slip-free condition, specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is 0mm/s;
(3) setting the boundary type of the air boundary surface as an input/output boundary, and calculating corresponding boundary conditions in real time through simulation; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is 0mm/s;
(4) setting the boundary type of the first deposition substrate surface as a slip-free boundary, and corresponding to a slip-free condition, specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: an initial pressure of 0MPa and an initial velocity of v n1 ，v n1 Is equal to the horizontal moving speed of the nozzle, v n1 The included angle between the direction of the first joint surface and the first joint surface is theta/2;
(5) the boundary type of the second deposition substrate surface 202 is set as a slip-free boundary, and the slip-free condition is specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: an initial pressure of 0MPa and an initial velocity of v n2 ，v n2 Is equal to the horizontal moving speed of the nozzle, v n2 Is in the direction of v n1 The included angle of (a) is theta, and theta is the angle of a deposition corner;
s4, solving by using a fluid volume numerical method to obtain a three-dimensional image of a deposition corner, and outputting a corresponding geometric file;
s5, importing the geometric file of the three-dimensional image of the deposition corner obtained in the step S4 into post-processing software, and adjusting the three-dimensional image of the deposition filament to an image in a mode of overlooking the deposition corner so as to obtain the outline of the deposition corner.
Further, the specific method in step S4 is as follows: and solving the phase fraction of each grid by using a fluid volume numerical method, and taking a curved surface with the phase fraction value of 0.5 as the three-dimensional shape of the deposited filament.
Further, the steps S1 to S4 are implemented by using OpenFORM software.
Further, step S5 is implemented using ParaView software.
Compared with the prior art, the method for predicting the outer contour of the deposition corner in the direct-writing 3D printing solves the problem that the existing direct-writing 3D printing simulation method cannot predict the deposition corner at any angle, achieves the purpose of predicting the outer contour of the deposition corner at any angle including an acute angle, a right angle and an obtuse angle by using the simulation method, and has the advantages that the maximum deviation of the prediction result is only 0.4mm according to the comparison between the direct-writing 3D printing reality and the prediction result, so that the method has better effectiveness, accuracy and practicability in the prediction of the outer contour of the deposition corner in the direct-writing 3D printing.
Drawings
FIG. 1 is a flow chart of a method for predicting deposited corner outline in direct-write 3D printing according to the present invention;
FIG. 2 is a schematic diagram of a complete three-dimensional geometric model of a direct-write 3D printing process constructed in step S1 according to the method for predicting deposition corner outer contours in direct-write 3D printing of the present invention;
FIG. 3 is a schematic diagram of a first calculation region in a three-dimensional geometric model of a direct-write 3D printing process constructed in step S101 in a method for predicting a deposited corner outline in direct-write 3D printing of the present invention;
FIG. 4 is a schematic diagram of key geometric parameters of a first calculation region in a three-dimensional geometric model of a direct-write 3D printing process constructed in step S101 according to a method for predicting a deposited corner outline in direct-write 3D printing of the present invention;
FIG. 5 is a schematic diagram of a second calculation region in the three-dimensional geometric model of the direct-write 3D printing process constructed in step S102 in the method for predicting the deposition corner outline in direct-write 3D printing of the present invention;
FIG. 6 (a) is a grid-partitioned overall schematic diagram of the three-dimensional geometric model obtained in step S2 by the method for predicting the deposited corner outline in direct-write 3D printing of the present invention;
FIG. 6 (b) is a schematic diagram of the grid division of the three-dimensional geometric model obtained in step S2 in the first calculation region by the method for predicting the deposited corner outline in direct-write 3D printing of the present invention;
FIG. 6 (c) is a schematic diagram of the grid division of the three-dimensional geometric model obtained in step S2 in the second calculation region by the method for predicting the deposited corner outline in direct-write 3D printing of the present invention;
FIG. 7 is a schematic diagram of initial conditions of phase fraction set in step S3 in the method for predicting deposited corner outline in direct-write 3D printing according to the present invention;
FIG. 8 is a schematic diagram showing the direction of the speeds of the first deposition substrate and the second deposition substrate set in step S3 according to the method for predicting the deposition corner outline in direct-write 3D printing of the present invention;
fig. 9 (a) is a schematic view of a three-dimensional geometric model of a predicted deposition corner in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention is set to 60 ° in the present embodiment;
fig. 9 (b) is a schematic view of a three-dimensional geometric model of a predicted deposition corner in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention is set to 90 ° in the present embodiment;
fig. 9 (c) is a schematic view of a three-dimensional geometric model of a predicted deposition corner in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention is set to 120 ° in the present embodiment;
fig. 10 (a) is an outline schematic diagram of a predicted deposition corner in the case where a corner obtained by a prediction method of a deposition corner outline in direct-write 3D printing of the present invention is set to 60 ° in the present embodiment;
fig. 10 (b) is an outline schematic diagram of a predicted deposition corner in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention is set to 90 ° in the present embodiment;
fig. 10 (c) is an outline schematic diagram of a predicted deposition corner in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention is set to 120 ° in the present embodiment;
FIG. 11 (a) is a diagram showing the comparison of the predicted outer contour of the deposited corner with the outer contour of the deposited corner set to 60℃obtained by the method for predicting the outer contour of the deposited corner in direct-write 3D printing according to the present embodiment;
FIG. 11 (b) is a diagram showing the comparison of the predicted outer contour of the deposited corner with the experimental result outer contour in the case where the corner obtained by the method for predicting the outer contour of the deposited corner in direct-write 3D printing of the present invention is set to 90 deg. in this embodiment;
fig. 11 (c) is a schematic diagram showing the comparison of the outline of the predicted deposition corner with the experimental result outline in the case where the corner obtained by the prediction method of the deposition corner outline in direct-write 3D printing of the present invention was set to 120 °.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and specific examples, which are in no way limiting.
In this embodiment, the outline prediction of the deposition corner of a certain ink in the direct-write 3D printing is further explained, and the direct-write 3D printing experiment is performed by the experimental setting under the same condition as in the prediction method, so as to verify the validity and accuracy of the method.
As shown in fig. 1, the specific steps of the method for predicting the deposited corner outline in direct-writing 3D printing are as follows:
s1, for a complete three-dimensional geometric model of a direct-write 3D printing process, boundary surfaces of the three-dimensional geometric model comprise a nozzle inlet surface 101, a nozzle inner surface 102, a nozzle outer surface 103, a nozzle bottom surface 104, an air boundary surface 105, a first deposition substrate surface 106 and a second deposition substrate surface 202; thus, as shown in fig. 2, a three-dimensional geometric model of a direct-write 3D printing process of a calculation domain is first constructed, the model being composed of two calculation regions, a first calculation region 1 and a second calculation region 2, respectively;
specifically, the specific steps of this step S1 are as follows:
s101, constructing a first calculation area 1 of a three-dimensional geometric model of a direct-writing 3D printing process; in particular, the method comprises the steps of,
as shown in fig. 3, the outer contour of the first calculation region 1 of the three-dimensional geometric model in the direct-writing 3D printing process is a three-dimensional cuboid, the top surface, the back surface, the left side surface and the right side surface of the three-dimensional cuboid are air boundary surfaces 105, the front surface of the three-dimensional cuboid is a first bonding surface 107, and the bottom surface of the three-dimensional cuboid is a first deposition substrate surface 106; a cylindrical blind hole is vertically downwards formed in the top surface of one side of the three-dimensional cuboid, and the diameter of the cylindrical blind hole is equal to the outer diameter of a nozzle in the direct-writing 3D printer; a cylindrical boss with the diameter smaller than the inner diameter of the cylindrical blind hole is arranged in the center of the cylindrical blind hole, the diameter of the cylindrical boss is equal to the inner diameter of the nozzle, the top surface of the cylindrical boss is flush with the top surface of the three-dimensional cuboid, and the bottom surface of the cylindrical boss is flush with the bottom surface of the blind hole; the top surface of the cylindrical boss is a nozzle inlet surface 101, the outer side surface of the cylindrical boss is a nozzle inner surface 102, the inner side surface of the cylindrical blind hole is a nozzle outer surface 103, and the annular bottom surface of the cylindrical blind hole between the inner side surface of the cylindrical blind hole and the outer side surface of the cylindrical boss is a nozzle bottom surface 104;
as shown in fig. 4, in the first calculation area 1 of the three-dimensional geometric model of the direct-writing 3D printing process, the key geometric parameters include: nozzle inner diameter d n Nozzle outer diameter D n Nozzle height L n And the distance h from the bottom surface of the nozzle to the deposition substrate;
s102, constructing a second calculation region 2 of the three-dimensional geometric model of the direct-writing 3D printing process;
as shown in fig. 5, the outer contour of the second calculation region 2 of the three-dimensional geometric model in the direct-writing 3D printing process is a three-dimensional cuboid consistent with the outer contour of the first calculation region 1 constructed in step S101, and the front, top, left side and right side of the three-dimensional cuboid are air boundary surfaces 105; the back of the three-dimensional cuboid is a second bonding surface 201; the bottom surface of the three-dimensional cuboid is a second deposition substrate surface 202;
s103, as shown in FIG. 2, the first calculation region 1 constructed in the step S101 and the second calculation region 2 constructed in the step S102 are combined into a three-dimensional geometric model of a complete direct-writing 3D printing process by aligning and completely overlapping the first bonding surface 107 of the first calculation region 1 and the second bonding surface 201 of the second calculation region 2;
in this embodiment, the three-dimensional geometric model of the direct-write 3D printing process is constructed based on the actual size of the selected direct-write 3D printing; according to the actual size measurement of direct-writing 3D printing, the inner diameter D of the nozzle n =0.84 mm, nozzle outer diameter D n Nozzle height L =1.22 mm n =2.44 mm; the distance h from the bottom surface of the nozzle to the deposition substrate was set to 0.75mm; based on the method, the three-dimensional geometric model of the direct-write 3D printing process utilizes OpenFOAM software (OpenFOAM v 1912), and the three-dimensional geometric model of the direct-write 3D printing process which is consistent with the actual direct-write 3D printing process is constructed by sequentially carrying out boundary point coordinate definition, different types of block division and boundary determination on the model in a block mesh component of the software;
s2, performing grid division on the three-dimensional geometric model constructed in the step S1 in calculation;
in order to ensure the accuracy of the deposition corner outline prediction result and minimize the calculation time, the principle of grid division of the three-dimensional geometric model for the direct-writing 3D printing process is as follows:
1) The area of the cylindrical shape (i.e. the area where the cylindrical boss is located) formed from the inner surface 102 of the nozzle to the inner diameter of the nozzle and the area of the cylindrical shape (i.e. the area where the cylindrical boss is located) formed from the bottom surface 104 of the nozzle to the cylindrical area where the outer diameter of the cylindrical shape formed between the projection surfaces of the first deposition substrate surface 106 is consistent with the outer diameter of the nozzle are all divided with the maximum density grid;
2) The cross section of the bottom surface 104 of the nozzle (i.e. the cross section parallel to the surface of the deposition substrate) is taken as an interface, and the grids divided by the lower area are denser than the grids divided by the upper area;
in the embodiment, in the step S2, openFOAM software (OpenFOAM v 1912) is adopted as mesh dividing software, and specifically, a block mesh component in the software is utilized to realize mesh division on the three-dimensional geometric model of the direct-writing 3D printing process established in the step S1; specifically, as shown in fig. 6 (a), a grid-divided overall schematic diagram of the three-dimensional geometric model in the present embodiment; FIG. 6 (b) is a schematic diagram showing the meshing of the three-dimensional geometric model in the present embodiment in the first calculation region; FIG. 6 (c) is a diagram showing the meshing of the three-dimensional geometric model in the present embodiment in the second calculation region; wherein the maximum single-side dimension of the grid divided from the nozzle inner surface 102 to the inside of the nozzle in the cylindrical region formed in accordance with the inner diameter of the nozzle and from the nozzle bottom surface 104 to the inside of the cylindrical region formed between the projection surfaces of the first deposition substrate surface 106 in accordance with the outer diameter of the nozzle is 0.1mm in the transverse cross section; taking the horizontal section of the nozzle bottom surface 104 in the three-dimensional model as an interface, wherein the maximum dimension of the grid divided by the lower area in the height direction is 0.1mm, and the maximum dimension of the grid divided by the upper area in the height direction is 0.4mm, so that the grid divided by the lower area of the interface in the three-dimensional model is denser than the grid divided by the upper area of the interface;
s3, setting ink material characteristics, phase fraction initial conditions, boundary conditions of each surface and boundary initial conditions in simulation;
specifically, the specific operation steps of the step S3 are as follows:
s301, setting the density rho, the surface tension coefficient sigma and the viscosity mu of the ink material in simulation; wherein, the density ρ and the surface tension coefficient sigma are constants and can be directly obtained by the ink material parameter test; the viscosity μ varies with the shear rate, and therefore the formula is used:
Figure BDA0003705731170000081
wherein μ is the viscosity of the ink, ">
Figure BDA0003705731170000082
Mu, shear rate 0 For zero shear viscosity of ink, τ 0 Is the yield stress of the ink, K is the viscosity coefficient of the ink, and n is the rheological coefficient of the ink; mu (mu) 0 ，τ 0 K, n are obtained by material parameter test of the ink;
in this embodiment, the settings of the ink material characteristics (including density ρ, surface tension coefficient σ, and viscosity μ) in the simulation are set using transport Properties in a constant folder in the simulation file under OpenFOAM software (OpenFOAM v 1912); specifically, in this embodiment, the material characteristics of a certain ink used are: density ρ=972 kg/m 3 The surface tension coefficient σ=43 mN/m, the viscosity μ of the ink varies with the shear rate, and is expressed by the formula
Figure BDA0003705731170000091
In the formula, < >>
Figure BDA0003705731170000092
Zero shear viscosity μ for shear rate 0 ＝1.58×10 6 Pa.s, yield stress τ 0 =563 Pa, viscosity coefficient k=867 pa·s n Rheological coefficient n=0.045;
s302, setting phase fraction initial conditions in simulation:
at the initial time of the write-through 3D printing process, the ink fills the nozzles and has not been extruded yet; based on this, the initial conditions for setting the phase fraction are: the phase fraction from the nozzle inner surface 102 to the nozzle inner region (i.e., the region where the cylindrical boss is located) is 1, and the phase fraction of the other regions is 0; as shown in fig. 7, darker areas represent a phase score of 1 and lighter areas represent a phase score of 0;
in this embodiment, the phase fraction initial condition is set using the set Fields Dict file in the system folder in the simulation file under OpenFOAM software (OpenFOAM v 1912): the phase fraction from the nozzle inner surface 102 to the nozzle inner region is 1, and the region phase fraction of the other regions is 0;
s303, setting boundary conditions and boundary initial conditions of each surface in simulation, wherein the specific setting mode is as follows:
(1) the type of boundary of the nozzle inlet face 101 is set as the inlet boundary, and the velocity is set as the ink velocity v of the nozzle inlet e ；
(2) Setting the boundary types of the inner surface 102, the outer surface 103 and the bottom surface 104 of the nozzle as slip-free boundaries, and corresponding to slip-free conditions;
(3) setting the boundary type of the air boundary surface 105 as an input/output boundary, and calculating corresponding boundary conditions in real time through simulation;
(4) setting the boundary type of the first deposition substrate surface 106 to be a slip-free boundary, and setting the speed to v in response to a slip-free condition n1 ，v n1 Is equal to the horizontal movement velocity v of the nozzle relative to the deposition substrate n See fig. 8,v n1 Is at an angle θ/2 to the first bonding surface 107, where θ is the angle of the deposited corner;
(5) setting the boundary type of the second deposition substrate surface 202 to be a slip-free boundary, and setting the speed to v in response to the slip-free condition n2 ，v n2 Numerical value of (v) and v n1 The same value of (a) is equal to the horizontal movement velocity v of the nozzle relative to the deposition substrate n See fig. 8,v n2 Is in the direction of v n1 The included angle of (a) is theta, and theta is the angle of a deposition corner;
in this embodiment, the boundary condition and the initial condition are set by using the p_ rhg file and the U file under the 0 folder in the simulation file of the OpenFOAM software (OpenFOAM v 1912); specifically, the p_ rhg file is used for setting the pressure boundary condition and the pressure initial condition of each surface, and the U file is used for setting the speed boundary condition and the speed initial condition of each surface; specific settings are shown in table 1 below;
table 1:
Figure BDA0003705731170000101
in this embodiment, in order to fully verify the effectiveness and accuracy of the method for depositing the corner outline in direct-write 3D printing provided by the invention for predicting the corner outline deposited at any angle, θ is set to 60 °, 90 ° and 120 °, respectively, to correspond to the situations of depositing the corner at any angle including acute angle, right angle and obtuse angle, respectively;
s4, solving by using a fluid volume numerical method to obtain a three-dimensional shape of a deposition corner;
solving the boundary of the ink extrusion filament and air by adopting a fluid volume method to obtain the shape of the ink extrusion filament and the corner, namely, taking the ink and the air as single continuous fluid, obtaining the phase fraction of each grid in the continuous fluid by constructing and solving a control equation of the single continuous fluid, and determining the shape of the extrusion filament by using a contour line with the phase fraction equal to 0.5; the specific solving process is as follows:
(1) Phase fraction is defined as
Figure BDA0003705731170000111
Wherein α is a phase fraction of a grid; v (V) b A volume of ink in the grid; v (V) m Is the total volume of the grid; wherein, the value of alpha is known from the definition of the phase fraction:
Figure BDA0003705731170000112
(2) The density and viscosity of the ink and air equivalent single continuous fluid are obtained from the phase fractions:
Figure BDA0003705731170000113
wherein ρ is the density of a single continuous fluid equivalent to ink and air; μ is the viscosity of the ink and air equivalent single continuous fluid; alpha is the phase fraction of a grid; ρ b Is the density of the ink; mu (mu) b Is the viscosity of the ink; ρ a Is the density of air; mu (mu) a Is the viscosity of air;
(3) Constructing a control equation in simulation, wherein the control equation consists of a continuity equation, a momentum conservation equation and a phase fraction equation; in particular, the method comprises the steps of,
(1) the continuity equation is:
Figure BDA0003705731170000114
in the method, in the process of the invention,
Figure BDA0003705731170000115
representing a divergence operator; u is the velocity field vector of a single continuous fluid equivalent of ink and air;
(2) the conservation of momentum equation is:
Figure BDA0003705731170000116
wherein t is time,
Figure BDA0003705731170000117
representing the vector versus time one-time derivative symbol, ρ being the density of the ink and air equivalent single continuous fluid, U being the velocity field vector of the ink and air equivalent single continuous fluid, +.>
Figure BDA0003705731170000118
Representing the divergence operator, ++>
Figure BDA0003705731170000119
Representing the gradient operator, p is the pressure scalar of the ink and air equivalent single continuous fluid, μ is the viscosity of the ink and air equivalent single continuous fluid, g is the gravitational acceleration vector, F σ Is a surface tension vector;
wherein, the surface tension vector formula is:
Figure BDA0003705731170000121
wherein σ is the surface tension coefficient of the ink; kappa is the surface shape curvature of the ink extruded filament, and kappa is determined by the shape calculated in real time during simulation; />
Figure BDA0003705731170000122
Representing gradient operators; alpha is the phase fraction of a grid;
(3) the phase fraction equation is:
Figure BDA0003705731170000123
wherein t is time,
Figure BDA0003705731170000124
one-time derivative symbol representing vector versus time, +.>
Figure BDA0003705731170000125
Representing the divergence operator, U is the velocity field vector of a single continuous fluid equivalent of ink and air, U r Is the velocity difference of the two fluids of ink and air on the surface of the extruded filament;
wherein U is r The formula is:
Figure BDA0003705731170000126
where min () represents a minimum operator, max () represents a maximum operator, i represents an absolute operator,
Figure BDA0003705731170000127
representing a gradient operator, c being a compression constant, c=1;
(4) Substituting the ink material characteristics, the initial conditions and the boundary conditions in the simulation set in the step S3 into the equations in the steps (1) - (3) so as to solve the phase fraction of each grid, and taking a curved surface with the phase fraction value of 0.5 as a three-dimensional image of a deposited corner; outputting a corresponding geometric file based on the obtained three-dimensional image of the deposition corner;
in this embodiment, using the inter FOAM solver value provided in OpenFOAM software (OpenFOAM v 1912), setting the ink material characteristics, the phase fraction initial conditions, and the boundary conditions and boundary initial conditions of each surface in the three-dimensional geometric model of the direct-write 3D printing process by using the three-dimensional geometric model of the direct-write 3D printing process subjected to the mesh division obtained in step S1 and step S2 and step S3, so as to solve the phase fraction of each mesh, wherein the curved surface with the phase fraction value of 0.5 is the three-dimensional shape of the deposited corner; fig. 9 (a) is a schematic diagram showing a three-dimensional geometric model of a deposited filament obtained by resolving by using the method for predicting the outer contour of a deposited corner in direct-writing 3D printing according to the present invention in the case where the deposited corner is set to 60 ° in the present embodiment; fig. 9 (b) is a schematic diagram showing a three-dimensional geometric model of a deposited filament obtained by resolving by using the method for predicting the outer contour of a deposited corner in direct-writing 3D printing according to the present invention in the case where the deposited corner is set to 90 ° in the present embodiment; fig. 9 (c) is a schematic diagram showing a three-dimensional geometric model of a deposited filament obtained by resolving by using the method for predicting the outer contour of a deposited corner in direct-writing 3D printing according to the present invention in the case where the deposited corner is set to 120 ° in the present embodiment;
s5, importing the geometric file of the three-dimensional image of the deposition corner obtained in the step S4 into post-processing software, and adjusting the three-dimensional image of the deposition corner to an image in a mode of overlooking the deposition corner so as to obtain the outline of the deposition corner:
in this embodiment, the three-dimensional geometric model of the predicted deposition corner obtained in step S4 is output in the form of a geometric file, the geometric file is imported into the post-processing software ParaView 5.8.0, and the deposition corner is placed in a top view direction by using the view direction adjustment function in the ParaView 5.8.0, so that the outer contour of the predicted deposition corner as shown in fig. 10 (a), 10 (b) and 10 (c) can be obtained; fig. 10 (a), 10 (b) and 10 (c) show the outer contours of the predicted deposition corners obtained in three cases where θ is set to 60 °, 90 ° and 120 °, respectively.
In order to verify the accuracy of the prediction method provided by the application, the ink is filled in an actual direct-writing 3D printer, direct-writing 3D printing is performed under the same process conditions as those set in simulation to obtain deposited filaments, and simultaneously, after printing is finished, a ruler is placed on the edge of a deposited corner; then shooting a deposition corner placed on the edge of the ruler by using a camera perpendicular to the substrate so as to obtain an experimental result photo of the outer contour of the deposition corner with the ruler; and processing the experimental result containing the outer contour of the deposition corner and the photo of the ruler, obtaining an outer contour curve of the deposition corner which is actually printed according to the comparison of the outer contour of the deposition corner and the ruler scale, and importing the outer contour curve into a top view image of the simulation result of the deposition corner, thereby obtaining the comparison of the simulation result of the deposition corner and the experimental result. As shown in fig. 11 (a), 11 (b) and 11 (c), the predicted results and experimental results of the deposition corner outer contours in the three cases where the deposition corner θ is set to 60 °, 90 ° and 120 °, respectively; as can be seen from the comparison chart, the method for predicting the outer contour of the deposition corner in direct-writing 3D printing can predict the deposition corner at any angle including an acute angle, a right angle and an obtuse angle, overcomes the problem that the conventional method cannot predict the deposition corner at any angle, and has good effectiveness and practicability; meanwhile, as can be further obtained from fig. 11 (a), 11 (b) and 11 (c), the maximum deviation between the predicted result and the actual experimental result is 0.4mm, which proves the accuracy of the method provided by the invention in the deposition corner outline prediction in direct-writing 3D printing.
The invention, in part, is not disclosed in detail and is well known in the art. While the foregoing describes illustrative embodiments of the present invention to facilitate an understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, but is to be construed as protected by the accompanying claims insofar as various changes are within the spirit and scope of the present invention as defined and defined by the appended claims.

Claims (4)

1. A prediction method of deposited corner outline in direct-writing 3D printing is characterized by comprising the following steps:
s1, constructing a three-dimensional geometric model of a direct-writing 3D printing process, wherein the three-dimensional geometric model consists of a first calculation area and a second calculation area; the outer contour of the first calculation area is a three-dimensional cuboid, the top surface, the back surface, the left side surface and the right side surface of the first calculation area are air boundary surfaces, the front surface of the first calculation area is a first bonding surface, and the bottom surface of the first calculation area is a first deposition substrate surface; a cylindrical blind hole is vertically and downwards formed in the top surface of one side of the three-dimensional cuboid, the diameter of the cylindrical blind hole is equal to the outer diameter of a nozzle in the direct-writing 3D printer, and the inner side surface of the cylindrical blind hole is the outer surface of the nozzle; a cylindrical boss is arranged in the center of the cylindrical blind hole, the diameter of the cylindrical boss is equal to the inner diameter of the nozzle, the top surface of the cylindrical boss is flush with the top surface of the three-dimensional cuboid, the bottom surface of the cylindrical boss is flush with the bottom surface of the blind hole, the top surface of the cylindrical boss is a nozzle inlet surface, and the outer side surface of the cylindrical boss is a nozzle inner surface; the annular bottom surface of the cylindrical blind hole between the inner side surface of the cylindrical blind hole and the outer side surface of the cylindrical boss is the bottom surface of the nozzle; the second calculation area is a three-dimensional cuboid consistent with the outer contour of the first calculation area, the front surface, the top surface, the left side surface and the right side surface of the second calculation area are air boundary surfaces, the back surface of the second calculation area is a second combination surface, and the bottom surface of the second calculation area is a second deposition substrate surface; the second bonding surface is completely overlapped with the first bonding surface;
s2, meshing the three-dimensional geometric model of the direct-writing printing process constructed in the step S1, wherein the principle is as follows: 1) The density maximum grid is divided from the inner surface of the nozzle to the cylindrical area formed in the nozzle and consistent with the inner diameter of the nozzle, and from the bottom surface of the nozzle to the cylindrical area formed between the projection surfaces of the first deposition substrate surface and consistent with the outer diameter of the nozzle; 2) The horizontal section of the bottom surface of the nozzle is taken as an interface, and the grids divided by the lower area of the nozzle are denser than the grids divided by the upper area of the nozzle;
s3, setting ink material characteristics, phase fraction initial conditions, boundary conditions of each surface and boundary initial conditions in simulation; wherein, the liquid crystal display device comprises a liquid crystal display device,
(1) Ink material properties include density ρ, surface tension coefficient σ, and viscosity μ;
(2) The initial conditions of the phase fraction are: the phase fraction from the inner surface of the nozzle to the inner region of the nozzle, namely the region where the cylindrical boss is located is 1, and the phase fraction of other regions is 0;
(3) The boundary conditions and boundary initial conditions of the respective surfaces are:
(1) setting the boundary type of the inlet face of the nozzle as an inlet boundary, wherein the boundary conditions comprise: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is the ink speed of the nozzle inlet;
(2) setting the boundary types of the inner surface, the outer surface and the bottom surface of the nozzle as non-slip boundaries, and corresponding to non-slip conditions; the boundary condition is a slip-free condition, specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is 0mm/s;
(3) setting the boundary type of the air boundary surface as an input/output boundary, and calculating corresponding boundary conditions in real time through simulation; the boundary initial conditions are: the initial pressure is 0MPa, and the initial speed is 0mm/s;
(4) setting the boundary type of the first deposition substrate surface as a slip-free boundary, and corresponding to a slip-free condition, specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: an initial pressure of 0MPa and an initial velocity of v n1 ，v n1 Is equal to the horizontal moving speed of the nozzle, v n1 The included angle between the direction of the first joint surface and the first joint surface is theta/2;
(5) setting the boundary type of the second deposition substrate surface as a slip-free boundary, and corresponding to a slip-free condition, specifically: the pressure is zero gradient pressure, and the speed is constant; the boundary initial conditions are: an initial pressure of 0MPa and an initial velocity of v n2 ，v n2 Is equal to the horizontal moving speed of the nozzle, v n2 Is in the direction of v n1 The included angle of (a) is theta, and theta is the angle of a deposition corner;
s4, solving by using a fluid volume numerical method to obtain a three-dimensional image of a deposition corner, and outputting a corresponding geometric file;
s5, importing the geometric file of the three-dimensional image of the deposition corner obtained in the step S4 into post-processing software, and adjusting the three-dimensional image of the deposition filament to an image in a mode of overlooking the deposition corner so as to obtain the outline of the deposition corner.
2. The method for predicting the deposited corner outline in direct-write 3D printing according to claim 1, wherein the specific method in step S4 is as follows: and solving the phase fraction of each grid by using a fluid volume numerical method, and taking a curved surface with the phase fraction value of 0.5 as the three-dimensional shape of the deposited corner.
3. The method for predicting deposited corner outline in direct-write 3D printing according to claim 1, wherein steps S1 to S4 are implemented using OpenFORM software.
4. The method for predicting deposited corner outline in direct-write 3D printing according to claim 1, wherein step S5 is implemented using ParaView software.
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