CN114834045A - Ink-jet 3D printing modeling and compensating method and closed-loop printing system - Google Patents
Ink-jet 3D printing modeling and compensating method and closed-loop printing system Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
- B29C64/30—Auxiliary operations or equipment
- B29C64/386—Data acquisition or data processing for additive manufacturing
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29C—SHAPING OR JOINING OF PLASTICS; SHAPING OF MATERIAL IN A PLASTIC STATE, NOT OTHERWISE PROVIDED FOR; AFTER-TREATMENT OF THE SHAPED PRODUCTS, e.g. REPAIRING
- B29C64/00—Additive manufacturing, i.e. manufacturing of three-dimensional [3D] objects by additive deposition, additive agglomeration or additive layering, e.g. by 3D printing, stereolithography or selective laser sintering
- B29C64/30—Auxiliary operations or equipment
- B29C64/386—Data acquisition or data processing for additive manufacturing
- B29C64/393—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B33—ADDITIVE MANUFACTURING TECHNOLOGY
- B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- B33Y50/00—Data acquisition or data processing for additive manufacturing
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B33—ADDITIVE MANUFACTURING TECHNOLOGY
- B33Y—ADDITIVE MANUFACTURING, i.e. MANUFACTURING OF THREE-DIMENSIONAL [3-D] OBJECTS BY ADDITIVE DEPOSITION, ADDITIVE AGGLOMERATION OR ADDITIVE LAYERING, e.g. BY 3-D PRINTING, STEREOLITHOGRAPHY OR SELECTIVE LASER SINTERING
- B33Y50/00—Data acquisition or data processing for additive manufacturing
- B33Y50/02—Data acquisition or data processing for additive manufacturing for controlling or regulating additive manufacturing processes
Abstract
The invention belongs to the technical field of ink-jet printing micro-manufacturing, and discloses an ink-jet 3D printing modeling and compensating method and a closed-loop printing system, which comprise the following steps: according to the relation between the spreading contact angle of the liquid drop and the roughness of the deposition surface, establishing a height evolution model of the ink-jet 3D printing part forming process, and describing a dynamic process of the height profile of the part; after printing a layer of pattern, measuring the height profile of the printed part by using a surface topography measuring device; according to the measurement profile, the reference profile and the established model, an algorithm is designed to generate a compensation pattern which is used as a next layer of printing pattern; and finishing printing all the layers to obtain a printing sample piece. And the measurement result is brought into a control algorithm to form a closed loop in the printing process, so that the surface quality and the electrical property of the molded part are effectively improved.
Description
Technical Field
The invention belongs to the technical field of inkjet printing micro-manufacturing, and particularly relates to an inkjet 3D printing modeling and compensating method and a closed-loop printing system.
Background
Inkjet 3D printing ejects a photocurable material in the form of tiny droplets through a nozzle and builds up a three-dimensional object by layer-by-layer curing. Inkjet 3D printing enables the formation of complex patterns and enables high precision, high resolution deposition of multiple materials. At present, the technology is applied to the fields of printed electronics and the like. In this field, it is commonly used for producing sensors, antennas, circuit boards, etc. Many electronic devices, such as microstrip patch antennas, have a significant impact on their electrical performance due to surface topography. However, during printing, the deposition surface characteristics cause the drop spreading topography to change. After the layers are stacked layer by layer, the effect is amplified continuously, the problem that the surface of a printed part is uneven is particularly obvious, and the electrical property of an electronic device is influenced finally. However, conventional inkjet 3D printing typically operates in an open-loop manner, i.e., the drop pattern printed per layer is predetermined and not adjusted according to the results of feedback measurements ([1] y.guo, j.pets, t.oomen, and s.mishra, "Control-oriented models for ink-jet 3D printing," mechanics, vol.56, pp.211-219, May 2018.). This printing method can cause the printing process to be influenced by some uncertain factors: such as uncertainty of position, shape and size of the liquid drops, and flowing and fusion of the liquid drops in the printing process, the printed parts may have defects, such as uneven printed surface, which further affects the performance of the printing device, so that the quality and stability of the printed sample are not high, and the improvement of the performance of the three-dimensional printing functional part is severely restricted. Therefore, a proper model needs to be established for the inkjet 3D printing process, feedback measurement results are incorporated into a control algorithm, and closed-loop control is performed on the existing printing process to further improve the printing quality and the stability of the printing system. Conventional finite element models ([2] radial Comminal, Marcin P.Serdczny, David B.Pedersen, and Jon Spanggenberg. numerical modeling of the strand displacement flow in excess-based additive Manufacturing,20: 68-76,2018; [3] GL Knapp, T Mukherjee, JS Zuback, HL Wei, TA Palmer, A De, and T DebRoy. structural blocks for a digital transition of additive Manufacturing, Acta Material 135:390, 2017; [4] additive Xia, Ji I Lu, Savoid David, Travy. Fuller.463) make it relatively unsuitable for computing the strand displacement flow 476, and the P.P.P.P.P.P.P.A.P.P.P.P.A.P.P.P.P.S. A.P.P.P.P.S. model, and P.S. P.P.S. A.P.P.P.S. A.P.P.P.P.S. A.P.P.S. A.P.P.P.S. A.P.P.S. A.P.P.P.P.P.S. A.P.P.P.P.A.P.P.A.A.P.S. A.P.P.A.A.P.A.B.B.B.B.A.B.B.A.A.A.B.A.A.A.B.B.A.B.B.B.A.A.A.A.A.A.B.A.A.A.B.B.A.A.A.B.B.A.A.A.B.A.A.A.A.A.A.A.A.A.A.A.B.B.A.A.A.A.A.B.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.4. A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.A.; the existing other process models assume that the shape of each layer of deposited liquid drop is fixed and unchanged, the difference of spreading contact angles of the liquid drop caused by different shapes of the deposited surfaces is ignored, and the model precision is to be further improved.
In summary, the problems of the prior art are as follows: traditional inkjet 3D prints and runs with the mode of ring-opening, prints the figure and does not carry out dynamic adjustment according to the measuring result, influences the surface quality who prints the device greatly, and then influences electronic device's electrical property.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides an ink-jet 3D printing modeling and compensating method and a closed-loop printing system, wherein a printing graph is dynamically adjusted according to a measurement result, and the surface quality of a printing device is improved.
In order to achieve the purpose, the invention adopts the technical scheme that:
an inkjet 3D printing modeling and compensation method comprises the following steps:
performing a droplet spreading experiment on base materials with different roughness to obtain the relation between a droplet spreading contact angle and the roughness of a deposition surface; according to the roughness value of each layer of outline, in an interval formed by two adjacent roughness values where the roughness value is located, obtaining a corresponding liquid drop contact angle of the layer in the model through linear interpolation;
substituting the relation between the droplet contact angle and the deposition surface roughness into the established ink-jet 3D printing highly-evolved model to obtain a specific layer-to-layer dynamic expression of the model;
before printing, initializing model parameters, initializing layer number variables and initial contours to zero, and printing a first layer of graph by using an initial layer printing graph generated by slicing the STL model by slicing software;
measuring the height profile of the printed part by using a surface topography measuring device, calculating the deviation between the actual measured profile and the reference profile, and judging whether the deviation is smaller than a set threshold value; if the deviation between the actual measurement contour and the reference contour is smaller than a set threshold value, the printing graph of the next layer is not adjusted; on the contrary, if the deviation between the actual measurement contour and the reference contour is greater than or equal to the set threshold value, calculating to obtain a compensation printing graph according to a printing compensation method;
step five, transmitting the printing graph determined in the step four to an ink-jet 3D printer, and printing the next layer according to the graph;
step six, judging whether the last layer is printed or not, if not, repeating the step four and the step five; if so, finally obtaining a printed sample piece, and finishing printing.
Further, the inkjet 3D printing model building process in the second step includes:
discretizing a printing area: discretizing the print area into an inner containing N l ×N w Grid region of nodes, discretized region being represented as a matrix
Wherein each element H (m, n) represents a position where the row-column index within the discretized region is m and n, respectively; at a given number of layers L, a scalar H (H (m, n), L) is used to represent the part height at the discretized location H (m, n) when printing to the L-th layer, and then the spatial height of the L-th layer is discretized using the region HDegree matrix H L Is represented as:
establishing a space dynamics state variable: h is L ∈R N Wherein N is N l ×N w ，
Establishing a preliminary expression of the model:
h L+1 ＝A L h L +B L f L
wherein h is L ,h L+1 ∈R N×1 Respectively taking the space height vectors of the L-th layer and the L + 1-th layer as state variables of the discrete system; a. the L ∈R N×N Is a system matrix, B L ∈R N×N For an input matrix, f L ∈R N×1 The space input vector is the graphic printed by the L-th layer;
identification system matrix A L And an input matrix B L ；A L ＝S(I+D g ) S is an N x N diagonal matrix describing part shrinkage during curing; i is an NxN unit array, D g For an N diagonal matrix, each element reflects the node height variation caused by local ink flow; in addition, B L ＝[b 1 b 2 ...b N ]Wherein each b is k Are all an N x 1 vector
The inner part comprises an identity matrix, and the other elements are 0; the position of the identity matrix reflects the position of the node where the center of the newly deposited droplet is located, and if a droplet is deposited at H (m, n) in a discrete region,
the row index at which the center of the unit matrix in the matrix is located is m,
the column index of the center of the unit array in the matrix is n;
is a single drop height distribution matrix and is used for describing the height profile of a single drop.
Further, the calculation formula of the deviation between the measurement profile and the reference profile in the fourth step is as follows:
wherein: r is L A reference profile of the L-th layer is shown,
showing the measured profile of the L-th layer.
Further, in the print compensation method of the fourth step, the compensation pattern
The calculation method comprises the following steps:
solving a single-layer minimization problem
Wherein epsilon L+1 (f) The prediction error function of the L +1 layer is expressed as:
when the optimization problem is solved, a gradient descent algorithm is adopted.
The gradient formula of the prediction error function is:
compensation pattern
The calculation formula of (2) is as follows:
wherein, is the predetermined pattern of the L +1 th layer, alpha is the learning rate, r L+1 Is the reference profile of the L +1 th layer.
The invention also aims to provide a closed-loop printing system formed by using the inkjet 3D printing modeling and compensating method, which comprises a PC upper computer, a motion system, an inkjet system, a negative pressure system, a sintering and curing system, a surface topography measuring system and the like; on one hand, the PC end sends a G code to the main controller, the main controller sends a control signal to the motor driver according to the corresponding G code so as to control the motor to move, sends a signal to the negative pressure controller so as to control the negative pressure pump and the ink to be extruded out, and sends a control signal to the sintering controller so as to be responsible for sintering and curing after printing is finished; on the other hand, the PC end sends printing data to the nozzle controller, the main controller communicates with the nozzle controller through SPI communication and sends a spraying signal to the nozzle controller, so that the nozzle driver is controlled to finish the printing of patterns; the sample surface appearance detection device is responsible for measuring the outline of the printing sample, the result is transmitted to the PC end after data processing, and the PC end adjusts the printing data of the next layer according to the measured appearance on the spot to form printing compensation.
The invention has the advantages and positive effects that:
1. a new highly-evolved model is provided for the modeling of the existing ink-jet 3D printing process, and the accuracy of the model for predicting the deposition morphology is effectively improved. Because the existing models all adopt the ideal assumption of droplet consistency, the shape difference of droplets caused by different deposition surface morphologies is not considered, and the model precision is to be further improved. The invention obtains the quantitative relation between the roughness of the deposition surface and the spreading contact angle of the liquid drop through the liquid drop deposition experiment, and effectively improves the precision of the model by dynamically changing the shape of the deposition liquid drop along with the difference of the number of printing layers in the height evolution model.
2. Aiming at an open-loop printing mode of traditional ink-jet 3D printing, a closed-loop printing method is provided. Because the open-loop printing mode is characterized in that the drop patterns printed on each layer are predetermined, the adjustment is not carried out according to the feedback measurement result. This printing method can cause the printing process to be influenced by some uncertain factors: such as uncertainty in droplet position, shape and size, and flow, fusion, etc. of droplets during printing, which may result in defects in the printed part, such as uneven printed surface, etc., and thus may affect the performance of the printing device. The surface appearance measuring device is introduced into the traditional printing system, and the subsequent printing graph is dynamically adjusted according to the measuring result and the model prediction result to form a closed loop of the printing process, so that the surface quality of the printing sample piece is effectively improved.
3. The invention obviously improves the surface quality and the electrical property of the formed electronic device for ink-jet 3D printing. The conventional open-loop printing mode formed sample piece has poor surface quality, high surface roughness and large peak-to-peak value of a measured profile, and the defects can reduce the conductivity of a conductive pattern and further influence the electrical property of a functional device. The model established by the invention can predict the defects and further compensate, thereby effectively improving the surface quality of the molded sample piece and improving the quality of the printed sample piece.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic diagram of discretization of a printing area in inkjet 3D printing according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of the correspondence between the 3D inkjet printing droplet pattern and the matrix in the embodiment of the invention.
FIG. 4 is a schematic view of partial ink flow for inkjet 3D printing according to an embodiment of the present invention.
FIG. 5 is a schematic diagram of a spatial height matrix updating process after a droplet is deposited in inkjet 3D printing according to an embodiment of the present invention.
Fig. 6 is a flowchart of the operation of a closed loop 3D inkjet printing system according to an embodiment of the present invention.
Fig. 7 is a schematic composition diagram of an inkjet 3D printing closed-loop printing system according to an embodiment of the present invention.
FIG. 8 is a schematic diagram illustrating a comparison between the printing compensation method and the uncompensated printing effect according to the embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, an inkjet 3D printing modeling and compensation method includes the following steps:
s101: performing a droplet spreading experiment on base materials with different roughness to obtain the relation between a droplet spreading contact angle and the roughness of the deposition surface; according to the roughness value of each layer of outline, in an interval formed by two adjacent roughness values where the roughness value is located, obtaining a corresponding liquid drop contact angle of the layer in the model through linear interpolation;
s102: modeling the process of inkjet 3D printing with vector h L The height profile of the part at level L is represented by a vector h L+1 Representing the height profile of the part on the L +1 th layer, and obtaining h through modeling L To h L+1 Substituting the result obtained in the step one into the model to obtain the concrete expression of each layer of the model;
s103: before printing is started, model parameters are initialized, the variable L of the layer number is 0, the initial contour hL is 0, and the pattern f is printed in the initial layer 0 Printed graphics generated for STL model sliced with slicing software
Printing a first layer of graph;
s104: measuring the height profile of the printed part by using a surface topography measuring device, calculating the deviation between the actual measured profile and the reference profile, and judging whether the deviation is less than a set threshold value; if the deviation between the actual measurement contour and the reference contour is smaller than a set threshold value, the printing graph of the next layer is not adjusted; on the contrary, if the deviation between the actual measurement profile and the reference profile is greater than or equal to the set threshold value, calculating to obtain a compensation printing graph according to the proposed printing compensation method;
s105: transmitting the printing pattern determined in the step S104 to an ink-jet 3D printer, and printing the next layer according to the pattern;
s106: judging whether the last layer is printed or not, if not, repeating S104 and S105; if so, finally obtaining a printed sample piece, and finishing printing.
The process modeling of the ink-jet 3D printing provided by the embodiment of the invention is carried out according to the following steps:
the first step is as follows: discretizing a printing area:
based on the idea of describing the evolution of the profile height of a printed part by matrix updating, a printing area is discretized into an inner containing N as shown in FIG. 2 l ×N w A grid area of nodes; to describe the height of the printed part at each location, the discretized area is represented as a matrix
Wherein each element H (m, n) represents a position where the row-column index within the discretized region is m and n, respectively; at a given number L of layers, a scalar H (m, n), L) is used to represent the part height at the discretized location H (m, n) when printing to the L-th layer; then the spatial height matrix H of the lth layer after discretization using region H L Can be expressed as:
the second step is that: establishing a space dynamics state variable: h is L ∈R N Wherein N is N l ×N w ，
The third step: establishing a preliminary expression of the model:
h L+1 ＝A L h L +B L f L
wherein h is L ,h L+1 ∈R N×1 Respectively taking the space height vectors of the L-th layer and the L + 1-th layer as state variables of the discrete system; a. the L ∈R N×N Is a system matrix, B L ∈R N×N For an input matrix, f L ∈R N×1 The space input vector is the graphic printed by the L-th layer; as shown in fig. 3, in the inkjet 3D printing modeling process provided by the embodiment of the present invention, the correspondence between the droplet patterns and the matrix is as follows: for patterned printing by an array of nozzles, the print pattern for each layer is made up of a number of droplets, the pattern of droplets deposited for each layer is represented by a matrix F, and each element F in the matrix F ij E {0,1}, where 1 represents a droplet is deposited, and 0 represents no droplet is deposited at the location; vectorizing the matrix F to obtain a spatial input vector F L Namely, the printing graph corresponding to the layer number L is obtained; the first term on the right of the equation describes the physical properties of the materials in successive printed layers and the height profile changes caused by the interactions, and the second term is used to capture the height stack caused by the deposition of the materials;
the fourth step: identification system matrix A L And an input matrix B L ；A L ＝S(I+D g ) S is an N x N diagonal matrix describing part shrinkage during curing; i is an NxN unit array, D g Is an N × N diagonal matrix, each element
Reflects the node height variation caused by local ink flow;
indicating that the node height is increasing and, conversely,
indicating a decrease in height; and assumes that the amount of height change due to local ink flow is inversely proportional to the node distance, as shown in the figure4, after the liquid drop is deposited, local ink flow behaviors exist among nodes in a dotted line circle, the ink flow direction is shown as an arrow in the figure, and the thickness of the arrow indicates the height variation caused by the local ink flow; as shown in fig. 5, in the inkjet 3D printing process provided by the embodiment of the present invention, a spatial height matrix before and after the deposition of the kth droplet in the lth layer is considered
And
the update relationship between them is expressed as:
wherein the content of the first and second substances,
respectively representing the spatial height matrix before and after a new droplet deposition;
the inner part comprises an identity matrix, and the other elements are 0; the position of the identity matrix reflects the position of the node where the center of the newly deposited droplet is located, and if a droplet is deposited at H (m, n) in a discrete region,
the row index at which the center of the unit matrix in the matrix is located is m,
the column index of the center of the unit array in the matrix is n;
for a single drop height distribution matrix to describe the height profile of a single drop, the input matrix in the third step model is B L ＝[b 1 b 2 ...b N ]. Wherein each b k Are all an N x 1 vector
The compensation printing method for ink-jet 3D printing provided by the embodiment of the invention is carried out according to the flow chart shown in FIG. 6, before printing is started, model parameters are initialized, the layer number variable and the initial contour are both initialized to zero, and the initial layer printing graph is a printing graph generated by slicing an STL model by slicing software so as to print a first layer graph; measuring the height profile of the printed portion using a surface topography measuring device, calculating the deviation between the actual measured profile and the reference profile, and determining whether the deviation is less than a predetermined threshold. If the deviation between the actual measurement contour and the reference contour is smaller than a set threshold value, the printing graph of the next layer is not adjusted; on the contrary, if the deviation between the actual measurement profile and the reference profile is greater than or equal to the established threshold, a compensation print pattern is calculated as the print pattern of the next layer according to the proposed print compensation method. Judging whether the last layer is printed or not, if not, repeating the steps; if so, finally obtaining a printed sample piece, and finishing printing.
The compensation printing graph of the ink-jet 3D printing provided by the embodiment of the invention is processed according to the following method:
solving a single-layer minimization problem
Wherein epsilon L+1 (f) The prediction error function of the L +1 layer is expressed as:
when the optimization problem is solved, a gradient descent algorithm is adopted.
The gradient formula of the prediction error function is:
compensation pattern
The calculation formula of (2) is as follows:
wherein, is the predetermined pattern of the L +1 th layer, alpha is the learning rate, r L+1 Is the reference profile of the L +1 th layer.
The composition block diagram of the inkjet 3D printing closed-loop printing system of the embodiment of the invention is shown in FIG. 7, and the whole system comprises a PC upper computer, a motion system, an inkjet system, a negative pressure system, a sintering and curing system, a surface topography measurement system and the like; on one hand, the PC end sends a G code to the main controller, the main controller sends a control signal to the motor driver according to the corresponding G code so as to control the motor to move, sends a signal to the negative pressure controller so as to control the negative pressure pump and the ink to be extruded out, and sends a control signal to the sintering controller so as to be responsible for sintering and curing after printing is finished; on the other hand, the PC end sends printing data to the nozzle controller, the main controller communicates with the nozzle controller through SPI communication and sends a spraying signal to the nozzle controller, so that the nozzle driver is controlled to finish the printing of patterns; the sample surface appearance detection device is responsible for measuring the outline of the printing sample, the result is transmitted to the PC end after data processing, and the PC end adjusts the printing data of the next layer according to the measured appearance on the spot to form printing compensation.
The following describes in detail the application effect of the embodiment of the present invention with reference to the accompanying drawings:
as shown in fig. 8, fig. 8(a) is the surface topography of a sample printed by the prior art printing strategy, fig. 8(b) is the surface topography of the sample after compensation printing according to the present invention, fig. 8(c) is the comparison effect of the cross-sectional profiles of the sample before and after compensation, the solid line is the uncompensated profile, and the dotted line is the compensated profile; as can be seen from the comparison of the surface appearance and the cross section profile of the printing sample piece, compared with the prior art, the printing compensation method provided by the invention obviously improves the surface flatness of the printing sample piece. The invention can ensure that the dielectric material has better flatness and the conductive pattern has good electrical property when being applied to the electronic field, and effectively improves the electrical property of a printed electronic functional device.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (5)
1. An inkjet 3D printing modeling and compensation method is characterized by comprising the following steps:
performing a droplet spreading experiment on base materials with different roughness to obtain the relation between a droplet spreading contact angle and the roughness of a deposition surface; according to the roughness value of each layer of outline, in an interval formed by two adjacent roughness values where the roughness value is located, obtaining a corresponding liquid drop contact angle of the layer in the model through linear interpolation;
substituting the relation between the droplet contact angle and the deposition surface roughness into the established ink-jet 3D printing highly-evolved model to obtain a specific layer-to-layer dynamic expression of the model;
before printing, initializing model parameters, initializing layer number variables and initial contours to zero, and printing a first layer of graph by using an initial layer printing graph generated by slicing the STL model by slicing software;
measuring the height profile of the printed part by using a surface topography measuring device, calculating the deviation between the actual measured profile and the reference profile, and judging whether the deviation is smaller than a set threshold value; if the deviation between the actual measurement contour and the reference contour is smaller than a set threshold value, the printing graph of the next layer is not adjusted; on the contrary, if the deviation between the actual measurement contour and the reference contour is greater than or equal to the set threshold value, calculating to obtain a compensation printing graph according to a printing compensation method;
step five, transmitting the printing graph determined in the step four to an ink-jet 3D printer, and printing the next layer according to the graph;
step six, judging whether the last layer is printed or not, and if not, repeating the step four and the step five; if so, finally obtaining a printed sample piece, and finishing printing.
2. The method according to claim 1, wherein the inkjet 3D printing modeling process in the second step comprises:
discretizing a printing area: discretizing the print area into an inner containing N l ×N w Grid region of nodes, discretized region being represented as a matrix
Wherein each element H (m, n) represents a position where the row-column index within the discretized region is m and n, respectively; at a given number of layers L, a scalar H (H (m, n), L) is used to represent the part height at the discretized location H (m, n) when printing to the L-th layer, and after discretization using region H, the spatial height matrix H for the L-th layer L Is represented as:
establishing a space dynamics state variable: h is L ∈R N Wherein N is N l ×N w ，
Establishing a preliminary expression of the model:
h L+1 ＝A L h L +B L f L
wherein h is L ，h L+1 ∈R N×1 The spatial height vectors of the L-th layer and the L + 1-th layer are respectively used as state variables of the discrete system; a. the L ∈R N×N In order to be a matrix of the system,B L ∈R N×N for an input matrix, f L ∈R N×1 The space input vector is the graphic printed by the L-th layer;
identification system matrix A L And an input matrix B L ；A L ＝S(I+D g ) S is an N x N diagonal matrix describing part shrinkage during curing; i is an NxN unit array, D g For an N diagonal matrix, each element reflects the node height variation caused by local ink flow; in addition, B L ＝[b 1 b 2 ... b N ]Wherein each b is k Are all an Nx 1 vector
The inner part comprises an identity matrix, and the other elements are 0; the position of the identity matrix reflects the position of the node where the center of the newly deposited droplet is located, and if a droplet is deposited at H (m, n) in a discrete region,
the row index at which the center of the unit matrix in the matrix is located is m,
the column index of the center of the unit array in the matrix is n;
is a single drop height distribution matrix and is used for describing the height profile of a single drop.
3. The method of claim 2, wherein the deviation of the measured profile from the reference profile in step four is calculated by:
wherein: r is L A reference profile of the L-th layer is shown,
showing the measured profile of the L-th layer.
4. The method according to claim 2, wherein in the printing compensation method of the fourth step, the compensation pattern
The calculation method comprises the following steps:
solving a single-layer minimization problem
Wherein epsilon L+1 (f) The prediction error function of the L +1 layer is expressed as:
when the optimization problem is solved, a gradient descent algorithm is adopted;
the gradient formula of the prediction error function is:
compensation pattern
The calculation formula of (c) is:
wherein, is the predetermined pattern of the L +1 th layer, alpha is the learning rate, r L+1 Is the reference profile of the L +1 th layer.
5. A closed loop printing system formed using the inkjet 3D printing modeling and compensation method of claim 1, wherein: the device comprises a PC upper computer, a motion system, an ink-jet system, a negative pressure system, a sintering and curing system and a surface topography measuring system; on one hand, the PC end sends a G code to the main controller, the main controller sends a control signal to the motor driver according to the corresponding G code so as to control the motor to move, sends a signal to the negative pressure controller so as to control the negative pressure pump and the ink to be extruded out, and sends a control signal to the sintering controller so as to be responsible for sintering and curing after printing is finished; on the other hand, the PC end sends printing data to the nozzle controller, the main controller communicates with the nozzle controller through SPI communication and sends a spraying signal to the nozzle controller, so that the nozzle driver is controlled to finish the printing of patterns; the sample surface appearance detection device is responsible for measuring the outline of the printing sample, the result is transmitted to the PC end after data processing, and the PC end adjusts the printing data of the next layer according to the measured appearance on the spot to form printing compensation.
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