Method for generating designable track of lattice structure for double-nozzle heterogeneous droplet freezing printing

Abstract

The invention discloses a lattice structure designable track generation method for double-nozzle heterogeneous liquid drop freezing printing. The lattice structure designable track generation method comprises the steps that the actual height of two kinds of material liquid drops after solidification and the optimal spraying frequency of spraying the two kinds of liquid drops through double nozzles are determined; determining space coordinates of each vertex of the dot matrix, and calculating space vectors corresponding to the branches forming the dot matrix structure by combining the space coordinates of the vertexes; the number of liquid drops needing to be deposited and the deposition step pitch of each branch rod are determined through iterative calculation; calculating a space coordinate of a liquid drop needing to be deposited on each branch rod, and determining a track coordinate of the lattice structure; combining a plurality of dot matrix structures according to any number and sequence, combining the actual heights of the two solidified liquid drops, performing printing layer number compensation on a structure formed by the liquid drops with smaller actual heights, and performing space array processing on the dot matrix structures to obtain double-nozzle track coordinates; and outputting according to a numerical control format after converting the coordinates of the double-nozzle tracks.

Description

Technical Field

[0001] This invention relates to the field of 3D printing technology, specifically to a method for generating designable trajectories for cryogenic printing of lattice structures using dual-nozzle heterogeneous droplets. Background Technology

[0002] Dual-nozzle uniform droplet cryo-printing is an emerging additive manufacturing technology. This technology precisely deposits graphene suspensions and water droplets onto a cryogenic substrate, and, combined with the ice template effect during cryogenic casting, enables the simultaneous integrated design and printing of complex three-dimensional macroscopic configurations and their microscopic porous structures of graphene. This technology shows broad application prospects in flexible electronic devices and high-efficiency energy storage systems, and can be used to fabricate large-size, high-precision, and diverse lattice structures. Lattice structures are lightweight porous structures composed of repeating unit cells connected by nodes. These structures typically exhibit excellent comprehensive properties, including low density (lightweight), high specific stiffness, high specific strength, ultra-large specific surface area, and good heat dissipation. Designing three-dimensional graphene into a lattice configuration to reinforce magnesium-based composites offers multiple significant advantages, such as synergistically achieving lightweight and high specific stiffness, constructing efficient load transfer, heat conduction, and electron transport networks, and significantly improving the overall performance of the composite material.

[0003] However, dual-nozzle uniform droplet cryogenic printing technology still faces significant challenges in trajectory generation. Even when adjusting printing parameters to maintain a consistent droplet cryogenic deposition diameter, the height of the droplets ejected from the dual nozzles will still differ significantly after spreading, contracting, oscillating, and solidifying on the cryogenic substrate due to material properties (such as surface tension, viscosity, and density). Therefore, the trajectory planning of the dual nozzles must be designed separately based on the characteristics of the two droplet materials: the droplet with the larger height needs fewer ejection layers, while the droplet with the smaller height needs more ejection layers to ensure precise spatial alignment. Simultaneously, the ejection frequency of the two droplets must be set separately, taking into account key parameters such as nozzle temperature, substrate temperature, and droplet volume—too high a frequency will cause the droplets to fuse due to insufficient cooling and solidification; too low a frequency will significantly reduce printing efficiency. Furthermore, existing methods are insufficient in their ability to autonomously design dual-nozzle lattice structures. Users typically can only choose from a predefined model library, lacking effective support for custom designs based on specific application scenarios, making it difficult to meet diverse manufacturing needs. Summary of the Invention

[0004] The purpose of this invention is to provide a method for generating a designable trajectory for a dot matrix structure in cryogenic printing of heterogeneous droplets with dual nozzles, so as to overcome the key problems of existing dual nozzle droplet height difference compensation, jetting parameter optimization and flexible generation of complex structures.

[0005] To achieve the above objectives, the present invention employs the following technical solution: A method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using a dual-nozzle system includes: First, based on the characteristics of the two types of droplets, the actual height of the droplets after solidification is determined. Then, using the parameters of the substrate, nozzle, and droplets, the optimal spraying frequency for spraying the two types of droplets using dual nozzles is calculated. Secondly, the spatial coordinates of each vertex of the lattice are determined based on the geometric dimensions of the lattice structure, and the spatial vectors corresponding to the branches constituting the lattice structure are calculated based on the connection relationship of the lattice structure and the spatial coordinates of the vertices; the number of droplets to be deposited and the deposition step distance of each branch are determined by iterative calculation. Next, by combining the vertex coordinates at the starting point of the branch with the number of droplets to be deposited, the spatial coordinates of the droplets to be deposited on each branch are obtained, thereby determining the trajectory coordinates of the lattice structure; Finally, characteristic parameters of the droplet material and the corresponding optimal spray frequency are added to the lattice structure; multiple lattice structures are combined in any number and order, and the actual height of the two types of droplets after solidification is combined. The number of printing layers is compensated for the structure composed of droplets with smaller actual heights, and the spatial array processing of the lattice structure is performed to obtain the dual-nozzle trajectory coordinates; the dual-nozzle trajectory coordinates are converted and output according to the CNC format.

[0006] Furthermore, based on the characteristics of the two material droplets, the actual height of the droplets after solidification is determined, specifically using the following calculation model for the actual height of droplet freezing and solidification:

[0007] in, This represents the actual height of the droplet after it solidifies. The diameter of the droplet after cryo-deposition. The initial volume of the droplet. The pinning strength coefficient; The Ornetzog number is calculated using droplet dynamic viscosity, droplet density, and droplet surface tension.

[0008] Furthermore, the optimal spray frequency for spraying two types of droplets using dual nozzles was calculated, specifically using the following optimal spray frequency calculation model:

[0009] in, To achieve the optimal injection frequency, The thermal conductivity of the substrate. This represents the contact area between the droplet and the substrate. For droplet density, For nozzle temperature, For substrate temperature, This represents the volume of the droplet after freezing and solidification. This represents the actual height of the droplet after it solidifies. The specific heat capacity of the droplet. This is the latent heat of solidification of the droplet.

[0010] Furthermore, based on the connection relationships of the lattice structure and the spatial coordinates of the vertices, the spatial vectors corresponding to the branches constituting the lattice structure are calculated, including: Let m be the number of branches in the lattice structure. Then, subtracting the spatial coordinates of the vertices at both ends of each branch will yield the spatial vector corresponding to that branch. ;in This represents the difference in the three-axis spatial coordinates of the two vertices of the branch numbered m.

[0011] Furthermore, iterative calculations determine the required number of droplets to be deposited on each branch and the deposition step distance, including: Given the initial number of droplets p and the step size w, perform iterative calculations: using the absolute values ​​of the spatial vectors of each branch. Divide by the initial step size w, round down to get the number of segments t, and then take the absolute value of the spatial vector. Divide by the number of segments t to obtain the actual step distance w'; if the error between the actual step distance w' and the initial step distance w is less than the preset value, then the actual step distance w' is determined to be the deposition step distance; otherwise, continue iterative calculation until the error meets the preset value requirement or the number of iterations is completed; and the final number of droplets on the branch p'=t+1.

[0012] Furthermore, by combining the vertex coordinates at the starting point of the branch with the required number of droplets to be deposited, the spatial coordinates of the droplets to be deposited on each branch are obtained, thereby determining the trajectory coordinates of the lattice structure, including: For each branch, generate an arithmetic sequence with an increment of 1 / t, increasing from 0 to 1. ; the spatial vector of the branch Multiply by the arithmetic sequence By obtaining t+1 values, and adding the coordinates of the vertex at the starting point of the branch to these t+1 values, we can obtain the spatial coordinates of the p' droplets to be deposited on the branch. Finally, by integrating the spatial coordinates of all the droplets on the branch, we can obtain the trajectory coordinates of the lattice structure.

[0013] Furthermore, multiple lattice structures are combined in any number and order, and the actual heights of the two types of droplets after solidification are considered. For structures composed of droplets with smaller actual heights, printing layer compensation is performed, and spatial array processing of the lattice structures is applied to obtain the dual-nozzle trajectory coordinates, including: After spatially arraying multiple dot structures, they are combined in any number and any order. During the combination process, based on the solidification height of the two material droplets, the number of printing layers is compensated for for structures composed of droplets with smaller heights. After the combination is completed, duplicate droplet coordinates are removed, and then the dot structure is arrayed again. The trajectory coordinates of the dual nozzles are obtained by combining the trajectory coordinates of the dot structure.

[0014] Furthermore, to compensate for the reduced number of printing layers in structures composed of smaller droplets, thereby enabling... ,in and This indicates the number of printing layers and the solidification height of the first type of material droplet. and This indicates the number of printing layers and the solidification height of the second type of material droplet.

[0015] Furthermore, based on the given distance, included angle, and characteristic parameters of the droplet material between the two nozzles, the spatial coordinates of the droplets in the trajectory coordinates of the two nozzles are calculated by distance compensation, and then output according to the CNC program format to complete the generation of the dual-nozzle printing trajectory.

[0016] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements a designable trajectory generation method for the dot matrix structure of the dual-nozzle heterogeneous droplet cryogenic printing.

[0017] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements a method for generating a lattice structure for cryogenic printing of dual-nozzle heterogeneous droplets.

[0018] Compared with the prior art, the present invention has the following technical features: 1. Precise coordination of heterogeneous droplets from dual nozzles: By accurately calculating the differences in the solidification height of droplets from different materials and implementing targeted layer compensation, the positional misalignment caused by material characteristics is effectively overcome, ensuring precise spatial coordination of heterogeneous droplets from dual nozzles and significantly improving the geometric accuracy and functional consistency of the lattice structure.

[0019] 2. Dual-nozzle jetting parameter optimization: Based on the heat conduction model, the optimal jetting frequency of the dual nozzles is scientifically calculated to balance the forming quality and printing efficiency, maximizing printing speed while ensuring structural clarity.

[0020] 3. Customizable lattice structure design: Adopting a modular combination approach, users can freely select and combine various lattice structures (including material properties and frequency parameters) as needed, breaking through the limitations of predefined model libraries and achieving highly flexible generation of complex lattice structure trajectories that meet diverse needs.

[0021] 4. Universal Trajectory Generation Algorithm: This algorithm first determines the spatial coordinates of the vertices based on the geometric dimensions of the lattice structure. Then, by calculating the vectors of the topological members and applying iterative calculations, it generates droplet deposition coordinates branch by branch, ultimately constructing the complete lattice structure printing trajectory. Compared to traditional methods limited to a single specific model, the unified algorithm framework proposed in this invention significantly reduces programming complexity, can efficiently build a rich lattice model library, and provides flexible solutions for diverse printing tasks. Attached Figure Description

[0022] Figure 1 This is a flowchart of the trajectory generation method of the present invention; Figure 2 This is a schematic diagram of different stages of the method of the present invention. Detailed Implementation

[0023] This invention proposes a designable trajectory generation method for dot matrix structures in cryogenic printing of heterogeneous droplets using dual nozzles. It closely integrates the droplet material properties with the characteristics of cryogenic printing technology, achieving high-precision collaborative trajectory planning between the two nozzles. Furthermore, through a modular design approach, it significantly enhances the customizable design capabilities of the dual-nozzle dot matrix structure. The method includes: first, determining the actual height of the two droplet materials after freezing using a calculation model based on their characteristics (e.g., surface tension, viscosity, and density); then, calculating the optimal ejection frequency for ejecting the two droplets using dual nozzles based on the parameters of the substrate, nozzles, and droplets using an optimal ejection frequency calculation model; finally, determining the spatial coordinates of each vertex of the dot matrix based on its geometric dimensions, and then determining the spatial coordinates of the dot matrix based on the connection of the dot matrix structure... The spatial vectors corresponding to the branches constituting the lattice structure are calculated by combining the spatial coordinates of the vertices; the number of droplets to be deposited and the deposition step distance for each branch are determined by iterative calculation; the spatial coordinates of the droplets to be deposited on each branch are obtained by combining the vertex coordinates at the starting point of the branch and the number of droplets to be deposited, thereby determining the trajectory coordinates of the lattice structure; characteristic parameters of the droplet material and the corresponding optimal spray frequency are added to the lattice structure; multiple lattice structures are combined in any number and order, and the actual height of the two types of droplets after solidification is combined, and the structure composed of droplets with smaller actual height is compensated for by the number of printing layers and the spatial array processing of the lattice structure is performed to obtain the trajectory coordinates of the dual nozzles; the trajectory coordinates of the dual nozzles are converted and output according to the CNC format to obtain the CNC code that can directly drive the equipment.

[0024] This invention first constructs a calculation model for the actual height of droplet freezing and solidification, and a calculation model for the optimal jet frequency of the droplet, combined with... Figure 2 The specific explanation is as follows: Define the initial diameter of the droplet during ejection as: (Equal to the nozzle diameter), the droplet shape is approximately spherical, and the initial droplet volume... for: (1) Define the diameter of the droplet after cryo-deposition as The actual height is After solidification, the droplet takes an approximately spherical shape, and its volume after freezing and solidification is... for: (2) Furthermore, the volume of the droplet is approximately equal before and after solidification, from Simplifying, we get: (3) Furthermore, the ideal height of the droplet after solidification is defined as... Substituting into formula (3), we get: (4) Furthermore, since the height of the sprayed droplets after solidification is much less than 1 mm, the ideal height can be derived from the above equation. (ignoring higher-order terms) ): (5) Define the dynamic viscosity of the droplet as The droplet density is The surface tension of the droplet is dimensionless Onezoglu numbers for: (6) Define the dimensionless pinning strength coefficient as Because the three-phase contact line between the substrate, droplet, and air is pinned, droplet spreading is inhibited, resulting in a decrease in the actual height of the droplet after solidification. Greater than the ideal height The relationship between the two is as follows: (7) Furthermore, the droplets are solidified to an ideal height. Substituting and simplifying, we obtain the calculation model for the actual height of droplet freezing and solidification as follows: (8) Define the specific heat capacity of a liquid droplet The nozzle temperature (initial droplet temperature) is The substrate temperature is The latent heat of solidification of the droplets is The total heat required for droplet freezing and solidification for: (9) Define the thermal conductivity of the substrate as The contact area between the droplet and the substrate is heat flow of droplets for: (10) Time required for droplet freezing and solidification for: (11) Furthermore, the optimal jetting frequency calculation model for droplets of different materials during cryogenic printing is as follows: (12) in, The optimal injection frequency.

[0025] The specific implementation process of the present invention will be further described below with reference to the accompanying drawings.

[0026] Step 1: Based on the characteristics of the two types of droplets, use the actual height calculation model (8) of the droplet freezing solidification to determine the actual height of the two types of droplets after solidification.

[0027] The two droplet materials mentioned refer to graphene and water; the property refers to the dynamic viscosity of the graphene and water droplets. Droplet density Surface tension Parameters were substituted into equation (8) to calculate the solidification height of the graphene droplets. And the height of the water droplets .

[0028] Step 2: Using the parameters of the substrate, nozzle and droplet, calculate the optimal spray frequency of the two droplets by spraying them with the dual nozzles using the optimal spray frequency calculation model (12).

[0029] The parameters of the substrate, nozzle, and droplets include the substrate temperature. Nozzle temperature and the latent heat of solidification of the two materials droplets The optimal spray frequencies for graphene droplets and water droplets were calculated using equation (12). and .

[0030] Step 3: Determine the spatial coordinates of each vertex of the lattice based on the geometric dimensions of the lattice structure.

[0031] Let n be the number of vertices in the lattice structure. Then, the spatial coordinates of each vertex can be determined based on the geometric dimensions. , This represents the three-dimensional coordinates of the nth vertex.

[0032] For example, consider the lattice structure of a triangular pyramid. The pyramid has four vertices, with three base vertices located on an equilateral triangle of side length L. Its spatial coordinates are as follows: The top vertex is located L / 2 above the intersection of the medians of the equilateral triangle, with spatial coordinates of... .

[0033] Step 4: Calculate the spatial vectors corresponding to the branches that make up the lattice structure based on the connection relationship of the lattice structure and the spatial coordinates of the vertices.

[0034] Let m be the number of branches in the lattice structure. Then, subtracting the spatial coordinates of the vertices at both ends of each branch yields the spatial vector corresponding to each branch (from 1 to m). ;in This represents the difference in the XYZ spatial coordinates of the two vertices at the ends of the branch numbered m.

[0035] Referring to the example in step 3, if the lattice structure of a triangular pyramid consists of 3 branches and has 4 vertices numbered 1-4, then the spatial vectors corresponding to the 3 branches are as follows: , , The result is obtained by subtracting vertices 1 and 4, 2 and 4, and 3 and 4 respectively.

[0036] Step 5: Iteratively calculate and determine the number of droplets to be deposited on each branch and the deposition step distance.

[0037] Given the initial number of droplets p and the step size w, perform iterative calculations: using the absolute values ​​of the spatial vectors of each branch calculated in step 2. Divide by the initial step size w, round down to get the number of segments t, and then take the absolute value of the spatial vector. Divide by the number of segments t to obtain the actual step size w'; if the error between the actual step size w' and the initial step size w is less than the preset value 10... -3 If the actual step size w' is determined to be the deposition step size, then the iterative calculation continues until the error meets the preset value requirement or the number of iterations max_n is completed; and the final number of droplets on the branch is p'=t+1.

[0038] Step 6: By combining the vertex coordinates at the starting point of the branch with the number of droplets to be deposited, the spatial coordinates of the droplets to be deposited on each branch are obtained, thereby determining the trajectory coordinates of the lattice structure.

[0039] For each branch, generate an arithmetic sequence with an increment of 1 / t, increasing from 0 to 1. ; the spatial vector of the branch Multiply by the arithmetic sequence By obtaining t+1 values, and adding the coordinates of the vertex P1 at the starting point of the branch to these t+1 values, we can obtain the spatial coordinates of the p' droplets to be deposited on the branch. Finally, by integrating the spatial coordinates of all the droplets on the branch, we can obtain the trajectory coordinates of the lattice structure.

[0040] Step 7: Add characteristic parameters of the droplet material and the corresponding optimal jetting frequency to the lattice structure.

[0041] In one embodiment of the present invention, the characteristic parameter IO1 is used to characterize the droplet material as graphene; the characteristic parameter IO2 is used to characterize the droplet material as water (which solidifies into ice); based on step 2, the optimal spray frequencies for these two materials are respectively... and .

[0042] Step 8: Combine multiple dot matrix structures in any number and order, combine the actual height of the two types of droplets after solidification, and perform printing layer compensation on the structure composed of droplets with smaller actual heights and spatial array processing of the dot matrix structure to obtain the trajectory coordinates of the dual nozzles.

[0043] After spatially arraying various lattice structures, they are combined in any number and order. During the combination process, the solidification heights of graphene droplets and water droplets are calculated according to step 1. and To determine the number of printing layers for structures composed of small droplets. n The quantitative compensation made ,in This indicates the number of graphene droplets printed. This indicates the number of printing layers of water droplets; after the combination is completed, duplicate droplet coordinates are removed, and then the lattice structure is arrayed again. The trajectory coordinates of the lattice structure are combined to obtain the trajectory coordinates of the dual nozzles; in the array processing, the droplet diameter, the number of deposited droplets and the deposition step, the array spacing and the number of arrays are integrated and input.

[0044] Step 9: After converting the trajectory coordinates of the dual nozzles, output them according to the CNC format to obtain CNC code that can directly drive the equipment.

[0045] Based on the given distance, included angle, and characteristic parameters of the droplet material between the two nozzles, the spatial coordinates of the droplets in the trajectory coordinates of the two nozzles are calculated by distance compensation, and then output according to the CNC program format to complete the generation of the dual-nozzle printing trajectory; the CNC program is written in MATLAB language.

[0046] Example: Example: Generation of trajectory for a custom-designed graphene lattice structure, referencing... Figure 1 and Figure 2 As shown.

[0047] Step 1, droplet diameter Graphene droplet density at a concentration of 10 mg / L , Onezog number Pinning coefficient solidification height Water droplet density , Onezog number Pinning coefficient solidification height .

[0048] Step 2, input the substrate temperature and nozzle temperature Parameters such as the specific heat capacity of graphene droplets. The latent heat of solidification of the droplets is The optimal jet frequency of water droplets was calculated using a model for calculating the optimal jet frequency of droplets. Specific heat capacity of water droplets The latent heat of solidification of the droplets is The optimal jet frequency of water droplets was calculated using a model for calculating the optimal jet frequency of droplets. .

[0049] Step 3: Input the vertex coordinates of the lattice structure into the lattice model library of the trajectory generation program. The vertex coordinates should be calculated based on the geometric dimensions of the lattice structure. For example, the BCC structure is composed of the diagonals inside a cube with side length L, therefore the coordinates of each vertex of the BCC are... , , , , , , , , .

[0050] Step 4: Parametric modeling and array processing of the lattice structure. Input various parameters of the lattice structure, such as droplet diameter, deposition step distance, number of branch droplets, array spacing, and number of arrays. In this embodiment, the droplet diameter is 0.5 mm, the deposition step distance is 0.8 mm, and the number of branch droplets is 10. Among them, the number of XY arrays in square one is 1, Z is 2, the array spacing in the Z direction is 7.2 mm, and the characteristic parameter is 1; the number of XY arrays in square two is 1, Z is 10, the array spacing in the Z direction is 0.8 mm, and the characteristic parameter is 2; the XYZ array spacing and number of arrays in BCC are both 1, and the characteristic parameter is 1; the number of XY arrays in the column is 2, Z is 1, the array spacing in the XY direction is 7.2 mm, and the characteristic parameter is 1. Step 5: Match the dot matrix structure combination with the number of printing layers for the dual printheads. Store the units generated in Step 4 into the program's register matrix in the order of squares, BCC, array columns, and array squares. Simultaneously, match the number of printing layers for square two with the columns to ensure... Changing the storage order or failing to match the number of printing layers for dual printheads will result in misalignment of the printed structure.

[0051] Step six: Remove duplicate droplet coordinates. Use the program's function tools to remove the coordinates of duplicate droplets to ensure that droplets are not repeatedly ejected from the same position during printing. After completion, release the combined dot matrix structure from the register matrix to obtain the custom-designed dot matrix structure. Perform distance compensation calculation on the droplet coordinates based on the nozzle spacing and angle, and finally perform spatial array to obtain the custom-designed dot matrix structure.

[0052] Step 7: Output the trajectory coordinates of the custom-designed dot matrix structure as a txt file in CNC program format to complete the generation of the print trajectory.

[0053] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for generating a designable trajectory for a dot matrix structure in cryogenic printing of heterogeneous droplets using a dual-nozzle nozzle, characterized in that, include: First, based on the characteristics of the two types of droplets, determine the actual height of the droplets after solidification. Subsequently, using the parameters of the substrate, nozzle, and droplets, the optimal spraying frequency for spraying two types of droplets using dual nozzles was calculated. Secondly, the spatial coordinates of each vertex of the lattice are determined based on the geometric dimensions of the lattice structure, and the spatial vectors corresponding to the branches constituting the lattice structure are calculated based on the connection relationship of the lattice structure and the spatial coordinates of the vertices; the number of droplets to be deposited and the deposition step distance of each branch are determined by iterative calculation. Next, by combining the vertex coordinates at the starting point of the branch with the number of droplets to be deposited, the spatial coordinates of the droplets to be deposited on each branch are obtained, thereby determining the trajectory coordinates of the lattice structure; Finally, characteristic parameters of the droplet material and the corresponding optimal jetting frequency are added to the lattice structure; Multiple dot matrix structures are combined in any number and order. The actual height of the two types of droplets after solidification is combined with the actual height of the droplets. The number of printing layers is compensated for the structure composed of droplets with smaller actual heights, and the spatial array processing of the dot matrix structure is performed to obtain the trajectory coordinates of the dual nozzles. The trajectory coordinates of the dual nozzles are converted and output according to the CNC format.

2. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, Based on the characteristics of the two material droplets, the actual height of the droplets after solidification is determined. Specifically, the following calculation model for the actual height of droplet freezing and solidification is used: in, This represents the actual height of the droplet after it solidifies. The diameter of the droplet after cryo-deposition. The initial volume of the droplet. The pinning strength coefficient; The Ornetzog number is calculated using droplet dynamic viscosity, droplet density, and droplet surface tension.

3. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, The optimal spray frequency for spraying two types of droplets using dual nozzles was calculated, specifically using the following optimal spray frequency calculation model: in, To achieve the optimal injection frequency, The thermal conductivity of the substrate. This represents the contact area between the droplet and the substrate. For droplet density, For nozzle temperature, For substrate temperature, This represents the volume of the droplet after freezing and solidification. This represents the actual height of the droplet after it solidifies. The specific heat capacity of the droplet. This is the latent heat of solidification of the droplet.

4. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, Based on the connection relationships of the lattice structure and the spatial coordinates of the vertices, the spatial vectors corresponding to the branches constituting the lattice structure are calculated, including: Let m be the number of branches in the lattice structure. Then, subtracting the spatial coordinates of the vertices at both ends of each branch will yield the spatial vector corresponding to that branch. ;in This represents the difference in the three-axis spatial coordinates of the two vertices of the branch numbered m.

5. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, Iterative calculations determine the number of droplets required for deposition on each branch and the deposition step distance, including: Given the initial number of droplets p and the step size w, perform iterative calculations: using the absolute values ​​of the spatial vectors of each branch. Divide by the initial step size w, round down to get the number of segments t, and then take the absolute value of the spatial vector. Divide by the number of segments t to obtain the actual step distance w'; if the error between the actual step distance w' and the initial step distance w is less than the preset value, then the actual step distance w' is determined to be the deposition step distance; otherwise, continue iterative calculation until the error meets the preset value requirement or the number of iterations is completed; and the final number of droplets on the branch p'=t+1.

6. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, By combining the vertex coordinates at the starting point of the branch with the required number of droplets to be deposited, the spatial coordinates of the droplets to be deposited on each branch are obtained, thereby determining the trajectory coordinates of the lattice structure, including: For each branch, generate an arithmetic sequence with an increment of 1 / t, increasing from 0 to 1. ; the spatial vector of the branch Multiply by the arithmetic sequence By obtaining t+1 values, and adding the coordinates of the vertex at the starting point of the branch to these t+1 values, we can obtain the spatial coordinates of the p' droplets to be deposited on the branch. Finally, by integrating the spatial coordinates of all the droplets on the branch, we can obtain the trajectory coordinates of the lattice structure.

7. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, Multiple lattice structures are combined in arbitrary numbers and orders. The actual heights of the two types of droplets after solidification are considered. For structures composed of droplets with smaller actual heights, printing layer compensation is performed, and spatial array processing of the lattice structures is applied to obtain the dual-nozzle trajectory coordinates, including: After spatially arraying multiple dot structures, they are combined in any number and any order. During the combination process, based on the solidification height of the two material droplets, the number of printing layers is compensated for for structures composed of droplets with smaller heights. After the combination is completed, duplicate droplet coordinates are removed, and then the dot structure is arrayed again. The trajectory coordinates of the dual nozzles are obtained by combining the trajectory coordinates of the dot structure.

8. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 7, characterized in that, To compensate for the reduced number of printing layers in structures composed of small droplets, thereby enabling... ,in and This indicates the number of printing layers and the solidification height of the first type of material droplet. and This indicates the number of printing layers and the solidification height of the second type of material droplet.

9. The method for designing trajectory generation of dot matrix structures for cryogenic printing of heterogeneous droplets using dual nozzles according to claim 1, characterized in that, Based on the given distance, included angle, and characteristic parameters of the droplet material between the two nozzles, the spatial coordinates of the droplets in the trajectory coordinates of the two nozzles are calculated by distance compensation, and then output according to the CNC program format to complete the generation of the dual-nozzle printing trajectory.

10. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes a computer program, it can design a trajectory generation method for the dot matrix structure of the dual-nozzle heterogeneous droplet cryogenic printing according to any one of claims 1-9.

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