Method and system for generating interface topology of multi-layer pcb board with enhanced interlayer bonding force

Abstract

The present application relates to the technical field of multi-layer PCB additive manufacturing, and discloses a method and system for generating an interface topology structure of a multi-layer PCB board with enhanced interlayer bonding force. The method comprises: extracting a rheological fingerprint based on a profile image of conductive ink, and constructing a rheological response function and a three-dimensional rheological erosion kernel; performing three-dimensional convolution on an original design model using the three-dimensional rheological erosion kernel to generate a physical entity set that reproduces the rheological smoothing effect; calculating a geometric deviation field to identify rheological shrinkage and expansion areas, and constructing a topology pre-distortion structure in accordance with the reverse geometric compensation principle; performing printability and minimum feature size constraint filtering to generate anti-flowing topology printing data. The present application solves the problem of interlocking feature degradation caused by the flowing effect of nano-ink, realizes physical fidelity of microscopic occlusion structure through pre-distortion compensation, and significantly enhances the interlayer bonding force and manufacturing reliability of the PCB.

Description

Technical Field

[0001] This invention relates to the field of multilayer PCB additive manufacturing technology, and more specifically, to a method and system for generating interface topology structures in multilayer PCB additive manufacturing to enhance interlayer bonding. Background Technology

[0002] With the application of additive manufacturing technology in the printed circuit board (PCB) field, constructing the microscopic interface of multilayer PCBs using nano-conductive inks has become a key technology for improving performance. To enhance interlayer bonding, designers typically construct "microscopic interlocking patterns" with mechanical anchoring effects at the interface. However, in actual reflow soldering or high-temperature thermal shock testing, interlayer delamination still occurs frequently. Failure analysis shows that the printed physical interface often presents a smooth, wavy shape rather than the sharp "interlocking" shape in the design data, resulting in mechanical interlocking forces far lower than expected. Existing slicing algorithms and manufacturing processes face serious yield and accuracy bottlenecks, the core contradiction of which lies in the geometric distortion between design and manufacturing. Traditional technologies are mostly based on WYSIWYG static geometric segmentation, ignoring the rheological properties of nano-inks at the microscale. During inkjet printing, the surface tension of liquid ink drives the droplets towards the minimum surface area state, producing a "rheological smoothing effect," causing sharp design features to be automatically smoothed out by physical tension before curing. Due to the lack of a time-integral prediction model based on rheological dynamics, it is impossible to predict the dynamic deformation process of geometric voxels after printing and before curing. The conformational degradation caused by this rheological constraint degenerates the ideal interlocked input data into invalid smooth undulations after the physical rheological process, severely limiting the generation quality of the interface topology. Therefore, how to shift from simple geometric slicing to geometric inverse reconstruction under rheological constraints, and construct an inverse solver that includes a "rheological erosion operator" to offset the smoothing effect of surface tension with pre-distortion compensation technology, is a technical problem that urgently needs to be solved in the field of multilayer PCB additive manufacturing.

[0003] In the prior art, Chinese Patent Publication No. CN114698268A discloses a method for additive manufacturing of multilayer circuit boards. This technology uses micro-stereolithography to print insulating substrates and construct microchannels, combined with laser-induced liquid phase deposition technology to deposit conductive lines within the channels. Multilayer PCB manufacturing is achieved by layering insulating substrates and conductive lines. The core architecture includes a micro-lithography forming unit, a laser deposition module, and interlayer positioning components, enabling the formation of high-precision conductive lines. This improves the structural stability and signal transmission performance of multilayer PCBs to a certain extent, providing a basic path for process optimization in additive manufacturing of PCBs. Chinese Patent Publication No. CN120129177A discloses a method and equipment for fabricating arbitrary-layer vertical interconnect PCBs based on 3D printing technology. This method directly forms vertical interconnect structures through 3D printing, replacing the traditional laser drilling and copper filling process. Simultaneously, it combines iterative optimization of printing parameters, adjusting the nozzle movement speed and ink jet volume to improve the connection accuracy between the vertical interconnect structure and the lines in each layer. The equipment integrates an online detection unit, which can provide real-time feedback on printing deviations and perform dynamic corrections, providing a technical solution for the efficient manufacturing of multilayer PCB vertical interconnects.

[0004] However, while the two existing technologies mentioned above have some reference value in the fields of multilayer PCB additive manufacturing processes and structural forming, they fail to solve the core pain point of geometric distortion under rheological constraints in current technologies. Among them, the patent with publication number CN114698268A focuses on the layer-by-layer forming process of insulating substrate and conductive lines, completely ignoring the rheological smoothing effect of nano-conductive ink in the inkjet printing process, and has not established a deformation prediction model based on rheological dynamics. As a result, the designed microchannels and other structures are smoothed out by surface tension before the ink cures, and cannot form an effective mechanical interlock. The patent with publication number CN120129177A focuses on the printing accuracy optimization of vertical interconnect structures, lacks a topology pre-distortion compensation mechanism, and has not built reverse correction logic for the rheological contraction and expansion regions, and cannot offset the morphological collapse of the ink from the jetting to the curing stage. Neither of them designed an inverse solver that includes a "rheological erosion operator". They could neither accurately predict the dynamic spreading and deformation process of ink droplets, nor generate inverse compensation data that could counteract the leveling effect. Ultimately, they could not meet the requirements of high mechanical interlocking force for multilayer PCBs in reflow soldering and high-temperature thermal shock testing. Summary of the Invention

[0005] This invention is applicable to additive manufacturing scenarios of multilayer PCBs using nano-conductive inks, meeting the stringent process requirements of high-frequency, high-speed circuits for interlayer bonding and geometric fidelity. By acquiring a time-series morphological dataset of the fluid's microscopic dynamic spreading characteristics and extracting a rheological fingerprint composed of balanced aspect ratio, leveling time constant, and maximum edge velocity, it achieves quantitative characterization of ink leveling dynamics and precise construction of the rheological response function. A three-dimensional rheological erosion kernel transforms the original design model into a set of physical entities that reproduce the rheological smoothing effect, converting traditional geometric design evaluation into dynamic prediction encompassing physical rheological processes, and accurately identifying rheological contraction and expansion regions in interlocking features. The topological pre-distortion structure generated based on the principle of inverse geometric compensation can offset feature collapse caused by surface tension with a "reverse distortion" morphology, significantly improving the physical fidelity of microscopic interlocking patterns such as dovetail grooves and barbs. By combining printability constraint filtering and minimum feature size constraint filtering, this invention not only solves the manufacturing stability problems of suspended voxel clusters, but also transforms the compensated geometric information into efficient anti-leveling topology printing data, fundamentally enhancing the mechanical anchoring force and interface stability of multilayer PCBs.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for generating interface topology in additive manufacturing of multilayer PCBs to enhance interlayer bonding includes:

[0008] The contour image of conductive ink on the surface of an insulating substrate is obtained. Edge detection and temporal extraction are performed on the contour image to obtain a temporal morphological dataset of fluid micro-dynamic spreading characteristics. The dynamic aspect ratio is calculated based on the temporal morphological dataset. Nonlinear regression fitting is performed on the dynamic aspect ratio to extract the rheological fingerprint of the leveling dynamics. A rheological response function is constructed based on the rheological fingerprint. A three-dimensional rheological erosion kernel is generated based on the rheological response function.

[0009] Three-dimensional convolution operations are performed based on a three-dimensional rheological erosion kernel to generate a set of physical entities. A geometric deviation field is calculated based on the set of physical entities, and a topological pre-distortion structure is constructed based on the geometric deviation field.

[0010] Printability constraint filtering is applied to the pre-distorted topology structure to obtain the corrected topology structure. Minimum feature size constraint filtering is then applied to the corrected topology structure to generate anti-leveling topology printing data.

[0011] Furthermore, the method for obtaining the time-series morphological dataset includes:

[0012] A conductive ink in a deposited state is obtained on the surface of an insulating substrate. An ink drop observation coordinate system is established with the geometric center of the conductive ink as the origin. The Z-axis of the ink drop observation coordinate system is defined as the geometric normal of the origin perpendicular to the plane of the insulating substrate. The two-dimensional extended plane that coincides with the surface of the insulating substrate is defined as the XY plane of the ink drop observation coordinate system.

[0013] Set the observation frequency and sampling time, and collect the contour image of the conductive ink corresponding to each sampling time according to the observation frequency;

[0014] The contour image at each sampling moment is analyzed using the ink droplet observation coordinate system to generate a morphological feature vector, which includes instantaneous height, instantaneous spreading radius, center height change rate, and edge radius change rate.

[0015] Arrange the morphological feature vectors of all sampling times in chronological order to obtain the temporal morphological dataset.

[0016] Furthermore, the rheological fingerprint includes:

[0017] The dynamic aspect ratio is calculated for each sampling moment based on the temporal morphology dataset. The dynamic aspect ratio is the ratio of the instantaneous height to the instantaneous spreading radius corresponding to each sampling moment. The dynamic aspect ratios of all sampling moments are arranged in temporal order to obtain the aspect ratio set.

[0018] A decay function containing an exponential decay term is constructed, and a global regression fitting is performed on the aspect ratio set to obtain the balanced aspect ratio, the initial aspect ratio, and the leveling time constant. The maximum value of the edge radius change rate is extracted by traversing the time-series morphology dataset and defined as the maximum edge rate.

[0019] The balanced aspect ratio, leveling time constant, and maximum edge velocity are combined to form a rheological fingerprint.

[0020] Furthermore, the method for constructing the three-dimensional rheological erosion core includes:

[0021] The product of the maximum edge rate and the leveling time constant is defined as the leveling length. A constant scaling factor is set, and the product of the leveling length and the constant scaling factor is defined as the horizontal standard deviation.

[0022] The reciprocal of the balanced aspect ratio is defined as the collapse factor, and the vertical standard deviation is defined as the horizontal standard deviation divided by the collapse factor.

[0023] Based on the law of conservation of mass, a normalization coefficient is set, and a rheological response function in the form of a three-dimensional Gaussian distribution is constructed based on the horizontal standard deviation, the vertical standard deviation, and the normalization coefficient.

[0024] The cutoff radius is set according to the horizontal length. A three-dimensional numerical matrix composed of discrete matrix elements is constructed based on the cutoff radius. The matrix elements in the three-dimensional numerical matrix are traversed. The probability density function value of each matrix element is calculated using the rheological response function as the weight value. All matrix elements are normalized to obtain the three-dimensional rheological erosion kernel.

[0025] Furthermore, the set of physical entities includes:

[0026] A micro-voxel space composed of three-dimensional orthogonally arranged voxel units is established. The set of voxel units with a value of one in the micro-voxel space is defined as the design entity, and the set of voxel units with a value of zero is defined as the background void, thereby obtaining the original design model.

[0027] A three-dimensional rheological erosion kernel is used to perform a global sliding scan on the original design model. Any voxel unit in the micro-voxel space is defined as the target voxel, and the coordinates of the target voxel in the micro-voxel space are defined as the global coordinates. The preset coordinate markers inside the three-dimensional rheological erosion kernel are traversed to obtain the binarized values ​​of the original design model at the positions of the global coordinates minus the coordinate markers. The binarized values ​​are then multiplied by the weight values ​​of the matrix elements of the three-dimensional rheological erosion kernel at the corresponding coordinate markers. All product results are summed to obtain the scalar field strength value.

[0028] Set a solidification threshold. If the scalar field strength value is greater than or equal to the solidification threshold, the target voxel is determined to be a physical entity and its binarized value is set to one. If the scalar field strength value is less than the solidification threshold, the target voxel is determined to be a physical void and its binarized value is set to zero. The set of all target voxels determined to be physical entities is defined as the physical entity set.

[0029] Furthermore, the topological predistortion structure includes:

[0030] Calculate the difference between the binarized values ​​of the original design model and the physical entity set at the target voxel. If the difference is 1, 0 or -1, the corresponding spatial region of the target voxel in the micro voxel space is defined as the rheological contraction region, the rheological expansion region and the geometric matching region, respectively.

[0031] For the rheological shrinkage region, morphological expansion operation is performed with the voxel unit of the rheological shrinkage region as the shrinkage compensation center to generate positive compensation voxels and superimpose them onto the original design model;

[0032] For the rheological expansion region, morphological expansion operation is performed with the voxel unit of the rheological expansion region as the center of the expansion mask to generate negative mask voxels and remove them from the original design model to obtain the topological predistortion structure.

[0033] Furthermore, the modified topology includes:

[0034] Set spatial adjacency rules, traverse the topological predistortion structure, and divide the voxel units that satisfy the spatial adjacency rules and have a binarized value of one into independent connected domains.

[0035] The number of voxel units contained within each independent connected region is counted and defined as the independent voxel number. A minimum droplet forming threshold is set.

[0036] Traverse all independent connected components: if the number of independent voxels is less than the minimum droplet formation threshold, define the independent connected component as a suspended voxel cluster and remove it from the topology predistortion structure; if the number of independent voxels is greater than or equal to the minimum droplet formation threshold, retain the independent connected component and obtain the corrected topology structure.

[0037] Furthermore, the minimum feature size constraint filtering includes:

[0038] Obtain the minimum physical resolution of the printing device to construct constraint structure elements, and define spatial neighborhoods based on the constraint structure elements;

[0039] Using constraint structuring elements, erosion and dilation operations are performed sequentially on the modified topology:

[0040] In the erosion operation, the voxel units within the modified topology are traversed and the corresponding spatial neighborhoods are obtained. If there is a voxel unit with a binary value of zero in the spatial neighborhood, the binary value of the current voxel unit is forcibly updated to zero.

[0041] In the dilation operation, if the binarized value of a voxel unit is detected to be one, the binarized values ​​of all voxel units in the corresponding spatial neighborhood are forcibly set to one.

[0042] A smooth topology is obtained by sequentially performing erosion and dilation operations on the modified topology.

[0043] Furthermore, the anti-leveling topology printing data includes:

[0044] The single-layer printing thickness and the voxel resolution of the micro voxel space in the Z-axis direction of the printing device are obtained. The ratio of the single-layer printing thickness to the voxel resolution is calculated and the ratio is rounded up to obtain the sampling step size.

[0045] Establish a slice index and increment the slice index by the sampling step size. For each slice index, create a two-dimensional numerical matrix consisting of control units arranged in a rectangular array and traverse the control units in the two-dimensional numerical matrix.

[0046] Based on the plane matrix index preset by the control unit, the voxel unit whose height is determined by the slice index and whose plane position is determined by the plane matrix index is located in the smooth topology, and the binarized value of the voxel unit is read.

[0047] If the read binary value is one, the preset injection state value of the control unit is set to one and defined as an effective injection point; if the read binary value is zero, the injection state value of the control unit is set to zero and defined as a blank avoidance point.

[0048] Stack all the generated two-dimensional numerical matrices in ascending order of slice index to obtain anti-leveling topology printing data.

[0049] A system for generating interface topology structures for multilayer PCB additive manufacturing that enhances interlayer bonding, used to implement the aforementioned method for generating interface topology structures for multilayer PCB additive manufacturing that enhances interlayer bonding, the system comprising:

[0050] Fingerprint extraction module: used to acquire the contour image of conductive ink on the surface of insulating substrate, perform edge detection and temporal extraction on the contour image to obtain a temporal morphological dataset of fluid micro-dynamic spreading characteristics, calculate the dynamic aspect ratio based on the temporal morphological dataset, perform nonlinear regression fitting on the dynamic aspect ratio to extract the rheological fingerprint of the flow dynamics behavior, construct the rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function.

[0051] Topology compensation module: used to perform three-dimensional convolution operation based on three-dimensional rheological erosion kernel, generate physical entity set, calculate geometric deviation field based on physical entity set, and construct topology pre-distortion structure based on geometric deviation field;

[0052] Manufacturing Constraint Module: Used to perform printability constraint filtering on the topology predistortion structure to obtain the corrected topology structure, perform minimum feature size constraint filtering on the corrected topology structure, and generate anti-leveling topology printing data.

[0053] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0054] This invention, based on rheological fingerprints and rheological response functions extracted from time-series morphological datasets, achieves a precise mapping from transient microfluidic motion to a digital rheological dynamics space, solving the pain point of traditional solutions neglecting the rheological properties of nano-inks, leading to geometric distortions in design and manufacturing. The three-dimensional rheological erosion kernel transforms the traditional "what you see is what you get" static slicing into a dynamic three-dimensional convolution operation encompassing physical rheological processes, accurately identifying and quantifying the geometric deviations between rheological contraction and expansion regions, overcoming the limitation of traditional techniques in predicting droplet deformation before solidification. The topological pre-distortion structure follows the principle of inverse geometric compensation, adjusting the interface... Qualitative design is transformed into quantitative reconstruction based on "reverse distortion" with compensation gain coefficient. By accurately offsetting the leveling smoothing effect caused by surface tension through positive compensation voxels and negative mask voxels, the physical fidelity of micro-interlocking patterns such as dovetail grooves is ensured. In addition, the introduction of printability constraint filtering and minimum feature size constraint filtering effectively eliminates suspended voxel clusters and eliminates high-frequency geometric jitter of edge contours, ensuring accurate adaptation of anti-leveling topology printing data and physical resolution of printing equipment. While achieving high-fidelity micro-interlocking features, it significantly enhances the interlayer mechanical anchoring force and manufacturing reliability of multilayer PCBs. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 A flowchart illustrating the method for generating interface topology in additive manufacturing of multilayer PCB boards to enhance interlayer bonding, as provided in an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram of a multilayer printed circuit board additive manufacturing process in an embodiment of the present invention;

[0058] Figure 3 This is a schematic diagram of the reverse geometric compensation logic for constructing a topological predistortion structure based on a geometric deviation field, provided in an embodiment of the present invention.

[0059] Figure 4 This is a functional block diagram of the interface topology generation system for additive manufacturing of multilayer PCB boards to enhance interlayer bonding, provided in an embodiment of the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] Example 1

[0062] Please see Figure 1 As shown, this embodiment provides a method for generating interface topology structures in additive manufacturing of multilayer PCB boards to enhance interlayer bonding, including:

[0063] Step S10: Obtain the contour image of conductive ink on the surface of the insulating substrate, perform edge detection and temporal extraction on the contour image to obtain a temporal morphology dataset of fluid micro-dynamic spreading characteristics, calculate the dynamic aspect ratio based on the temporal morphology dataset, perform nonlinear regression fitting on the dynamic aspect ratio to extract the rheological fingerprint of the leveling dynamics, construct the rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function.

[0064] Further, step S10 includes:

[0065] Step S11: Obtain the contour image of the conductive ink on the surface of the insulating substrate, perform edge detection and temporal extraction on the contour image, and obtain the temporal morphological dataset of the fluid micro-dynamic spreading characteristics.

[0066] In the additive manufacturing process of multilayer printed circuit boards, the circuit formation process occurs on an insulating substrate, which is a plate-like carrier used to hold conductive ink and support the multilayer circuit structure. During inkjet printing, conductive ink, as the material basis of the micro-interlocking structure, is discretely sprayed onto the surface of the insulating substrate by the print head. The micro-morphological evolution of the conductive ink determines the geometric fidelity of the final solidified structure. The leveling effect, that is, the physical process of spontaneous transformation from a high-potential-energy sharp shape to a low-potential-energy rounded shape driven by surface tension after the conductive ink contacts the insulating substrate, is the main physical root cause of the failure of the designed micro-interlocking structure. The occurrence of the leveling effect is highly time-varying and anisotropic, and the evolution trajectory of the leveling effect depends on the viscosity of the conductive ink, the surface tension, and the wetting angle between the conductive ink and the insulating substrate. Therefore, it is necessary to establish an observation framework that can accurately map the hydrodynamic behavior of conductive ink to the time dimension and output a structured time-series morphological dataset. The aim is to transform the transient and elusive micro-fluidic motion into a static, computable, and predictive digital description. See Figure 2This diagram illustrates a scenario of additive manufacturing of a multilayer printed circuit board in an embodiment of the present invention, showcasing the microscopic physical process of conductive ink from jetting to deposition. At the top is the printhead, performing the core manufacturing task. The printhead is in operation, discretely releasing conductive ink, forming a series of vertically falling, discretely jetted conductive ink particles in flight. The discretely jetted conductive ink eventually lands on the surface of the supporting carrier, i.e., the insulating substrate. Upon contact with the insulating substrate, influenced by fluid physics, its morphology evolves from an initial high-potential-energy state to a low-potential-energy, rounded shape as shown in the diagram. This landed and stabilized droplet is the conductive ink in the deposition state marked in the diagram.

[0067] Specifically, to describe the geometric changes of the conductive ink spreading microscopic event on the insulating substrate, a fixed microscopic three-dimensional Cartesian coordinate system, namely the droplet observation coordinate system, is established with the geometric center of the deposited conductive ink on the insulating substrate as the origin. The Z-axis of the droplet observation coordinate system is defined as the geometric normal perpendicular to the plane of the insulating substrate and pointing to the location of the print head; the X-axis is defined as a straight line located within the surface of the insulating substrate and parallel to the tangent direction of the print head's movement trajectory during the ejection action; the Y-axis is defined as a straight line located within the surface of the insulating substrate, passing through the origin, and perpendicular to both the Z-axis and the X-axis; the XY plane of the droplet observation coordinate system, formed by the X-axis and Y-axis, is a two-dimensional extended plane macroscopically coinciding with the microscopically rough upper surface of the insulating substrate, thus establishing a spatial measurement system with the insulating substrate as the absolute reference and the printing path as the directional guide. Taking the moment when the printhead performs discrete ejection as the zero point of time, the conductive ink in its deposition state that has just landed on the surface of the insulating substrate is tracked and photographed in situ using a high-speed stroboscopic microscopy unit integrated in the printing device. The high-speed stroboscopic microscopy unit is a photoelectric capture component integrated in the data acquisition link, which has a precisely calibrated optical field of view, and the geometric center of the optical field of view is mechanically locked and aligned with the origin of the ink droplet observation coordinate system. The working logic utilizes short-pulse illumination to freeze the high-speed fluid motion posture within microseconds, thereby acquiring clear transient images within the optical field of view. A high-speed stroboscopic microscopy unit periodically acquires contour images of the deposited conductive ink according to a preset observation frequency. The observation frequency is set to ensure that the morphological changes of the conductive ink from contact with the insulating substrate to complete solidification are captured; for example, one frame is acquired every microsecond. The sampling time is set to M, with t representing the index of the sampling time, ranging from 1 to M. The value of M is greater than the product of the fluid relaxation time constant of the conductive ink and the observation frequency to satisfy the Nyquist sampling theorem's requirement for complete reproduction of the rheological curve inflection point, preventing aliasing of leveling dynamics characteristics due to insufficient sampling points. The fluid relaxation time constant is defined as the characteristic physical time required for the conductive ink to evolve from its unstable state at the moment of contact to its final static equilibrium state under the drive of surface tension. Meanwhile, an effective detection area is defined within the optical field of view. The size setting logic is: the physical wetting limit range determined by the standard jet volume of the conductive ink and the limit balance contact angle on the insulating substrate, multiplied by a preset process redundancy coefficient as the side length.The limiting equilibrium contact angle is defined as the angle between the tangents at the solid-liquid-gas three-phase interface when the conductive ink stops spreading on the insulating substrate and reaches a state of static equilibrium. Its value is obtained by measuring a single droplet static test. The process redundancy coefficient is set to cover the deviation of the wetting boundary position caused by the mechanical positioning error of the print head and the slight volume fluctuation of the conductive ink. For example, the value is 1.2. The standard jet volume is obtained from the nameplate of the print head equipment. The purpose of setting the effective detection area is to ensure the complete envelopment of the physical wetting boundary of the conductive ink while effectively eliminating invalid background noise at the edge of the field of view, thereby maximizing the use of the spatial resolution advantage of optical imaging technology at the microscale.

[0068] The acquired contour images are analyzed using the ink droplet observation coordinate system to generate a structured morphological feature vector S. For each contour image acquired at sampling time t, the corresponding morphological feature vector S(t) is: ,in, For the t-th sampling time, the coordinates of the highest point of the deposited conductive ink on the Z-axis of the ink droplet observation coordinate system are used to characterize the instantaneous height H of the fluid. Let R be the maximum projected radius of the edge of the deposited conductive ink on the XY plane of the ink droplet observation coordinate system at the t-th sampling time, used to characterize the instantaneous spreading radius R of the fluid. This represents the instantaneous rate of change of the center height of the conductive ink over time, i.e., the center height change rate. The calculation is performed using the first-order backward difference formula, which is as follows: ,in, For the (t-1)th sampling time, the coordinates of the highest point of the deposited conductive ink on the Z-axis of the ink droplet observation coordinate system are: The time interval between two adjacent samples; This represents the instantaneous rate of change of the edge radius of the conductive ink over time, i.e., the edge radius change rate. The calculation is performed using the first-order backward difference formula, which is as follows: ,in, At the (t-1)th sampling time, the maximum projected radius of the edge of the deposited conductive ink on the XY plane of the ink droplet observation coordinate system, i.e., the morphological feature vector at each sampling time, includes instantaneous height, instantaneous spreading radius, rate of change of center height, and rate of change of edge radius. The logic for constructing the morphological feature vector is: through direct measurement values... and Capture the static profile of the fluid and calculate values ​​through differential calculation. and Capturing the dynamic trends of fluids; among which, This reflects the intensity of gravity and longitudinal collapse. This reflects the intensity of the lateral flow driven by surface tension. The morphological feature vectors of all M sampling times are arranged in chronological order to obtain a temporal morphological dataset. The temporal morphological dataset essentially maps the continuous, simulated flow spreading process of conductive ink in the physical world into a discretized numerical trajectory that can be recognized by a computer.

[0069] Step S12: Calculate the dynamic aspect ratio based on the time-series morphological dataset, perform nonlinear regression fitting on the dynamic aspect ratio, and extract the rheological fingerprint of the leveling dynamics behavior.

[0070] The temporal morphology dataset, as a holographic record of the microscopic evolution of conductive ink, contains the dynamic laws of fluids under the combined action of surface tension and viscous force. In order to further transform the microscopic geometric evolution trajectory recorded in the temporal morphology dataset into dynamic parameters that can reveal the physical essence of the leveling effect, dimensionless processing and nonlinear regression analysis are performed on the temporal morphology dataset to extract rheological fingerprints.

[0071] Specifically, based on a time-series morphological dataset, the dynamic aspect ratio is calculated for each sampling moment. This dynamic aspect ratio is a dimensionless physical parameter characterizing the sharpness of the geometric shape of the deposited conductive ink during leveling. Its numerical value is obtained by the ratio of the corresponding instantaneous height to the instantaneous spreading radius. The purpose of introducing the dynamic aspect ratio is to construct a dimensionless evaluation index independent of minute fluctuations in the absolute volume of the conductive ink, thereby quantifying the degree of morphological collapse of the conductive ink during leveling. Because the instantaneous height of the deposited conductive ink continuously decreases over time under the combined effects of gravity and surface tension, while the instantaneous spreading radius continuously expands, the dynamic aspect ratio exhibits a monotonically decreasing trend over time. This evolution process accurately maps the spontaneous transformation of the conductive ink from a high-potential unstable state upon contact with the insulating substrate to a low-potential static equilibrium state. The dynamic aspect ratios at M sampling times are sequentially arranged to obtain an aspect ratio set. To analyze the underlying physical mechanism controlling this transition process, a nonlinear least squares method is used, and a decay function is employed to perform a global regression fitting on the aspect ratio set containing data from all sampling times. It is important to note that this global regression fitting is not based on numerical solutions for any single sampling time, but rather on statistical optimization of the entire time domain data. The dynamic aspect ratios corresponding to all M sampling times are considered as constraints and participate in the calculation simultaneously. The aim is to find an optimal set of coefficients A, B, and C that remain constant throughout the entire time domain, minimizing the sum of squared residuals between the theoretical curve of the decay function and all M actual observed data points. The decay function formula is as follows: ,in, Let represent the dynamic aspect ratio fitted value corresponding to the t-th sampling time, and e represent the base of the natural logarithm. The specific fitting logic is as follows: as the sampling time t approaches infinity, the exponential decay term... As the value approaches 0, the theoretically fitted value of the dynamic aspect ratio approaches A. Given that conductive ink inevitably reaches a static steady state after an infinitely long time, this mathematical behavior corresponds to a physical steady-state characteristic. The coefficient A is physically mapped to the equilibrium aspect ratio, which characterizes the final stable geometric shape at the end of the leveling dynamics process. When the sampling time t is extrapolated backward to 0, the exponential decay term is 1. At this point, the theoretically fitted value of the dynamic aspect ratio is always equal to B. Given that t = 0 corresponds to the physical instant of fluid contact with the substrate, this mathematical behavior corresponds to a physical initial characteristic. The coefficient B is physically mapped to the initial aspect ratio, which characterizes the initial geometric shape at the instant the conductive ink contacts the insulating substrate. The coefficient C, as the denominator of the exponential term, mathematically determines the decay rate of the decay function as t increases. Physically, the coefficient C is mapped to the leveling time constant, characterizing the standard characteristic proportion of the total evolution amplitude, BA, during the evolution of the dynamic aspect ratio from the initial aspect ratio B to the equilibrium aspect ratio A. The required number of sampling time intervals. The balanced aspect ratio and leveling time constant obtained through the global regression fitting analysis are combined with the maximum value of the edge radius change rate extracted by traversing the time-series morphology dataset to form a rheological fingerprint, wherein the maximum value of the edge radius change rate is defined as the maximum edge rate.

[0072] Step S13: Construct a rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function.

[0073] Rheological fingerprinting quantitatively reveals the physical decay law of conductive ink on a macroscopic time scale. In order to transform this physical law into a geometric operation operator that can be executed by a computer in a three-dimensional digital manufacturing space, a three-dimensional rheological erosion kernel that can accurately describe the spatial migration probability of ink mass is constructed.

[0074] Specifically, a voxelization discretization algorithm based on ray projection is used to discretize the multilayer printed circuit board to be printed, establishing a micro-voxel space that matches the physical resolution of the printing device. This micro-voxel space is a discrete set composed of three-dimensionally orthogonally arranged voxel units. Each voxel unit has a binary state attribute to characterize whether the spatial location is filled with conductive ink. The physical size of the voxel unit is set to match the minimum physical resolution of the print head. Using the ink droplet observation coordinate system as a mathematical reference, and employing rheological fingerprinting to define a rheological response function describing ink diffusion behavior, this function is a three-dimensional Gaussian probability density function G(X,Y,Z) characterizing the physical probability density of mass transfer to surrounding spatial positions during the leveling dynamics of conductive ink. X, Y, and Z are strictly aligned with the directions of the ink droplet observation coordinate system. The construction logic is as follows: the product of the maximum edge velocity and the leveling time constant is defined as the leveling length, which represents the characteristic spreading distance that the fluid can complete in the XY plane of the ink droplet observation coordinate system under surface tension; the standard deviation of the rheological response function in the XY plane of the ink droplet observation coordinate system, i.e., the horizontal standard deviation, is defined as follows: Set to be positively correlated with the leveling length, i.e. Where K is a constant scaling factor set according to the three sigma statistical criterion, for example, it is set to 0.3. This represents the leveling length. The positive correlation is set because the leveling length physically quantifies the dynamic limit distance at which conductive ink can undergo lateral displacement driven by surface tension; while the standard deviation of the Gaussian function mathematically determines the effective coverage width of the probability distribution. The stronger the physical dynamic spreading ability, i.e., the larger the leveling length, the wider the mathematical probability range of ink mass diffusion in all directions should be, i.e., the larger the horizontal standard deviation. The distribution shape of the rheological response function in the Z-axis direction of the ink droplet observation coordinate system is corrected using the balanced aspect ratio in the rheological fingerprint. Specifically, a collapse factor is set, which is the reciprocal of the balanced aspect ratio, and the standard deviation of the rheological response function in the Z-axis direction of the ink droplet observation coordinate system, i.e., the vertical standard deviation, is calculated. Set as Divide by the collapse factor, i.e. The reason is that the equilibrium aspect ratio directly reflects the geometric "flatness" of the ink under static steady state. When the equilibrium aspect ratio is small, for example, less than 1, it means that the ink height is low and the spread is wide, which physically manifests as a significant collapse effect in the vertical direction. By setting the vertical standard deviation to be proportional to the equilibrium aspect ratio, when the aspect ratio decreases proportionally, the vertical standard deviation also decreases. In a Gaussian distribution, this means that the vertical distribution is "narrower" and more concentrated. Therefore, combining the above horizontal and vertical standard deviations, the rheological response function is obtained, and its calculation formula is: ,in, The normalization coefficient is set according to the law of conservation of mass, meaning that the leveling process only changes the geometric distribution of the conductive ink without changing its total volume. Therefore, the normalization coefficient forces the integral of the rheological response function over the entire space to be 1. exp(·) represents the abbreviation for exponential function, and X, Y, and Z all represent coordinate variables in the ink droplet observation coordinate system.

[0075] Specifically, the cutoff radius is set based on the leveling length. The setting is based on the statistical cutoff criterion of the Gaussian distribution. According to statistical principles, regions more than three standard deviations from the center have a probability density integral value of less than 0.3%. Therefore, the cutoff radius is set to the smallest integer voxel unit greater than or equal to the leveling length. Based on the cutoff radius, a three-dimensional numerical matrix, i.e., a three-dimensional rheological erosion kernel, is constructed. To cover the physical influence domains in both positive and negative directions, for example, the dimensions of this three-dimensional numerical matrix in the X, Y, and Z dimensions are all set to twice the cutoff radius plus one. That is, the three-dimensional rheological erosion kernel is structurally composed of cubic units arranged in a three-dimensional array, which are the matrix elements of the three-dimensional rheological erosion kernel. Each matrix element is assigned a unique set of coordinate identifiers (I, J, L), where I, J, and L correspond to discrete position numbers in the X, Y, and Z axes, respectively, with values ​​ranging from the negative cutoff radius to the positive cutoff radius. The matrix element with coordinates (0,0,0) is defined as the geometric center unit of the 3D rheological erosion kernel. Spatial sampling calculations are performed on each matrix element within the 3D rheological erosion kernel. The calculation logic is as follows: the index coordinates (I,J,L) of the matrix element are directly used as relative coordinate variables in physical space, i.e., physical coordinates X=I, Y=J, Z=L, and substituted into the rheological response function to obtain a probability density function value. This probability density function value is written into the matrix element as a weight value for that position. After assigning values ​​to all matrix elements, the sum of the values ​​of all matrix elements within the 3D rheological erosion kernel is calculated. The value in each matrix element is divided by this sum, and the matrix element is updated with the calculation result.

[0076] Step S10, through rheological fingerprinting, rheological response function, and three-dimensional rheological erosion kernel, solves the technical problem of the mismatch between the microscopic rheological properties of nano-conductive ink and the slice data, which causes the sharp "interlocking features" in the design data to degrade and fail before curing due to the "rheological smoothing effect" driven by surface tension. This achieves a precise mapping from transient microfluidic motion to a digital, predictable rheological dynamics model space. Specifically, the rheological fingerprint quantitatively reveals the physical decay law of conductive ink on a macroscopic timescale; the rheological response function establishes the physical probability density of ink mass transfer to the surrounding spatial position; and the three-dimensional rheological erosion kernel transforms the rheological response function into a three-dimensional numerical matrix, providing core geometric operators for subsequent simulation of the rheological dynamics process.

[0077] Step S20: Perform three-dimensional convolution operation based on the three-dimensional rheological erosion kernel to generate a physical entity set, calculate the geometric deviation field based on the physical entity set, and construct a topological predistortion structure based on the geometric deviation field.

[0078] Further, step S20 includes:

[0079] Step S21: Perform a three-dimensional convolution operation based on the three-dimensional rheological erosion kernel to generate a physical entity set.

[0080] After obtaining the three-dimensional rheological erosion core, in order to quantitatively evaluate the form in which the designed micro-interlocking structure will degenerate in actual printing, the three-dimensional rheological erosion core is used to perform forward simulation of the design data.

[0081] Specifically, the original design model within the micro-voxel space is obtained. This original design model is a binary scalar field generated by mapping ideal CAD design data of a multilayer printed circuit board into the micro-voxel space. The set of voxel units with a value of 1 in the micro-voxel space is defined as the design entity, representing the expected conductive material filling area; the set of voxel units with a value of 0 in the micro-voxel space is defined as background voids, representing the air region without material. A three-dimensional rheological erosion kernel is used as a mathematical operator to simulate rheological dynamics, performing a global three-dimensional spatial convolution operation on the original design model to generate a rheological potential energy field. This operation mathematically simulates the probabilistic migration of conductive ink mass driven by surface tension and gravity from the high-potential-energy design entity region to the low-potential-energy background void region. The generation of the rheological potential energy field is achieved through a three-dimensional convolution operation. The specific operational logic is as follows: using a three-dimensional rheological erosion kernel as the convolution operator, a global sliding scan is performed on the original design model. During the scanning process, any voxel unit in the micro voxel space is defined as the target voxel, and the coordinates of the target voxel in the micro voxel space are defined as the global coordinates. The rheological potential energy intensity at the target voxel is calculated by: traversing all coordinate markers inside the three-dimensional rheological erosion core; for each traversed coordinate marker, obtaining the binarized value of the original design model at the position after subtracting the coordinate marker from the global coordinates; multiplying the binarized value by the matrix element weight value of the three-dimensional rheological erosion core at the corresponding coordinate marker; summing all the calculated product results within the traversal range; the calculated product sum is the physical probability density intensity of the conductive ink migrating to the target voxel under the leveling effect; and assigning the product sum as the scalar field strength value of the rheological potential energy field at the target voxel.

[0082] To restore the continuously changing rheological potential energy field to a solidified structure with a clear gas-liquid physical interface, a solidification threshold is set. This threshold is based on the principle of conservation of conductive solute volume, ensuring that the volume of the entity generated by numerical truncation remains consistent with the original designed volume within a preset tolerance range, preventing virtual volume expansion or contraction due to numerical calculation errors. For example, the solidification threshold is set to 0.5. The scalar field strength at each target voxel is determined. If the scalar field strength is greater than or equal to the solidification threshold, the target voxel is determined to be a physical entity after solidification, and its binarized value is set to 1. If the scalar field strength is less than the solidification threshold, the target voxel is determined to be a physical void after solidification, and its binarized value is set to 0. All physical entities and target voxels that have been assigned binary values ​​are combined into a physical entity set. The physical entity set quantitatively reproduces the rheological smoothing effect of conductive ink in the actual additive manufacturing process in terms of geometric features. This causes the sharp edges of the micro-interlocking patterns such as barbs, dovetail grooves or overhang structures that originally existed in the original design model to degenerate into smooth wavy or collapsed shapes in the predicted physical entity structure.

[0083] Step S22: Calculate the geometric deviation field based on the physical entity set, and construct the topological predistortion structure based on the geometric deviation field.

[0084] To accurately quantify the degree of geometric distortion of conductive ink under rheological smoothing effects and construct inverse compensation data capable of offsetting this distortion, the original design model and the generated physical entity set are used as computational inputs. A geometric deviation field is established to characterize the differential distribution, using the microscopic voxel space as the computational domain. The computational logic of the geometric deviation field is as follows: traversing each target voxel in the microscopic voxel space, calculating the difference between the binarized value of the original design model at the target voxel and the binarized value of the physical entity set at the target voxel, and defining this difference as the value of the geometric deviation field at the target voxel. The geometric deviation field obtained based on this calculation logic includes three numerical states, each corresponding to a different type of physical distortion: When the value of the geometric deviation field is 1, the spatial region corresponding to the target voxel in the micro-voxel space is defined as the rheological shrinkage region, indicating that the position exists in the design but disappears after actual curing, i.e., underfilling has occurred; when the value of the geometric deviation field is -1, the spatial region corresponding to the target voxel in the micro-voxel space is defined as the rheological expansion region, indicating that the position does not exist in the design but is filled by ink after actual curing, i.e., overfilling or collapse has occurred; when the value of the geometric deviation field is 0, the spatial region corresponding to the target voxel in the micro-voxel space is defined as the geometric matching region, indicating that the printing result is consistent with the design expectation.

[0085] A topological pre-distortion structure capable of pre-compensating rheological deformation is constructed based on a geometric deviation field. The construction logic follows the principle of inverse geometric compensation, i.e., adding material in the rheological contraction region to offset the volume shrinkage caused by surface tension, and reducing material in the rheological expansion region to suppress the collapse propagation caused by gravity. Specifically, a compensation gain coefficient is introduced. The compensation gain coefficient is a dimensionless scalar used to adjust the amplitude of the geometric compensation space. Its setting is based on the ratio of the leveling length to the inherent resolution of the micro-voxel space. This ratio physically reflects the range of voxel units that the conductive ink can laterally diffuse and cover under the driving force of leveling dynamics; for example, it is set to 1. A three-dimensional morphological expansion algorithm based on spherical structural elements is used to spatially correct the original design model. The correction logic is as follows: traverse the geometric deviation field and read the discrete deviation value stored in each target voxel. The discrete deviation value is the value of 1 used to characterize contraction or the value of -1 used to characterize expansion, which is calculated above. Specifically, for the target voxel with a discrete deviation value of 1, it is marked as the contraction compensation center, and the global coordinates of the contraction compensation center in the micro-voxel space are obtained. Morphological dilation is performed using global coordinates as the origin. The process is as follows: Construct a discrete spherical structuring element with a radius equal to the compensation gain coefficient. Traverse every voxel unit in the micro-voxel space and define the currently traversed voxel unit as a candidate voxel. Calculate the Euclidean distance between the global coordinates of the candidate voxel and the global coordinates of the contraction compensation center. Find all candidate voxels whose Euclidean distance is less than or equal to the radius of the discrete spherical structuring element. Mark the set of all found candidate voxels in the micro-voxel space as positive compensation voxels, thus forming a convex, sharp feature. For the target voxel with a discrete deviation of -1, mark it as the center of the dilation mask and obtain the global coordinates of the dilation mask center in the micro-voxel space. Morphological dilation is then performed using these global coordinates as the origin. The process is as follows: Construct a discrete spherical structuring element with a radius equal to the compensation gain coefficient. Traverse every candidate voxel in the micro-voxel space. Calculate the Euclidean distance between the global coordinates of the candidate voxel and the three-dimensional global coordinates of the dilation mask center. Find all candidate voxels whose Euclidean distance is less than or equal to the radius of the discrete spherical structural element. Mark the set of all found candidate voxels in the microscopic voxel space as negative mask voxels, thus forming a concave void-avoidance feature. Superimpose positive compensation voxels onto the original design model and remove the negative mask voxels from the original design model to obtain the topological predistortion structure. See also... Figure 3This is a schematic diagram of the reverse geometric compensation logic for constructing a topological predistortion structure based on a geometric deviation field, provided by an embodiment of the present invention. As shown in the figure, the schematic diagram includes two related mapping states: the left side shows the geometric deviation field identification state, and the right side shows the morphological reverse correction state. In the geometric deviation field identification state on the left, an example is shown as a local slice of the microscopic voxel space at a specific height, with the background grid representing discrete voxel units; the area enclosed by the black dashed line in the figure represents the original design model, and the area enclosed by the gray solid line represents the physical entity set; the red grid area located inside the original design model but not covered by physical entities is marked as a rheological contraction region with a value of 1; the blue grid area located outside the outline of the original design model but occupied by physical entities is marked as a rheological expansion region with a value of -1. The non-overlapping area between the rheological contraction region and the rheological expansion region constitutes the geometric deviation field. In the morphological inverse correction state on the right, the compensation process for the aforementioned deviation areas is demonstrated: For the red rheological contraction region, the central voxel is selected as the contraction compensation center, and a discrete spherical structural element with a radius equal to the compensation gain coefficient is constructed (shown as a yellow semi-transparent circle in the figure). Morphological expansion is performed to generate a set of outwardly protruding dark green voxels, defined as positive compensation voxels, thus forming a sharp, convex feature that counteracts contraction. For the blue rheological expansion region, the central voxel is selected as the expansion mask center, and expansion is performed using the discrete spherical structural element to determine a set of purple voxels that need to be removed, defined as negative mask voxels, thus forming a concave, hollow feature that counteracts collapse. The final generated topological predistortion structure exhibits a "reverse distortion" morphology that is completely opposite to the physical leveling trend.

[0086] Step S20, through physical entity sets, geometric deviation fields, and topological pre-distortion structures, solves the technical problem of traditional slicing algorithms neglecting rheological deformation, which prevents the physical interface from forming the designed "interlocking" shape, leading to a significant decrease in mechanical interlocking force. It achieves quantitative prediction of the degree of rheological distortion and reconstruction optimization based on the principle of inverse geometric compensation. Specifically, the physical entity set reproduces the collapse morphology and smoothing effect of conductive ink during actual processing; the geometric deviation field identifies and defines the rheological contraction region, rheological expansion region, and geometric matching region; and the topological pre-distortion structure, following the principle of inverse geometric compensation, generates reverse distortion data that can pre-compensate rheological deformation.

[0087] Step S30: Perform printability constraint filtering on the pre-distorted topology structure to obtain the corrected topology structure. Perform minimum feature size constraint filtering on the corrected topology structure to generate anti-leveling topology printing data.

[0088] Further, step S30 includes:

[0089] Step S31: Perform printability constraint filtering on the pre-distorted topology structure to obtain the corrected topology structure.

[0090] After obtaining the topology predistortion structure, printability constraint filtering is applied to the topology predistortion structure to ensure the stability and physical manufacturability of the additive manufacturing process.

[0091] Specifically, a spatial adjacency rule is defined: if the absolute value of the difference between the global coordinates of two voxel units along the X, Y, and Z axes is less than or equal to 1, then the two voxel units are considered to satisfy the spatial adjacency rule, meaning they are physically connected in space. A marker matrix with the same size as the micro-voxel space is initialized, and all elements in the marker matrix are initialized to 0, with 0 defined as an unvisited state. Each voxel unit in the topology predistortion structure is traversed sequentially. During the traversal, the global coordinates of the current voxel unit are obtained. The binarized value of this global coordinate in the topology predistortion structure and the value at the same global coordinate position in the marker matrix are then read using these global coordinates. If the current voxel unit has a value of 1 in the topology predistortion structure and a value of 0 at the same global coordinate position in the label matrix, a new independent connected component is identified. This voxel unit is defined as the starting seed point of the independent connected component, a unique connected component identifier is assigned to it, and the values ​​at the same global coordinate positions in the label matrix are updated to this identifier, thus marking it as visited. Using this starting seed point as the center, all voxel units that satisfy the spatial adjacency rules are searched. For each searched voxel unit, its corresponding global coordinates are obtained, and it is determined whether its value in the topology predistortion structure is 1 and whether its value at the same global coordinate position in the label matrix is ​​0. If both conditions are met, the values ​​at the same global coordinate positions of neighboring voxel units in the label matrix are also updated to the connected component identifier, and the voxel unit is added to the search queue. The recursive search continues outward from the newly marked voxel unit until no new voxel unit satisfying the spatial adjacency rules and with a label matrix value of 0 is found, thus completing the definition of an independent connected component. Repeat the above process of selecting the initial seed point and recursively searching until there are no more matrix elements in the marker matrix whose corresponding topology predistortion structure value is 1 and whose own value is 0. This divides all voxel units with a value of 1 into several independent connected components. The number of voxel units contained within each independent connected component is counted and defined as the independent voxel count. A minimum droplet formation threshold is introduced, which is a fixed integer value determined based on the ratio of the physical volume of a single standard ink droplet to the volume of a single voxel unit. All independent connected components are traversed: if the independent voxel count is less than the minimum droplet formation threshold, the independent connected component is defined as a suspended voxel cluster, and the values ​​of all voxel units within the suspended voxel cluster are forcibly modified to 0, thus removing the suspended voxel cluster from the topology predistortion structure; if the independent voxel count is greater than or equal to the minimum droplet formation threshold, the independent connected component is retained. By completing the traversal, judgment, and filtering of all independent connected components, invalid data that does not meet the physical forming conditions is eliminated, resulting in the corrected topology predistortion structure, defined as the corrected topology structure.

[0092] Step S32: Perform minimum feature size constraint filtering on the modified topology to generate anti-leveling topology printing data.

[0093] The modified topology removes dangling noise. To further eliminate high-frequency geometric jitter in the edge contours of the modified topology, which manifests as tiny burrs or protrusions, minimum feature size constraint filtering is applied to the modified topology.

[0094] Specifically, a constraint structuring element is constructed. This constraint structuring element is not a physical entity, but rather a set of discrete relative coordinates defined within a microscopic voxel space. Its construction logic is as follows: obtain the minimum physical resolution of the printing device, calculate the ratio of this minimum physical resolution to the side length of the voxel unit, and round this ratio up to define the feature constraint radius. The constraint structuring element is defined as all relative coordinate offsets that satisfy the following conditions. The set of: where , and All values ​​are integers, and their absolute values ​​are all less than or equal to the feature constraint radius. Based on the constraint structuring element, a spatial neighborhood is defined. For any voxel unit with global coordinates in the micro voxel space, its spatial neighborhood is defined as the set of all voxel units in the micro voxel space that satisfy the following coordinate condition: the global coordinates of the voxel unit are... ,in, This is a set of discrete relative coordinates defined by constraint structuring elements. Erosion and dilation operations are sequentially performed on the modified topology using these constraint structuring elements. The erosion operation involves traversing the voxel units within the modified topology and obtaining their corresponding spatial neighborhoods. The binary value of each voxel unit within its neighborhood is checked: if any voxel unit in the neighborhood has a value of 0, its value is forcibly updated to 0; only when all voxel units in the neighborhood have values ​​of 1 are their values ​​retained. This removes geometric features whose surface dimensions are smaller than the feature constraint radius. Dilation is then performed. Specifically, the micro-voxel space processed by the erosion operation is traversed again. If a voxel unit with a value of 1 is detected, its spatial neighborhood is obtained, and the values ​​of all voxel units whose global coordinates lie within this neighborhood are forcibly set to 1. This results in a smooth topology. The smooth topology represents a low-pass filtered geometry, eliminating all high-frequency geometric features smaller than the feature constraint radius, and retaining only the main geometric contour that can be stably reproduced by the print head in physical space.

[0095] Transform the smooth topology into low-level control commands for driving additive manufacturing equipment. Specifically, the sampling step size is calculated by obtaining the single-layer printing thickness specified on the printer's nameplate and the voxel resolution in the micro-voxel space along the Z-axis. The sampling step size is the ratio of the single-layer printing thickness to the voxel resolution, and this ratio is rounded up to obtain the sampling step size. A slice index U is established in the micro-voxel space, starting from 0 and incrementing by the sampling step size until it exceeds the maximum dimension index of the smooth topology in the Z-axis direction. For each determined slice index, a two-dimensional numerical matrix with a resolution of W×N is created, where W and N are equal to the total number of voxels in the micro-voxel space along the X and Y axes, respectively. The two-dimensional numerical matrix consists of W×N control units arranged in a rectangular array. The control unit is the smallest information carrier that constitutes the bitmap image. Each control pixel unit has a unique planar matrix index (P,Q), where P is the row index, ranging from 0 to W-1; Q is the column index, ranging from 0 to N-1. Each control unit stores an injection state value F(P,Q), whose value is only 0 or 1. Specifically, an all-zero matrix is ​​initialized as the current two-dimensional numerical matrix. Each control unit in the two-dimensional numerical matrix is ​​traversed. For the target discrete control unit with the planar matrix index (P, Q), addressing is performed within the smooth topology, and the binarized value of the voxel unit at the corresponding position is read. If the read voxel unit value is 1, the injection state value of the control unit is set to 1, and the control unit is defined as an effective injection point; if the read voxel unit value is 0, the injection state value of the control unit is set to 0, and the control unit is defined as a blank avoidance point. As the slice index accumulates incrementally with the discrete sampling step size, until the slice index value is greater than the maximum coordinate index value of the smooth topology in the Z-axis direction, the overall height of the smooth topology has been traversed. At this point, all the two-dimensional numerical matrices generated during the traversal are stacked in ascending order of their corresponding slice indices to obtain the anti-leveling topology printing data. The anti-leveling topology printing data is then transmitted to the control system of the additive manufacturing equipment. The control system parses the control unit in each two-dimensional numerical matrix. The printhead moves to the corresponding physical printing position based on the planar matrix index of the control unit. This physical printing position is a spatial location determined by the droplet observation coordinate system. The X-axis position of the physical printing position is calculated by multiplying the row index value in the planar matrix index by the physical dimension of the voxel unit in the X-axis direction. The Y-axis position of the physical printing position is calculated by multiplying the column index value in the planar matrix index by the physical dimension of the voxel unit in the Y-axis direction. The Z-axis value of this physical printing position in the droplet observation coordinate system is calculated by multiplying the slice index value corresponding to the current two-dimensional jet control matrix by the physical dimension of the voxel unit in the Z-axis direction.Subsequently, actions are executed based on the ejection state values ​​stored in the control unit: when the ejection state value is 1, ink droplets are ejected; when the ejection state value is 0, the printhead remains silent. This process creates, layer by layer, a multi-layer PCB board interface in the physical world that resists leveling effects and possesses high-fidelity micro-interlocking characteristics.

[0096] Step S30, by executing printability constraint filtering, minimum feature size constraint filtering, and anti-leveling topology printing data, solves the problem that suspended voxel clusters or high-frequency geometric burrs generated after pre-distortion processing cannot be stably reproduced by the printing equipment, thus affecting the manufacturability of physical entities and the stability of the bonding interface. It achieves a reliable transformation from the topology optimization model to high-fidelity, anti-leveling underlying driving instructions. Specifically, printability constraint filtering eliminates invalid suspended data that does not meet the minimum droplet forming threshold, ensuring the physical stability of the manufacturing process; minimum feature size constraint filtering eliminates high-frequency geometric jitter of edge contours, making the feature size accurately matched with the physical resolution of the printing equipment; and anti-leveling topology printing data transforms the compensated geometric information into underlying control information that drives the nozzle to perform discrete jetting actions, ultimately realizing the manufacturing of multilayer PCB board interfaces with high-fidelity micro-interlocking features.

[0097] Example 2

[0098] This embodiment, based on Embodiment 1, provides a multilayer PCB additive manufacturing interface topology generation system that enhances interlayer bonding, such as... Figure 4 As shown, it includes:

[0099] Fingerprint extraction module: used to acquire the contour image of conductive ink on the surface of insulating substrate, perform edge detection and temporal extraction on the contour image to obtain a temporal morphological dataset of fluid micro-dynamic spreading characteristics, calculate the dynamic aspect ratio based on the temporal morphological dataset, perform nonlinear regression fitting on the dynamic aspect ratio to extract the rheological fingerprint of the flow dynamics behavior, construct the rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function.

[0100] Topology compensation module: used to perform three-dimensional convolution operation based on three-dimensional rheological erosion kernel, generate physical entity set, calculate geometric deviation field based on physical entity set, and construct topology pre-distortion structure based on geometric deviation field;

[0101] Manufacturing Constraint Module: Used to perform printability constraint filtering on the topology predistortion structure to obtain the corrected topology structure, perform minimum feature size constraint filtering on the corrected topology structure, and generate anti-leveling topology printing data.

[0102] The fingerprint extraction module acquires the contour image of conductive ink on the surface of an insulating substrate, performs edge detection and temporal extraction on the contour image to obtain a temporal morphological dataset of the fluid's microscopic dynamic spreading characteristics, calculates the dynamic aspect ratio based on the temporal morphological dataset, performs nonlinear regression fitting on the dynamic aspect ratio to extract the rheological fingerprint of the leveling dynamics, constructs a rheological response function based on the rheological fingerprint, and generates a three-dimensional rheological erosion kernel based on the rheological response function, including:

[0103] Step S11: Obtain the contour image of the conductive ink on the surface of the insulating substrate, perform edge detection and temporal extraction on the contour image to obtain a temporal morphological dataset of the fluid micro-dynamic spreading characteristics.

[0104] Step S12: Calculate the dynamic aspect ratio based on the time-series morphological dataset, perform nonlinear regression fitting on the dynamic aspect ratio, and extract the rheological fingerprint of the horizontal dynamic behavior.

[0105] Step S13: Construct a rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function.

[0106] The topology compensation module describes performing three-dimensional convolution operations based on a three-dimensional rheological erosion kernel to generate a physical entity set, calculating a geometric deviation field based on the physical entity set, and constructing a topology predistortion structure based on the geometric deviation field, including:

[0107] Step S21: Perform a three-dimensional convolution operation based on the three-dimensional rheological erosion kernel to generate a physical entity set;

[0108] Step S22: Calculate the geometric deviation field based on the physical entity set, and construct the topological predistortion structure based on the geometric deviation field.

[0109] The manufacturing constraint module describes performing printability constraint filtering on the pre-distorted topology structure to obtain a corrected topology structure, and then performing minimum feature size constraint filtering on the corrected topology structure to generate anti-leveling topology printing data, including:

[0110] Step S31: Perform printability constraint filtering on the pre-distorted topology structure to obtain the corrected topology structure;

[0111] Step S32: Perform minimum feature size constraint filtering on the modified topology to generate anti-leveling topology printing data.

[0112] In addition, the parts of the technical solutions provided in the embodiments of this application that are consistent with the implementation principles of the corresponding technical solutions in the prior art have not been described in detail, so as to avoid excessive elaboration.

[0113] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for generating interface topology structures in additive manufacturing of multilayer PCBs to enhance interlayer bonding, characterized in that, The method includes: The contour image of conductive ink on the surface of an insulating substrate is obtained. Edge detection and temporal extraction are performed on the contour image to obtain a temporal morphological dataset of fluid micro-dynamic spreading characteristics. Based on the temporal morphological dataset, the dynamic aspect ratio of conductive ink at each sampling time is calculated. Nonlinear regression fitting is performed on the dynamic aspect ratio to extract the rheological fingerprint of the leveling dynamics. A rheological response function is constructed based on the rheological fingerprint. A three-dimensional rheological erosion kernel describing the spatial migration probability of ink mass is constructed based on the rheological response function. Three-dimensional convolution operations are performed based on a three-dimensional rheological erosion kernel to generate a set of physical entities. A geometric deviation field is calculated based on the set of physical entities. A topological pre-distortion structure that can pre-compensate rheological deformation is constructed based on the geometric deviation field. Printability constraint filtering is applied to the pre-distorted topology structure to obtain the corrected topology structure. Minimum feature size constraint filtering is then applied to the corrected topology structure to generate anti-leveling topology printing data.

2. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 1, characterized in that, The method for obtaining the time-series morphological dataset includes: A conductive ink in a deposited state is obtained on the surface of an insulating substrate. An ink drop observation coordinate system is established with the geometric center of the conductive ink as the origin. The Z-axis of the ink drop observation coordinate system is defined as the geometric normal of the origin perpendicular to the plane of the insulating substrate. The two-dimensional extended plane that coincides with the surface of the insulating substrate is defined as the XY plane of the ink drop observation coordinate system. Set the observation frequency and sampling time, and collect the contour image of the conductive ink corresponding to each sampling time according to the observation frequency; The contour image at each sampling moment is analyzed using the ink droplet observation coordinate system to generate a morphological feature vector, which includes instantaneous height, instantaneous spreading radius, center height change rate, and edge radius change rate. Arrange the morphological feature vectors of all sampling times in chronological order to obtain the temporal morphological dataset.

3. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 2, characterized in that, The rheological fingerprint includes: The dynamic aspect ratio is calculated for each sampling moment based on the temporal morphology dataset. The dynamic aspect ratio is the ratio of the instantaneous height to the instantaneous spreading radius corresponding to each sampling moment. The dynamic aspect ratios of all sampling moments are arranged in temporal order to obtain the aspect ratio set. A decay function containing an exponential decay term is constructed, and a global regression fitting is performed on the aspect ratio set to obtain the balanced aspect ratio, the initial aspect ratio, and the leveling time constant. The maximum value of the edge radius change rate is extracted by traversing the time-series morphology dataset and defined as the maximum edge rate. The balanced aspect ratio, leveling time constant, and maximum edge velocity are combined to form a rheological fingerprint.

4. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 3, characterized in that, The method for constructing the three-dimensional rheological erosion core includes: The product of the maximum edge rate and the leveling time constant is defined as the leveling length. A constant scaling factor is set, and the product of the leveling length and the constant scaling factor is defined as the horizontal standard deviation. The reciprocal of the balanced aspect ratio is defined as the collapse factor, and the vertical standard deviation is defined as the horizontal standard deviation divided by the collapse factor. Based on the law of conservation of mass, a normalization coefficient is set, and a rheological response function in the form of a three-dimensional Gaussian distribution is constructed based on the horizontal standard deviation, the vertical standard deviation, and the normalization coefficient. The cutoff radius is set according to the horizontal length. A three-dimensional numerical matrix composed of discrete matrix elements is constructed based on the cutoff radius. The matrix elements in the three-dimensional numerical matrix are traversed. The probability density function value of each matrix element is calculated using the rheological response function as the weight value. All matrix elements are normalized to obtain the three-dimensional rheological erosion kernel.

5. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 4, characterized in that, The set of physical entities includes: A micro-voxel space composed of three-dimensional orthogonally arranged voxel units is established. The set of voxel units with a value of one in the micro-voxel space is defined as the design entity, and the set of voxel units with a value of zero is defined as the background void, thereby obtaining the original design model. A three-dimensional rheological erosion kernel is used to perform a global sliding scan on the original design model. Any voxel unit in the micro-voxel space is defined as the target voxel, and the coordinates of the target voxel in the micro-voxel space are defined as the global coordinates. The preset coordinate markers inside the three-dimensional rheological erosion kernel are traversed to obtain the binarized values ​​of the original design model at the positions of the global coordinates minus the coordinate markers. The binarized values ​​are then multiplied by the weight values ​​of the matrix elements of the three-dimensional rheological erosion kernel at the corresponding coordinate markers. All product results are summed to obtain the scalar field strength value. Set a solidification threshold. If the scalar field strength value is greater than or equal to the solidification threshold, the target voxel is determined to be a physical entity and its binarized value is set to one. If the scalar field strength value is less than the solidification threshold, the target voxel is determined to be a physical void and its binarized value is set to zero. The set of all target voxels determined to be physical entities is defined as the physical entity set.

6. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 5, characterized in that, The topology predistortion structure includes: Calculate the difference between the binarized values ​​of the original design model and the physical entity set at the target voxel. If the difference is 1, 0 or -1, the corresponding spatial region of the target voxel in the micro voxel space is defined as the rheological contraction region, the rheological expansion region and the geometric matching region, respectively. For the rheological shrinkage region, morphological expansion operation is performed with the voxel unit of the rheological shrinkage region as the shrinkage compensation center to generate positive compensation voxels and superimpose them onto the original design model; For the rheological expansion region, morphological expansion operation is performed with the voxel unit of the rheological expansion region as the center of the expansion mask to generate negative mask voxels and remove them from the original design model to obtain the topological predistortion structure.

7. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 6, characterized in that, The modified topology includes: Set spatial adjacency rules, traverse the topological predistortion structure, and divide the voxel units that satisfy the spatial adjacency rules and have a binarized value of one into independent connected domains. The number of voxel units contained within each independent connected region is counted and defined as the independent voxel number. A minimum droplet forming threshold is set. Traverse all independent connected components: if the number of independent voxels is less than the minimum droplet formation threshold, define the independent connected component as a suspended voxel cluster and remove it from the topology predistortion structure; if the number of independent voxels is greater than or equal to the minimum droplet formation threshold, retain the independent connected component and obtain the corrected topology structure.

8. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 7, characterized in that, The minimum feature size constraint filtering includes: Obtain the minimum physical resolution of the printing device to construct constraint structure elements, and define spatial neighborhoods based on the constraint structure elements; Using constraint structuring elements, erosion and dilation operations are performed sequentially on the modified topology: In the erosion operation, the voxel units within the modified topology are traversed and the corresponding spatial neighborhoods are obtained. If there is a voxel unit with a binary value of zero in the spatial neighborhood, the binary value of the current voxel unit is forcibly updated to zero. In the dilation operation, if the binarized value of a voxel unit is detected to be one, the binarized values ​​of all voxel units in the corresponding spatial neighborhood are forcibly set to one. A smooth topology is obtained by sequentially performing erosion and dilation operations on the modified topology.

9. The method for generating interface topology of multilayer PCB additive manufacturing to enhance interlayer bonding as described in claim 8, characterized in that, The anti-leveling topology printing data includes: The single-layer printing thickness and the voxel resolution of the micro voxel space in the Z-axis direction of the printing device are obtained. The ratio of the single-layer printing thickness to the voxel resolution is calculated and the ratio is rounded up to obtain the sampling step size. Establish a slice index and increment the slice index by the sampling step size. For each slice index, create a two-dimensional numerical matrix consisting of control units arranged in a rectangular array and traverse the control units in the two-dimensional numerical matrix. Based on the plane matrix index preset by the control unit, the voxel unit whose height is determined by the slice index and whose plane position is determined by the plane matrix index is located in the smooth topology, and the binarized value of the voxel unit is read. If the read binary value is one, the preset injection state value of the control unit is set to one and defined as an effective injection point; if the read binary value is zero, the injection state value of the control unit is set to zero and defined as a blank avoidance point. Stack all the generated two-dimensional numerical matrices in ascending order of slice index to obtain anti-leveling topology printing data.

10. A system for generating interface topology structures for multilayer PCB additive manufacturing that enhances interlayer bonding, used to implement the method for generating interface topology structures for multilayer PCB additive manufacturing that enhances interlayer bonding as described in any one of claims 1-9, characterized in that... The system includes: Fingerprint extraction module: used to acquire the contour image of conductive ink on the surface of insulating substrate, perform edge detection and temporal extraction on the contour image to obtain a temporal morphological dataset of fluid micro-dynamic spreading characteristics, calculate the dynamic aspect ratio based on the temporal morphological dataset, perform nonlinear regression fitting on the dynamic aspect ratio to extract the rheological fingerprint of the flow dynamics behavior, construct the rheological response function based on the rheological fingerprint, and generate a three-dimensional rheological erosion kernel based on the rheological response function. Topology compensation module: used to perform three-dimensional convolution operation based on three-dimensional rheological erosion kernel, generate physical entity set, calculate geometric deviation field based on physical entity set, and construct topology pre-distortion structure based on geometric deviation field; Manufacturing Constraint Module: Used to perform printability constraint filtering on the topology predistortion structure to obtain the corrected topology structure, perform minimum feature size constraint filtering on the corrected topology structure, and generate anti-leveling topology printing data.

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