Flexible circuit board three-dimensional deformation prediction and compensation method based on deep learning

Abstract

The invention provides a flexible circuit board three-dimensional deformation prediction and compensation method based on deep learning, and relates to the technical field of circuit boards, and the method comprises the steps: building a relation data set through obtaining technological parameters and actual deformation data, constructing a variable density grid unit to calculate a stress gradient matrix, and forming a deformation prediction parameter matrix to carry out three-dimensional deformation prediction. And a feedback compensation matrix is constructed after a deformation deviation value is calculated, process parameters are adjusted according to a compensation transmission link sequence, welding processing is performed on the flexible circuit board, and deformation compensation is realized. According to the method, the three-dimensional deformation prediction precision and the welding quality of the flexible circuit board can be effectively improved.

Description

Technical Field

[0001] This invention relates to circuit board technology, and more particularly to a method for predicting and compensating three-dimensional deformation of flexible circuit boards based on deep learning. Background Art

[0002] As electronic devices become increasingly thinner and more portable, flexible printed circuit boards (FPCs) are widely used in smartphones, wearable devices, and other fields due to their lightweight, thinness, and flexibility. During the production of FPCs, especially in the soldering process, factors such as mismatched thermal expansion coefficients of materials, soldering temperature gradients, and mechanical stress often cause three-dimensional deformation of the FPCs, including bending, twisting, and warping. This severely affects the assembly accuracy, electrical performance, and reliability of electronic products.

[0003] Traditional methods for controlling the deformation of flexible circuit boards rely primarily on empirical formulas and simplified models for prediction, making it difficult to accurately reflect the actual deformation under complex process conditions. With increasingly stringent manufacturing precision requirements, existing technologies exhibit significant shortcomings. First, traditional deformation prediction methods typically employ uniform mesh generation, failing to provide refined analysis for densely populated solder joint areas, resulting in insufficient prediction accuracy in stress concentration regions. Second, existing compensation methods often utilize static adjustment strategies, neglecting to consider the stress transfer relationships between multiple solder joints, leading to unsatisfactory compensation effects, especially prone to overcompensation or undercompensation under the interactive influence of multiple solder joints. Furthermore, most existing methods fail to establish an accurate mapping relationship between process parameters and deformation, unable to adaptively adjust to dynamic changes in actual production, resulting in low accuracy and efficiency in deformation compensation.

[0004] As the requirements for assembly precision in flexible electronic products continue to increase, there is an urgent need to develop a method that can accurately predict the three-dimensional deformation of flexible circuit boards and implement effective compensation in order to improve product quality and production efficiency. Summary of the Invention

[0005] This invention provides a method for predicting and compensating three-dimensional deformation of flexible circuit boards based on deep learning, which can solve the problems in the prior art.

[0006] A first aspect of this invention provides a method for predicting and compensating three-dimensional deformation of flexible circuit boards based on deep learning, comprising:

[0007] The process parameters in the production process of flexible circuit boards are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit boards.

[0008] A variable density grid cell is constructed along the distribution direction of the solder joints on the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress deformation characteristic data of the variable density grid cell. A deformation prediction parameter matrix is ​​constructed based on the stress gradient matrix.

[0009] Input the process parameter-deformation relationship dataset into the deformation prediction parameter matrix to calculate the three-dimensional deformation prediction data. Compare the actual three-dimensional deformation data with the three-dimensional deformation prediction data to calculate the deformation deviation value.

[0010] A feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters.

[0011] The flexible circuit board is welded according to the adjusted process parameters to perform three-dimensional deformation compensation.

[0012] The process parameters for flexible circuit board manufacturing are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit board, including:

[0013] The process parameters of the flexible circuit board during the welding process are collected, and the process parameters are arranged according to the execution sequence of the welding process based on the collection time of the process parameters to generate a process parameter timing sequence.

[0014] The actual three-dimensional deformation data of the flexible circuit board under the action of the process parameter timing sequence is collected in real time, and the deformation gradient of the actual three-dimensional deformation data at adjacent collection times is calculated.

[0015] The deformation compensation direction is determined based on the deformation gradient. A process parameter change matrix is ​​constructed by the process parameter difference between adjacent time nodes of the process parameter time sequence. The deformation compensation coefficient is calculated based on the weight distribution of the temperature process parameter difference and the pressure process parameter difference in the process parameter change matrix.

[0016] The deformation compensation direction is applied to the deformation compensation coefficient to generate the deformation compensation amount for each time node;

[0017] The deformation compensation amount is used to construct compensation adjustment curves in the temperature process parameter correlation region and the pressure process parameter correlation region, respectively. Based on the compensation adjustment curves, the time series of process parameters is gradually compensated in different regions to establish the process parameter-deformation relationship dataset.

[0018] A variable-density mesh element is constructed along the solder joint distribution direction of the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress-deformation characteristic data of the variable-density mesh element. A deformation prediction parameter matrix is ​​then constructed based on the stress gradient matrix, including:

[0019] A variable-density grid cell is generated along the solder joint distribution direction of the flexible circuit board. The variable-density grid cell is set as a micro-scale grid cell in the solder joint distribution area and as a macro-scale grid cell in the non-solder joint area.

[0020] First stress-deformation characteristic data are obtained in the microscale grid cell, which characterizes the stress distribution and deformation trend of the weld joint area. Second stress-deformation characteristic data are obtained in the macroscale grid cell, which characterizes the stress distribution and deformation trend of the non-weld joint area.

[0021] Based on the grid density distribution of the first stress deformation feature data and the second stress deformation feature data, a multi-scale deformation field reconstruction is performed to obtain the stress field reconstruction matrix.

[0022] The stress gradient of the variable density grid cell is calculated based on the stress field reconstruction matrix, and the stress gradient is used to generate a stress gradient matrix according to the distribution position of the variable density grid cell.

[0023] The stress field reconstruction matrix and the stress gradient matrix are decoupled by feature extraction, stress-deformation correlation features are extracted, and a deformation prediction parameter matrix is ​​constructed based on the stress-deformation correlation features.

[0024] Based on the grid density distribution of the first and second stress deformation feature data, a multi-scale deformation field reconstruction is performed to obtain the stress field reconstruction matrix, including:

[0025] The microscale grid cells and the macroscale grid cells are divided into deformation reconstruction regions according to the density gradient magnitude. The density change rate of the deformation reconstruction region is calculated, and a reconstruction feature vector is constructed based on the density change rate.

[0026] A spiral reconstruction path is generated based on the density distribution of the reconstructed feature vector. The geometric parameters of the spatial configuration of the spiral reconstruction path are matched with the density change process of the reconstructed feature vector. The first stress deformation feature data and the second stress deformation feature data are reconstructed and mapped along the spiral reconstruction path to generate reconstruction enhancement data.

[0027] A reconstruction data transmission channel is established within the deformation reconstruction region. The direction of the reconstruction data transmission channel is consistent with the density gradient direction of the reconstruction feature vector. The reconstruction enhancement data is transmitted along the reconstruction data transmission channel to obtain the transmitted reconstruction enhancement data.

[0028] The reconstructed and enhanced data after transmission is used to generate a stress field reconstruction matrix according to the density gradient direction of the reconstructed feature vector.

[0029] The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix to calculate three-dimensional deformation prediction data. The actual three-dimensional deformation data of the flexible circuit board is compared with the three-dimensional deformation prediction data to calculate the deformation deviation value, including:

[0030] The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix. The process parameters are graded and quantized based on the stress transmission channels in the deformation prediction parameter matrix. The deformation prediction flow field is generated in the stress transmission channels based on the quantized process parameters.

[0031] The deformation prediction flow field is unfolded in three-dimensional space to obtain three-dimensional deformation prediction data, and a three-dimensional deformation prediction surface is generated based on the three-dimensional deformation prediction data;

[0032] Curvature constraints are constructed based on the ratio of deformation between adjacent feature positions in the actual three-dimensional deformation data. Tensor completion is performed on the actual three-dimensional deformation data to generate a three-dimensional deformation measured surface. The curvature constraints are used to limit the spatial continuity features of the actual three-dimensional deformation data.

[0033] A continuous transition surface is constructed between the three-dimensional deformation prediction surface and the three-dimensional deformation measured surface, and a hyperboloid interferogram is constructed based on the hyperbolic transition characteristics of the continuous transition surface;

[0034] Extract the peak and trough positions of the hyperboloid interferogram, and calculate the spatial coordinate difference between the peak and trough positions as the deformation deviation value.

[0035] A feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters, including:

[0036] Deformation feature points are determined based on the distribution of the deformation deviation values. A deformation coordinate system is established using the deformation feature points, and the stress transmission direction of the deformation feature points is calculated.

[0037] Within the deformation coordinate system, a compensation unit array is divided according to the stress transmission direction. The deformation deviation value of each compensation unit and the positional relationship between the deformation feature point are calculated. The deformation deviation values ​​are arranged according to the position of the compensation unit to generate a feedback compensation matrix.

[0038] Based on the stress distribution characteristics of the compensation units in the feedback compensation matrix, the main transmission node is determined, and a compensation transmission link is established from the main transmission node. The compensation values ​​in the compensation transmission link are spatially reconstructed through the positional relationship between the compensation units to generate a compensation distribution matrix.

[0039] Based on the compensation values ​​in the compensation distribution matrix, the compensation values ​​of each compensation unit in the compensation unit array are transferred and adjusted to generate a continuous compensation field.

[0040] The spatial positional relationship of the compensation units in the compensation distribution matrix is ​​converted into adjustment coordinates of the process parameters. The adjustment order of the process parameters on the adjustment coordinates is determined according to the transmission direction of the compensation transmission link. The compensation values ​​in the continuous compensation field are applied to the process parameters according to the adjustment order to obtain the adjusted process parameters.

[0041] Based on the stress distribution characteristics of the compensation units in the feedback compensation matrix, the main transfer node is determined. A compensation transfer link is established starting from the main transfer node. The compensation values ​​in the compensation transfer link are spatially reconstructed using the positional relationships between the compensation units to generate a compensation distribution matrix, including:

[0042] Stress field analysis is performed on the compensation units in the feedback compensation matrix to extract the principal stress direction and principal stress intensity of each compensation unit;

[0043] A stress intensity field is constructed based on the distribution of principal stress intensity in the deformation coordinate system, and a stress direction field is constructed based on the distribution of principal stress direction in the deformation coordinate system. The stress intensity field and the stress direction field are combined to form a stress distribution feature.

[0044] Based on the stress intensity field, the compensation unit with the largest principal stress intensity is selected as the main transmission node. A stress transmission region is established based on the stress direction field. A transmission axis is established in the stress direction of the main transmission node. The transmission priority is determined based on the distance between the adjacent transmission sub-regions in the stress transmission region and the transmission axis.

[0045] The transmission relationship of each compensation unit is determined based on the stress distribution characteristics of each compensation unit in the stress transmission area. The transmission relationship is optimized based on the transmission priority, and the optimized transmission relationship is determined as the compensation transmission link.

[0046] Based on the relative positions of the compensation units in the deformation coordinate system, the spatial distance and orientation angle between the compensation units are calculated. The spatial distance and orientation angle are used as position association parameters. The compensation values ​​of each compensation unit in the compensation transmission link are spatially reconstructed according to the position association parameters to generate a compensation distribution matrix.

[0047] A second aspect of the present invention provides an electronic device, comprising:

[0048] processor;

[0049] Memory used to store processor-executable instructions;

[0050] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0051] A third aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0052] The beneficial effects of this application are as follows:

[0053] This invention proposes a method for predicting and compensating three-dimensional deformation of flexible circuit boards based on deep learning. By establishing a dataset on the relationship between process parameters and deformation, and using variable density mesh elements and stress gradient matrix to perform accurate deformation prediction, high-precision prediction and compensation of three-dimensional deformation of flexible circuit boards are achieved.

[0054] This invention employs a feedback compensation matrix and a compensation transmission link, which can sequentially adjust process parameters based on deformation deviation values. This ensures that the influence of stress transmission is taken into account during the compensation process, effectively avoiding new deformation problems caused during the compensation process and improving the effectiveness and stability of the compensation.

[0055] This invention combines deep learning with materials mechanics analysis to establish a complete three-dimensional deformation prediction and compensation system for flexible circuit boards. This not only improves the processing accuracy of flexible circuit boards but also reduces material waste and time costs caused by traditional trial-and-error methods, and has significant practical value for the mass production of flexible electronic products. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating the three-dimensional deformation prediction and compensation method for flexible circuit boards based on deep learning, according to an embodiment of the present invention.

[0057] Figure 2 This is a complete flowchart of the process parameter-deformation relationship dataset established based on process parameters and actual three-dimensional deformation data in an embodiment of the present invention;

[0058] Figure 3 This is a complete flowchart of an embodiment of the present invention for constructing a feedback compensation matrix based on deformation deviation values ​​and adjusting process parameters. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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.

[0060] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0061] Figure 1 This is a flowchart illustrating the deep learning-based three-dimensional deformation prediction and compensation method for flexible circuit boards according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0062] The process parameters in the production process of flexible circuit boards are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit boards.

[0063] A variable density grid cell is constructed along the distribution direction of the solder joints on the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress deformation characteristic data of the variable density grid cell. A deformation prediction parameter matrix is ​​constructed based on the stress gradient matrix.

[0064] Input the process parameter-deformation relationship dataset into the deformation prediction parameter matrix to calculate the three-dimensional deformation prediction data. Compare the actual three-dimensional deformation data with the three-dimensional deformation prediction data to calculate the deformation deviation value.

[0065] A feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters.

[0066] The flexible circuit board is welded according to the adjusted process parameters to perform three-dimensional deformation compensation.

[0067] In one optional implementation, process parameters during the flexible circuit board manufacturing process are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit board, including:

[0068] The process parameters of the flexible circuit board during the welding process are collected, and the process parameters are arranged according to the execution sequence of the welding process based on the collection time of the process parameters to generate a process parameter timing sequence.

[0069] The actual three-dimensional deformation data of the flexible circuit board under the action of the process parameter timing sequence is collected in real time, and the deformation gradient of the actual three-dimensional deformation data at adjacent collection times is calculated.

[0070] The deformation compensation direction is determined based on the deformation gradient. A process parameter change matrix is ​​constructed by the process parameter difference between adjacent time nodes of the process parameter time sequence. The deformation compensation coefficient is calculated based on the weight distribution of the temperature process parameter difference and the pressure process parameter difference in the process parameter change matrix.

[0071] The deformation compensation direction is applied to the deformation compensation coefficient to generate the deformation compensation amount for each time node;

[0072] The deformation compensation amount is used to construct compensation adjustment curves in the temperature process parameter correlation region and the pressure process parameter correlation region, respectively. Based on the compensation adjustment curves, the time series of process parameters is gradually compensated in different regions to establish the process parameter-deformation relationship dataset.

[0073] like Figure 2 As shown, the method includes:

[0074] The process parameters for welding flexible circuit boards are collected, including key parameters such as welding temperature, welding pressure, welding time, and solder joint location. In actual production environments, these parameters can be collected in real time using devices such as temperature sensors, pressure sensors, and time controllers. The acquisition accuracy for welding temperature is typically ±1℃, with a sampling frequency of 10Hz; the acquisition accuracy for welding pressure is ±0.01MPa, with a sampling frequency of 20Hz; and the control accuracy for welding time is ±0.01s. For the welding process of a certain type of flexible circuit board, the typical temperature parameter range is 220℃-260℃, the pressure parameter range is 0.3MPa-0.6MPa, and the time parameter range is 1.5s-3.0s.

[0075] The weld point location is acquired via a vision system with an accuracy of ±0.02mm. Based on the acquisition time of the process parameters, they are arranged according to the execution sequence of the welding process to generate a process parameter time sequence. For example, in a certain welding process, at t=0s, the temperature is 25℃ and the pressure is 0MPa; at t=1.0s, the temperature rises to 150℃ and the pressure increases to 0.2MPa; at t=2.0s, the temperature rises to 220℃ and the pressure increases to 0.4MPa; at t=3.0s, the temperature reaches 240℃ and the pressure stabilizes at 0.5MPa; at t=5.0s, the temperature remains at 240℃ and the pressure remains at 0.5MPa; at t=5.5s, cooling begins, the temperature drops to 220℃, and the pressure decreases to 0.3MPa; at t=6.0s, the temperature drops to 180℃ and the pressure decreases to 0.1MPa; at t=7.0s, the temperature returns to room temperature, and the pressure drops to 0. Arranging these data in chronological order forms a complete process parameter time sequence.

[0076] Real-time acquisition of actual 3D deformation data of flexible circuit boards under the action of process parameters is performed. This data is acquired using a high-precision 3D scanning system, typically composed of a structured light projector and a high-resolution camera, capable of capturing minute changes on the flexible circuit board surface. The scanning accuracy reaches ±0.01mm, with a scanning frequency of 5Hz, covering the entire flexible circuit board surface. During the welding process, a 3D scan is performed every 0.2s to record the 3D coordinate data of the flexible circuit board surface. For example, for a 100mm × 80mm flexible circuit board, approximately 10,000 3D coordinate points are acquired at each scan moment, forming the 3D deformation data for that moment. The flexible circuit board exhibits different deformation characteristics at different stages of the welding process. During the heating stage, due to thermal expansion, the board surface bends upwards, with a maximum deformation of 0.5mm. During the isothermal stage, due to material softening and pressure, the board surface gradually flattens, and the deformation decreases to 0.3mm. During the cooling stage, due to material shrinkage and residual stress release, localized deformation occurs on the board surface, with uneven deformation distribution ranging from 0.1mm to 0.4mm.

[0077] The deformation gradient of actual 3D deformation data at adjacent acquisition times is calculated. The deformation gradient reflects the rate of change of deformation over time and is an important parameter for analyzing the dynamic characteristics of deformation. For each acquisition point, the deformation difference between two adjacent acquisition times is calculated and divided by the time interval to obtain the deformation gradient of that point. For example, for a point located at coordinates (50mm, 40mm), the height is 0.15mm at t=2.0s and 0.18mm at t=2.2s. Then, the deformation gradient of this point during this time interval is (0.18mm-0.15mm) / 0.2s=0.15mm / s. By calculating the deformation gradient of all acquisition points, the deformation gradient distribution of the entire flexible circuit board is obtained. The deformation gradient distribution varies significantly at different stages of the welding process. In the initial stage of heating, the deformation gradient is relatively large, reaching 0.2 mm / s-0.3 mm / s; in the isothermal stage, the deformation gradient is relatively small, about 0.05 mm / s-0.1 mm / s; in the cooling stage, the direction of the deformation gradient changes, ranging from -0.15 mm / s to 0.05 mm / s.

[0078] The deformation compensation direction is determined based on the deformation gradient. The deformation compensation direction should be opposite to the deformation gradient direction to counteract the deformation trend. For each data acquisition point, the compensation direction is determined based on the direction of its deformation gradient. For example, if the deformation gradient at a point is positive, it indicates that the height of that point is increasing, so the compensation direction is negative; conversely, if the deformation gradient is negative, it indicates that the height of that point is decreasing, so the compensation direction is positive. In practical applications, considering the overall deformation characteristics of the flexible circuit board, areas with similar deformation gradients are usually divided into the same compensation area and the same compensation direction is used.

[0079] For example, the region with a deformation gradient between 0.1 mm / s and 0.2 mm / s is designated as region A, with a negative compensation direction; the region with a deformation gradient between -0.05 mm / s and 0.05 mm / s is designated as region B, with the compensation direction determined according to the trend; and the region with a deformation gradient between -0.2 mm / s and -0.1 mm / s is designated as region C, with a positive compensation direction.

[0080] A process parameter variation matrix is ​​constructed by analyzing the differences in process parameters at adjacent time points in the time series of process parameters. This matrix records the changes in each process parameter at adjacent time points, reflecting the dynamic characteristics of the process parameters. For example, from t=2.0s to t=3.0s, the temperature increases from 220℃ to 240℃, a change of 20℃; the pressure increases from 0.4MPa to 0.5MPa, a change of 0.1MPa. These changes are organized according to process parameter type and time point to form the process parameter variation matrix. The rows of the matrix represent different process parameters, and the columns represent different time point pairs. By analyzing the process parameter variation matrix, process parameters and time stages that have a significant impact on deformation can be identified.

[0081] The deformation compensation coefficient is calculated based on the weighted distribution of the temperature and pressure differences in the process parameter variation matrix. The deformation compensation coefficient describes the degree of influence of process parameter changes on deformation and is used to quantify the magnitude of compensation adjustment. By analyzing historical data and experimental results, the weights of temperature and pressure parameters on deformation are determined. In this embodiment, the weight of the temperature parameter is 0.7, and the weight of the pressure parameter is 0.3, indicating that the effect of temperature change on deformation is 2.33 times that of pressure change. Based on these weights and the differences in the process parameter variation matrix, the deformation compensation coefficient is calculated. For example, for a certain time node, if the temperature change is 20℃ and the pressure change is 0.1MPa, then the deformation compensation coefficient is 20℃ × 0.7 + 0.1MPa × 0.3 = 14.03 (after unit conversion). The magnitude of the deformation compensation coefficient reflects the degree of compensation adjustment required; the larger the coefficient, the greater the required compensation adjustment.

[0082] The deformation compensation direction is applied to the deformation compensation coefficient to generate the deformation compensation amount for each time node. This deformation compensation amount is the actual adjustment applied to the process parameters and is determined by both the deformation compensation direction and the deformation compensation coefficient. For each time node, the deformation compensation direction is multiplied by the deformation compensation coefficient to obtain the deformation compensation amount. For example, if the deformation compensation direction for a time node is negative and the deformation compensation coefficient is 14.03, then the deformation compensation amount is -14.03. Based on the magnitude and direction of the deformation compensation amount, the process parameters are adjusted accordingly to offset or reduce the deformation. In practical applications, the deformation compensation amount is usually converted into specific process parameter adjustment values, such as temperature and pressure adjustment values. For example, a deformation compensation amount of -14.03 corresponds to a temperature reduction of 10℃ and a pressure reduction of 0.05 MPa.

[0083] Compensation adjustment curves were constructed for the deformation compensation amount in both the temperature-related and pressure-related process parameter regions. These curves describe how the deformation compensation amount is converted into specific process parameter adjustment values, and how these values ​​change over time. The temperature-related process parameter region refers to the area where deformation is primarily affected by temperature, such as the high-temperature zone around the weld joint; the pressure-related process parameter region refers to the area where deformation is primarily affected by pressure, such as the stress concentration zone around the stress point. For each region, a corresponding compensation adjustment curve was constructed based on the deformation characteristics and process parameter sensitivity of that region. For example, for the temperature-related process parameter region, the compensation adjustment curve exhibits a linear relationship between the deformation compensation amount and the temperature adjustment value, with a slope of 0.5℃ / unit compensation amount; for the pressure-related process parameter region, the compensation adjustment curve exhibits a non-linear relationship between the deformation compensation amount and the pressure adjustment value, with a smaller slope within a small compensation range and a larger slope within a large compensation range.

[0084] Based on the compensation adjustment curve, the time series of process parameters is progressively compensated in different regions to establish a process parameter-deformation relationship dataset. Regional progressive compensation refers to adopting different compensation strategies and gradually adjusting process parameters according to the deformation characteristics and compensation requirements of different regions to achieve precise compensation. For each time series node, the corresponding compensation adjustment curve is queried based on the deformation compensation amount at that node to determine the temperature and pressure adjustment values. Then, these adjustment values ​​are applied to the original process parameters to obtain the compensated process parameters. For example, for the time series node t=3.0s, the original temperature is 240℃, the deformation compensation amount is -14.03, and the temperature compensation adjustment curve shows a temperature adjustment value of -7℃, resulting in a compensated temperature of 233℃. Through similar calculations, the compensated process parameters for all time series nodes are obtained, forming a complete process parameter-deformation relationship dataset. This dataset records the deformation status of the flexible circuit board under different combinations of process parameters, including information such as original process parameters, compensated process parameters, deformation amount, and deformation gradient. For example, a data item contains the following information: time t=3.0s, original temperature 240℃, original pressure 0.5MPa, compensated temperature 233℃, compensated pressure 0.48MPa, deformation 0.3mm, deformation gradient 0.15mm / s.

[0085] By analyzing patterns and trends in the dataset, a mapping relationship between process parameters and deformation can be established, providing data support for deformation prediction. Simultaneously, the compensation experience in the dataset can guide the design of process parameters for new products, improving production efficiency and product quality. In practical applications, as production data accumulates, the process parameter-deformation relationship dataset will continuously expand and optimize, leading to continuous improvement in the accuracy of deformation prediction and compensation.

[0086] The method provided by this invention achieves precise process parameter compensation and deformation control by real-time acquisition of process parameters and deformation data, analysis of deformation gradient and process parameter changes, calculation of deformation compensation coefficient and compensation amount, and construction of compensation adjustment curve. Compared with traditional methods, this method considers the dynamic characteristics of deformation during welding and the comprehensive influence of process parameters, resulting in more accurate compensation and meeting the stringent requirements of high-precision electronic products for deformation control of flexible circuit boards.

[0087] In one optional implementation, a variable-density mesh element is constructed along the solder joint distribution direction of the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress-deformation characteristic data of the variable-density mesh element. A deformation prediction parameter matrix is ​​then constructed based on the stress gradient matrix, including:

[0088] A variable-density grid cell is generated along the solder joint distribution direction of the flexible circuit board. The variable-density grid cell is set as a micro-scale grid cell in the solder joint distribution area and as a macro-scale grid cell in the non-solder joint area.

[0089] First stress-deformation characteristic data are obtained in the microscale grid cell, which characterizes the stress distribution and deformation trend of the weld joint area. Second stress-deformation characteristic data are obtained in the macroscale grid cell, which characterizes the stress distribution and deformation trend of the non-weld joint area.

[0090] Based on the grid density distribution of the first stress deformation feature data and the second stress deformation feature data, a multi-scale deformation field reconstruction is performed to obtain the stress field reconstruction matrix.

[0091] The stress gradient of the variable density grid cell is calculated based on the stress field reconstruction matrix, and the stress gradient is used to generate a stress gradient matrix according to the distribution position of the variable density grid cell.

[0092] The stress field reconstruction matrix and the stress gradient matrix are decoupled by feature extraction, stress-deformation correlation features are extracted, and a deformation prediction parameter matrix is ​​constructed based on the stress-deformation correlation features.

[0093] Variable-density mesh cells are generated along the solder joint distribution direction of the flexible circuit board. These variable-density mesh cells have different densities in different regions. Micro-scale mesh cells are set in the solder joint distribution area, while macro-scale mesh cells are set in the non-solder joint area. The side length of the micro-scale mesh cells is typically 0.05 mm to 0.1 mm, used to accurately describe stress concentration and deformation details near the solder joints; the side length of the macro-scale mesh cells is typically 0.5 mm to 2 mm, used to describe the overall stress distribution and deformation trend in the non-solder joint area.

[0094] In practical applications, for a flexible circuit board with dimensions of 100mm × 80mm, the number of microscale grid cells in the solder joint area (approximately 5mm in diameter) is about 10,000, while the number of macroscale grid cells in the non-solder joint area is about 5,000. The generation of variable-density grid cells requires consideration of the solder joint distribution characteristics. For common electronic components such as chips, resistors, and capacitors, their solder joints are typically arranged in a certain direction. For example, for a certain type of chip, its solder joints are rectangularly distributed along the edge with a spacing of 0.3mm; for resistor arrays, the solder joints are linearly distributed with a spacing of 0.5mm. Based on these solder joint distribution characteristics, grid cells with gradually varying density are generated along the solder joint arrangement direction, with the highest grid density at the solder joint and gradually decreasing as the distance from the solder joint increases.

[0095] The first stress-deformation characteristic data is obtained from microscale mesh elements. This data includes parameters such as the magnitude and direction of principal stresses, strain, and deformation. The data can be obtained using finite element analysis or experimental measurement. In finite element analysis, based on the material properties, geometry, and boundary conditions of the flexible circuit board, mechanical analysis is performed on the microscale mesh elements to calculate the stress and deformation of each element.

[0096] In practical applications, for flexible circuit boards after soldering, the principal stresses of the microscale mesh cells near the solder joints typically range from 30 MPa to 50 MPa, with the principal stress directions forming an angle of 30° to 45° with the solder joint connection line, and the deformation ranging from 0.05 mm to 0.2 mm. For example, for a microscale mesh cell near a solder joint on a certain chip, the principal stress is 42 MPa, the principal stress direction is 35°, and the deformation is 0.12 mm. These data reflect the stress concentration phenomenon and local deformation characteristics in the solder joint area.

[0097] Second-scale stress-deformation characteristic data are obtained from macroscopic-scale grid cells. This data also includes parameters such as principal stress magnitude, principal stress direction, strain, and deformation, but its spatial resolution is lower, primarily reflecting the overall deformation trend. In non-solder joint regions, the stress distribution is relatively uniform, with principal stress magnitudes typically between 5 MPa and 15 MPa and deformation between 0.01 mm and 0.05 mm. For example, in a macroscopic-scale grid cell 10 mm from a solder joint, the principal stress magnitude is 8 MPa, the principal stress direction is 60°, and the deformation is 0.03 mm. This second-scale stress-deformation characteristic data is crucial for understanding the overall deformation behavior of flexible circuit boards. It complements the first-scale stress-deformation characteristic data, comprehensively describing the stress distribution and deformation trend of the flexible circuit board.

[0098] Multi-scale deformation field reconstruction is performed based on the grid density distribution of the first and second stress deformation feature data to obtain the stress field reconstruction matrix. Multi-scale deformation field reconstruction is the process of fusing stress deformation feature data at different scales to generate a continuous stress field covering the entire flexible circuit board. In this embodiment, the multi-scale deformation field reconstruction uses a density-weighted fusion method, which performs a weighted average of the stress deformation feature data according to the density distribution of the grid cells. Specifically, for any point P within the reconstruction region, its distance to surrounding micro-scale and macro-scale grid cells is calculated, weights are determined based on these distances, and then a weighted average is calculated.

[0099] For example, point P is surrounded by three micro-scale grid cells M1, M2, and M3, with distances of 0.2 mm, 0.3 mm, and 0.5 mm, respectively, and principal stresses of 40 MPa, 38 MPa, and 35 MPa. There are also two macro-scale grid cells L1 and L2, with distances of 1.0 mm and 1.5 mm, respectively, and principal stresses of 10 MPa and 8 MPa. Using the inverse distance weighting method, M1 has a weight of 5, M2 has a weight of 3.33, M3 has a weight of 2, L1 has a weight of 1, and L2 has a weight of 0.67, for a total weight of 12. The reconstructed principal stress of point P is (40×5 + 38×3.33 + 35×2 + 10×1 + 8×0.67) / 12 = 34.4 MPa.

[0100] Through similar calculations, the stress distribution at all points on the entire flexible circuit board is obtained, forming a stress field reconstruction matrix. The size of the stress field reconstruction matrix is ​​m×n×k, where m and n correspond to the number of discrete points in the length and width directions of the flexible circuit board, respectively, and k corresponds to the number of stress parameters stored in the matrix. In this embodiment, m=200, n=160, and k=6, corresponding to a spatial resolution of 0.5mm×0.5mm. The stored parameters include the magnitude and direction of the principal stresses in three directions.

[0101] The stress gradient of variable-density grid cells is calculated based on the stress field reconstruction matrix. The stress gradient is then used to generate a stress gradient matrix according to the distribution of the variable-density grid cells. The stress gradient reflects the rate of change of stress in space and is an important parameter for predicting deformation. The stress gradient is calculated using the central difference method, which performs differential calculations on the stress data in the stress field reconstruction matrix. In the x-direction, the stress gradient equals the stress difference between two adjacent points divided by the distance between the two points; the calculation methods for the y and z directions are similar. For example, for the point at position (100, 80, 3) in the stress field reconstruction matrix, its stress gradient in the x-direction is calculated as [stress(101,80,3) - stress(99,80,3)] / (2×0.5mm) = 10MPa / mm.

[0102] For boundary points, forward or backward differencing is used to calculate the stress gradient matrix by calculating the stress gradient at all points. The stress gradient matrix has the same spatial structure as the stress field reconstruction matrix, but each location stores the stress gradient value rather than the stress value. In practical applications, the stress gradient near the weld joint is typically large, reaching 20 MPa / mm to 50 MPa / mm; the stress gradient in areas far from the weld joint is smaller, typically 1 MPa / mm to 5 MPa / mm. The stress gradient matrix intuitively reflects the non-uniformity of stress distribution, helping to identify areas with a high risk of deformation.

[0103] Feature decoupling is performed between the stress field reconstruction matrix and the stress gradient matrix to extract stress-strain correlation features. Feature decoupling refers to decomposing the complex stress-strain relationship into multiple independent feature components to more accurately describe the correlation between stress and deformation. In this embodiment, principal component analysis is used for feature decoupling. The stress field reconstruction matrix and the stress gradient matrix are combined to form a feature matrix, and principal component analysis is performed on the feature matrix to extract the main feature components. Typically, the first 5 to 10 principal components are selected, as these principal components can explain more than 80% of the total variance.

[0104] For example, in the feature matrix of a flexible circuit board, the first five principal components explain 40%, 25%, 10%, 8%, and 5% of the total variance, respectively, cumulatively explaining 88% of the variance. The eigenvectors corresponding to these five principal components reflect the stress concentration characteristics of the solder joint area, the bending deformation characteristics of the board edge, the thermal deformation characteristics caused by the temperature gradient, the local deformation characteristics caused by material inhomogeneity, and the dynamic deformation characteristics caused by vibration, respectively. By analyzing the physical meaning of these eigenvectors, a correlation model between stress and deformation is established, and the stress-deformation correlation characteristics are extracted.

[0105] Stress-strain correlation characteristics are quantitative parameters describing how stress affects deformation, including stress sensitivity coefficient, stress direction factor, and gradient influence coefficient. For example, for the weld joint area, a stress sensitivity coefficient of 0.005 mm / MPa means that for every 1 MPa increase in stress, the deformation increases by 0.005 mm; a stress direction factor of 0.8 means that the consistency between the principal stress direction and the deformation direction is 80%; and a gradient influence coefficient of 0.002 mm² / MPa means that for every 1 MPa / mm increase in stress gradient, the deformation increases by 0.002 mm.

[0106] A deformation prediction parameter matrix is ​​constructed based on the stress-deformation correlation characteristics. This matrix is ​​a data structure used to store various parameters required for deformation prediction, including stress sensitivity coefficient, stress direction factor, and gradient influence coefficient. The spatial structure of the deformation prediction parameter matrix is ​​the same as that of the stress field reconstruction matrix, but each location stores a prediction parameter instead of a stress value. When constructing the deformation prediction parameter matrix, corresponding prediction parameters are set according to the stress-deformation correlation characteristics of different regions.

[0107] For high-stress areas near solder joints, the stress sensitivity coefficient is relatively high, typically between 0.004 mm / MPa and 0.008 mm / MPa; for non-solder joint areas, the stress sensitivity coefficient is relatively low, typically between 0.001 mm / MPa and 0.003 mm / MPa. Simultaneously, the influence of stress direction and stress gradient is considered to comprehensively determine the prediction parameters. The deformation prediction parameter matrix also contains information on stress transmission channels, used to describe the path and manner of stress transmission in the flexible circuit board. Stress transmission channels typically extend along the high stiffness direction of the material, forming connections between solder joints. For example, for the region between two adjacent solder joints, the direction of the stress transmission channel is consistent with the direction of the line connecting the two solder joints, with a transmission efficiency of 85%, indicating that the stress attenuates by 15% during transmission.

[0108] Once the deformation prediction parameter matrix is ​​constructed, it can be used for subsequent deformation prediction calculations. The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix, and the three-dimensional deformation prediction data is calculated using the prediction model within the parameter matrix. In practical applications, the deformation prediction parameter matrix can accurately predict the deformation of flexible circuit boards under different process conditions, with a prediction accuracy exceeding 90%, providing strong support for the design optimization and process parameter adjustment of flexible circuit boards.

[0109] The method of this invention achieves accurate prediction of the three-dimensional deformation of flexible circuit boards by constructing variable density mesh elements, acquiring multi-scale stress deformation characteristic data, reconstructing multi-scale deformation fields, calculating stress gradient matrices, and constructing deformation prediction parameter matrices. This provides technical support for deformation compensation and reliability improvement of flexible circuit boards.

[0110] In one optional implementation, a multi-scale deformation field reconstruction is performed based on the grid density distribution of the first stress deformation feature data and the second stress deformation feature data to obtain a stress field reconstruction matrix, including:

[0111] The microscale grid cells and the macroscale grid cells are divided into deformation reconstruction regions according to the density gradient magnitude. The density change rate of the deformation reconstruction region is calculated, and a reconstruction feature vector is constructed based on the density change rate.

[0112] A spiral reconstruction path is generated based on the density distribution of the reconstructed feature vector. The geometric parameters of the spatial configuration of the spiral reconstruction path are matched with the density change process of the reconstructed feature vector. The first stress deformation feature data and the second stress deformation feature data are reconstructed and mapped along the spiral reconstruction path to generate reconstruction enhancement data.

[0113] A reconstruction data transmission channel is established within the deformation reconstruction region. The direction of the reconstruction data transmission channel is consistent with the density gradient direction of the reconstruction feature vector. The reconstruction enhancement data is transmitted along the reconstruction data transmission channel to obtain the transmitted reconstruction enhancement data.

[0114] The reconstructed and enhanced data after transmission is used to generate a stress field reconstruction matrix according to the density gradient direction of the reconstructed feature vector.

[0115] The micro-scale and macro-scale mesh units are divided into deformation reconstruction regions based on their density gradient. Micro-scale mesh units are typically small in size and high in density, suitable for describing local details; macro-scale mesh units are larger in size and low in density, suitable for describing overall trends. In this embodiment, the size of the micro-scale mesh unit is 0.1mm × 0.1mm, and the size of the macro-scale mesh unit is 2mm × 2mm. For a flexible circuit board with a size of 100mm × 80mm, the total number of micro-scale mesh units is approximately 800,000, and the total number of macro-scale mesh units is approximately 2,000. The mesh units are divided according to their density gradient, with a density gradient greater than 0.5 units / mm. 2 The region is divided into high-gradient deformation reconstruction regions, with density gradients ranging from 0.2 to 0.5 units / mm. 2 The region between them is divided into a medium-gradient deformation reconstruction region, with a density gradient of less than 0.2 units / mm. 2 The region is divided into low-gradient deformation reconstruction regions.

[0116] The density change rate of the deformed reconstruction region is calculated to construct the reconstruction feature vector. The density change rate describes the change of mesh density along a specific direction and is a key parameter for constructing the reconstruction feature vector. In this embodiment, the density change rate is calculated along the x-axis, y-axis, and z-axis respectively. For high-gradient deformed reconstruction regions, the average density change rate along the x-axis is 0.8 elements / mm. 2 The average density change rate in the y-axis direction is 0.6 units / mm. 2 The average density change rate along the z-axis is 0.4 units / mm. 2 / mm; For the medium-gradient deformation reconstruction region, the density change rates in the three directions are 0.4, 0.3, and 0.2 units / mm, respectively. 2 / mm; For the low-gradient deformation reconstruction region, the density change rates in the three directions are 0.15, 0.12, and 0.08 elements / mm, respectively. 2 / mm. Based on these density change rates, a reconstructed feature vector is constructed. The reconstructed feature vector is a three-dimensional vector whose direction points to the direction of the fastest density increase, and its magnitude is equal to the density change rate in that direction. For example, at a point in the high-gradient deformation reconstruction region, if the density change rate in the x-axis direction is 0.9 units / mm. 2 / mm, 0.5 units / mm in the y-axis direction. 2 / mm, 0.3 units / mm in the z-axis direction. 2 If the reconstructed feature vector at this point has a radius of 1.07 units per mm, then the angle between the direction of the reconstructed feature vector and the x-axis is 29.1 degrees, the angle with the y-axis is 62.5 degrees, and the angle with the z-axis is 73.2 degrees. 2 / mm.

[0117] A spiral reconstruction path is generated based on the density distribution of the reconstructed feature vectors. The spiral reconstruction path is a special spatial curve whose geometric parameters (such as pitch, radius, and rotational angular velocity) match the density change process of the reconstructed feature vectors. In this embodiment, the basic form of the spiral reconstruction path is a three-dimensional spiral. The central axis of the spiral is aligned with the average direction of the reconstructed feature vectors. The pitch of the spiral is inversely proportional to the density change rate, and the radius of the spiral is directly proportional to the local mesh density. For example, in a high-gradient deformation reconstruction region, the average direction of the reconstructed feature vectors is (0.7, 0.5, 0.3), and the average density change rate is 0.8 units / mm. 2 / mm, with an average grid density of 25 elements / mm 2 Therefore, the central axis of the spiral reconstruction path in this region is (0.7, 0.5, 0.3), the pitch is 1 / 0.8 = 1.25 mm, and the radius is 25 × 0.02 = 0.5 mm. In the medium-gradient and low-gradient deformation reconstruction regions, a similar method is used to generate spiral reconstruction paths, forming a continuous path network covering the entire deformation reconstruction region.

[0118] The first and second stress deformation feature data are density-reconstructed and mapped along a spiral reconstruction path to generate enhanced reconstruction data. The first stress deformation feature data comes from microscale grid cells and contains local detail information; the second stress deformation feature data comes from macroscale grid cells and contains overall trend information. Density reconstruction mapping is a data fusion technique that maps data at different scales to a unified space according to specific rules. In this embodiment, a weighted average method is used for density reconstruction mapping. For each point on the spiral reconstruction path, its distance to surrounding microscale and macroscale grid cells is calculated, weights are determined based on the distances, and then a weighted average is calculated as the enhanced reconstruction data for that point. The weight calculation uses an inverse distance weighting method, where closer distances result in larger weights, and farther distances result in smaller weights. For example, for point P on the spiral reconstruction path, it is surrounded by three micro-scale grid cells M1, M2, and M3, with distances of 0.2 mm, 0.3 mm, and 0.5 mm, respectively, and stress-deformation characteristic data of 35 MPa, 32 MPa, and 30 MPa; and two macro-scale grid cells L1 and L2, with distances of 1.0 mm and 1.5 mm, respectively, and stress-deformation characteristic data of 28 MPa and 26 MPa. The weights of each cell are calculated as follows: M1 = 1 / 0.2 = 5, M2 = 1 / 0.3 = 3.33, M3 = 1 / 0.5 = 2, L1 = 1 / 1.0 = 1, and L2 = 1 / 1.5 = 0.67. The total weight is 5 + 3.33 + 2 + 1 + 0.67 = 12. The reconstructed augmentation data for point P is (35×5+32×3.33+30×2+28×1+26×0.67) / 12=32.4MPa. Through similar calculations, the reconstructed augmentation data for all points along the spiral reconstruction path are obtained.

[0119] A reconstruction data transfer channel is established within the deformation reconstruction region. This channel is the path for data transfer in space, and its direction is consistent with the density gradient direction of the reconstruction feature vector. It is used to transfer reconstruction enhancement data. In this embodiment, the reconstruction data transfer channel adopts a tree structure, extending from high-density regions to low-density regions. Branch points are located at positions where the density gradient direction changes significantly. For high-gradient deformation reconstruction regions, the trunk of the transfer channel extends along the average density gradient direction, with a length of approximately 20 mm. A branch point is set every 2 mm, and each branch point extends 3-5 branches with a branch length of 2-5 mm. For medium-gradient and low-gradient deformation reconstruction regions, the structural parameters of the transfer channel are correspondingly reduced. For example, in a certain high-gradient region, the average density gradient direction is (0.6, 0.4, 0.3), the trunk length is 18 mm, and the branch points are located at positions 2 mm, 4 mm, and 6 mm from the trunk starting point. Each branch point extends 4 branches with an average branch length of 3.5 mm.

[0120] The reconstructed enhancement data is transferred along the reconstructed data transfer channel to obtain the transferred reconstructed enhancement data. Data transfer refers to the process of transferring the reconstructed enhancement data along the spiral reconstructed path to the entire deformation reconstructed region. In this embodiment, the data transfer adopts an attenuation transfer model, where the transfer intensity decreases with increasing distance. Starting from the beginning of the transfer channel, the reconstructed enhancement data is transferred outward along the transfer channel with a transfer coefficient of 0.9, meaning that the data intensity decreases by 10% for every 1 mm transferred. For example, if the reconstructed enhancement data at the beginning of the transfer channel is 40 MPa, after transferring 1 mm it becomes 40 × 0.9 = 36 MPa, after transferring 2 mm it becomes 36 × 0.9 = 32.4 MPa, and so on. During the transfer process, if a branch point is encountered, the data is diverted to each branch while keeping the total transfer amount constant. In this way, the reconstructed enhancement data is transferred to each position in the deformation reconstructed region to obtain the transferred reconstructed enhancement data.

[0121] The transmitted reconstructed and enhanced data is used to generate a stress field reconstruction matrix according to the density gradient direction of the reconstructed feature vectors. The stress field reconstruction matrix is ​​a data structure describing the stress distribution, and its arrangement direction is consistent with the density gradient direction of the reconstructed feature vectors. In this embodiment, the stress field reconstruction matrix adopts a three-dimensional matrix structure, with the three dimensions corresponding to the x, y, and z directions in space, respectively. The values ​​of the matrix elements represent the stress values ​​at the corresponding locations. The size of the matrix is ​​determined based on the size of the flexible circuit board and the analysis accuracy, typically 200×160×20, corresponding to a spatial resolution of 0.5mm×0.5mm×0.05mm. The transmitted reconstructed and enhanced data is mapped to the corresponding positions in the matrix to form a complete stress field reconstruction matrix. For example, a point located at coordinates (25mm, 30mm, 0.5mm) has a transmitted reconstructed and enhanced data of 35MPa, which is stored at position (50, 60, 10) in the matrix (assuming the matrix index starts from 0). For positions where data is not directly calculated, it is obtained through interpolation methods. Commonly used interpolation methods include linear interpolation, bilinear interpolation, and trilinear interpolation.

[0122] The stress field reconstruction matrix can be used for subsequent stress analysis and deformation prediction. By analyzing the stress distribution characteristics in the matrix, stress concentration areas and potential deformation risk points can be identified. For example, in the stress field reconstruction matrix of a flexible circuit board, a significant stress concentration phenomenon was found around the main chip, with a maximum stress value reaching 45 MPa, far higher than the 20-25 MPa in other areas, indicating that this area is a potential deformation risk point. Based on this finding, the chip packaging process can be optimized, or a reinforcing structure can be added to this area to reduce the degree of stress concentration.

[0123] This method, through multi-scale deformation field reconstruction, fully leverages the advantages of both micro- and macro-scale mesh cells to achieve an accurate description of stress distribution in flexible circuit boards. Compared to traditional single-scale analysis methods, this method significantly improves analytical accuracy while maintaining computational efficiency, particularly in its ability to characterize stress concentration regions. In practical applications, this method has been successfully applied to the analysis of various types of flexible circuit boards, improving prediction accuracy by over 35%, and providing strong support for the design optimization and reliability enhancement of flexible circuit boards.

[0124] In one optional implementation, the process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix to calculate three-dimensional deformation prediction data. The actual three-dimensional deformation data of the flexible circuit board is compared with the three-dimensional deformation prediction data to calculate the deformation deviation value, including:

[0125] The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix. The process parameters are graded and quantized based on the stress transmission channels in the deformation prediction parameter matrix. The deformation prediction flow field is generated in the stress transmission channels based on the quantized process parameters.

[0126] The deformation prediction flow field is unfolded in three-dimensional space to obtain three-dimensional deformation prediction data, and a three-dimensional deformation prediction surface is generated based on the three-dimensional deformation prediction data;

[0127] Curvature constraints are constructed based on the ratio of deformation between adjacent feature positions in the actual three-dimensional deformation data. Tensor completion is performed on the actual three-dimensional deformation data to generate a three-dimensional deformation measured surface. The curvature constraints are used to limit the spatial continuity features of the actual three-dimensional deformation data.

[0128] A continuous transition surface is constructed between the three-dimensional deformation prediction surface and the three-dimensional deformation measured surface, and a hyperboloid interferogram is constructed based on the hyperbolic transition characteristics of the continuous transition surface;

[0129] Extract the peak and trough positions of the hyperboloid interferogram, and calculate the spatial coordinate difference between the peak and trough positions as the deformation deviation value.

[0130] The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix. This dataset contains a large amount of historical production data, recording the deformation of flexible circuit boards under different combinations of process parameters. In this embodiment, the process parameters mainly include welding temperature, welding pressure, welding time, solder joint distribution, and material properties. For example, in a certain production run, when the welding temperature was 240℃, the welding pressure was 0.5MPa, and the welding time was 2.5s, the deformation of a certain type of flexible circuit board at a specific location was 0.22mm. By collecting a large amount of such data, a process parameter-deformation relationship dataset containing 5000 sets of data was established. The deformation prediction parameter matrix is ​​pre-calculated using stress-deformation characteristic data of variable density mesh elements, which includes information on stress transmission channels. The stress transmission channels describe the path of stress transmission in the flexible circuit board, typically extending along the high stiffness direction of the material.

[0131] The process parameters are quantified in a hierarchical manner based on the stress transmission channels in the deformation prediction parameter matrix. This hierarchical quantization process converts continuous process parameter values ​​into discrete levels, facilitating transmission calculations within the stress transmission channels. In this embodiment, the welding temperature is divided into 5 levels (220℃-230℃ is level 1, 230℃-240℃ is level 2, 240℃-250℃ is level 3, 250℃-260℃ is level 4, and 260℃-270℃ is level 5), the welding pressure is divided into 4 levels (0.3MPa-0.4MPa is level 1, 0.4MPa-0.5MPa is level 2, 0.5MPa-0.6MPa is level 3, and 0.6MPa-0.7MPa is level 4), and the welding time is divided into 3 levels (1.5s-2.0s is level 1, 2.0s-2.5s is level 2, and 2.5s-3.0s is level 3). Through this graded and quantified process, process parameters can be effectively transmitted within the stress transmission channel.

[0132] Based on the quantified process parameters, a deformation prediction flow field is generated within the stress transmission channel. This predicted flow field describes the dynamic process of deformation propagation in the flexible circuit board and can be viewed as a flow field where stress is transferred through the material, causing deformation. In this embodiment, the stress transmission channel is divided into multiple sub-channels, each corresponding to different transmission characteristics. Process parameters are transmitted through these sub-channels, generating deformation flows of varying intensities. The intensity of the deformation flow is related to the level of the process parameters and the transmission coefficient of the stress transmission channel. For example, a combination of process parameters—welding temperature level 3, welding pressure level 2, and welding time level 3—generates a deformation flow intensity of 0.25 mm / mm in a sub-channel with a transmission coefficient of 0.85. By calculating the deformation flow intensity of all sub-channels, a complete deformation prediction flow field is generated.

[0133] The deformation prediction flow field is unfolded in three-dimensional space to obtain three-dimensional deformation prediction data. Since the deformation prediction flow field is a two-dimensional plane flow field, it needs to be converted into three-dimensional deformation data. The conversion process considers factors such as the material properties, thickness distribution, and solder joint locations of the flexible circuit board. In this embodiment, a layered integration method is used to convert the flow field into three-dimensional deformation data. The flexible circuit board is divided into 10 layers, each with a thickness of 0.02 mm. The deformation of each layer is calculated, and then integrated to obtain the overall deformation. For example, the deformation prediction flow field intensity at the point located at coordinates (25 mm, 30 mm) is 0.25 mm / mm. After layered integration calculation, the three-dimensional deformation prediction value of this point is 0.20 mm, with a direction of 45° and a height increase of 0.12 mm. By calculating the three-dimensional deformation prediction values ​​of all points on the flexible circuit board, complete three-dimensional deformation prediction data is obtained.

[0134] A three-dimensional deformation prediction surface is generated based on three-dimensional deformation prediction data. This surface is a continuous surface describing the predicted deformation state of a flexible circuit board, generated by interpolating discrete three-dimensional deformation prediction data. In this embodiment, radial basis function interpolation is used to generate the three-dimensional deformation prediction surface. Deformation feature points are selected as interpolation base points, with an interpolation radius of 5 mm and a smoothing coefficient of 0.8. In this way, a three-dimensional deformation prediction surface covering the entire flexible circuit board is generated with a resolution of 0.5 mm × 0.5 mm. The prediction surface visually displays the expected deformation state of the flexible circuit board under given process parameters.

[0135] Curvature constraints are constructed based on the ratio of deformation between adjacent feature locations in actual 3D deformation data. This actual 3D deformation data is obtained through high-precision 3D scanning, recording the actual deformation of feature points on the flexible circuit board. Due to measurement limitations, the actual deformation data is usually discrete and needs to be completed using curvature constraints. Curvature constraints limit the spatial continuity of the deformed surface, ensuring its smoothness. In this embodiment, the ratio of deformation between adjacent feature points is calculated as the curvature constraint. For example, if feature point A has a deformation of 0.18 mm, feature point B has a deformation of 0.15 mm, and the distance between the two points is 3 mm, then the deformation ratio is 0.15 / 0.18 = 0.833. The curvature constraint is set to allow this ratio to vary within the range of 0.8-0.9.

[0136] Tensor completion is performed on actual 3D deformation data to generate a measured 3D deformation surface. Tensor completion is a data completion technique used to infer the values ​​of unknown data points based on known data points. In this embodiment, the actual 3D deformation data is organized into 3D tensors, and missing data points are filled in using a tensor completion algorithm. The completion process considers curvature constraints to ensure the continuity and rationality of the completion results. For example, given feature point A (25mm, 30mm, 0.18mm) and feature point B (28mm, 30mm, 0.15mm), it is necessary to complete the deformation of the intermediate point C (26.5mm, 30mm, ?). According to the curvature constraint, the deformation of point C should be 0.166mm. Through similar calculations, all missing data points are filled in, generating a complete measured 3D deformation surface.

[0137] A continuous transition surface is constructed between the predicted 3D deformation surface and the measured 3D deformation surface. This continuous transition surface describes the transition process from the predicted surface to the measured surface and is used to analyze the differences between the two. The construction process considers the spatial position and shape characteristics of the two surfaces to ensure a smooth transition. In this embodiment, a weighted average method is used to construct the continuous transition surface. For each point P on the surface, its coordinates on the transition surface are a weighted average of the predicted surface coordinates and the measured surface coordinates, with the weights continuously varying from 0 to 1. For example, when the weight is 0.3, the coordinates of the point on the transition surface are 70% of the predicted surface coordinates plus 30% of the measured surface coordinates. By varying the weights, a series of transition surfaces are generated, forming a continuous transition process.

[0138] Hyperbolic interferograms are constructed based on the hyperbolic transition features of continuous transition surfaces. Hyperbolic interferograms are a visualization technique used to visually represent the differences between two surfaces. Hyperbolic transition features refer to the hyperbolic characteristics exhibited by the transition surface in certain directions; these characteristics appear as interference fringes in the interferogram. In this embodiment, the interference threshold is set to 0.02 mm, meaning that an interference fringe is formed when the height difference between two adjacent points on the transition surface reaches 0.02 mm. A complete hyperbolic interferogram is generated by calculating the height differences of all points on the transition surface. The fringe density in the interferogram reflects the magnitude of the deformation difference, and the fringe direction reflects the direction of the deformation difference.

[0139] The peak and trough positions of the hyperboloid interferogram are extracted. Peak positions correspond to bright fringes in the interferogram, representing areas where the predicted deformation value is greater than the measured value; trough positions correspond to dark fringes, representing areas where the predicted deformation value is less than the measured value. Image processing techniques are used to identify bright and dark fringes in the interferogram and determine their spatial locations. In this embodiment, the interferogram resolution is 0.2 mm, and the identification thresholds are 80% and 20% of the brightness value, corresponding to peak and trough positions, respectively. In this way, all peak and trough positions in the interferogram are extracted, totaling approximately 300 peaks and 280 troughs.

[0140] The spatial coordinate difference between the peak and trough positions is calculated as the deformation deviation value, which directly reflects the degree of deviation between the predicted and measured deformation. The calculation process considers distance and direction factors in three-dimensional space to comprehensively evaluate the spatial distribution of deformation deviation. In this embodiment, for each pair of adjacent peak and trough points, their coordinate differences in the x, y, and z directions, as well as the Euclidean distance, are calculated. For example, the coordinate difference between peak point P1 (25.2mm, 30.1mm, 0.22mm) and trough point P2 (25.4mm, 30.3mm, 0.18mm) is (0.2mm, 0.2mm, -0.04mm), and the Euclidean distance is 0.28mm. By statistically analyzing the coordinate differences of all peak and trough pairs, the spatial distribution characteristics of deformation deviation are obtained.

[0141] The calculated deformation deviation values ​​are used in the subsequent feedback compensation process. In this embodiment, the maximum deformation deviation value is 0.32 mm, occurring near the main chip solder joint; the minimum deformation deviation value is 0.05 mm, occurring in the board edge area; and the average deformation deviation value is 0.18 mm. These deviation values ​​intuitively reflect the accuracy of deformation prediction and provide an important basis for deformation compensation. By analyzing the spatial distribution of deformation deviation values, weak links in deformation prediction can be identified, allowing for targeted prediction models and compensation strategies.

[0142] The calculation process for deformation deviation considers various factors such as the material properties, geometry, and welding process of the flexible circuit board, accurately reflecting the difference between the predicted and actual deformation. Through continuous iterative calculation and compensation adjustments, the deformation deviation can be gradually reduced, ultimately achieving high-precision deformation prediction and compensation. In practical applications, when the deformation deviation is less than 0.05mm, the prediction accuracy can be considered satisfactory, requiring no further adjustment.

[0143] This method is applicable to various types of flexible circuit boards, including single-layer, double-layer, and multilayer boards. For different types of flexible circuit boards, parameters and models can be adjusted to adapt to their specific deformation characteristics. The implementation of this method is highly effective, improving the deformation prediction accuracy of flexible circuit boards by more than 50%, providing strong support for the manufacturing of high-precision electronic products.

[0144] In one optional implementation, a feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters, including:

[0145] Deformation feature points are determined based on the distribution of the deformation deviation values. A deformation coordinate system is established using the deformation feature points, and the stress transmission direction of the deformation feature points is calculated.

[0146] Within the deformation coordinate system, a compensation unit array is divided according to the stress transmission direction. The deformation deviation value of each compensation unit and the positional relationship between the deformation feature point are calculated. The deformation deviation values ​​are arranged according to the position of the compensation unit to generate a feedback compensation matrix.

[0147] Based on the stress distribution characteristics of the compensation units in the feedback compensation matrix, the main transmission node is determined, and a compensation transmission link is established from the main transmission node. The compensation values ​​in the compensation transmission link are spatially reconstructed through the positional relationship between the compensation units to generate a compensation distribution matrix.

[0148] Based on the compensation values ​​in the compensation distribution matrix, the compensation values ​​of each compensation unit in the compensation unit array are transferred and adjusted to generate a continuous compensation field.

[0149] The spatial positional relationship of the compensation units in the compensation distribution matrix is ​​converted into adjustment coordinates of the process parameters. The adjustment order of the process parameters on the adjustment coordinates is determined according to the transmission direction of the compensation transmission link. The compensation values ​​in the continuous compensation field are applied to the process parameters according to the adjustment order to obtain the adjusted process parameters.

[0150] like Figure 3 As shown, the method includes:

[0151] Deformation feature points are determined based on the distribution of deformation deviation values ​​to form the basis of the deformation coordinate system. These feature points are the points on the flexible circuit board where deformation is most significant, typically corresponding to the location of the maximum deformation deviation value. In practical applications, a high-precision 3D scanner can be used to scan the flexible circuit board, obtaining 3D coordinate data of the entire board surface. This data is then compared with the design model to calculate the deformation deviation value at each point. For example, after soldering, a flexible circuit board exhibits a maximum deformation deviation of 0.28mm in the main chip area. The point with the largest deformation in this area is selected as the deformation feature point. Using this feature point as the origin, an x-axis is established along the main deformation direction, a y-axis is established perpendicular to the main deformation direction, and a z-axis is established perpendicular to the xy-plane, thus constructing the deformation coordinate system.

[0152] After determining the deformation feature point, it is necessary to calculate the stress transmission direction at that point. The stress transmission direction refers to the main direction in which stress propagates on the flexible circuit board, and it is usually consistent with the principal stress direction. The principal stress direction of the deformation feature point can be determined through finite element analysis. In this embodiment, the principal stress direction of the deformation feature point is 45°, indicating that the stress is mainly transmitted along this direction. The accurate determination of the stress transmission direction is crucial for the subsequent division of compensation units and the establishment of the compensation transmission link.

[0153] An array of compensation units is divided according to the stress transmission direction within the deformation coordinate system. Each compensation unit is a tiny area on the flexible circuit board used for localized deformation compensation. The size and shape of the compensation units should be determined based on the dimensions and deformation characteristics of the flexible circuit board. In this embodiment, a square with a side length of 2mm is used as the basic compensation unit, arranged at 45° along the stress transmission direction to form an array of compensation units. For a flexible circuit board with dimensions of 100mm × 80mm, approximately 2000 compensation units are divided. The center coordinates of each compensation unit can be represented by the deformation coordinate system; for example, coordinates (10, 8, 0.15) indicate that the compensation unit is located 10mm to the right, 8mm above, and 0.15mm above the deformation feature point.

[0154] The deformation deviation value of each compensation unit and its positional relationship with the deformation feature point are calculated. This positional relationship includes two parameters: distance and angle. Distance represents the spatial distance from the compensation unit to the deformation feature point, and angle represents the orientation angle of the compensation unit relative to the deformation feature point. In this embodiment, the distance is calculated using three-dimensional Euclidean distance, and the angle is represented by the azimuth and elevation angles in a spherical coordinate system. For example, the compensation unit located at coordinates (10, 8, 0.15) has a distance of 12.82 mm from the deformation feature point, an azimuth angle of 38.7°, and an elevation angle of 0.67°. Simultaneously, the deformation deviation value of this compensation unit is measured to be 0.18 mm.

[0155] The deformation deviation values ​​are arranged according to the positions of the compensation units to generate a feedback compensation matrix. This matrix is ​​a data structure describing the deformation distribution of the flexible circuit board, with each element corresponding to the deformation deviation value of a compensation unit. In this embodiment, the feedback compensation matrix is ​​a 50×40 two-dimensional array covering the entire flexible circuit board area. Each element value in the matrix represents the deformation deviation at the corresponding position, in millimeters. For example, the element at position (5, 4) has a value of 0.18, indicating that the deformation deviation of the compensation unit at that position is 0.18 mm. The feedback compensation matrix visually reflects the deformation distribution characteristics of the flexible circuit board, providing a basis for subsequent compensation.

[0156] The main transfer node is determined based on the stress distribution characteristics of the compensation units in the feedback compensation matrix. The main transfer node is the starting point for the transfer of compensation values, and typically, the compensation unit with the highest stress is selected as the main transfer node. In this embodiment, by analyzing the stress state of each compensation unit in the feedback compensation matrix, it was found that the compensation unit located near the main chip solder joint has the highest stress, reaching 42 MPa. Therefore, this compensation unit is determined as the main transfer node. The position coordinates of the main transfer node are (8, 6, 0.22), and the deformation deviation value is 0.25 mm.

[0157] A compensation transfer link is established starting from the main transfer node. This link describes the path through which the compensation value is transferred from the main transfer node to its surroundings. Based on the stress transfer direction, multiple transfer links radiate outwards from the main transfer node, connecting adjacent compensation units along that direction. In this embodiment, eight main transfer links are established, extending along the directions of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°, respectively. Each transfer link contains 10-15 compensation units, covering the main stress area surrounding the main transfer node. For example, the transmission link along the 45° direction contains the following compensation unit: (8,6,0.22)--(10,8,0.15)--(12,10,0.12)--(14,12,0.09)--(16,14,0.07)--(18,16,0.05)--(20,18,0.04)--(22,20,0.03)--(24,22,0.02)--(26,24,0.01).

[0158] The compensation values ​​in the compensation transmission link are spatially reconstructed based on the positional relationships between compensation units, generating a compensation distribution matrix. The positional relationships include two parameters: relative distance and relative direction, used to describe the spatial relationships between compensation units. Spatial reconstruction refers to the process of adjusting the compensation values ​​according to the positional relationships, considering both spatial attenuation and directional offset. In this embodiment, the spatial attenuation of the compensation values ​​adopts an exponential attenuation model with an attenuation coefficient of 0.8; the directional offset adopts a linear offset model with an offset coefficient of 0.1 rad / mm. Through spatial reconstruction, the compensation value of each compensation unit is calculated, forming a compensation distribution matrix. For example, the compensation unit located 5 mm from the main transmission node has a compensation value of 0.25 × 0.8. 5 =0.082mm, compensation direction offset 0.1×5=0.5rad, approximately 28.6°.

[0159] The compensation values ​​of each compensation unit in the compensation unit array are adjusted based on the compensation values ​​in the compensation distribution matrix to generate a continuous compensation field. The adjustment refers to the process of adjusting the compensation values ​​of all compensation units in the array according to the compensation values ​​of each compensation unit in the compensation transmission link. A spatial interpolation method is used to interpolate the discrete compensation values ​​in the compensation distribution matrix to obtain the compensation value at any position, forming a continuous compensation field. In this embodiment, for compensation units not on the transmission link, their compensation values ​​are calculated using a distance-weighted average method. For example, for the compensation unit at position (15, 15, 0.1), the compensation values ​​of the compensation units on the four surrounding transmission links are 0.09mm, 0.08mm, 0.07mm, and 0.06mm, respectively, with distances of 2.5mm, 3.2mm, 3.8mm, and 4.5mm. Therefore, the compensation value of this unit is (0.09×2.5+0.08×3.2+0.07×3.8+0.06×4.5) / (2.5+3.2+3.8+4.5)=0.072mm. In this way, the compensation values ​​at all positions on the flexible circuit board are calculated, forming a continuous compensation field.

[0160] The spatial positional relationships of the compensation units in the compensation distribution matrix are converted into adjustment coordinates for process parameters. These adjustment coordinates refer to their positions in the welding equipment coordinate system and are used to guide the adjustment of welding process parameters. Through coordinate transformation, the positions of the compensation units in the deformation coordinate system are converted to their positions in the welding equipment coordinate system. In this embodiment, the welding equipment uses a Cartesian coordinate system, with the origin located at the lower left corner of the equipment, the x-axis pointing to the right, the y-axis pointing upwards, and the z-axis perpendicular to the xy-plane. Through translation and rotation transformations, the coordinates (x, y, z) in the deformation coordinate system are converted to coordinates (X, Y, Z) in the welding equipment coordinate system. For example, the point (10, 8, 0.15) in the deformation coordinate system is converted to the point (25, 30, 0.15) in the welding equipment coordinate system.

[0161] The adjustment order of process parameters on the adjustment coordinates is determined based on the transmission direction of the compensation transmission link. The adjustment order refers to the sequence in which the process parameters are adjusted, typically starting from the main transmission node and proceeding sequentially along the compensation transmission link. In this embodiment, the process parameters at the position corresponding to the main transmission node are adjusted first, and then adjusted sequentially outward along each transmission link. For example, for a transmission link along the 45° direction, the adjustment order is: (8,6,0.22)--(10,8,0.15)--(12,10,0.12)--...--(26,24,0.01). This adjustment order ensures the continuity and consistency of stress transmission.

[0162] The compensation values ​​in the continuous compensation field are applied to the process parameters in an adjustment order to obtain the adjusted process parameters. Process parameters include welding temperature, pressure, and time, and different parameters have different effects on deformation. Based on experimental data and empirical models, a mapping relationship between the compensation values ​​and the adjustment amounts of the process parameters is established. In this embodiment, the adjustment amount of welding temperature is directly proportional to the compensation value, with a coefficient of 20℃ / mm; the adjustment amount of welding pressure is inversely proportional to the compensation value, with a coefficient of -0.5MPa / mm; and the adjustment amount of welding time is directly proportional to the compensation value, with a coefficient of 2s / mm. For example, for a position with a compensation value of 0.1mm, the welding temperature is adjusted by -2℃, the welding pressure by +0.05MPa, and the welding time by -0.2s. In this way, the adjustment amounts of the process parameters at all positions are calculated, resulting in the adjusted process parameter distribution.

[0163] The adjusted process parameters are used to guide the welding process of flexible circuit boards. During the welding process, the welding conditions are precisely controlled according to the process parameter settings at different locations to achieve deformation compensation. Experimental results show that after deformation compensation using this method, the maximum deformation deviation of the flexible circuit board is reduced from the original 0.28mm to 0.05mm, demonstrating a significant deformation compensation effect that meets the assembly requirements of high-precision electronic products.

[0164] This method is not only applicable to deformation compensation of flexible circuit boards, but can also be extended to the manufacturing process of other flexible electronic products. By precisely controlling the process parameters, it effectively reduces product deformation errors, improves product assembly accuracy and reliability, and has broad application prospects.

[0165] In one optional implementation, a main transfer node is determined based on the stress distribution characteristics of the compensation units in the feedback compensation matrix. A compensation transfer link is established starting from the main transfer node. The compensation values ​​in the compensation transfer link are spatially reconstructed using the positional relationships between the compensation units to generate a compensation distribution matrix, including:

[0166] Stress field analysis is performed on the compensation units in the feedback compensation matrix to extract the principal stress direction and principal stress intensity of each compensation unit;

[0167] A stress intensity field is constructed based on the distribution of principal stress intensity in the deformation coordinate system, and a stress direction field is constructed based on the distribution of principal stress direction in the deformation coordinate system. The stress intensity field and the stress direction field are combined to form a stress distribution feature.

[0168] Based on the stress intensity field, the compensation unit with the largest principal stress intensity is selected as the main transmission node. A stress transmission region is established based on the stress direction field. A transmission axis is established in the stress direction of the main transmission node. The transmission priority is determined based on the distance between the adjacent transmission sub-regions in the stress transmission region and the transmission axis.

[0169] The transmission relationship of each compensation unit is determined based on the stress distribution characteristics of each compensation unit in the stress transmission area. The transmission relationship is optimized based on the transmission priority, and the optimized transmission relationship is determined as the compensation transmission link.

[0170] Based on the relative positions of the compensation units in the deformation coordinate system, the spatial distance and orientation angle between the compensation units are calculated. The spatial distance and orientation angle are used as position association parameters. The compensation values ​​of each compensation unit in the compensation transmission link are spatially reconstructed according to the position association parameters to generate a compensation distribution matrix.

[0171] Stress field analysis is performed on the compensation units in the feedback compensation matrix to extract the principal stress directions and intensities of each unit. Each compensation unit can be considered a tiny region on the flexible circuit board, whose deformation characteristics are influenced by the surrounding stress distribution. The stress field analysis employs the finite element method, dividing the flexible circuit board into several tiny units and calculating the stress state of each unit. For a specific compensation unit, its principal stress directions and intensities can be obtained through eigenvalue decomposition of the stress tensor. For example, for a compensation unit located near a solder joint, its principal stress intensity is typically between 30-50 MPa, and the principal stress direction forms an angle of 30°-45° with the direction of the solder joint connection.

[0172] After stress field analysis, stress intensity and stress direction fields are constructed in the deformation coordinate system. The stress intensity field describes the spatial distribution of principal stress intensities in the deformation coordinate system and can be represented by a three-dimensional scalar field; the stress direction field describes the spatial distribution of principal stress directions in the deformation coordinate system and can be represented by a three-dimensional vector field. Combining the stress intensity and stress direction fields forms a stress distribution characteristic, comprehensively describing the stress state on the flexible circuit board. In practical applications, the stress intensity field of a typical flexible circuit board exhibits a "ridge" distribution, with the peak region located near the solder joints, and the intensity decreasing from the center outwards; the stress direction field, on the other hand, exhibits a radial distribution, radiating outwards from the solder joints, with the direction changing with position.

[0173] Based on the constructed stress intensity field, the compensation unit with the highest principal stress intensity is selected as the main transfer node. In practical cases, the compensation unit located near the main chip solder joints typically has the highest principal stress intensity, reaching 45 MPa, and this unit is determined as the main transfer node. The main transfer node is the starting point for compensation value transfer; the compensation values ​​of subsequent compensation units will be calculated based on their association with the main transfer node.

[0174] A stress transfer region is established based on the stress direction field. This region can be considered as the path of stress propagation on the flexible circuit board, typically extending along the principal stress direction. A transfer axis is established in the stress direction of the main transfer node, representing the main path of stress transfer. The transfer axis usually starts from the main transfer node and extends to the edge of the board, with a length of approximately 50-80 mm. The stress transfer region is divided into multiple transfer sub-regions, and the transfer priority is determined based on the distance of each sub-region from the transfer axis. The closer the transfer sub-region is to the transfer axis, the higher its transfer priority. In practical implementation, the distance between the transfer sub-region and the transfer axis is divided into three levels: 0-5 mm is high priority, 5-15 mm is medium priority, and above 15 mm is low priority.

[0175] The stress transfer relationship between compensation units is determined based on the stress distribution characteristics of each unit within the stress transfer region. The transfer relationship describes how stress is transferred from one compensation unit to another, including both the transfer direction and the transfer intensity. The transfer direction is typically along the principal stress direction, and the transfer intensity is proportional to the principal stress intensity. For two adjacent compensation units A and B, if the principal stress direction of A points towards B, and the difference in their principal stress intensities is less than 10 MPa, then a stress transfer relationship is considered to exist between A and B.

[0176] The transfer relationship is optimized based on transfer priority, considering three factors: transfer priority, consistency of transfer direction, and uniformity of transfer intensity. Transfer relationships in high-priority areas are retained first; transfer relationships where the angle between the transfer direction and the transfer axis is less than 30° are retained first; and transfer relationships between compensation units with similar transfer intensities are retained first. Through optimization, the most reasonable transfer relationship is selected, forming a complete compensation transfer link. In a typical case, starting from the main transfer node, five main transfer links are formed, each containing 8-12 compensation units, covering the main stress concentration areas on the flexible circuit board.

[0177] Once the compensation transmission link is determined, the spatial distance and orientation angle between the compensation units are calculated based on their relative positions in the deformation coordinate system. The spatial distance is calculated using three-dimensional coordinate differences, and the orientation angle is calculated using vector angles. These spatial distances and orientation angles are used as position association parameters to describe the spatial relationship between the compensation units. In practical cases, the spatial distance between adjacent compensation units is typically between 2-5 mm, and the orientation angle is between 15° and 45°. These parameters directly affect the transmission attenuation and orientation shift of the compensation value.

[0178] Based on the location association parameters, the compensation values ​​of each compensation unit in the compensation transmission link are spatially reconstructed to generate a compensation distribution matrix. The spatial reconstruction process considers two factors: spatial attenuation and directional offset of the compensation values. Spatial attenuation represents the characteristic that the compensation value decreases with increasing spatial distance, and can be described by an exponential attenuation function; directional offset represents the characteristic that the compensation direction changes with spatial position, and can be described by an angular offset function. By comprehensively considering these two factors, the compensation value of each compensation unit in the compensation transmission link can be accurately calculated.

[0179] In a specific example, the initial compensation value of the main transmission node is 0.15 mm. As it propagates outward along the transmission link, the spatial attenuation coefficient is 0.85, and the directional offset coefficient is 0.12 rad / mm. The first-stage transmission unit is located 3.5 mm from the main transmission node, and its calculated compensation value is 0.15 × 0.85. 3.5 =0.078mm, the compensation direction is offset relative to the main transmission node by 0.12×3.5=0.42rad, approximately 24°. The second-stage transmission unit is located 4.2mm from the first-stage transmission unit, and its calculated compensation value is 0.078×0.85. 4.2 =0.035mm, the compensation direction is offset from the first-stage transmission unit by 0.12×4.2=0.50rad, approximately 29°. Similarly, the compensation value and direction of all compensation units in the entire transmission link are calculated.

[0180] The compensation values ​​and directions of all compensation units are integrated to form a complete compensation distribution matrix. This three-dimensional matrix contains the compensation amount and direction at each location on the flexible circuit board. In practical applications, the resolution of the compensation distribution matrix is ​​typically 0.5mm × 0.5mm, covering the entire flexible circuit board area. Through interpolation calculations, compensation values ​​at any location can be obtained, achieving continuous deformation compensation.

[0181] After the compensation distribution matrix is ​​generated, it is used to guide the adjustment of process parameters. Based on the compensation values ​​in the compensation distribution matrix, process parameters such as welding temperature, pressure, and time are precisely adjusted. For example, for areas with positive compensation values, the welding temperature is appropriately reduced by 5-10℃ and the welding time is shortened by 0.5-1s; for areas with negative compensation values, the welding temperature is appropriately increased by 5-10℃ and the welding time is extended by 0.5-1s. In this way, precise compensation for the three-dimensional deformation of the flexible circuit board is achieved.

[0182] After applying this method to compensate for the deformation of flexible circuit boards, the deformation error was reduced from 0.25mm to less than 0.05mm, and the deformation compensation accuracy was improved by 80%. At the same time, the product yield increased from 92% to 98.5%, significantly improving production efficiency and product quality.

[0183] This method is applicable not only to single-layer flexible circuit boards but also to multi-layer flexible circuit boards. For multi-layer flexible circuit boards, each layer can be treated as an independent deformation type, and compensation transmission links and compensation distribution matrices can be established separately. Then, the inter-layer effects are comprehensively considered to achieve overall deformation compensation. Practice shows that this method is also very effective on double-layer flexible circuit boards, with deformation errors controlled within 0.08mm, meeting the assembly requirements of high-precision electronic products.

[0184] A second aspect of the present invention provides an electronic device, comprising:

[0185] processor;

[0186] Memory used to store processor-executable instructions;

[0187] The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0188] A third aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0189] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting and compensating three-dimensional deformation of flexible circuit boards based on deep learning, characterized in that, include: The process parameters in the production process of flexible circuit boards are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit boards. A variable density grid cell is constructed along the distribution direction of the solder joints on the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress deformation characteristic data of the variable density grid cell. A deformation prediction parameter matrix is ​​constructed based on the stress gradient matrix. Input the process parameter-deformation relationship dataset into the deformation prediction parameter matrix to calculate the three-dimensional deformation prediction data. Compare the actual three-dimensional deformation data with the three-dimensional deformation prediction data to calculate the deformation deviation value. A feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters. The flexible circuit board is welded according to the adjusted process parameters to perform three-dimensional deformation compensation.

2. The method according to claim 1, characterized in that, The process parameters for flexible circuit board manufacturing are obtained, and a process parameter-deformation relationship dataset is established based on the process parameters and the actual three-dimensional deformation data of the flexible circuit board, including: The process parameters of the flexible circuit board during the welding process are collected, and the process parameters are arranged according to the execution sequence of the welding process based on the collection time of the process parameters to generate a process parameter timing sequence. The actual three-dimensional deformation data of the flexible circuit board under the action of the process parameter timing sequence is collected in real time, and the deformation gradient of the actual three-dimensional deformation data at adjacent collection times is calculated. The deformation compensation direction is determined based on the deformation gradient. A process parameter change matrix is ​​constructed by the process parameter difference between adjacent time nodes of the process parameter time sequence. The deformation compensation coefficient is calculated based on the weight distribution of the temperature process parameter difference and the pressure process parameter difference in the process parameter change matrix. The deformation compensation direction is applied to the deformation compensation coefficient to generate the deformation compensation amount for each time node; The deformation compensation amount is used to construct compensation adjustment curves in the temperature process parameter correlation region and the pressure process parameter correlation region, respectively. Based on the compensation adjustment curves, the time series of process parameters is gradually compensated in different regions to establish the process parameter-deformation relationship dataset.

3. The method according to claim 1, characterized in that, A variable-density mesh element is constructed along the solder joint distribution direction of the flexible circuit board. A stress gradient matrix is ​​calculated based on the stress-deformation characteristic data of the variable-density mesh element. A deformation prediction parameter matrix is ​​then constructed based on the stress gradient matrix, including: A variable-density grid cell is generated along the solder joint distribution direction of the flexible circuit board. The variable-density grid cell is set as a micro-scale grid cell in the solder joint distribution area and as a macro-scale grid cell in the non-solder joint area. First stress-deformation characteristic data are obtained in the microscale grid cell, which characterizes the stress distribution and deformation trend of the weld joint area. Second stress-deformation characteristic data are obtained in the macroscale grid cell, which characterizes the stress distribution and deformation trend of the non-weld joint area. Based on the grid density distribution of the first stress deformation feature data and the second stress deformation feature data, a multi-scale deformation field reconstruction is performed to obtain the stress field reconstruction matrix. The stress gradient of the variable density grid cell is calculated based on the stress field reconstruction matrix, and the stress gradient is used to generate a stress gradient matrix according to the distribution position of the variable density grid cell. The stress field reconstruction matrix and the stress gradient matrix are decoupled by feature extraction, stress-deformation correlation features are extracted, and a deformation prediction parameter matrix is ​​constructed based on the stress-deformation correlation features.

4. The method according to claim 3, characterized in that, Based on the grid density distribution of the first and second stress deformation feature data, a multi-scale deformation field reconstruction is performed to obtain the stress field reconstruction matrix, including: The microscale grid cells and the macroscale grid cells are divided into deformation reconstruction regions according to the density gradient magnitude. The density change rate of the deformation reconstruction region is calculated, and a reconstruction feature vector is constructed based on the density change rate. A spiral reconstruction path is generated based on the density distribution of the reconstructed feature vector. The geometric parameters of the spatial configuration of the spiral reconstruction path are matched with the density change process of the reconstructed feature vector. The first stress deformation feature data and the second stress deformation feature data are reconstructed and mapped along the spiral reconstruction path to generate reconstruction enhancement data. A reconstruction data transmission channel is established within the deformation reconstruction region. The direction of the reconstruction data transmission channel is consistent with the density gradient direction of the reconstruction feature vector. The reconstruction enhancement data is transmitted along the reconstruction data transmission channel to obtain the transmitted reconstruction enhancement data. The reconstructed and enhanced data after transmission is used to generate a stress field reconstruction matrix according to the density gradient direction of the reconstructed feature vector.

5. The method according to claim 1, characterized in that, The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix to calculate three-dimensional deformation prediction data. The actual three-dimensional deformation data of the flexible circuit board is compared with the three-dimensional deformation prediction data to calculate the deformation deviation value, including: The process parameter-deformation relationship dataset is input into the deformation prediction parameter matrix. The process parameters are graded and quantized based on the stress transmission channels in the deformation prediction parameter matrix. The deformation prediction flow field is generated in the stress transmission channels based on the quantized process parameters. The deformation prediction flow field is unfolded in three-dimensional space to obtain three-dimensional deformation prediction data, and a three-dimensional deformation prediction surface is generated based on the three-dimensional deformation prediction data; Curvature constraints are constructed based on the ratio of deformation between adjacent feature positions in the actual three-dimensional deformation data. Tensor completion is performed on the actual three-dimensional deformation data to generate a three-dimensional deformation measured surface. The curvature constraints are used to limit the spatial continuity features of the actual three-dimensional deformation data. A continuous transition surface is constructed between the three-dimensional deformation prediction surface and the three-dimensional deformation measured surface, and a hyperboloid interferogram is constructed based on the hyperbolic transition characteristics of the continuous transition surface; Extract the peak and trough positions of the hyperboloid interferogram, and calculate the spatial coordinate difference between the peak and trough positions as the deformation deviation value.

6. The method according to claim 1, characterized in that, A feedback compensation matrix is ​​constructed based on the deformation deviation value. Each compensation unit in the feedback compensation matrix forms a compensation transmission link according to the stress transmission direction. The process parameters are sequentially adjusted according to the transmission characteristics of the compensation transmission link to obtain the adjusted process parameters, including: Deformation feature points are determined based on the distribution of the deformation deviation values. A deformation coordinate system is established using the deformation feature points, and the stress transmission direction of the deformation feature points is calculated. Within the deformation coordinate system, a compensation unit array is divided according to the stress transmission direction. The deformation deviation value of each compensation unit and the positional relationship between the deformation feature point are calculated. The deformation deviation values ​​are arranged according to the position of the compensation unit to generate a feedback compensation matrix. Based on the stress distribution characteristics of the compensation units in the feedback compensation matrix, the main transmission node is determined, and a compensation transmission link is established from the main transmission node. The compensation values ​​in the compensation transmission link are spatially reconstructed through the positional relationship between the compensation units to generate a compensation distribution matrix. Based on the compensation values ​​in the compensation distribution matrix, the compensation values ​​of each compensation unit in the compensation unit array are transferred and adjusted to generate a continuous compensation field. The spatial positional relationship of the compensation units in the compensation distribution matrix is ​​converted into adjustment coordinates of the process parameters. The adjustment order of the process parameters on the adjustment coordinates is determined according to the transmission direction of the compensation transmission link. The compensation values ​​in the continuous compensation field are applied to the process parameters according to the adjustment order to obtain the adjusted process parameters.

7. The method according to claim 6, characterized in that, Based on the stress distribution characteristics of the compensation units in the feedback compensation matrix, the main transfer node is determined. A compensation transfer link is established starting from the main transfer node. The compensation values ​​in the compensation transfer link are spatially reconstructed using the positional relationships between the compensation units to generate a compensation distribution matrix, including: Stress field analysis is performed on the compensation units in the feedback compensation matrix to extract the principal stress direction and principal stress intensity of each compensation unit; A stress intensity field is constructed based on the distribution of principal stress intensity in the deformation coordinate system, and a stress direction field is constructed based on the distribution of principal stress direction in the deformation coordinate system. The stress intensity field and the stress direction field are combined to form a stress distribution feature. Based on the stress intensity field, the compensation unit with the largest principal stress intensity is selected as the main transmission node. A stress transmission region is established based on the stress direction field. A transmission axis is established in the stress direction of the main transmission node. The transmission priority is determined based on the distance between the adjacent transmission sub-regions in the stress transmission region and the transmission axis. The transmission relationship of each compensation unit is determined based on the stress distribution characteristics of each compensation unit in the stress transmission area. The transmission relationship is optimized based on the transmission priority, and the optimized transmission relationship is determined as the compensation transmission link. Based on the relative positions of the compensation units in the deformation coordinate system, the spatial distance and orientation angle between the compensation units are calculated. The spatial distance and orientation angle are used as position association parameters. The compensation values ​​of each compensation unit in the compensation transmission link are spatially reconstructed according to the position association parameters to generate a compensation distribution matrix.

8. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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