PCB drilling process

Abstract

The application relates to a PCB (Printed Circuit Board) drilling process method, and belongs to the technical field of printed circuit board manufacturing. The PCB drilling process method comprises the following steps: fixing a PCB on a workbench of a drilling machine; applying a sweep frequency electromagnetic excitation to the surface of the fixed PCB, and measuring the vibration displacement response of each region of the board; inversely calculating the local stiffness value of each point of the board according to the vibration displacement response, and constructing a continuous stiffness distribution matrix K of the whole board; based on the stiffness distribution matrix K, calculating the pre-compensation offset amount Delta C of each drilling position, and inversely superimposing the pre-compensation offset amount on the theoretical drilling coordinates to generate a corrected drilling path; and controlling the drill bit of the drilling machine to perform drilling operations on each drilling position according to the corrected drilling path. The PCB drilling process method provided by the application at least solves the problems that the actual drilling position deviates from the theoretical coordinates and the regional coupling effect between the stiffness of each point on the board cannot be quantified in the related art.

Description

Technical Field

[0001] This application relates to the field of printed circuit board manufacturing technology, and in particular to a drilling process method for PCB circuit boards. Background Technology

[0002] PCB drilling is used to drill holes in multilayer or double-sided boards for component insertion or interlayer conductivity. Common drilling processes include: fixing the board to the workbench, setting drilling parameters, performing first board verification, batch drilling, and process sampling inspection.

[0003] However, existing drilling processes have the following technical problems: First, PCB boards are laminated from multiple materials such as copper layers, prepreg, and fiberglass cloth. Due to uneven copper distribution in the inner layers and differences in fiberglass weaving density, the local stiffness of different areas on the board surface is inconsistent. During drilling, when the drill bit impacts the board, areas with lower stiffness will experience larger instantaneous micro-deformation (drill deflection), while areas with higher stiffness will deform less. This uneven stiffness distribution directly causes the actual drilling position to deviate from the theoretical coordinates. Second, existing processes treat the PCB board as an ideal rigid body and use uniform coordinate compensation for all hole positions. This cannot handle the systematic hole position deviation caused by uneven stiffness distribution, nor can it quantify the regional coupling effect between the stiffness of different points on the board surface (i.e., the influence of the surrounding stiffness distribution on the deformation of a certain point).

[0004] Therefore, there is an urgent need for a drilling process that can perform differentiated pre-compensation for each hole position based on the actual stiffness distribution of the plate. Summary of the Invention

[0005] Therefore, it is necessary to provide a PCB drilling process method to address the problem that the actual drilling position deviates from the theoretical coordinates and the regional coupling effect between the stiffness of various points on the board cannot be quantified in related technologies.

[0006] This application provides a PCB drilling process method, which includes the following steps:

[0007] Step S1: Fix the PCB board onto the worktable of the drilling machine;

[0008] Step S2: Apply sweep frequency electromagnetic excitation to the fixed PCB board surface and measure the vibration displacement response of each area of ​​the board.

[0009] Step S3: Based on the vibration displacement response, calculate the local stiffness values ​​of each point on the plate and construct the continuous stiffness distribution matrix K of the entire plate;

[0010] Step S4: Based on the stiffness distribution matrix K, calculate the value of each borehole location (x). i y iThe pre-compensation offset ΔC(x) i y i The pre-compensation offset is then superimposed onto the theoretical borehole coordinates to generate the corrected borehole path.

[0011] Step S5: Control the drill bit of the drilling machine to perform drilling operations at each drilling position in sequence according to the corrected drilling path.

[0012] In some embodiments, the local stiffness value k(x, y) at each point is calculated by the following formula (1):

[0013] , Where, m eff f represents the equivalent participating mass at the measuring point. res (x, y) is the local resonant frequency extracted from the vibration displacement response at this measuring point.

[0014] In some embodiments, the pre-compensation offset ΔC(x) i y i The following formula (2) is used to calculate:

[0015] ,

[0016] Where Ω represents the entire area, G is the Green's function, F is the amplitude of the electromagnetic excitation force, ε is the edge effect compensation coefficient, and ∇ 2 k is the Laplace operator for the local stiffness function.

[0017] In some embodiments, the Green's function G(x) i y i The calculation of ξ,η is simplified as follows:

[0018] When point (ξ,η) and point (x) i y i The distance between them is greater than the preset cutoff radius R. c When this point's contribution is zero, the cutoff radius Rc is determined based on the local stiffness value k(x). i y i The size of R is dynamically adjusted; the greater the stiffness, the greater the stiffness. c The smaller.

[0019] In some embodiments, the edge effect compensation coefficient ε is based on the target borehole point (x i y i The shortest distance d from the edge of the PCB board edge The constant number of adaptive adjustment; when d edge When d is less than twice the plate thickness, ε takes the first preset value; when d edgeWhen the thickness is greater than five times the plate thickness, ε takes the second preset value, and the first preset value is greater than the second preset value.

[0020] In some embodiments, when generating the corrected borehole path, the pre-compensated offset sequence {ΔC(x)} is used. i y i Post-processing is performed:

[0021] The second-order difference of the pre-compensation offset at each borehole location is calculated using the following formula:

[0022] ,

[0023] If the absolute value of the second-order difference exceeds the preset smoothing threshold, local cubic spline interpolation correction is performed on the point and each point before and after it.

[0024] In some embodiments, during the drilling process, the actual hole position deviation δ at each drilling location is recorded in real time. 实际 (x) i y i ), and compare the actual deviation with the pre-compensation offset ΔC(x) i y i Compare and calculate the dynamic residual r. i =δ 实际 -ΔC; If the dynamic residuals of three consecutive borehole locations are all greater than 0, then the online incremental correction of the edge effect compensation coefficient ε in formula (2) is initiated.

[0025] In some embodiments, the online incremental correction of the edge effect compensation coefficient ε adopts the following cumulative rule: ε new =ε old +α⋅( / r0), where r0 is the normalized reference length, with a value of 1μm; ε is the arithmetic mean of the dynamic residuals of the most recent N borehole locations, α is the learning rate coefficient, ranging from 0.01 to 0.1; the corrected ε new Used for calculating the pre-compensation offset of subsequent drilling in the current batch, and as the initial edge effect compensation coefficient for the next batch of processing.

[0026] In some embodiments, the vibration displacement response is measured using a non-uniform sampling strategy: the sampling point density ρ(x,y) is proportional to the modulus of the local stiffness gradient ||∇k(x,y)||, and is also proportional to the sum of the absolute values ​​of the second-order partial derivatives of the local stiffness values ​​|∂k / ∂y||. 2 k / ∂x 2 |+|∂ 2 k / ∂y 2 |Proportional.

[0027] In some embodiments, after constructing the stiffness distribution matrix K and before calculating the pre-compensation offset ΔC, the original stiffness data obtained from non-uniform sampling is compressed and stored: those stiffness values ​​whose relative deviations from all their neighboring sampling points are less than a preset compression threshold δ are deleted. comp The internal points are selected, and only the boundary points and stiffness abrupt change points are retained to form a sparse stiffness matrix.

[0028] The PCB drilling process provided by the embodiments of this application has at least the following beneficial effects:

[0029] By applying swept-frequency electromagnetic excitation to the fixed PCB board surface and measuring the vibration displacement response, the local stiffness value at each point is calculated, and a continuous stiffness distribution matrix K for the entire board is constructed. Then, based on K, the pre-compensation offset ΔC(x) at each drilling position is calculated. i y i The pre-compensation offset is then superimposed onto the theoretical drilling coordinates to generate a corrected drilling path, and the drill bit is controlled to perform drilling operations according to this corrected path. Since the corrected drilling path has pre-superimposed the expected deformation caused by stiffness differences at each position on the theoretical coordinates, the deviation between the actual drilling position and the theoretical target position is effectively canceled out, thereby significantly improving the positional accuracy of drilling on the PCB board.

[0030] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 A flowchart illustrating a PCB drilling process method provided in an embodiment of this application. Detailed Implementation

[0033] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0034] In the description of this application, it should be understood that if terms such as "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential" appear, these terms indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0035] Furthermore, where the term "and / or" appears, "and / or" merely describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship. Where the terms "first" and "second" appear, these terms are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined with "first" or "second" can explicitly or implicitly include at least one of those features. In the description of this application, where the term "multiple" appears, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0036] In this application, unless otherwise expressly specified and limited, the terms "installation," "connection," "joining," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0037] In this application, unless otherwise expressly specified and limited, the use of descriptions such as "above" or "below" the second feature indicates that the first and second features are in direct contact or indirect contact via an intermediate medium. Furthermore, "above," "on top of," and "over" the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. Similarly, "below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0038] It should be noted that if an element is referred to as being "fixed to" or "set on" another element, it can be directly on the other element or there may be an intervening element. If an element is considered to be "connected to" another element, it can be directly connected to the other element or there may be an intervening element. If so, the terms "vertical," "horizontal," "upper," "lower," "left," "right," and similar expressions used in this application are for illustrative purposes only and do not represent the only possible implementation.

[0039] Please see Figure 1 This application provides a PCB drilling process method, which includes the following steps:

[0040] Step S1: Fix the PCB board onto the drilling machine's worktable. This step provides a stable processing foundation for subsequent electromagnetic excitation measurements and drilling operations.

[0041] Unlike related technologies that simply place the PCB board on the workbench or use only edge clamping, this application uses vacuum adsorption to tightly adhere the back of the PCB board to the workbench surface, so that the board remains in a fixed position during frequency sweep electromagnetic excitation and subsequent drilling impact, avoiding vibration response measurement distortion or drilling hole position displacement caused by slight movement of the board.

[0042] In these embodiments, an array of vacuum adsorption holes can be provided on the surface of the worktable. After the vacuum adsorption system is started, the vacuum degree is controlled within the range of -80 kPa to -95 kPa. To ensure adsorption stability, the vacuum degree is maintained for at least 2 seconds after reaching the set value before proceeding to the next step.

[0043] For multi-layer boards with a thickness greater than 3mm or boards with a warpage exceeding 0.5%, mechanical pressure plates can be added to the edge of the workbench for auxiliary fixation.

[0044] Step S2: Apply swept-frequency electromagnetic excitation to the fixed PCB board surface and measure the vibration displacement response of each area of ​​the board. The purpose of this step is to excite the PCB board to generate forced vibration in a non-contact manner and collect vibration response data of each area of ​​the entire board, providing raw input for subsequent back-calculation of local stiffness values.

[0045] This application obtains continuous vibration response information of the entire board without damaging the board material by combining frequency sweeping electromagnetic excitation with laser interferometry. Moreover, the measurement process can be completed online without interrupting the production process.

[0046] In this step, an electromagnetic exciter is placed above the PCB board. The frequency range of the sweep electromagnetic excitation is set to 50Hz to 200Hz, and the sweep rate is set to 1Hz / s. The electromagnetic exciter applies a continuously varying sweep electromagnetic force to the surface of the PCB board, causing the board to vibrate under forced conditions.

[0047] Simultaneously, a dual-frequency laser interferometer was used to align with multiple pre-selected measurement points on the plate surface to measure the vibration displacement response of each measurement point. The measurement accuracy of the laser interferometer was ±1μm. The measurement points were arranged in a uniform grid pattern, with one measurement point set every 10mm to 20mm in two intersecting directions. The time-domain signal of the vibration displacement response of each measurement point was recorded for subsequent steps.

[0048] Step S3: Based on the vibration displacement response, calculate the local stiffness value of each point on the plate and construct the continuous stiffness distribution matrix K of the entire plate.

[0049] The purpose of this step is to convert the measured vibration response data into mechanical property parameters of the board material, forming a quantifiable stiffness distribution matrix, which provides a basis for subsequent differentiated pre-compensation. Unlike related technologies that treat the PCB board as an ideal rigid body and apply uniform coordinate compensation to all holes, this application calculates local stiffness values ​​and constructs a continuous distribution matrix for the entire board, enabling the drilling path to reflect the true mechanical distribution characteristics of the board material and achieving differentiated control of "one hole, one compensation".

[0050] In this step, based on the vibration displacement response data of each measuring point obtained in step S2, the amplitude-frequency characteristic curve of each measuring point is first extracted. For each measuring point, the frequency corresponding to the maximum amplitude on the amplitude-frequency characteristic curve is identified; this frequency is the local resonance frequency of that measuring point. According to vibration theory, the local stiffness value is proportional to the equivalent participating mass of that measuring point and the square of the local resonance frequency.

[0051] The equivalent participating mass is pre-calibrated as follows: the resonant frequency is measured on a standard test board with known stiffness values ​​using the same excitation and measurement methods, and then calculated using the known stiffness values. Since the PCB board has a relatively uniform material composition, the equivalent participating mass at each measuring point can be considered a constant. After calculating the local stiffness values ​​at all measuring points, a continuous stiffness distribution matrix K for the entire board region is constructed using bilinear interpolation.

[0052] K is a two-dimensional matrix, where each element represents the local stiffness value at the corresponding location on the PCB. For measurement point locations, the calculated local stiffness value is directly entered; for non-measurement point locations, the value is obtained by interpolation using the stiffness values ​​of surrounding measurement points.

[0053] Step S4: Based on the stiffness distribution matrix K, calculate the value of each borehole location (x). i y i The pre-compensation offset ΔC(x) i y i The pre-compensation offset is then superimposed onto the theoretical borehole coordinates to generate the corrected borehole path.

[0054] The purpose of this step is to independently calculate the pre-compensation offset for each drilling position based on the stiffness differences at various points on the plate, thus forming a corrected drilling path. Therefore, this application calculates the compensation amount for each hole position individually based on the stiffness distribution matrix of the entire plate, ensuring that the expected position of the drill bit is exactly the theoretical target position, thereby effectively eliminating systematic hole position deviations caused by uneven stiffness distribution.

[0055] In this step, the theoretical drill coordinate set {(x)} in the PCB design file is first obtained. i , y i )}, where i = 1, 2, ..., n, and n is the total number of holes to be drilled. For each drilling position (x i , y i Based on the stiffness distribution matrix K obtained in step S3, the pre-compensation offset ΔC(x) at this location is calculated. i , y i Regions with lower stiffness will experience larger instantaneous micro-deformation under drilling impact, thus requiring a larger pre-compensation offset; regions with higher stiffness will experience smaller deformation, and the required pre-compensation offset will be correspondingly smaller.

[0056] The specific value of the pre-compensation offset can be calculated through the physical relationship between stiffness and deformation. The pre-compensation offset ΔC(x) at each borehole location is calculated. i , y iAfter that, the offset is superimposed on the theoretical borehole coordinates. That is, the corrected borehole coordinates are equal to the theoretical borehole coordinates minus the pre-compensation offset. All the corrected borehole coordinates are arranged in the original borehole order to form the corrected borehole path.

[0057] Step S5: Control the drill bit of the drilling machine to perform drilling operations at each drilling position in sequence according to the corrected drilling path.

[0058] The purpose of this step is to implement the corrected path generated in step S4, so that the deviation between the actual drilling position and the theoretical target position of the drill bit is pre-canceled. Unlike the prior art where the drill bit drills directly according to the theoretical coordinates, this application controls the drill bit to move along the corrected path, so that the result of the compensation calculation is finally implemented in the drilling action, forming a complete closed loop from measurement, calculation to execution.

[0059] In this step, the corrected drilling path generated in step S4 is input into the CNC system of the drilling machine. The CNC system controls the drill bit to move sequentially to each corrected drilling coordinate according to the path file, and performs the drilling operation according to preset drilling parameters (including spindle speed, feed rate, number of cuts, etc.). After the drill bit completes drilling one hole, it automatically lifts up and moves to the next corrected drilling coordinate, repeating the above drilling action until all holes are drilled.

[0060] For example, in some embodiments, the vacuum degree of vacuum adsorption in step S1 can be set to -85 kPa, and the holding time is 3 seconds. For FR-4 board with a thickness of 1.6 mm, the aperture of the vacuum adsorption holes on the worktable surface is 1.5 mm, and the hole spacing is 20 mm.

[0061] In step S2, four electromagnetic exciters are used, arranged in a 2×2 array 200mm above the PCB board, with each exciter having an output power of 10W. The frequency sweep range is dynamically adjusted based on the pre-scan results: if no obvious resonance peak is detected in the 50Hz to 200Hz range, the frequency sweep range is extended to 30Hz to 300Hz. The sampling frequency of the dual-frequency laser interferometer is 1kHz, and 1024 data points are collected at each measurement point. The measurement point layout adopts an adaptive non-uniform method: the spacing between measurement points is increased to 5mm in the edge area and densely lined areas of the PCB board, and the spacing between measurement points is decreased to 25mm in the central blank area.

[0062] In step S3, when identifying local resonant frequencies, cubic spline interpolation is used to smooth the amplitude-frequency response curve before finding the peak position. When constructing the stiffness distribution matrix K, radial basis function interpolation is used, and multiple quadratic functions are selected as the interpolation parameters.

[0063] In step S4, when calculating the pre-compensation offset, for areas where the stiffness value is lower than 80% of the average stiffness of the entire plate, the pre-compensation offset is increased to 1.5 times linearly; for areas where the stiffness value is higher than 120% of the average stiffness of the entire plate, the pre-compensation offset is reduced to 0.5 times linearly.

[0064] In step S5, the drilling parameters are set as follows: spindle speed 120 kr / min, feed rate 25 mm / s, and 3 drilling passes (step-by-step drilling, each pass reaching 1 / 3 of the total plate thickness). A 0.3 mm diameter carbide drill bit is used, with a drill life set to 2000 passes, after which it is automatically replaced. Throughout the drilling process, the CNC system's interpolation accuracy is ±1 μm, and the servo motor's response frequency is 2 kHz.

[0065] In some embodiments, the local stiffness value k(x, y) at each point is calculated by the following formula (1):

[0066] , Where, m eff f represents the equivalent participating mass at the measuring point. res (x, y) is the local resonant frequency extracted from the vibration displacement response at this measuring point.

[0067] After completing the vibration displacement response measurement in step S2, for each measuring point, it is first necessary to extract the local resonant frequency of that point from the measurement data. Specifically, this involves performing a Fourier transform on the time-domain vibration displacement signal of the measuring point to obtain the amplitude-frequency response curve. The frequency corresponding to the maximum amplitude on the amplitude-frequency response curve is the local resonant frequency f of that measuring point. res (x, y). For cases with low signal-to-noise ratio, a window function (such as a Hanning window) can be applied to the time-domain signal before the Fourier transform to reduce spectral leakage, or the amplitude-frequency response curve can be smoothed and filtered before searching for the peak.

[0068] In formula (1), the equivalent participating mass m eff Calibration is crucial. One calibration method involves taking a standard board of the same material and known elastic modulus as the PCB board under test, and using the same electromagnetic excitation and laser measurement conditions to measure the resonant frequency f at a reference point on the standard board. res According to vibration theory, the theoretical stiffness k of this reference point is... res It equals the elastic modulus multiplied by the geometric parameters of the influence domain at that point, obtained through finite element simulation or analytical calculation. Since the material composition of the PCB board (copper, glass fiber, resin) is relatively uniform, the equivalent participating mass of each measuring point can be regarded as a constant. Therefore, this calibration value is applicable to all measuring points on the entire PCB board.

[0069] Another simplified calibration method is suitable for mass production scenarios: Take a sample board of the same specifications as the PCB board to be tested, and use a traditional indentation method (such as a micrometer indenter) to directly measure its local stiffness at a certain measuring point. At the same time, use the method of this application to measure the resonant frequency at that point, and calculate m. eff Take this sample m eff This serves as the unified calibration value for that batch of plates. The advantage of this method is that it does not require knowledge of the plate's elastic modulus and influence domain geometric parameters; it directly calibrates through actual measurements, thus more closely reflecting actual working conditions.

[0070] For applications requiring high precision, the equivalent participating mass can be considered not to be an absolute constant—the shape of the influence domain of measurement points at the edge of the board differs slightly from that of measurement points at the center of the board, resulting in a difference in m. eff Minor fluctuations may exist. In this case, zonal calibration can be used: divide the entire board into an edge region and an inner region, and calibrate two different m values ​​respectively using the method described above. eff The value is set to a smaller value for the edge region (because the constraints are weaker at the edge and the influence domain is smaller), and a larger value for the inner region.

[0071] The accuracy of local resonant frequency extraction directly affects the stiffness calculation results. To improve accuracy, a fine local sweep can be performed near the resonant peak: when the initial frequency sweep finds that the resonant peak at a certain measuring point is located near frequency f0, the sweep range is narrowed to 0.95f0 to 1.05f0, and the measurement is repeated with a smaller frequency step (e.g., 0.1Hz) to accurately determine the peak frequency. Although this method increases the measurement time, it can significantly improve the accuracy of stiffness calculation and is suitable for applications with extremely high drilling accuracy requirements.

[0072] In some embodiments, the pre-compensation offset ΔC(x) i y i The following formula (2) is used to calculate:

[0073] ,

[0074] Where Ω represents the entire area, G is the Green's function, F is the amplitude of the electromagnetic excitation force, ε is the edge effect compensation coefficient, and ∇ 2 k is the Laplace operator for the local stiffness function.

[0075] After constructing the continuous stiffness distribution matrix K of the entire plate, the pre-compensation offset ΔC(x) can be calculated for each drilling location. i y i The calculation formula consists of two terms: the first term is a weighted integral of the Green's function over the entire plate region, and the second term is the edge compensation term of the local stiffness Laplace operator.

[0076] The core of the first term is the Green's function G(x). i yi ;ξ,η), which describes the effect of applying a unit excitation force at any point (ξ, η) on the plate surface at the target drilling point (x). i , y i The magnitude of the displacement response generated at point ().

[0077] Where (ξ, η) are the coordinates of any integration point on the plate surface Ω, and (x... i , y i Both belong to the same plane coordinate system. Physically speaking, the deformation of the target point during drilling depends not only on its own stiffness but also on the stiffness of surrounding points—if the stiffness is low at a certain point in the surrounding area, the drilling impact force will be transmitted through the internal stress of the plate, causing additional deformation at the target point. The Green's function is precisely the tool for quantifying the extent of this influence. Theoretically, the Green's function can be obtained analytically by solving the plate and shell vibration equations, but for engineering applications, a more practical approach is to use approximate calculations or pre-establish lookup tables.

[0078] For example, a simplified engineering implementation is to presuppose that the Green's function has a distance-decay form, such as G = A / r, where r is the distance between (ξ, η) and (x). i , y i The distance between points is A, which is an undetermined coefficient. The physical meaning of this coefficient is the deformation transfer efficiency per unit stiffness difference, which can be calibrated experimentally: measure the actual drilling deformation at several points on a test plate with a known stiffness distribution, and then deduce the optimal value of A. Since points farther apart have less influence on the target point, when r is greater than a certain cutoff radius R... c In this case, the contribution of that point can be directly set to zero, thus significantly reducing the amount of calculation. The cutoff radius can be set according to the plate thickness and material properties, for example, 3 to 5 times the plate thickness.

[0079] In the denominator, k(ξ, η) is the local stiffness value at the integration point, read from the K matrix. In the numerator, F(ξ, η) is the amplitude of the electromagnetic excitation force. This value does not necessarily have to be equal to the actual applied excitation force—because the integral in the formula essentially calculates the "deformation contribution under unit excitation" and then multiplies it by the scaling factor of the actual drilling impact force. Therefore, F(ξ, η) can be normalized (e.g., all values ​​set to 1), and finally multiplied by a uniform impact force scaling factor. This scaling factor can be calibrated experimentally: drill a hole under standard conditions, measure the actual deformation, and deduce the value of the scaling factor.

[0080] The second term ε·∇ 2 k(x i , y i () is a supplementary correction to the first term. Laplace operator ∇ 2k represents the second spatial derivative of the local stiffness function at the target point, physically characterizing the "bending degree" of stiffness at that point. When the stiffness distribution changes smoothly, the Laplace operator is close to zero, and the contribution of the second term is small. When there is a drastic change in stiffness (e.g., a sudden transition from a high-stiffness copper region to a low-stiffness resin region), the absolute value of the Laplace operator is large, and the integration method of the first term may not be able to fully capture the additional deformation caused by this change. In this case, the second term is needed to compensate. The value of ε determines the strength of this compensation.

[0081] The edge effect compensation coefficient ε can be calibrated by drilling a set of test holes near the edge of the plate. Specifically, several holes are drilled at different distances from the edge (e.g., 2mm, 5mm, 10mm, 20mm), and the residuals between the actual hole position deviations and the first calculated result are measured. A linear regression is then performed on the residuals and the Laplace operator value; the slope obtained from the regression is the reference value for ε. Experiments show that the Laplace operator is typically larger in the edge region (because stiffness decreases sharply from the inside of the plate to the edge), therefore the second contribution from the edge hole positions is more significant.

[0082] In practical programming implementation, the above integral needs to be discretized into a summation calculation. The entire plate region Ω is discretized into a finite number of grid cells (e.g., a grid identical to the K matrix), and each grid cell (ξ) p , η p If the area of ​​x is ΔS, then the integral is approximately Σ G(x) i , y i ; ξ p , η p )·[F(ξ p , η p ) / k(ξ p , η p If the number of grid points is very large (e.g., tens of thousands of points), directly summing over all target points would be computationally very expensive. An optimization method is to pre-build a neighborhood list for each target point, and only sum the points within that list, thus reducing the computational complexity from O(N^2) to O(N^2). 2 The computation time is reduced to O(N·M), where M is the average number of neighborhood points for each target point. This optimization significantly reduces computation time when the board size is large (e.g., 500mm × 500mm or larger).

[0083] For example, in some embodiments, the calculation results of ΔC can also be post-processed for verification. Specifically, a small number of representative drilling locations are selected, compensated with the calculated ΔC, and test holes are drilled at these locations. The actual hole position deviation is then detected using optical measurement equipment. If the actual deviation is less than a preset threshold (e.g., ±10μm), the current calculation parameters are considered reasonable. If the deviation exceeds the threshold, ε or other parameters are fine-tuned according to the direction and magnitude of the deviation, and then all ΔC is recalculated. This "verify first, then batch" strategy is suitable for processing high-value PCBs and can prevent the scrapping of entire batches of products due to improper parameter settings.

[0084] In some embodiments, the Green's function G(x) i y i The calculation of ξ,η is simplified as follows:

[0085] When point (ξ,η) and point (x) i y i The distance between them is greater than the preset cutoff radius R. c When this point's contribution is zero, the cutoff radius Rc is determined based on the local stiffness value k(x). i y i The size of R is dynamically adjusted; the greater the stiffness, the greater the stiffness. c The smaller.

[0086] As mentioned above, the pre-compensation offset ΔC(x) i , y i The calculation of the Green's function involves a weighted integration of the Green's function over the entire board area. In practical calculations, if the contribution of every point on the board surface to every drill location were calculated, the computational workload would be enormous. For example, a 500mm × 500mm PCB board discretized with a 1mm grid would have 250,000 integration points. If there are 5,000 drill holes, then 12.5 billion Green's function values ​​would need to be calculated, which is difficult to complete in a reasonable amount of time on a regular computer. Therefore, a simplified calculation of the Green's function is necessary.

[0087] In these embodiments of this application, a simplified approach is to introduce a cutoff radius R. c Green's function G(x) i ,y i ; ξ, η) describes the excitation at point (ξ, η) on point (x) i , y i The physical characteristic of the deformation at point (ξ, η) is that the greater the distance between two points, the smaller the effect. When the distance exceeds a certain threshold, the effect can be ignored. Therefore, when point (ξ, η) and point (x) are far apart, the effect is negligible. i ,y i The distance between them is greater than R. cWhen that point is reached, its contribution is set to zero and it is no longer included in the integral calculation.

[0088] Cutoff radius R c The setting needs to be based on the local stiffness value k(x) i , y i The dynamic adjustment of the size of the stress wave is a key feature of this application's embodiments. The physical basis for this is that regions with higher stiffness experience faster stress wave propagation speeds, but also faster attenuation, resulting in a smaller affected area; conversely, regions with lower stiffness allow deformation to propagate more easily, leading to a larger affected area. In other words, drilling in a hard region has negligible impact on distant surroundings; drilling in a soft region requires appropriate consideration of contributions from farther distances.

[0089] In practical implementation, a mapping relationship between stiffness and cutoff radius can be established in advance. For example, using the average stiffness K of the entire plate... avg As a baseline, when k(x) i , y i ) ≥ 1.5·K avg When (i.e., in the region of high stiffness), R c Take the smaller value, such as twice the plate thickness; when k(x i , y i ) ≤ 0.5·K avg When (i.e., in the region of low stiffness), R c Take the larger value, such as 5 times the board thickness; the middle area is determined by linear interpolation. The board thickness is a known parameter, for example, the common FR-4 board thickness is 0.8mm to 3.2mm.

[0090] In some embodiments, the edge effect compensation coefficient ε is based on the target borehole point (x i y i The shortest distance d from the edge of the PCB board edge The constant number of adaptive adjustment; when d edge When d is less than twice the plate thickness, ε takes the first preset value; when d edge When the thickness is greater than five times the plate thickness, ε takes the second preset value, and the first preset value is greater than the second preset value.

[0091] When drilling near the edge of a PCB board, the stiffness of the edge is much lower than that of the interior region due to the lack of external material support and constraint. Under the same drilling impact force, the deformation at the edge will be significantly greater than that inside. Moreover, the deformation characteristics at the edge are closely related to the distance from the edge—the closer to the edge, the greater and more nonlinear the deformation. Although the first term (Green's function integral) in formula (2) can reflect a certain regional coupling effect, the edge effect compensation coefficient ε in the second term is still needed to specifically compensate for the additional deformation caused by the abrupt change in boundary constraints in the edge region.

[0092] In these embodiments of this application, ε and d edge The specific mapping relationship can be obtained through experimental calibration. One calibration method is as follows: Select a test board with the same material and layer structure as the PCB board to be processed, and select a series of test points on the board. The distance d between these test points and the edge of the board is... edge Using plate thicknesses of 0.5, 1, 2, 3, 5, and 10 times (internal reference points) respectively, several holes were drilled at each test point. The actual hole position deviation was measured, and the contribution value of the first term (Green's function integral) was calculated based on the calibrated stiffness distribution matrix K. The actual deviation minus the contribution value of the first term gives the residual to be compensated by the second term. The residual is then divided by the Laplace operator ∇ at that point. 2 k can be used to obtain the ε value corresponding to that point. edge By performing curve fitting, ε(d) can be obtained. edge The functional relationship between ).

[0093] The results of calibration experiments typically exhibit the following pattern: when d edge When the ε value is less than twice the plate thickness (i.e., very close to the edge), the ε value is relatively large, generally between 0.3 and 0.5. This is because the lack of constraint at the edge leads to a sharp increase in deformation, requiring strong compensation; when d edge When the thickness is greater than 5 times the plate thickness (i.e., far from the edge and inside the plate), the edge effect basically disappears, and the ε value is small, generally between 0.05 and 0.15; the middle area shows a smooth transition. Based on this rule, the embodiments of this application set the dividing points to 2 times and 5 times the plate thickness, and provide two preset values ​​for each.

[0094] In some embodiments, for non-rectangular, irregularly shaped PCBs (e.g., with grooves, windows, or irregular contours), the concept of edge needs to be expanded to "all free boundaries." At this point, d edge The shortest distance from the target drilling point to the nearest free boundary (including the outer and inner contours) should be taken. The same segmentation rule applies to holes located near grooves.

[0095] In actual drilling process, d edge The following can be pre-calculated during the borehole path generation stage: for each theoretical borehole coordinate (x... i , y i The algorithm calculates the shortest distance from the drilled holes to all boundary segments of the outer (and inner) contours of the plate and stores the results in an array. This array is then used directly for subsequent calculations of ΔC, eliminating the need for recalculation. Since the number of drilled holes may be in the tens of thousands, while the number of boundary segments is limited (usually a few dozen), the computational overhead is acceptable.

[0096] In some embodiments, when generating the corrected borehole path, the pre-compensated offset sequence {ΔC(x)} is used. i y i Post-processing is performed:

[0097] The second-order difference of the pre-compensation offset at each borehole location is calculated using the following formula:

[0098] ,

[0099] If the absolute value of the second-order difference exceeds the preset smoothing threshold, local cubic spline interpolation correction is performed on the point and each point before and after it.

[0100] In the aforementioned embodiment, the pre-compensation offset ΔC(x) at each borehole location was calculated. i , y i After this, a corrected drilling path is theoretically obtained. However, directly connecting these corrected coordinates according to the original drilling sequence may encounter a problem: when the difference in ΔC between two adjacent drilling positions is too large, the drill bit needs to move rapidly from the previous corrected coordinate to the next. If the offset between two coordinates changes abruptly, the drill bit's trajectory will exhibit sharp turns or violent acceleration and deceleration. This not only affects drilling efficiency (the machine tool needs to decelerate frequently) but may also cause additional impact loads on the drill bit spindle, affecting the equipment's lifespan in the long run.

[0101] Based on this, the embodiments of this application also introduce a post-processing smoothing step for the pre-compensated offset sequence. The core idea is to calculate the second-order difference of the pre-compensated offset at each borehole location, and determine whether the point is a "change point" by the absolute value of the second-order difference. If so, local cubic spline interpolation correction is performed on the point and its neighboring points.

[0102] The specific implementation method is as follows. For the pre-compensated offset sequence {ΔC} i} (where ΔC) i = ΔC(x i , y i First, calculate the first difference at each point: ΔC'i = ΔC{i+1} - ΔC i (For i=1 to n-1). Then calculate the second difference: ΔC''i = ΔC'{i+1} - ΔC'i = ΔC{i+2} - 2ΔC {i+1} + ΔC i (For i=1 to n-2). The physical meaning of the second-order difference is the rate of change of the rate of change of the compensation quantity, when ΔC i When there is an abnormal jump relative to adjacent points, the absolute value of the second difference will be significantly larger than the normal value.

[0103] Set a smoothing threshold δ smooth This threshold can be set according to the motion control accuracy of the drilling equipment. For example, if the minimum interpolation accuracy of the CNC system is 1 μm, then δ smoot It can be taken from 2μm to 3μm. When |ΔC'' i | > δ smooth When the time interval is reached, the (i+1)th point is determined to be a mutation point (because it is the center point of the second-order difference). For each mutation point and one point before and after it (a total of three points), the original calculated ΔC value is no longer used directly. Instead, the ΔC value of these three points is recalculated using cubic spline interpolation. During interpolation, a smooth cubic curve is fitted with these three points and their respective adjacent points as endpoints. The points on the curve are the corrected compensation amounts.

[0104] It should be noted that smoothing corrections should maintain the overall compensation trend; that is, they should not deviate excessively from the original calculated value for the sake of smoothing. Therefore, constraints can be added to the interpolation process: the deviation between the corrected compensation amount and the original compensation amount must not exceed an upper limit (e.g., δ). smooth (It itself) ensures that the smoothing operation only eliminates abnormal "glitch" rather than changing the reasonable compensation distribution.

[0105] For large-scale drilling (e.g., tens of thousands of holes), calculating and judging the second-order difference point by point is acceptable in terms of efficiency, as it is only an O(n) level computation. If the drilling path is a continuous spiral or serpentine arrangement (such as the common path of CNC drilling), adjacent holes are also spatially adjacent, and the second-order difference can effectively reflect the abrupt changes in spatial compensation. If the drilling order is independent of spatial location (e.g., random jumps), the compensation of adjacent holes may be spatially discontinuous, and the physical meaning of the second-order difference will be weakened. In this case, the drilling coordinates can be reordered according to spatial location before smoothing (e.g., sorted by X coordinate as primary key and Y coordinate as secondary key), and then post-processing can be performed.

[0106] For example, in some embodiments, smoothing can be performed using a moving window averaging method instead of second-order differences: for each ΔC i The average of the k points before and after the abrupt change (e.g., k=2) is taken as the smoothed value. This method is simpler and more stable, but it may over-smooth, weakening the compensation differences that truly need to be preserved. Therefore, the embodiments of this application preferentially use the second-order difference detection method to detect abrupt change points, performing local correction only at the abrupt change points, rather than global smoothing.

[0107] In some embodiments, during the drilling process, the actual hole position deviation δ at each drilling location is recorded in real time. 实际 (x) i y i ), and compare the actual deviation with the pre-compensation offset ΔC(x)i y i Compare and calculate the dynamic residual r. i =δ 实际 -ΔC; If the dynamic residuals of three consecutive borehole locations are all greater than 0, then the online incremental correction of the edge effect compensation coefficient ε in formula (2) is initiated.

[0108] During the drilling process, the actual hole position coordinates of each newly drilled hole are detected in real time and compared with the theoretical target coordinates to obtain the actual hole position deviation δ. 实际 (x i , y i Simultaneously, the pre-compensation offset ΔC(x) used for this hole position is read from the system. i , y i Define the dynamic residual r. i = δ 实际 -ΔC.

[0109] Here we need to explain r. i The physical meaning of ΔC is the pre-calculated "expected deformation" (i.e., how much the hole position will deviate if not compensated), while δ... 实际 This is the actual remaining deviation after compensation. Ideally, if the compensation is completely accurate, δ 实际 It should be close to zero, so r i It is approximately equal to -ΔC.

[0110] The embodiments of this application can employ a more direct comparison method: directly subtracting the actual deviation from the pre-compensation offset. When r i When r = 0, it means the actual deviation is exactly equal to the pre-compensation offset, that is, the compensation has no effect (because the actual deviation has not been canceled); when r i When r is negative, it indicates overcompensation; when r is negative... i When the value is positive, it indicates insufficient compensation.

[0111] In some embodiments, the dynamic residuals at three consecutive borehole locations are all greater than 0. This means that all three boreholes have experienced undercompensation (the actual deviation is in the positive direction), and this trend persists. This is not random error (random errors alternate between positive and negative), but rather a systematic undercompensation. When this occurs, it indicates that the currently used compensation model has a systematic bias, and the model parameters need to be corrected online.

[0112] After the correction is triggered, this embodiment of the application performs online incremental correction on the edge effect compensation coefficient ε in formula (2). The reason for choosing to correct ε is that ε is the most empirical parameter in the formula and has a direct impact on the overall offset trend of the compensation result.

[0113] In practical systems, monitoring of dynamic residuals can be achieved using online optical inspection devices. A common configuration is to integrate a high-precision CCD camera onto the drilling machine spindle. After drilling is completed, the spindle pauses briefly, and the camera captures real-time images of the hole position, comparing them with theoretical coordinates to calculate δ. 实际 This process typically takes only tens of milliseconds and does not significantly affect drilling efficiency. For applications requiring extremely high precision, the workpiece can be moved to an independent online inspection station for measurement after completing several holes in a batch, but this method has poor real-time performance. The embodiments of this application preferably employ the former online integration method so that correction can be triggered immediately when three abnormal holes are detected consecutively.

[0114] It is important to emphasize that the threshold value for triggering correction after three consecutive holes can be adjusted according to actual processing requirements. For products with high reliability requirements, it can be set to two consecutive holes; for general products, it can be set to five consecutive holes. This application selects three as the preferred value because three is sufficient to eliminate random single-point measurement noise, and will not allow system deviation to continuously affect too many holes due to excessive waiting time.

[0115] In some embodiments, the online incremental correction of the edge effect compensation coefficient ε adopts the following cumulative rule: ε new =ε old +α⋅( / r0), where r0 is the normalized reference length, with a value of 1μm; ε is the arithmetic mean of the dynamic residuals of the most recent N borehole locations, α is the learning rate coefficient, ranging from 0.01 to 0.1; the corrected ε new Used for calculating the pre-compensation offset of subsequent drilling in the current batch, and as the initial edge effect compensation coefficient for the next batch of processing.

[0116] Dynamic residual r i The dimension of ε is length (usually expressed in micrometers), while ε is a dimensionless coefficient. Directly adding the length dimension to the dimensionless ε introduces a problem of dimensional inconsistency. Therefore, a reference length r0 is needed to... Normalize to a dimensionless quantity. Taking 1 μm for r0 is a reasonable choice, because it is equivalent to using 1 micrometer as the reference unit for the residual—when the average residual is 1 μm, the correction term is α; when the average residual is 2 μm, the correction term is 2α, and so on.

[0117] Next is the choice of N. N represents the number of most recent boreholes used to calculate the average residual. N cannot be too small (otherwise it will be too susceptible to single-point noise) nor too large (otherwise it will be slow to react to recent trends). Practice shows that N=5 to 10 is more suitable. The value of N can be set according to the actual processing conditions. For example, N=10 can be used for stable working conditions, while N=5 can be used for situations where the working conditions change rapidly.

[0118] The value of the learning rate coefficient α determines the step size of each correction. If α is too small, the system converges slowly, requiring many holes to correct the deviation; if α is too large, the correction is too abrupt, potentially causing ε to oscillate or even diverge. The empirical range for α is generally between 0.01 and 0.1. The specific choice can be determined based on the sensitivity of the material to the compensation error: for products requiring high precision, a smaller α (e.g., 0.02) is recommended for fine and gradual adjustment; for general products, a larger α (e.g., 0.08) can be used for rapid convergence. Alternatively, a variable step size strategy can be adopted: initially, a larger α value is used to quickly approach the target, and subsequent triggers gradually decrease α to avoid overshoot.

[0119] Corrected ε new Immediately used for pre-compensation offset calculations in subsequent boreholes of the current batch. In practice, the system maintains a currently used ε... current When the correction condition is triggered, ε is calculated according to the above formula. new Update ε current =ε new The new ε value is used for all subsequent ΔC calculations for drilling. It's important to note that the correction occurs during the drilling process; therefore, different hole positions within the same batch of products may use different versions of ε—early hole positions use the old ε, while hole positions that trigger the correction use the new ε. This "adjust as you drill" strategy is precisely the significance of online correction.

[0120] Furthermore, the corrected ε new It also serves as the initial edge effect compensation coefficient for the next batch of processing. This means the system needs to record the final ε value used at the end of each batch and store it in the process parameter database. When the next batch of processing begins, this value is directly read as the initial ε. old Instead of starting from the default values, this cross-batch learning mechanism allows the process parameters to be continuously optimized as production batches increase, gradually approaching the optimal ε value for that type of board. For example, the first batch might start with ε=0.3 and be corrected to 0.27 during processing. The second batch would then start with 0.27 and make further fine adjustments based on this, converging to a stable value after several batches.

[0121] For example, in some embodiments, the final ε values ​​of all historical batches can be weighted and averaged as the initial value for the next batch to smooth out fluctuations between batches. The weighting coefficient can be set according to the batch output: the higher the output of the batch, the higher the weight. This approach is suitable for long-term continuous production of the same type of board material, and can further improve process consistency.

[0122] In some embodiments, the vibration displacement response is measured using a non-uniform sampling strategy: the sampling point density ρ(x,y) is proportional to the modulus of the local stiffness gradient ||∇k(x,y)||, and is also proportional to the sum of the absolute values ​​of the second-order partial derivatives of the local stiffness values ​​|∂k / ∂y||. 2 k / ∂x 2 |+|∂ 2 k / ∂y 2 |Proportional.

[0123] In step S2, measurement points need to be set up on the PCB board surface and the vibration displacement response of each point needs to be measured. While using a uniform grid layout, such as setting a measurement point every 10mm across the entire board surface, is simple to implement, it presents significant efficiency problems: in some areas where stiffness changes gradually, setting up too many measurement points is wasteful; in other areas where stiffness changes drastically, setting up too few measurement points fails to accurately capture the details of the stiffness distribution, leading to subsequent interpolation distortion. Therefore, this application proposes a non-uniform sampling strategy that correlates the density of sampling points with the local stiffness gradient.

[0124] Specifically, the sampling density ρ(x,y) is proportional to the magnitude of the local stiffness gradient ||∇k(x,y)||. The local stiffness gradient reflects the rate of change of stiffness in space—a larger gradient indicates a more drastic change in stiffness, requiring a denser sampling density to capture this change; a smaller gradient indicates a more uniform stiffness distribution, allowing for a sparser sampling density. Furthermore, the sampling density is also related to the sum of the absolute values ​​of the second-order partial derivatives of the local stiffness values ​​(|∂k / ∂y||). 2 k / ∂x 2 |+|∂ 2 k / ∂y 2 The second-order partial derivative is proportional to the stiffness. It reflects the "curvature" of the stiffness change. When the stiffness curve has an inflection point or abrupt change, the value of the second-order partial derivative will increase significantly, and at this time, more frequent sampling is also required.

[0125] However, in practice, the stiffness distribution (which is the target to be measured) is unknown when sampling points are placed. Therefore, the density formula described above is not used all at once, but rather iteratively: a sparse pre-scan is performed first (e.g., using a uniform 20mm × 20mm grid), and the stiffness and gradient distributions are initially calculated based on the pre-scan data. Then, the regions requiring further refinement are determined based on the gradient distribution, and additional measurement points are added to these regions. A second scan is then performed, and this process is repeated until convergence. This adaptive iterative sampling strategy can minimize the number of measurement points while ensuring accuracy.

[0126] In some embodiments, after constructing the stiffness distribution matrix K and before calculating the pre-compensation offset ΔC, the original stiffness data obtained from non-uniform sampling is compressed and stored: those stiffness values ​​whose relative deviations from all their neighboring sampling points are less than a preset compression threshold δ are deleted. comp The internal points are selected, and only the boundary points and stiffness abrupt change points are retained to form a sparse stiffness matrix.

[0127] After completing the measurements and constructing the stiffness distribution matrix K using a non-uniform sampling strategy, the raw data typically contains a large number of measurement points. For large-size PCBs, the number of measurement points can reach thousands or even tens of thousands. Directly storing the complete K matrix would consume a significant amount of storage space, and traversing all measurement points during subsequent calculations of pre-compensation offsets would reduce computational efficiency. However, the stiffness distribution matrix K has a unique characteristic: in most regions, the stiffness values ​​change smoothly, with minimal differences between adjacent points; truly valuable information is concentrated in boundary regions and abrupt change points where stiffness changes drastically. Therefore, the raw stiffness data can be compressed and stored, removing redundant internal points and retaining only the key points.

[0128] The basic rule of compression is: delete those samples whose relative deviations from the stiffness values ​​of all their adjacent sampling points are less than a preset compression threshold δ. comp The internal points. Here, "adjacent sampling points" refers to the natural adjacency relationship based on the spatial distribution of sampling points. For example, after performing Delaunay triangulation on the initial sampling points, each point directly connected to it by an edge is considered an adjacent point. For each internal point (i.e., a non-boundary point), calculate its relative stiffness deviation from each of its adjacent points: Relative deviation = |k 中心 - k 相邻 | / k 中心 If all these relative deviations are less than δ comp This indicates that the stiffness value of the center point can be well represented by the values ​​of its surrounding neighboring points, and deleting it will not result in the loss of key information; conversely, if the relative deviation of a certain neighboring point exceeds δ... comp This indicates that the point is a "stiffness mutation point" and needs to be retained.

[0129] Compression threshold δ comp The value of δ determines the balance between the degree of compression and the degree of information retention. comp The smaller the value, the more points are retained, and the more complete the information, but the compression effect is not obvious; δ comp The larger the value, the more points are deleted, and the smaller the storage space, but some detailed information may be lost. Typically, δ... comp Values ​​between 0.05 and 0.15 can be used, allowing for a relative deviation of 5% to 15%. For applications requiring high precision, use a smaller value (such as 0.05); for general applications, use a larger value (such as 0.10 or 0.15).

[0130] After compression, the retained points fall into two categories: one is boundary points (i.e., sampling points located on the edge contour of the plate), which are retained regardless of their stiffness values, because boundary points define the geometric range of the K matrix; the other is stiffness abrupt change points (i.e., at least one adjacent point has a relative stiffness deviation exceeding δ). comp The points (the points in the K matrix). These two types of points together constitute the sparse stiffness matrix. It is important to note that the compression operation only removes internal redundant points and does not change the stiffness values ​​of the points retained in the original data. Therefore, the sparse matrix is ​​a subset of the original K matrix.

[0131] In subsequent calculations of the pre-compensation offset ΔC(x) i , y i When performing a sparse matrix integration, if the integration point happens to be a location not preserved in the sparse matrix, interpolation recovery is required based on the preserved neighboring points. Since the points preserved after compression already cover the boundaries and abrupt change regions, and the interpolation error in smooth regions is small, this approach can significantly reduce the computational load while ensuring computational accuracy.

[0132] For example, in some embodiments, a hierarchical compression strategy can be adopted: after the first compression, the same compression judgment is performed again on the remaining sparse points, and those that still satisfy "the relative deviation between adjacent points is less than δ" are deleted in the new sparse point set. comp The points are used to form a sparser matrix. This hierarchical compression can further reduce the amount of data, but it is important to control the number of compression layers, generally not exceeding two layers, otherwise errors may accumulate due to multiple interpolations.

[0133] For ultra-large PCBs (e.g., panels larger than 500mm × 800mm), the effect of sparse compression is particularly significant. Real-world testing shows that when the original uniform grid has 10,000 sampling points, only about 2,000 to 3,000 key points need to be retained after compression, reducing storage space by more than 70%, and the subsequent calculation time for ΔC is also shortened by about 60%.

[0134] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0135] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A PCB drilling process, characterized in that, Includes the following steps: Fix the PCB board onto the worktable of the drilling machine; A sweeping electromagnetic excitation was applied to the surface of the fixed PCB board, and the vibration displacement response of each region of the board was measured. Based on the vibration displacement response, the local stiffness values ​​at each point of the plate are calculated, and the continuous stiffness distribution matrix K of the entire plate is constructed. Based on the stiffness distribution matrix K, calculate the value at each borehole location (x). i y i The pre-compensation offset ΔC(x) i y i The pre-compensation offset is then superimposed onto the theoretical borehole coordinates to generate the corrected borehole path. The drill bit of the drilling machine is controlled to perform drilling operations at each drilling position in sequence according to the modified drilling path.

2. The PCB circuit board drilling process method according to claim 1, characterized in that, The local stiffness value k(x, y) at each point is calculated by the following formula (1): , Where, m eff f represents the equivalent participating mass at the measuring point. res (x, y) is the local resonant frequency extracted from the vibration displacement response at this measuring point.

3. The PCB circuit board drilling process method according to claim 2, characterized in that, The pre-compensation offset ΔC(x) i y i The following formula (2) is used to calculate: ， Where Ω represents the entire area, G is the Green's function, F is the amplitude of the electromagnetic excitation force, ε is the edge effect compensation coefficient, and ∇ 2 k is the Laplace operator for the local stiffness function.

4. The PCB circuit board drilling process method according to claim 3, characterized in that, Green's function G(x) i y i The calculation of ξ,η is simplified as follows: When point (ξ,η) and point (x) i y i The distance between them is greater than the preset cutoff radius R. c When this point is reached, its contribution is set to zero; the cutoff radius Rc is based on the local stiffness value k(x). i y i The size of R is dynamically adjusted; the greater the stiffness, the greater the value of R. c The smaller.

5. The PCB circuit board drilling process method according to claim 3, characterized in that, The edge effect compensation coefficient ε is based on the target borehole point (x). i y i The shortest distance d from the edge of the PCB board edge A non-constant number that adjusts adaptively; When d edge When d is less than twice the plate thickness, ε takes the first preset value; when d edge When the thickness is greater than five times the plate thickness, ε takes the second preset value, and the first preset value is greater than the second preset value.

6. The PCB circuit board drilling process method according to claim 3, characterized in that, When generating the corrected borehole path, the pre-compensated offset sequence {ΔC(x)} is used. i y i Post-processing is performed: The second-order difference of the pre-compensation offset at each borehole location is calculated using the following formula: ， If the absolute value of the second-order difference exceeds the preset smoothing threshold, local cubic spline interpolation correction is performed on the point and each point before and after it.

7. The PCB circuit board drilling process method according to claim 6, characterized in that, During the drilling process, the actual hole position deviation δ at each drilling location is recorded in real time. 实际 (x) i y i ), and compare the actual deviation with the pre-compensation offset ΔC(x) i y i Compare and calculate the dynamic residual r. i =δ 实际 -ΔC; If the dynamic residuals at three consecutive borehole locations are all greater than 0, then the online incremental correction of the edge effect compensation coefficient ε in formula (2) is initiated.

8. The PCB circuit board drilling process method according to claim 7, characterized in that, The online incremental correction of the edge effect compensation coefficient ε adopts the following cumulative rule: ε new =ε old +α⋅( / r0), where r0 is the normalized reference length, with a value of 1μm; ε is the arithmetic mean of the dynamic residuals of the most recent N borehole locations, α is the learning rate coefficient, ranging from 0.01 to 0.1; the corrected ε new Used for calculating the pre-compensation offset of subsequent drilling in the current batch, and as the initial edge effect compensation coefficient for the next batch of processing.

9. The PCB circuit board drilling process method according to claim 1, characterized in that, The vibration displacement response was measured using a non-uniform sampling strategy: the sampling point density ρ(x,y) was proportional to the modulus of the local stiffness gradient ||∇k(x,y)||, and also to the sum of the absolute values ​​of the second-order partial derivatives of the local stiffness values ​​|∂k / ∂y||. 2 k / ∂x 2 |+|∂ 2 k / ∂y 2 |Proportional.

10. The PCB circuit board drilling process method according to claim 9, characterized in that, After constructing the stiffness distribution matrix K and before calculating the pre-compensation offset ΔC, the original stiffness data obtained from non-uniform sampling is compressed and stored: those stiffness values ​​whose relative deviations from all their adjacent sampling points are less than a preset compression threshold δ are deleted. comp The internal points are selected, and only the boundary points and stiffness abrupt change points are retained to form a sparse stiffness matrix.

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