A metal processing flatness detection method based on laser measurement

Abstract

The present application relates to the technical field of metal processing detection, in particular to a metal processing flatness detection method based on laser measurement, comprising: constructing an initial state vector of the initial deformation characteristics of the short axis and long axis of the bearing metal plate, inputting an elastic thin plate mechanics model and solving the inverse problem, and inverting the internal stress distribution field of the plate surface deformation; extracting the maximum principal stress direction and the maximum shear stress value, correcting the two-dimensional height distribution matrix accordingly to eliminate the non-planar error caused by springback, and obtaining the theoretical plane data; calculating the normal deviation of each measuring point to form the flatness deviation value, dividing the out-of-tolerance and qualified areas and counting the related parameters, and finally generating a structured detection and deformation reason analysis report. The method improves the flatness detection precision, realizes the accurate tracing of the deformation reason, is suitable for high-precision flatness detection in the field of metal processing, and is a metal processing flatness detection method based on laser measurement.

Description

Technical Field

[0001] This invention relates to the field of metal processing inspection technology, and in particular to a method for detecting the flatness of metal processing based on laser measurement. Background Technology

[0002] In metal processing, surface flatness is a crucial indicator of product quality. Laser measurement technology, due to its high accuracy and fast response speed, is widely used in the flatness inspection of metal sheets. Existing laser inspection methods typically obtain a two-dimensional height distribution matrix of the metal sheet surface through laser scanning, and then calculate the deviation of each measuring point relative to a preset plane to determine whether the surface flatness is up to standard.

[0003] Conventional testing methods of this type only focus on the height deviation of the sheet surface, failing to consider the impact of internal stress generated during metal sheet processing on the sheet surface deformation, nor to correct for non-planar errors caused by the sheet's own springback. Since internal stress can cause irreversible deformation of the sheet surface, the springback effect will cause discrepancies between the measured height deviation and the actual flatness deviation, leading to inaccurate identification of out-of-tolerance areas, inability to determine the root cause of the sheet surface deformation, and ultimately failing to meet the testing requirements of high-precision metal processing.

[0004] Conventional testing methods can only output flatness deviation results, but cannot reflect the internal stress distribution that causes the deformation of the board surface. They cannot distinguish whether the surface deviation is caused by processing error or internal stress and springback effect, which makes it difficult to rectify the deformation and makes it difficult to achieve the integration of flatness testing and deformation cause analysis. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a method for detecting the flatness of metal processing based on laser measurement.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a method for detecting the flatness of metal processing based on laser measurement, comprising: An initial state vector is constructed for the metal plate to be tested, wherein the initial state vector carries the initial deformation characteristics of the plate surface in the directions of the minor axis and the major axis, respectively; The initial state vector is input into a preset elastic thin plate mechanical model. By solving the inverse problem of the elastic thin plate mechanical model, the internal stress distribution field that causes the current plate deformation is inverted. The maximum principal stress direction and maximum shear stress value are extracted from the internal stress distribution field. Based on the internal stress distribution field obtained by inversion, the two-dimensional height distribution matrix is ​​geometrically corrected to eliminate the non-planar error caused by the springback of the plate itself, and the corrected theoretical plane data is obtained. Based on the corrected theoretical plane data, the normal deviation of each measuring point on the plate surface relative to the theoretical plane is calculated to form a set of discrete flatness deviation values. The flatness deviation values ​​are divided into regions to identify out-of-tolerance and acceptable regions, and the peak value and root mean square value of the deviation for each region are calculated. Based on the identified out-of-tolerance area location, the peak deviation, the root mean square value, and the inverted stress distribution field, a structured flatness detection and deformation cause analysis report is generated.

[0007] As a further aspect of the present invention, the construction of the initial state vector of the metal plate to be detected includes: The surface of the metal plate to be tested is scanned by a line laser sensor in a continuous state to collect raw point cloud data containing height information. The original point cloud data is denoised and registered, and the processed point cloud data is converted into a two-dimensional height distribution matrix with the direction of metal plate movement as the horizontal axis and the direction perpendicular to the plate surface as the vertical axis. Based on the two-dimensional height distribution matrix, its row slope field and column slope field along the direction of travel are calculated. The row slope field is used to describe the warping of the short side edge, and the column slope field is used to describe the collapse of the long side edge. Based on the row slope field and the column slope field, two independent initial state vectors are constructed respectively; The original point cloud data is subjected to denoising and coordinate registration processing. The processed point cloud data is then converted into a two-dimensional height distribution matrix with the direction of travel of the metal plate as the horizontal axis and the direction perpendicular to the plate surface as the vertical axis, including: Apply a filtering algorithm based on statistical outliers to the original point cloud data to remove noise points caused by splashes or oxide scale interference, and obtain a clean point cloud; Using a long straight edge of the metal plate as a reference, a rigid transformation is performed on the pure point cloud so that the position of the point cloud data in the global coordinate system coincides with the actual physical position of the metal plate, thus completing coordinate registration; The registered point cloud data is resampled according to the motion trajectory of the metal plate. Fixed column intervals are set in the horizontal direction and fixed row intervals are set in the vertical direction to form a regular grid-like point matrix. The height value of each grid vertex in the gridded point matrix is ​​extracted and arranged in row-major order to construct the two-dimensional height distribution matrix. The number of rows in the two-dimensional height distribution matrix corresponds to the number of horizontal sampling points, and the number of columns corresponds to the number of vertical sampling points.

[0008] As a further aspect of the present invention, the step of calculating the row slope field and column slope field along the direction of travel based on the two-dimensional height distribution matrix includes: For each row of data in the two-dimensional height distribution matrix, the height change rate between two adjacent measuring points in the row is calculated using the central difference method. The calculated height change rates are stored row by row to form the row slope field. For each column of the two-dimensional height distribution matrix, the central difference method is also used to calculate the height change rate between two adjacent measuring points in the column. The calculated height change rates are stored by column to form the column slope field. The calculated row slope field and column slope field are smoothed to eliminate calculation spikes caused by high-frequency vibrations and obtain stable slope field data. The smoothed row slope field and column slope field are normalized so that their numerical range is mapped to a preset standard interval, providing consistent data input for subsequent state inversion.

[0009] As a further aspect of the present invention, the step of constructing two independent initial state vectors based on the row slope field and the column slope field includes: Extract all row slope values ​​from the row slope field, arrange them in the order of row index, and combine them into a one-dimensional array. The one-dimensional array is the initial state vector that carries the short edge warping feature. Extract all column slope values ​​from the column slope field, arrange them in the order of column index, and combine them into another one-dimensional array. The one-dimensional array is the initial state vector that carries the long edge collapse feature. The initial state vector bearing the short edge warping feature and the initial state vector bearing the long edge collapse feature are concatenated to form an extended state vector, which fully describes the current overall deformation trend of the board surface.

[0010] As a further aspect of the present invention, the initial state vector is input into a preset elastic thin plate mechanical model, and the internal stress distribution field leading to the current plate deformation is derived by solving the inverse problem of the elastic thin plate mechanical model, including: The preset elastic thin plate mechanical model is invoked, which defines the physical relationship between plate thickness, Young's modulus, Poisson's ratio and deformation displacement. Using the initial state vector as the observation boundary condition, the objective function of the elastic thin plate mechanical model is set to minimize the residual between the observed deformation and the actual measured deformation; The mechanical model of the elastic thin plate is discretized using the finite element analysis method, dividing the continuous plate surface into several tiny mesh elements; On each of the grid cells, the internal stress value that generates the deformation described by the initial state vector is solved by iterative calculation. All the internal stress values ​​are arranged according to their positions on the plate surface to form the internal stress distribution field.

[0011] As a further aspect of the present invention, the direction of the maximum principal stress and the value of the maximum shear stress are extracted from the internal stress distribution field, and these are used as constraints in the subsequent flatness evaluation process, including: For each spatial location in the internal stress distribution field, calculate the stress tensor at the corresponding point; The calculated stress tensor is decomposed into eigenvalues ​​to obtain the magnitudes and directions of the three principal stresses. The principal stress with the largest value is selected and its direction is recorded as the direction of the maximum principal stress. Calculate half the difference between the maximum principal stress and the minimum principal stress in the stress tensor to obtain the shear stress value at the spatial location point, and search the entire plate surface to find the maximum shear stress value; The extracted maximum principal stress direction and the calculated maximum shear stress value are respectively assigned to a status flag bit and a value limit bit. When calculating the flatness deviation in the subsequent calculation, only the data in the plane where the maximum principal stress direction is located are processed, and high stress anomalies exceeding the maximum shear stress value are ignored.

[0012] As a further aspect of the present invention, the step of geometrically correcting the two-dimensional height distribution matrix based on the internal stress distribution field obtained by inversion to eliminate the non-planar error caused by the springback of the sheet metal itself, and obtaining corrected theoretical planar data, includes: By traversing the internal stress distribution field, for each grid cell with residual stress, a theoretical springback compensation amount is calculated based on the relationship between the stress value at the grid cell and the yield strength of the material. The calculated theoretical rebound compensation is taken as the opposite of the value, and used as the height correction of the mesh cell. All calculated height corrections are mapped back to the corresponding positions in the two-dimensional height distribution matrix. The height values ​​in the original matrix are subtracted point by point to offset the rise or fall of the plate surface caused by residual stress. The modified two-dimensional height distribution matrix is ​​fitted with a plane to obtain a best-fitting theoretical plane equation. The plane represented by the theoretical plane equation is the modified theoretical plane data.

[0013] As a further aspect of the present invention, based on the corrected theoretical plane data, the normal deviation of each measuring point on the plate surface relative to the theoretical plane is calculated to form a set of discrete flatness deviation values, including: Read the corrected theoretical plane data, which includes the normal vector of the theoretical plane and a point on the plane; For each measuring point in the two-dimensional height distribution matrix, calculate the vector difference between the position vector of the measuring point and the position vector of the nearest point on the theoretical plane; The dot product of the vector difference and the normal vector of the theoretical plane is calculated, and the result is the signed normal deviation of the measured point relative to the theoretical plane. All calculated signed normal deviation values ​​are stored according to their coordinate positions on the plate surface to form a set of discrete flatness deviation values, with positive values ​​indicating convexity and negative values ​​indicating depression.

[0014] As a further aspect of the present invention, the flatness deviation values ​​are divided into regions to identify out-of-tolerance and acceptable regions, and the peak value and root mean square value of the deviation for each region are statistically analyzed, including: A maximum allowable flatness tolerance zone is defined, which extends equidistantly upwards and downwards from the modified theoretical plane as a reference. All flatness deviation values ​​outside the tolerance zone are marked as out-of-tolerance points, and all flatness deviation values ​​within the tolerance zone are marked as acceptable points. The connected component analysis algorithm is used to group adjacent out-of-tolerance points, and all out-of-tolerance points belonging to the same group are aggregated into an independent out-of-tolerance region. The qualified points that are not aggregated constitute the qualified region. For each identified out-of-tolerance region, calculate the maximum absolute value of all flatness deviations within it as the deviation peak value of the out-of-tolerance region, and calculate its standard deviation as the root mean square value of the out-of-tolerance region.

[0015] As a further aspect of the present invention, a structured flatness inspection and deformation cause analysis report is generated based on the identified out-of-tolerance area location, the peak deviation, the root mean square value, and the inverted stress distribution field, including: The coordinate range of each out-of-tolerance region on the plate surface, the peak deviation of the out-of-tolerance region, the root mean square value of the out-of-tolerance region, and the direction of the maximum principal stress obtained by inversion at the center point of the out-of-tolerance region are organized into a structured data record. All the structured data records of the out-of-tolerance areas, along with the overall size information of the board and the batch number of this test, are assembled into a standardized data package; The standardized data packet is filled into a preset report template, and a schematic diagram with out-of-tolerance area markings is drawn in the report template. A detailed list of values ​​is listed below the diagram. The data in the report template is exported as a file format that can be read by the production management system, thus completing the generation of the flatness inspection and deformation cause analysis report.

[0016] Compared with the prior art, the advantages and positive effects of the present invention are as follows: The initial state vectors, representing the initial deformation characteristics of the metal plate surface in the minor and major axes, are input into a pre-set elastic thin-plate mechanical model. By solving the inverse problem of this model, the internal stress distribution field leading to the current surface deformation is derived. Compared to conventional methods that rely solely on laser scanning to obtain surface height deviations, this approach overcomes the limitations of surface measurement, captures the intrinsic driving factors of surface deformation, avoids the bias of judging flatness based solely on surface height data, and makes the test results more closely reflect the actual deformation state of the plate. Furthermore, it clarifies the relationship between surface deformation and internal stress, enabling precise tracing of the deformation cause and overcoming the limitations of conventional testing methods that can only determine whether the plate is qualified but cannot analyze the root cause of the deformation.

[0017] The maximum principal stress direction and maximum shear stress value are extracted from the internal stress distribution field obtained by inversion. Based on this internal stress distribution field, the two-dimensional height distribution matrix is ​​geometrically corrected to eliminate non-planar errors caused by the springback of the sheet metal itself. This effectively avoids measurement deviations caused by neglecting the springback effect in conventional testing, making the corrected theoretical plane data closer to the true plane state of the sheet metal. Consequently, the calculated normal deviations of each measuring point on the sheet surface relative to the theoretical plane are more accurate, and the discrete flatness deviation values ​​are more valuable for reference. This allows for clearer differentiation between out-of-tolerance and acceptable areas, reducing misjudgments caused by springback errors, improving the accuracy and reliability of flatness testing, and adapting to the testing requirements of high-precision metal processing. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for detecting the flatness of metal processing based on laser measurement, as described in this invention. Figure 2 A flowchart for calculating the row slope field and column slope field; Figure 3 A flowchart for inverting the internal stress distribution field; Figure 4 A three-dimensional surface plot of the normal deviation for flatness testing of metal plates; Figure 5 This is a heat map showing the distribution of flatness deviation in a metal plate. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0020] See Figure 1An initial state vector is constructed for the metal plate to be tested, which carries the initial deformation characteristics of the plate surface in the minor and major axis directions. The initial state vector is input into a preset elastic thin plate mechanical model. By solving the inverse problem of the elastic thin plate mechanical model, the internal stress distribution field that causes the current plate surface deformation is inverted. The direction of the maximum principal stress and the value of the maximum shear stress are extracted from the internal stress distribution field. Based on the inverted internal stress distribution field, the two-dimensional height distribution matrix is ​​geometrically corrected to eliminate the non-planar error caused by the springback of the plate itself, and the corrected theoretical plane data is obtained. Based on the corrected theoretical plane data, the normal deviation of each measuring point on the plate surface relative to the theoretical plane is calculated to form a set of discrete flatness deviation values. The flatness deviation values ​​are divided into regions to identify out-of-tolerance regions and qualified regions, and the peak value and root mean square value of the deviation in each region are statistically calculated. Based on the identified out-of-tolerance region location, the peak value of the deviation, the root mean square value, and the inverted internal stress distribution field, a structured flatness detection and deformation cause analysis report is generated.

[0021] In one embodiment of the present invention, the process of constructing the initial state vector of the metal plate to be inspected involves high-precision scanning and data conversion of the metal plate surface. Taking a cold-rolled steel plate in continuous motion as an example of the metal plate to be inspected, a line laser sensor mounted above the production line scans the surface of the steel plate. As the laser line sweeps across the surface, the sensor records the positional changes of the laser line on the surface, thereby acquiring raw point cloud data containing three-dimensional coordinate information. The raw point cloud data reflects the height information of each sampling point on the surface of the plate.

[0022] In some embodiments, the original point cloud data undergoes denoising and coordinate registration. The original point cloud data may contain noise points caused by oxide scale adhering to the steel plate surface, coolant splashes, or environmental dust reflection. A statistical outlier-based filtering algorithm is applied to process the original point cloud data. This algorithm calculates the average distance between each point and its nearest neighbors, assuming this distance follows a Gaussian distribution. Points with a mean distance exceeding a set standard deviation are identified as outliers and removed. For example, the original point cloud may contain 105,000 points, and the processed clean point cloud retains 102,000 valid points. Coordinate registration uses a long straight edge of the steel plate as a reference. At least three feature points located on this long straight edge are manually or automatically selected in the clean point cloud. Based on the theoretical coordinates of these feature points in a preset world coordinate system, a rigid transformation matrix is ​​calculated. A rigid transformation is then performed on the clean point cloud, ensuring that the position of the clean point cloud data in the global coordinate system precisely coincides with the actual physical position of the steel plate.

[0023] In practice, the processed point cloud data is converted into a two-dimensional height distribution matrix with the direction of metal plate movement as the horizontal axis and the direction perpendicular to the plate surface as the vertical axis. The coordinate-registered point cloud data is resampled according to the movement trajectory of the steel plate on the production line. A fixed column interval is set horizontally (the width of the steel plate), for example, a column interval of 2 mm, and a fixed row interval is set vertically (the length of the steel plate), for example, a row interval of 2.5 mm. The resampling process is performed on a virtual regular grid. For each grid vertex, the height value corresponding to that position is calculated using an interpolation algorithm, ultimately forming a regular gridded point matrix. The height value of each grid vertex in the gridded point matrix is ​​extracted and arranged in row-major order to construct a two-dimensional height distribution matrix. The number of rows in the two-dimensional height distribution matrix corresponds to the number of horizontal sampling points. For example, if the steel plate is 1200 mm wide and the column spacing is 2 mm, then 601 columns are generated. The number of columns in the two-dimensional height distribution matrix corresponds to the number of vertical sampling points. For example, if the scan length is 1500 mm and the row spacing is 2.5 mm, then 601 rows are generated. Finally, a matrix with 601 rows and 601 columns is formed. Each element in the matrix stores the height value of the corresponding grid point.

[0024] In some embodiments, the row slope field and column slope field along the direction of travel are calculated based on a two-dimensional height distribution matrix. For each row of data in the two-dimensional height distribution matrix, the rate of change of height between two adjacent measurement points within the row is calculated using the central difference method. For a given row vector, where the _i_th ... The height value of each element is Then its slope It can be calculated using a formula, which is:

[0025] in: This is the lateral sampling interval. All height change rates calculated for each row are stored row-wise, forming a row slope field describing the warping of the short side edges. For each column of the two-dimensional height distribution matrix, the central difference method is also used to calculate the height change rate between two adjacent measurement points within the column. For a given column vector, the height value of the i-th element is... Then its column slope The calculation formula is:

[0026] in: It is the longitudinal sampling interval. All the height change rates calculated for each column are stored column by column to form a column slope field describing the collapse of the long edge.

[0027] In practice, two independent initial state vectors are constructed based on the row slope field and the column slope field, respectively. All row slope values ​​are extracted from the row slope field, which is a matrix with the same size as the two-dimensional height distribution matrix. The slope values ​​of all rows are arranged in ascending order of row index, forming a one-dimensional array. This one-dimensional array is the initial state vector carrying the short-side edge warping feature. All column slope values ​​are extracted from the column slope field, which is also a matrix. The slope values ​​of all columns are arranged in ascending order of column index, forming another one-dimensional array. This one-dimensional array is the initial state vector carrying the long-side edge collapse feature. Optionally, the initial state vector carrying the short-side edge warping feature and the initial state vector carrying the long-side edge collapse feature are concatenated end-to-end to form an extended state vector. This extended state vector fully describes the overall deformation trend of the slab surface at the current stage, providing input for subsequent mechanical inversion.

[0028] In one embodiment of the present invention, the process of calculating the row slope field and column slope field based on a two-dimensional height distribution matrix involves differential operations and data post-processing. The two-dimensional height distribution matrix is ​​a regular grid array containing height values. (See also...) Figure 2 For each row of the two-dimensional height distribution matrix, the central difference method is applied to calculate the rate of change of height between two adjacent measurement points within the row. For a given row vector with index P, the height value of its q-th element is... The value at the corresponding position in the slope field. Calculated using the central difference, with the lateral sampling interval used in the calculation. The central difference method is also applied to calculate the rate of change of height between two adjacent measuring points in each column of the two-dimensional height distribution matrix. For a given column vector with column index q, the height value of its Pth element is... Then the value at the corresponding position in the slope field Calculated using the central difference, with the longitudinal sampling interval used in the calculation. All height change rates calculated for each row are stored row by row to form a row slope field, which is used to describe the warping of the short edge. All height change rates calculated for each column are stored column by column to form a column slope field, which is used to describe the collapse of the long edge.

[0029] In some embodiments, the calculated row slope fields and column slope fields are smoothed to eliminate computational glitches caused by high-frequency vibrations. The smoothing process employs a mean filtering algorithm, which replaces each slope value with the arithmetic mean of all slope values ​​within a fixed-size neighborhood, for example, using a 3x3 sliding window to traverse the entire row and column slope fields. After mean filtering, local abrupt changes in the row and column slope fields are suppressed, resulting in stable slope field data. The smoothed row and column slope fields are then normalized, mapping their numerical range to a preset standard interval. Normalization is achieved through a linear transformation, with the following formula:

[0030] in: This represents the original slope value in the smoothed slope field. This represents the global minimum value in the slope field. This represents the global maximum value in the slope field. and These are the lower and upper limits of the preset standard interval, and n represents the normalized slope value.

[0031] In practice, two independent initial state vectors are constructed based on the row slope field and the column slope field, respectively. All row slope values ​​are extracted from the row slope field, which is a two-dimensional array. The extraction operation visits each row of the row slope field in ascending order of row index, and appends all slope values ​​from each row to a one-dimensional array. This one-dimensional array is the initial state vector carrying the short-side edge warping feature, and its length is equal to the total number of elements in the row slope field. Similarly, all column slope values ​​are extracted from the column slope field, which is also a two-dimensional array. The extraction operation visits each column of the column slope field in ascending order of column index, and appends all slope values ​​from each column to another one-dimensional array. This one-dimensional array is the initial state vector carrying the long-side edge collapse feature, and its length is equal to the total number of elements in the column slope field.

[0032] It is understandable that the construction of the initial state vectors needs to ensure that the data order corresponds to the spatial location. The order of elements in the initial state vector carrying the warping feature of the short edge is consistent with the row-first traversal order of the row slope field, and the order of elements in the initial state vector carrying the collapsing feature of the long edge is consistent with the column-first traversal order of the column slope field. Optionally, a concatenation operation can be performed on the initial state vectors carrying the warping feature of the short edge and the collapsing feature of the long edge. The concatenation operation directly appends all elements of the initial state vector carrying the collapsing feature of the long edge to all elements of the initial state vector carrying the warping feature of the short edge, forming a longer extended state vector. The extended state vector fully describes the current overall deformation trend of the board surface, and the dimension of the extended state vector is equal to the sum of the dimensions of the two independent initial state vectors.

[0033] In one embodiment of the present invention, an initial state vector is input into a preset elastic thin plate mechanical model, and the internal stress distribution field leading to the current plate deformation is retrieved by solving the inverse problem of the elastic thin plate mechanical model. See also... Figure 3 The system invokes a pre-defined elastic thin-plate mechanical model, a physical model based on classical plate and shell theory, which defines the physical relationships between plate thickness, Young's modulus, Poisson's ratio, and deformation displacement. Using the initial state vector as the observation boundary condition, the objective function of the elastic thin-plate mechanical model is set to minimize the residual between the observed deformation and the actual measured deformation. The objective function is typically expressed as the squared L2 norm of the difference. The elastic thin-plate mechanical model is discretized using the finite element method, dividing the continuous metal plate surface into numerous tiny triangular or quadrilateral mesh elements. In a specific example, a steel plate measuring 1.5 meters by 1.2 meters can be discretized into approximately 10,000 quadrilateral elements. On each mesh element, the internal stress value that generates the deformation described by the initial state vector is solved iteratively. The iterative calculation can employ the Newton-Raphson method or the conjugate gradient method. All internal stress values ​​are arranged according to their positions on the plate surface to form an internal stress distribution field, which is an array of stress values ​​corresponding to the nodes or centers of the finite element mesh.

[0034] In some embodiments, after obtaining the internal stress distribution field, the direction of the maximum principal stress and the value of the maximum shear stress are extracted from the internal stress distribution field. For each spatial location in the internal stress distribution field, i.e., the center point of each finite element mesh element, the stress tensor at the corresponding point is calculated. The stress tensor is a 3x3 symmetric matrix containing the normal stress and shear stress components at that point. Eigenvalue decomposition is performed on the calculated stress tensor. Eigenvalue decomposition solves for the eigenvalues ​​and eigenvectors of the stress tensor. The mathematical expression of eigenvalue decomposition involves solving the characteristic equation. Eigenvalue decomposition yields the magnitudes and directions of the three principal stresses, which are arranged in descending order of their algebraic values. The principal stress with the largest value is selected from the three principal stresses, and its direction is recorded as the direction of the maximum principal stress, which is given by the corresponding eigenvector.

[0035] In practical implementation, the shear stress value at a spatial location is obtained by calculating half the difference between the maximum and minimum principal stresses in the stress tensor. The formula for calculating the shear stress value is:

[0036] in: Represents the maximum principal stress. Represents the minimum principal stress. This represents the shear stress value at that point. The shear stress values ​​calculated for the center points of all mesh elements across the entire plate surface are searched to find the maximum value among all shear stress values; this maximum value is the maximum shear stress value. The maximum shear stress value reflects the peak level of shear stress within the plate surface. The extracted direction of the maximum principal stress and the calculated maximum shear stress value are assigned to a status flag and a numerical limit bit, respectively. The status flag stores the angular information of the direction of the maximum principal stress, and the numerical limit bit stores the specific value of the maximum shear stress. In subsequent calculations of flatness deviation, the status flag and numerical limit bits guide the data processing logic.

[0037] Optionally, during the iterative solution of the internal stress distribution field, the maximum shear stress value can be used as a reference for convergence judgment. If the maximum shear stress value calculated during the iteration exceeds a preset proportion of the material's yield strength, an early warning can be triggered or the iteration step size can be adjusted. In some embodiments, the extracted maximum principal stress direction can be visualized as a vector field diagram, superimposed on the plate topography diagram, for intuitive analysis of the directional characteristics of the stress concentration region. The calculation process for extracting the maximum principal stress direction and the maximum shear stress value from the internal stress distribution field is independent of the stress inversion iteration loop and is usually performed only after the iteration converges and the final internal stress distribution field is obtained.

[0038] In one embodiment of the invention, the two-dimensional height distribution matrix is ​​geometrically corrected based on the inverted internal stress distribution field to eliminate non-planar errors caused by the springback of the sheet metal itself. The internal stress distribution field is an array of stress values ​​corresponding to finite element mesh elements. Traversing the internal stress distribution field, for each mesh element with residual stress, a theoretical springback compensation amount is calculated based on the relationship between the stress value at the mesh element and the material's yield strength. The theoretical springback compensation amount... This characterizes the expected height change of the plate surface point corresponding to the mesh element under an ideal state assuming complete stress release, with the sign indicating the springback direction. The calculation process references the material's elastoplastic constitutive relation; one calculation method involves the ratio of stress intensity to the material's yield strength. The material's yield strength is understood to be an inherent property of the sheet metal, serving as a known constant input. The inverse of the calculated theoretical springback compensation is used as the height correction for the corresponding mesh element. The height correction is numerically equal to the theoretical springback compensation but with the opposite sign; its function is to counteract the predicted springback deformation.

[0039] In some embodiments, all calculated height corrections are mapped back to their corresponding positions in the two-dimensional height distribution matrix. The grid of the internal stress distribution field corresponds spatially to the grid of the two-dimensional height distribution matrix, with the center point of each grid cell corresponding to a measurement point determined by a specific row and column index in the two-dimensional height distribution matrix. The height correction calculated for each grid cell is assigned to the corresponding measurement point in the two-dimensional height distribution matrix via interpolation or direct assignment. Then, a point-by-point subtraction operation is performed on the height values ​​in the original matrix, subtracting the height correction for the corresponding point from the original height value. This operation cancels out the plate elevation or depression caused by residual stress, resulting in a corrected height data matrix. Referring to Table 1, an example correspondence between a simplified set of stress values ​​and the calculated theoretical springback compensation is shown.

[0040] Table 1: Relationship between stress values ​​and theoretical springback compensation

[0041] In practice, a plane fitting is performed on the modified two-dimensional height distribution matrix to obtain a best-fitting theoretical plane equation. Plane fitting typically employs the least squares method, which finds a plane such that the sum of the squared distances from this plane to all three-dimensional points in the modified two-dimensional height distribution matrix is ​​minimized. The general form of the theoretical plane equation is:

[0042] Where X, Y, and Z are spatial coordinate variables, A, B, C, and D are the fitted plane coefficients, and the vector (A, B, C) represents the normal vector of the plane. The plane represented by the theoretical plane equation is the corrected theoretical plane data. The corrected theoretical plane data includes the plane coefficients and reference point information used to define the plane.

[0043] In practice, the normal deviation of each measuring point on the board surface relative to the theoretical plane is calculated based on the corrected theoretical plane data. The corrected theoretical plane data is read, which includes the normal vector of the theoretical plane and a point on the plane. For each measuring point in the two-dimensional height distribution matrix, its spatial coordinates are determined by its row and column index in the matrix and its corresponding height value. The vector difference between the measuring point's position vector and the position vector of the nearest point on the theoretical plane is calculated. The dot product of this vector difference and the theoretical plane's normal vector is then calculated; the result is the signed normal deviation of the measuring point relative to the theoretical plane. A positive signed normal deviation indicates that the measuring point is located on the positive normal side of the theoretical plane, i.e., it is convex; a negative signed normal deviation indicates that the measuring point is located on the negative normal side of the theoretical plane, i.e., it is concave.

[0044] Optionally, the nearest point can be calculated quickly using vector projection. In some embodiments, the theoretical plane equations can be converted into point normals, thereby simplifying the calculation process. It is understood that the calculated normal deviation is a direct measure of flatness. All calculated signed normal deviation values ​​are stored according to their coordinate positions on the board surface, forming a set of discrete flatness deviation values. Flatness deviation values ​​are typically stored in a matrix of the same size as the original two-dimensional height distribution matrix, or as a data list containing coordinates and deviation values.

[0045] See Figure 4 This is a 3D surface plot of the normal deviation for flatness testing of a metal plate. It visually presents the distribution of the vertical deviation of each measuring point relative to the theoretical plane after geometric correction. The red / orange areas have positive normal deviations, with peak values ​​close to 4mm, representing the areas with the most significant bulges in the metal plate. The blue areas have negative normal deviations, with valley values ​​close to -4mm, representing the areas with the most severe indentations in the metal plate. The yellow / light blue areas have deviation values ​​close to 0, indicating that the flatness of this area is relatively good. It visually presents the degree of deviation between the actual plate surface and the ideal theoretical plane after springback correction, and is the core visualization result for evaluating flatness, directly locating high-deviation areas. If the deviation in a certain area continues to exceed the standard, it can be used to infer whether the input parameters of the flexural thin plate mechanical model are accurate, or whether parameters such as the material yield strength match the actual working conditions, guiding the optimization of the mechanical model.

[0046] In one embodiment of the invention, the flatness deviation values ​​are divided into regions to identify out-of-tolerance and acceptable regions. The flatness deviation values ​​are a set of discrete, signed normal deviation data corresponding to the positions of measuring points on the plate surface. A maximum allowable flatness tolerance zone is set, which extends equidistantly upwards and downwards from the corrected theoretical plane. The tolerance zone range is determined by the product technical requirements, for example, set to ±0.5 mm. Measuring points corresponding to all flatness deviation values ​​outside the tolerance zone are marked as out-of-tolerance points, and measuring points within the tolerance zone are marked as acceptable points. In a specific example, a steel plate surface has 10,000 measuring points, of which 9,500 measuring points with deviation values ​​within ±0.5 mm are marked as acceptable points, and the remaining 500 measuring points with deviation values ​​exceeding this range are marked as out-of-tolerance points.

[0047] In some embodiments, a connected component analysis algorithm is used to group adjacent out-of-tolerance points. The algorithm traverses all measured points marked as out-of-tolerance points, checking the connectivity between each out-of-tolerance point and other measured points within its eight or four neighborhoods. All spatially adjacent out-of-tolerance points that satisfy the connectivity relationship are grouped into the same set, thus aggregating all out-of-tolerance points belonging to the same group into a single out-of-tolerance region. Acceptable points not aggregated by any connected component analysis constitute continuous acceptable regions. Through this process, 500 scattered out-of-tolerance points may be aggregated into 5 independent out-of-tolerance regions with irregular boundaries.

[0048] In practice, for each identified out-of-tolerance region, its peak deviation and root mean square (RMS) value are statistically analyzed. The maximum absolute value of all smoothness deviations within the out-of-tolerance region is calculated; this maximum absolute value is taken as the peak deviation of the out-of-tolerance region. The standard deviation of all smoothness deviations within the out-of-tolerance region is calculated; this standard deviation is taken as the RMS value of the out-of-tolerance region, characterizing the dispersion of smoothness deviations in that region. The RMS value of the Kth out-of-tolerance region is then calculated. The formula is:

[0049] in: This represents the total number of measuring points contained in the Kth out-of-tolerance region. This represents the flatness deviation value of the i-th measuring point in the region. This represents the arithmetic mean of all flatness deviations within the region. The peak value and root mean square value of the deviations are the core indicators for quantitatively evaluating the severity of out-of-tolerance areas.

[0050] In practice, a structured flatness inspection and deformation cause analysis report is generated based on the identified out-of-tolerance areas, peak deviation values, root mean square values, and the internal stress distribution field obtained through inversion. The coordinate range of each out-of-tolerance area on the board surface, the peak deviation value of the out-of-tolerance area, the root mean square value of the out-of-tolerance area, and the direction of the maximum principal stress obtained through inversion at the center point of the out-of-tolerance area are compiled into a structured data record. The coordinate range is represented in pixel coordinates or physical millimeter coordinates, for example, recorded as "Area 1: X[150-180], Y[320-350]". The direction of the maximum principal stress is represented by an angle value. In some embodiments, the structured data records of all out-of-tolerance areas, along with the overall size information of the board and the batch number of this inspection, are assembled into a standardized data package. The overall size information of the board includes length, width, and thickness, and the inspection batch number is used to uniquely identify this inspection task. The standardized data package can be organized using JSON, XML, or a custom binary format to ensure the integrity and parsability of the data fields.

[0051] In practice, standardized data packages are entered into a pre-defined report template. The report template is an electronic document containing a fixed title, chart areas, and data table areas. The chart area of ​​the report template displays a schematic diagram with out-of-tolerance areas marked. This diagram is presented as a two-dimensional contour plot or a three-dimensional rendering, clearly outlining the boundaries of each out-of-tolerance area using striking colors or fill patterns. Below the data table area of ​​the report template, a detailed list of values ​​is listed, presenting structured data records for all out-of-tolerance areas in tabular form. Optionally, the data in the report template can be exported to a format readable by the production management system. The export format can be a PDF document for archiving and viewing, a CSV file, or directly written to a database for subsequent data analysis and process monitoring. It can be understood that generating a flatness inspection and deformation cause analysis report is the final output of the methodology, integrating comprehensive information from morphology measurement, stress inversion, and defect statistics.

[0052] See Figure 5 This is a heatmap showing the flatness deviation distribution of a metal plate, primarily displaying the signed deviation of the plate's overall height relative to the theoretical plane. It visually presents the distribution, shape, and intensity of bulges (red) and depressions (blue) across the plate, transforming abstract deviation data into a directly interpretable spatial distribution. It clearly distinguishes between acceptable areas (light colors) and out-of-tolerance areas (dark colors), providing direct evidence for subsequent connected component analysis and defect clustering. Color codes directly correspond to normal deviation values, allowing for rapid reading of deviation peaks in each area and assessment of defect severity. It provides raw data for calculating the deviation peaks and root mean square values ​​of out-of-tolerance areas, supporting the structured index statistics required by the patent. The location of out-of-tolerance areas is directly correlated with subsequent stress inversion results, providing clues for locating the root cause of deformation.

[0053] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for detecting the flatness of metal processing based on laser measurement, characterized in that, include: An initial state vector is constructed for the metal plate to be tested, wherein the initial state vector carries the initial deformation characteristics of the plate surface in the directions of the minor axis and the major axis, respectively; The initial state vector is input into a preset elastic thin plate mechanical model. By solving the inverse problem of the elastic thin plate mechanical model, the internal stress distribution field that causes the current plate deformation is inverted. The maximum principal stress direction and maximum shear stress value are extracted from the internal stress distribution field. Based on the internal stress distribution field obtained by inversion, the two-dimensional height distribution matrix is ​​geometrically corrected to eliminate the non-planar error caused by the springback of the plate itself, and the corrected theoretical plane data is obtained. Based on the corrected theoretical plane data, the normal deviation of each measuring point on the plate surface relative to the theoretical plane is calculated to form a set of discrete flatness deviation values. The flatness deviation values ​​are divided into regions to identify out-of-tolerance and acceptable regions, and the peak value and root mean square value of the deviation for each region are calculated. Based on the identified out-of-tolerance area location, the peak deviation, the root mean square value, and the inverted stress distribution field, a structured flatness detection and deformation cause analysis report is generated.

2. The method for detecting the flatness of metal processing based on laser measurement as described in claim 1, characterized in that, The initial state vector for constructing the metal plate to be detected includes: The surface of the metal plate to be tested is scanned by a line laser sensor in a continuous state to collect raw point cloud data containing height information. The original point cloud data is denoised and registered, and the processed point cloud data is converted into a two-dimensional height distribution matrix with the direction of metal plate movement as the horizontal axis and the direction perpendicular to the plate surface as the vertical axis. Based on the two-dimensional height distribution matrix, its row slope field and column slope field along the direction of travel are calculated. The row slope field is used to describe the warping of the short side edge, and the column slope field is used to describe the collapse of the long side edge. Based on the row slope field and the column slope field, two independent initial state vectors are constructed respectively; The original point cloud data is subjected to denoising and coordinate registration processing. The processed point cloud data is then converted into a two-dimensional height distribution matrix with the direction of travel of the metal plate as the horizontal axis and the direction perpendicular to the plate surface as the vertical axis, including: Apply a filtering algorithm based on statistical outliers to the original point cloud data to remove noise points caused by splashes or oxide scale interference, and obtain a clean point cloud; Using a long straight edge of the metal plate as a reference, a rigid transformation is performed on the pure point cloud so that the position of the point cloud data in the global coordinate system coincides with the actual physical position of the metal plate, thus completing coordinate registration; The registered point cloud data is resampled according to the motion trajectory of the metal plate. Fixed column intervals are set in the horizontal direction and fixed row intervals are set in the vertical direction to form a regular grid-like point matrix. The height value of each grid vertex in the gridded point matrix is ​​extracted and arranged in row-major order to construct the two-dimensional height distribution matrix. The number of rows in the two-dimensional height distribution matrix corresponds to the number of horizontal sampling points, and the number of columns corresponds to the number of vertical sampling points.

3. The method for detecting the flatness of metal processing based on laser measurement as described in claim 2, characterized in that, The calculation of the row slope field and column slope field along the direction of travel based on the two-dimensional height distribution matrix includes: For each row of data in the two-dimensional height distribution matrix, the height change rate between two adjacent measuring points in the row is calculated using the central difference method. The calculated height change rates are stored row by row to form the row slope field. For each column of the two-dimensional height distribution matrix, the central difference method is also used to calculate the height change rate between two adjacent measuring points in the column. The calculated height change rates are stored by column to form the column slope field. The calculated row slope field and column slope field are smoothed to eliminate calculation spikes caused by high-frequency vibrations and obtain stable slope field data. The smoothed row slope field and column slope field are normalized so that their numerical range is mapped to a preset standard interval, providing consistent data input for subsequent state inversion.

4. The method for detecting the flatness of metal processing based on laser measurement as described in claim 3, characterized in that, Based on the row slope field and the column slope field, two independent initial state vectors are constructed respectively, including: Extract all row slope values ​​from the row slope field, arrange them in the order of row index, and combine them into a one-dimensional array. The one-dimensional array is the initial state vector that carries the short edge warping feature. Extract all column slope values ​​from the column slope field, arrange them in the order of column index, and combine them into another one-dimensional array. The one-dimensional array is the initial state vector that carries the long edge collapse feature. The initial state vector bearing the short edge warping feature and the initial state vector bearing the long edge collapse feature are concatenated to form an extended state vector, which fully describes the current overall deformation trend of the board surface.

5. The method for detecting the flatness of metal processing based on laser measurement as described in claim 4, characterized in that, The initial state vector is input into a preset elastic thin plate mechanical model. By solving the inverse problem of the elastic thin plate mechanical model, the internal stress distribution field that causes the current plate deformation is derived, including: The preset elastic thin plate mechanical model is invoked, which defines the physical relationship between plate thickness, Young's modulus, Poisson's ratio and deformation displacement. Using the initial state vector as the observation boundary condition, the objective function of the elastic thin plate mechanical model is set to minimize the residual between the observed deformation and the actual measured deformation; The mechanical model of the elastic thin plate is discretized using the finite element analysis method, dividing the continuous plate surface into several tiny mesh elements; On each of the grid cells, the internal stress value that generates the deformation described by the initial state vector is solved by iterative calculation. All the internal stress values ​​are arranged according to their positions on the plate surface to form the internal stress distribution field.

6. The method for detecting the flatness of metal processing based on laser measurement as described in claim 5, characterized in that, The maximum principal stress direction and maximum shear stress value are extracted from the internal stress distribution field and used as constraints in the subsequent flatness evaluation process, including: For each spatial location in the internal stress distribution field, calculate the stress tensor at the corresponding point; The calculated stress tensor is decomposed into eigenvalues ​​to obtain the magnitudes and directions of the three principal stresses. The principal stress with the largest value is selected and its direction is recorded as the direction of the maximum principal stress. Calculate half the difference between the maximum principal stress and the minimum principal stress in the stress tensor to obtain the shear stress value at the spatial location point, and search the entire plate surface to find the maximum shear stress value; The extracted maximum principal stress direction and the calculated maximum shear stress value are respectively assigned to a status flag bit and a value limit bit. When calculating the flatness deviation in the subsequent calculation, only the data in the plane where the maximum principal stress direction is located are processed, and high stress anomalies exceeding the maximum shear stress value are ignored.

7. The method for detecting the flatness of metal processing based on laser measurement as described in claim 6, characterized in that, The step involves geometrically correcting the two-dimensional height distribution matrix based on the internal stress distribution field obtained through inversion, eliminating non-planar errors caused by the springback of the sheet metal itself, and obtaining corrected theoretical planar data, including: By traversing the internal stress distribution field, for each grid cell with residual stress, a theoretical springback compensation amount is calculated based on the relationship between the stress value at the grid cell and the yield strength of the material. The calculated theoretical rebound compensation is taken as the opposite of the value, and used as the height correction of the mesh cell. All calculated height corrections are mapped back to the corresponding positions in the two-dimensional height distribution matrix. The height values ​​in the original matrix are subtracted point by point to offset the rise or fall of the plate surface caused by residual stress. The modified two-dimensional height distribution matrix is ​​fitted with a plane to obtain a best-fitting theoretical plane equation. The plane represented by the theoretical plane equation is the modified theoretical plane data.

8. The method for detecting the flatness of metal processing based on laser measurement as described in claim 7, characterized in that, Based on the corrected theoretical plane data, the normal deviation of each measuring point on the plate surface relative to the theoretical plane is calculated, forming a set of discrete flatness deviation values, including: Read the corrected theoretical plane data, which includes the normal vector of the theoretical plane and a point on the plane; For each measuring point in the two-dimensional height distribution matrix, calculate the vector difference between the position vector of the measuring point and the position vector of the nearest point on the theoretical plane; The dot product of the vector difference and the normal vector of the theoretical plane is calculated, and the result is the signed normal deviation of the measured point relative to the theoretical plane. All calculated signed normal deviation values ​​are stored according to their coordinate positions on the plate surface to form a set of discrete flatness deviation values, with positive values ​​indicating convexity and negative values ​​indicating depression.

9. The method for detecting the flatness of metal processing based on laser measurement as described in claim 8, characterized in that, The flatness deviation values ​​are divided into regions to identify out-of-tolerance and acceptable regions, and the peak value and root mean square value of the deviation for each region are statistically analyzed, including: A maximum allowable flatness tolerance zone is defined, which extends equidistantly upwards and downwards from the modified theoretical plane as a reference. All flatness deviation values ​​outside the tolerance zone are marked as out-of-tolerance points, and all flatness deviation values ​​within the tolerance zone are marked as acceptable points. The connected component analysis algorithm is used to group adjacent out-of-tolerance points, and all out-of-tolerance points belonging to the same group are aggregated into an independent out-of-tolerance region. The qualified points that are not aggregated constitute the qualified region. For each identified out-of-tolerance region, calculate the maximum absolute value of all flatness deviations within it as the deviation peak value of the out-of-tolerance region, and calculate its standard deviation as the root mean square value of the out-of-tolerance region.

10. The method for detecting the flatness of metal processing based on laser measurement as described in claim 9, characterized in that, Based on the identified out-of-tolerance area locations, the peak deviation, the root mean square value, and the inverted stress distribution field, a structured flatness inspection and deformation cause analysis report is generated, including: The coordinate range of each out-of-tolerance region on the plate surface, the peak deviation of the out-of-tolerance region, the root mean square value of the out-of-tolerance region, and the direction of the maximum principal stress obtained by inversion at the center point of the out-of-tolerance region are organized into a structured data record. All the structured data records of the out-of-tolerance areas, along with the overall size information of the board and the batch number of this test, are assembled into a standardized data package; The standardized data packet is filled into a preset report template, and a schematic diagram with out-of-tolerance area markings is drawn in the report template. A detailed list of values ​​is listed below the diagram. The data in the report template is exported as a file format that can be read by the production management system, thus completing the generation of the flatness inspection and deformation cause analysis report.

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