A kind of aluminum veneer multi-axis linkage numerical control bending method based on springback compensation

Abstract

The present application belongs to the technical field of metal sheet plastic forming and digital control cross, and discloses a kind of aluminum veneer multi-axis linkage numerical control bending method based on springback compensation.The method collects historical bending process data, with sheet thickness, bending radius, die slot width and feed speed as input features to divide process feature subspace, and establishes a bending angle springback amount mapping matrix in each subspace to obtain initial down pressure depth compensation value for performing feedforward control.In the multi-axis linkage bending stage, real-time servo motor torque feedback signal and grating displacement signal are collected, and the real-time plastic deformation resistance of the current bending zone is calculated, and the online compensation correction amount is solved using the dynamic differential equation of deformation resistance and springback angle, and the correction amount is added to the remaining trajectory planning of multi-axis interpolation algorithm.The present application makes the down pressure trajectory self-adaptive correction according to real-time resistance, eliminates the fixed compensation deviation, and improves the compliance of bending angle to target value.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of metal sheet plastic forming and digital control, specifically involving a springback compensation control method for bending aluminum single panels using multi-axis linkage CNC equipment, and discloses a multi-axis linkage CNC bending method for aluminum single panels based on springback compensation. Background Technology

[0002] In multi-axis CNC bending of aluminum panels, springback of the sheet metal after unloading is the direct cause of dimensional deviations. Existing CNC bending equipment generally employs a static compensation strategy to control springback. Specifically, this involves inputting geometric and process parameters such as sheet thickness, bending radius, lower die slot width, and feed speed into the control system. The control system then calculates a fixed compression depth compensation based on built-in empirical formulas or a static data mapping table established through offline testing. During actual bending operations, the CNC system drives each axis according to a pre-planned multi-axis interpolation trajectory and directly applies this fixed compression depth compensation when the bending reaches the bottom dead center. The motion trajectory and compression depth remain unchanged throughout the multi-axis linkage process, without adjusting to changes in the physical state of the sheet metal during deformation.

[0003] The core technical problem with the aforementioned static compensation strategy is that the fixed downward pressure depth compensation cannot match the real-time physical state changes of the aluminum panel during multi-axis linkage bending. Fluctuations in the mechanical properties of aluminum panels from the same or different batches exist. During the plastic deformation process caused by the slider downward pressure, the actual yield strength and plastic deformation resistance of the panel are dynamically changing. Because existing technology relies solely on preset static parameters for one-time feedforward calculations, it cannot detect real-time changes in deformation resistance in the middle and later stages of bending. This leads to a disconnect between the applied fixed compensation amount and the actual springback requirements of the panel, ultimately causing a systematic deviation in the bending angle from the target value. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-axis linkage CNC bending method for aluminum single panels based on springback compensation, which can solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation includes: collecting historical bending process data, using plate thickness, bending radius, lower die V-groove width and feed speed as input features, dividing the process feature subspace through a clustering algorithm, and fitting and establishing a bending angle springback mapping matrix in each process feature subspace;

[0007] During the actual bending process, the current aluminum panel parameters and target bending angle are read, and the initial pressing depth compensation value is obtained by looking up the table to execute feedforward control;

[0008] In the multi-axis linkage stage, the torque feedback signal of the servo motor and the displacement signal of the grating ruler are collected in real time to calculate the real-time plastic deformation resistance of the current bending zone. The online compensation correction amount is obtained by using the established dynamic differential equation of deformation resistance and springback angle. The online compensation correction amount is then superimposed on the remaining trajectory planning of the multi-axis interpolation algorithm.

[0009] Preferably, the step of dividing the process feature subspace by clustering algorithm includes: standardizing the input features and calculating the Mahalanobis distance between each input feature to eliminate the correlation interference between different physical dimensions;

[0010] A clustering algorithm based on density peaks is adopted, and local decision values ​​are constructed according to the Mahalanobis distance. Input features whose local decision values ​​satisfy the preset density conditions are clustered into the same process feature subspace, so that the bending conditions in the same process feature subspace have similar stress and strain distribution states.

[0011] For input features with sparse edge distribution, a forced attribution determination is made based on the distribution variance of adjacent process feature subspaces to ensure that all historical bending process data fall into a unique process feature subspace.

[0012] Preferably, the step of fitting and establishing a bending angle springback mapping matrix in each process feature subspace includes: in the process feature subspace, taking the target bending angle as the dependent variable and the difference between the initial pressing depth and the measured springback angle as the independent variable, using partial least squares regression to establish a mapping matrix reflecting the nonlinear relationship between pressing depth and springback.

[0013] The step of obtaining the initial pressure depth compensation value by looking up a table includes: calculating the interpolation node coordinates of the current plate parameters and the target bending angle in the mapping matrix, and outputting the corresponding initial pressure depth compensation value using a bilinear interpolation algorithm.

[0014] Preferably, the real-time acquisition of the torque feedback signal of the servo motor and the displacement signal of the grating ruler during the multi-axis linkage stage includes: during the pressing stage of the multi-axis linkage, synchronously reading the current feedback value of the servo driver and the position pulse value of the grating ruler at a fixed sampling period.

[0015] The current feedback value is converted into a torque feedback signal, and the torque feedback signal and the grating ruler displacement signal are respectively subjected to sliding mean filtering to remove high-frequency glitch signals caused by mechanical transmission chain gaps and external vibrations, so as to obtain smooth torque time series and displacement time series.

[0016] Preferably, the calculation of the real-time plastic deformation resistance of the current bending zone includes: calculating the real-time downward displacement of the slider based on the displacement signal of the grating ruler, and calculating the real-time bending force output by the hydraulic cylinder of the bending machine based on the torque feedback signal;

[0017] Combining the bending span and real-time downward displacement of the aluminum single panel, a mechanical equilibrium equation for bending force and plastic deformation resistance is constructed based on the principle of virtual work. The real-time bending force and the real-time downward displacement of the slider are substituted into the mechanical equilibrium equation to solve for the real-time plastic deformation resistance of the current bending zone.

[0018] Preferably, the step of solving the online compensation correction amount using the established dynamic differential equation of deformation resistance and rebound angle, and superimposing the online compensation correction amount into the remaining trajectory planning of the multi-axis interpolation algorithm, includes: inputting the real-time plastic deformation resistance into the pre-constructed dynamic differential equation, solving for the transient rebound angle change rate at the current moment, and performing an integral operation on the transient rebound angle change rate over the remaining compression time to obtain the online compensation correction amount;

[0019] Obtain the remaining unexecuted trajectory points of the multi-axis interpolation algorithm in the current interpolation cycle, and allocate the online compensation correction amount to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points.

[0020] Preferably, after aggregating the input features whose local decision values ​​meet the preset density conditions into the same process feature subspace, the method further includes: real-time monitoring of the distribution density changes of newly added historical bending process data in each process feature subspace;

[0021] When the distribution density of a certain process feature subspace exceeds the preset capacity threshold, a splitting operation is triggered. Based on the principal component direction of the new data in the Mahalanobis distance space, the original process feature subspace is divided into two subspaces, and the bending angle springback mapping matrix corresponding to the two subspaces is recalculated to achieve adaptive evolution of the process feature subspace.

[0022] Preferably, before calculating the interpolation node coordinates of the current sheet parameters and the target bending angle in the mapping matrix, the method further includes: obtaining the measured yield strength value of the current aluminum single panel, and comparing the measured yield strength value with the standard yield strength value in the historical bending process data;

[0023] If the difference between the two exceeds the allowable fluctuation range, then based on the positive correlation between yield strength and springback, the plate thickness feature in the current plate parameters is equivalently converted, and the converted equivalent plate thickness is used as a new input feature to participate in the calculation of interpolation node coordinates.

[0024] Preferably, after obtaining the smooth torque time series and displacement time series, the method further includes: performing a first-order difference operation on the displacement time series to obtain a velocity time series, and performing a first-order difference operation on the torque time series to obtain a torque change rate time series.

[0025] The speed time series and the torque change rate time series are multiplied together, and the inflection point when the product result turns from negative to positive is identified.

[0026] The inflection point is taken as the critical switching point for the aluminum panel to enter the plastic deformation stage from the elastic deformation stage. Only the torque feedback signal and the grating ruler displacement signal after the critical switching point are collected to calculate the real-time plastic deformation resistance.

[0027] Preferably, when allocating the online compensation correction amount to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points, the method further includes: obtaining the maximum allowable tensile strain threshold corresponding to the aluminum single-panel material;

[0028] Calculate the maximum permissible downward displacement boundary of the remaining trajectory points based on the maximum permissible tensile strain threshold;

[0029] Determine whether the position coordinates of the remaining trajectory points after allocating the online compensation correction amount exceed the maximum allowable downward displacement boundary;

[0030] If the amount exceeds the limit, the excess compensation will be truncated and transferred to the pressure parameter adjustment during the pressure holding stage.

[0031] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0032] 1. This invention solves the problem of the disconnect between static compensation and real-time springback requirements by integrating offline feedforward and online feedback. By real-time acquisition of servo motor torque feedback signals and grating ruler displacement signals, and calculating the real-time plastic deformation resistance of the current bending zone based on the principle of virtual work, the system can obtain the actual physical changes during the bending process. The online compensation correction is solved using dynamic differential equations and superimposed on the remaining trajectory planning of the multi-axis interpolation algorithm. This allows the multi-axis linkage downward pressing trajectory to adaptively correct itself based on the real-time resistance of the current sheet material, thereby eliminating fixed compensation deviations caused by fluctuations in material mechanical properties and improving the conformity of the aluminum single-panel bending angle to the target value.

[0033] 2. This invention uses Mahalanobis distance clustering to divide the process feature subspace, eliminating correlation interference between different physical dimensions, ensuring that the springback mapping matrix within the same subspace closely matches the stress-strain distribution. By using moving average filtering to process torque and displacement signals, and combining the inflection point of the product of velocity and torque change rate to determine the critical switching point from elastic to plastic deformation, high-frequency interference caused by mechanical transmission clearances and external vibrations is eliminated, ensuring the physical authenticity of the resistance signals used in the calculation. By introducing a maximum allowable tensile strain threshold to constrain the position coordinates of the remaining trajectory points, and transferring compensation exceeding the boundary to the holding pressure stage, over-correction of the multi-axis interpolation trajectory is prevented, avoiding tearing of the aluminum panel due to excessive local deformation. Attached Figure Description

[0034] Figure 1 Flowchart of the multi-axis linkage CNC bending method for aluminum single panels based on springback compensation

[0035] Figure 2 Flowchart of clustering and adaptive evolution of process feature subspace

[0036] Figure 3 Flowchart for feedforward control and initial compensation value acquisition

[0037] Figure 4 Flowchart for signal processing and deformation identification in multi-axis linkage stage

[0038] Figure 5 Flowchart for real-time plastic deformation resistance calculation

[0039] Figure 6 Flowchart for online compensation correction allocation and boundary constraints. Detailed Implementation

[0040] Please refer to Figure 1 and Figure 2This embodiment provides a multi-axis linkage CNC bending method for aluminum single-panel bending based on springback compensation. Historical bending process data is collected, with valid samples derived from the historical operation records of the multi-axis linkage CNC bending equipment. Each valid sample includes core fields such as plate thickness, bending radius, lower die V-groove width, feed speed, target bending angle, actual pressing depth, measured springback angle, bending force, and material grade. Invalid samples with bending angle deviations exceeding preset ranges, equipment alarms, or plate breakage are removed to ensure the validity and consistency of the sample data. Plate thickness, bending radius, lower die V-groove width, and feed speed are used as input features. These four input features are the core process and geometric parameters affecting the springback of aluminum single-panel bending. Plate thickness is negatively correlated with springback, while bending radius and lower die V-groove width are positively correlated with springback. Feed speed affects yield strength by changing the material strain rate, and thus is positively correlated with springback. The input features are standardized using the Z-score standardization method. For each input feature, the mean and standard deviation of all historical samples are calculated, transforming the feature values ​​of each sample into standardized feature vectors with a mean of 0 and a variance of 1, thus eliminating the influence of different physical dimensions on subsequent calculations. A clustering algorithm is used to divide the process feature subspace, and the Mahalanobis distance between each input feature is calculated. The formula for calculating the Mahalanobis distance is:

[0041]

[0042] in, Let be the Mahalanobis distance between sample i and sample j. Let i be the standardized input feature vector of the i-th sample. Let j be the standardized input feature vector of the j-th sample. The covariance matrix of the input eigenvectors, This is the inverse of the covariance matrix. Mahalanobis distance eliminates the interference of linear correlation between different input features by using the inverse of the covariance matrix, avoiding distance calculation errors caused by process matching correlation between features. A density peak-based clustering algorithm is adopted, and local decision values ​​are constructed based on Mahalanobis distance. First, the local density of each sample is calculated, and the calculation formula is:

[0043]

[0044] in, Let be the local density value of the i-th sample. The preset cutoff distance, This is an indicator function; the function value is 1 when the value within the parentheses is less than 0, and 0 otherwise. The cutoff distance is chosen to ensure that the average number of neighbors for each sample is 1% to 2% of the total number of samples, thus guaranteeing the statistical validity of the local density calculation. The minimum distance from each sample to the sample with the higher local density value is calculated. For the sample with the highest local density, Find the maximum Mahalanobis distance among all samples. Calculate the local decision value based on local density and minimum distance, using the following formula:

[0045]

[0046] in, Let be the local decision value of the i-th sample. Input features whose local decision values ​​satisfy a preset density condition are clustered into the same process feature subspace. The preset density condition is that the local decision value is greater than a decision threshold determined by the cumulative distribution function. The decision threshold is the value corresponding to the cumulative distribution of local decision values ​​reaching 95%. Samples above the threshold are selected as cluster centers, and samples not belonging to cluster centers are assigned to the subspace of the nearest cluster center, so that bending conditions within the same process feature subspace have similar stress-strain distribution states. For input features with sparse edge distribution, forced assignment is performed based on the distribution variance of neighboring process feature subspaces to ensure that all historical bending process data fall into a unique process feature subspace, avoiding unassigned condition samples.

[0047] Within each process feature subspace, a bending angle springback mapping matrix is ​​fitted and established. Within this subspace, the target bending angle is used as the dependent variable, and the difference between the initial compression depth and the measured springback angle is used as the independent variable. Independent and dependent variable matrices are constructed, and a multiple regression method is employed to establish a mapping matrix reflecting the nonlinear relationship between compression depth and springback. The rows of the mapping matrix correspond to the discrete values ​​of the target bending angle, the columns correspond to the standardized value ranges of the input features, and the matrix elements are the initial compression depth compensation values ​​required to offset springback under the corresponding operating conditions.

[0048] During the actual bending process, the current aluminum panel's sheet parameters and target bending angle are read. The sheet parameters include the measured sheet thickness, bending radius, lower die V-groove width, and feed speed. First, the process feature subspace to which the current parameters belong is determined. The initial pressing depth compensation value is obtained by looking up a table, and feedforward control is executed. The nearest neighbor matching method is used to select the compensation value corresponding to the node in the mapping matrix that is closest to the current parameters. The initial pressing depth compensation value is superimposed on the preset pressing trajectory to complete the feedforward compensation setting before bending.

[0049] During the multi-axis linkage phase, the torque feedback signal of the servo motor and the displacement signal of the grating ruler are synchronously acquired with a fixed sampling period of 0.5ms to 2ms to ensure the real-time performance and time synchronization of the signal acquisition. The torque feedback signal of the servo motor is obtained by converting the q-axis current feedback value of the servo driver. The torque and q-axis current are linearly proportional. The grating ruler displacement signal comes from an absolute grating ruler mounted on the bending slider and is used to obtain the real-time downward displacement of the slider, with a displacement resolution of not less than 1μm. The real-time downward displacement of the slider is calculated based on the grating ruler displacement signal, and the real-time bending force output by the hydraulic cylinder of the bending machine is calculated based on the torque feedback signal. The calculation formula is as follows:

[0050]

[0051] in, The real-time bending force at the k-th sampling time is... This represents the torque feedback signal at the k-th sampling time. This refers to the transmission ratio from the servo motor to the hydraulic cylinder. For the mechanical efficiency of the transmission system. Let be the radius of action of the hydraulic cylinder piston. Combining the bending span and real-time downward displacement of the aluminum panel, a mechanical equilibrium equation for the bending force and plastic deformation resistance is constructed based on the principle of virtual work. The core of the virtual work principle is that the virtual work done by the external force is equal to the virtual work done by the internal force in the plastic deformation zone. The mechanical equilibrium equation is:

[0052]

[0053] in, This represents the real-time plastic deformation resistance of the bending zone at the k-th sampling time. The volume of the plastic deformation zone in the bending area. Let be the rate of change of the equivalent strain with respect to the downward displacement at the k-th sampling time. Substituting the real-time bending force and the real-time downward displacement of the slider into the mechanical equilibrium equation, the real-time plastic deformation resistance of the current bending zone is solved. The solution formula is:

[0054]

[0055] Plastic deformation resistance is the actual flow stress of a material at the current stage of plastic deformation. It directly reflects the real-time mechanical properties of the material and is directly related to the amount of springback after unloading.

[0056] A dynamic differential equation for the relationship between deformation resistance and springback angle is pre-constructed. This equation, derived from the theory of elastoplastic mechanics of materials, reflects the dynamic relationship between changes in plastic deformation resistance and changes in springback angle. The dynamic differential equation is as follows:

[0057]

[0058] in, The transient rate of change of the rebound angle. The rate of change of resistance to plastic deformation. This is a proportionality coefficient related to the material's elastic modulus. The work hardening coefficient of the material. Let be the plastic deformation resistance at time t. The proportionality coefficient K and hardening coefficient C are obtained by calibrating historical data within the corresponding process feature subspace to ensure the prediction accuracy of the equation. The real-time plastic deformation resistance is input into the dynamic differential equation, and the transient rebound angle change rate at the current time is obtained by solving it. The online compensation correction amount is obtained by integrating the transient rebound angle change rate over the remaining compression time. The calculation formula is as follows:

[0059]

[0060] in, To compensate for corrections online, For the current moment, This is the preset end time of the downward pressure. This is the conversion factor between the rebound angle and the compression depth, in mm / rad. The remaining unexecuted trajectory points of the multi-axis interpolation algorithm in the current interpolation cycle are obtained. These are the compression phase trajectory points that have been planned but not yet executed. Each trajectory point contains the position coordinates, velocity, and acceleration parameters of each linkage axis. The online compensation correction is allocated to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points. The allocation formula is:

[0061]

[0062] in, The compensation amount allocated to the m-th remaining trajectory point. This is the preset total downward displacement. Let be the original downward displacement of the m-th remaining trajectory point. This represents the completed downward displacement at the current moment. The compensation is smoothly superimposed through proportional displacement allocation, avoiding motion impacts during multi-axis linkage and enabling real-time adaptive correction of the downward trajectory.

[0063] This embodiment achieves feedforward compensation for bending springback by offline process feature subspace partitioning and springback mapping matrix fitting. Through real-time signal acquisition, plastic deformation resistance calculation, and dynamic differential equation solving in the multi-axis linkage stage, online feedback correction of springback compensation is achieved. By integrating offline feedforward and online feedback, the downward trajectory of multi-axis linkage can be adaptively adjusted according to the real-time physical state of the sheet material, eliminating compensation deviations caused by fluctuations in material mechanical properties and ensuring that the bending angle meets the target value.

[0064] Specifically, the range of input feature values ​​and the dimension of the springback mapping matrix for each process feature subspace obtained in this embodiment are shown in Table 1. This table clarifies the bending condition boundary corresponding to each process feature subspace, ensuring that the samples in each subspace have similar stress and strain distribution states, thus providing a basis for high-precision fitting of the springback mapping matrix.

[0065] Table 1. Range of Input Feature Values ​​in Process Feature Subspace and Dimensions of Springback Mapping Matrix

[0066]

[0067] In Table 1, the rows of the springback mapping matrix correspond to the target bending angle, with a value range of 30° to 180° and an interval of 10°, for a total of 15 rows; the columns correspond to the standardized value range of the input features, for a total of 10 columns, and the matrix elements are the initial downward pressure depth compensation values ​​under the corresponding working conditions.

[0068] In another embodiment, when standardizing the input features, for each input feature, the mean of the feature is calculated by iterating through all historical bending process samples. with standard deviation For each sample, this feature value Perform the transformation to obtain standardized eigenvalues. This method unifies the statistical distribution of all input features to a standard normal distribution with a mean of 0 and a variance of 1, eliminating the interference of different physical dimensions such as plate thickness and feed rate on the distance calculation and preventing features with larger dimensional values ​​from dominating the clustering results. When calculating the Mahalanobis distance between each input feature, the covariance matrix of the input features is first constructed, and the elements of the covariance matrix... ,in For the p-th input feature, For the q-th input feature, Let be the mean of the p-th input feature. Let q be the mean of the q-th input feature. The covariance matrix fully reflects the linear correlation between different input features. By inverting the covariance matrix, Mahalanobis distance can completely eliminate the interference of process matching correlation between features, such as the positive correlation between plate thickness and lower mold V-groove width, ensuring that the distance calculation result only reflects the process differences between samples.

[0069] When using a density peak-based clustering algorithm, the cutoff distance The selection of the cutoff distance was completed through iterative calculation. The initial cutoff distance was set to 10% of the mean Mahalanobis distance among all samples. The value of the cutoff distance was iteratively adjusted until the average number of neighbors of each sample was 1.5% of the total number of samples. This ensured that the local density calculation was both statistically valid and did not suffer from insufficient local density discrimination due to an excessively large cutoff distance. The minimum distance for each sample was calculated. When the current sample has a local density greater than that of the current sample, iterate through all samples with a density greater than that of the current sample, calculate the Mahalanobis distance from the current sample to these samples, and take the minimum value as the maximum value. For the sample with the highest global local density, The maximum value of the Mahalanobis distance among all samples is taken to ensure that the local decision value of that sample is the global maximum. All samples are sorted in descending order of their local decision values. Inflection points where local decision values ​​change abruptly after sorting are identified, and samples before these inflection points are designated as cluster centers. The location of the inflection point is determined by the second-order difference extremum of the local decision values, ensuring that the number and location of cluster centers are entirely determined by the distribution characteristics of the sample data, avoiding partitioning bias caused by manually setting the number of clusters. Each non-cluster center sample is assigned to the process feature subspace of the nearest cluster center, ensuring that samples within the same subspace have similar stress-strain distributions for their corresponding bending conditions, thus ensuring consistency in the springback behavior within the same subspace.

[0070] For input features with sparse edge distribution, the Mahalanobis distance from the sample to all cluster centers is first calculated. If the minimum Mahalanobis distance is greater than a preset edge threshold (which is twice the average Mahalanobis distance from the sample to the cluster center within the corresponding subspace), the sample is determined to be a sparsely distributed edge sample. The Mahalanobis distance from this edge sample to each neighboring subspace, as well as the variance of the Mahalanobis distance from the sample to the cluster center within each neighboring subspace, are calculated. The ratio of the Mahalanobis distance to the variance for each neighboring subspace is calculated, and the sample is assigned to the process feature subspace with the smallest ratio. Through variance normalization, edge samples are avoided from being assigned to subspaces with high dispersion, ensuring that all historical bending process data fall into a unique process feature subspace, achieving full coverage of all bending conditions.

[0071] After the initial partitioning of the process feature subspace, the distribution density changes of newly added historical bending process data in each process feature subspace are monitored in real time. For every 100 sets of newly added valid historical bending process data, the local density mean of all samples in each subspace is recalculated. When the local density mean of a certain process feature subspace exceeds the preset capacity threshold, a splitting operation is triggered. The preset capacity threshold is 1.5 times the local density mean of the subspace at the time of initial partitioning. The local density mean exceeding the threshold indicates that there are too many samples in the subspace, the dispersion of process parameters increases, the consistency of stress and strain distribution decreases, and the fitting accuracy of the springback mapping matrix will be affected. After triggering the split operation, principal component analysis is performed on the standardized input feature vectors of all samples in the subspace to extract the first principal component direction. The first principal component direction is the direction with the largest variance of the sample data, corresponding to the dimension with the largest difference in process parameters. Using the coordinates of the original cluster center of the subspace in the first principal component direction as the dividing point, the original samples are divided into two groups, forming two new process feature subspaces. New cluster centers are determined for the two new subspaces, and the bending angle springback mapping matrix corresponding to the two subspaces is recalculated to achieve the adaptive evolution of the process feature subspace.

[0072] This embodiment eliminates interference from dimensions and correlations between different input features by calculating Mahalanobis distance, achieves accurate division of the process feature subspace through a density peak-based clustering algorithm, ensures full coverage of all bending conditions through mandatory assignment of edge samples, and enables the process feature subspace to dynamically adjust with newly added process data through an adaptive evolution mechanism, always maintaining the consistency of stress and strain distribution of samples within the subspace, further improving the fitting accuracy and applicability of the springback mapping matrix.

[0073] Specifically, Table 2 shows a comparison of the distribution parameters before and after the splitting operation of a certain process feature subspace in this embodiment. The table shows the changes in sample distribution during the adaptive evolution of the subspace, verifying that the splitting operation can effectively reduce the dispersion of process parameters of samples in the subspace and improve the consistency of stress and strain distribution in the subspace.

[0074] Table 2 Comparison of Distribution Parameters Before and After Adaptive Evolution of Process Feature Subspace Table

[0075]

[0076] In Table 2, the original subspace No. 3 was split because the local density mean exceeded the preset capacity threshold of 0.3 after the addition of new samples. The principal component analysis results showed that the direction with the largest sample variance in this subspace was the thickness direction of the board. Therefore, the original space was divided into two subspaces along the thickness direction of the board. The local density mean of the two subspaces after the split returned to the preset reasonable range, ensuring the fitting accuracy of the rebound mapping matrix.

[0077] refer to Figure 3 In another preferred embodiment, within the process feature subspace, the target bending angle is used as the dependent variable, and the difference between the initial pressing depth and the measured springback angle is used as the independent variable. Simultaneously, standardized sheet thickness, bending radius, lower die V-groove width, and feed speed are included as auxiliary independent variables to construct an independent variable matrix X and a dependent variable matrix Y. Each row of the independent variable matrix X corresponds to a historical sample, and each column corresponds to an independent variable. Each row of the dependent variable matrix Y corresponds to a historical sample, and each column corresponds to the target bending angle. Partial least squares regression is used to establish a mapping matrix reflecting the nonlinear relationship between pressing depth and springback. Partial least squares regression performs principal component decomposition on both the independent variable matrix X and the dependent variable matrix Y, extracting principal components that best explain the variance of both the independent and dependent variable matrices. This avoids the regression coefficient distortion problem caused by multicollinearity of independent variables in ordinary least squares regression and adapts to working conditions where bending process parameters are correlated. The regression coefficient matrix is ​​calculated based on the extracted principal components, using the following formula:

[0078]

[0079] in, This is the regression coefficient matrix. A regression model between the independent and dependent variables is established using the regression coefficient matrix. Based on the regression model, a bending angle springback mapping matrix is ​​constructed. The rows of the mapping matrix correspond to the discrete values ​​of the target bending angle, the columns correspond to the discrete values ​​of the plate thickness, and the matrix elements are the initial compression depth compensation values ​​required to offset springback under the corresponding working conditions, fully reflecting the nonlinear relationship between compression depth and springback.

[0080] During the actual bending process, the current aluminum panel's sheet parameters and target bending angle are read. After determining the process feature subspace to which the current parameters belong, the coordinates of the interpolation nodes in the mapping matrix are calculated. The interpolation nodes are the four adjacent nodes in the mapping matrix that are closest to the current parameters, with coordinates as follows: , , , ,in , For adjacent plate thickness nodes, , For adjacent target bending angle nodes, the corresponding initial downward pressure depth compensation value is output using the bilinear interpolation algorithm. The calculation formula is as follows:

[0081]

[0082] in, This is the initial compression depth compensation value for the interpolated output. The interpolation weights are in the x-direction. The interpolation weights are in the y-direction. , , , This represents the numerical values ​​of the mapping matrix for four adjacent interpolation nodes. Interpolation weights. ,in This represents the actual measured thickness of the current board material. for Corresponding plate thickness, for Corresponding plate thickness; interpolation weight ,in For the current target bending angle, for The corresponding target bending angle, for The corresponding target bending angle. The bilinear interpolation algorithm realizes the continuous calculation of the discrete mapping matrix, ensuring that a smooth and accurate initial pressing depth compensation value can be obtained under any sheet material parameters and target bending angle, avoiding the step error caused by discrete table lookup.

[0083] Before calculating the interpolation node coordinates of the current sheet metal parameters and the target bending angle in the mapping matrix, the measured yield strength value of the current aluminum panel is obtained. This measured yield strength value is obtained from the sheet metal material certificate or by testing the hardness with a portable hardness tester and then calculating it using a preset hardness-yield strength conversion relationship. The measured yield strength value is compared with the standard yield strength value in historical bending process data. The standard yield strength value is the benchmark yield strength value used in historical process data for the corresponding grade of aluminum panel. If the difference exceeds the allowable fluctuation range (±5% of the standard yield strength value), then based on the positive correlation between yield strength and springback, the sheet thickness characteristic in the current sheet metal parameters is equivalently converted. Yield strength and springback are positively correlated; the higher the yield strength, the greater the elastic recovery after unloading, and the greater the springback. Sheet thickness and springback are negatively correlated; the greater the sheet thickness, the smaller the springback. Therefore, the change in springback caused by yield strength fluctuations can be compensated by converting the sheet thickness. The formula for converting the equivalent sheet thickness is:

[0084]

[0085] in, For equivalent plate thickness, To measure the actual thickness of the sheet metal, The measured yield strength of the current aluminum single-panel The standard yield strength is used in historical bending process data. When the measured yield strength is greater than the standard yield strength, the converted equivalent plate thickness is greater than the measured thickness, resulting in a larger initial compression depth compensation value during bilinear interpolation to offset the increased springback caused by the increased yield strength. Conversely, when the measured yield strength is less than the standard yield strength, the converted equivalent plate thickness is less than the measured thickness, resulting in a smaller initial compression depth compensation value to offset the decreased springback caused by the decreased yield strength. The converted equivalent plate thickness is used as a new input feature in the calculation of the interpolation node coordinates to ensure that the initial compression depth compensation value matches the actual mechanical properties of the current plate.

[0086] This embodiment establishes a nonlinear mapping matrix between compression depth and rebound amount using partial least squares regression, solving the problem of insufficient fitting accuracy caused by multicollinearity of independent variables. It achieves continuous and accurate calculation of the initial compression depth compensation value through bilinear interpolation algorithm. By comparing yield strength and converting equivalent plate thickness, it eliminates the influence of mechanical property fluctuations between material batches on the feedforward compensation accuracy, further improving the accuracy of feedforward control and providing a good foundation for subsequent online feedback compensation.

[0087] Specifically, the core interpolation node data of the bending angle springback mapping matrix obtained by fitting within the process feature subspace 3-1 in this embodiment is shown in Table 3. This table provides basic data for bilinear interpolation calculation, ensuring that an accurate initial pressure depth compensation value can be obtained under any target bending angle and plate thickness.

[0088] Table 3. Interpolation Nodes of the Bending Angle Springback Mapping Matrix and Corresponding Initial Downward Depth Compensation Values

[0089]

[0090] In Table 3, the initial compression depth compensation value is the additional compression depth required to offset the springback under the corresponding working conditions. This value is calculated by the partial least squares regression model and reflects the nonlinear relationship between the target bending angle, plate thickness and springback amount. When performing bilinear interpolation, the node data in the table is used as the benchmark to calculate the compensation value corresponding to any intermediate value.

[0091] refer to Figure 4 In a preferred embodiment, during the downward pressing phase of multi-axis linkage, the current feedback value of the servo driver and the position pulse value of the grating ruler are synchronously read with a fixed sampling period of 1ms. This ensures that the time synchronization error between the torque signal and the displacement signal does not exceed one sampling period, avoiding mechanical calculation deviations caused by time asynchrony. The current feedback value is converted into a torque feedback signal, and the conversion relationship is as follows: ,in The torque constant of the servo motor. Let be the q-axis current feedback value at the k-th sampling time. The torque feedback signal and the grating ruler displacement signal are respectively subjected to moving average filtering. The filtering calculation formula is:

[0092]

[0093] in, This represents the filtered output value at the k-th sampling time. This represents the original sampled value at the kn-th sampling time. The sliding window length is 5 in this embodiment. The sliding mean filter effectively removes high-frequency glitches caused by mechanical transmission chain gaps and external vibrations, obtaining smooth torque and displacement time series, thus avoiding fluctuations in subsequent mechanical calculation results caused by high-frequency interference.

[0094] After obtaining the smoothed torque and displacement time series, a first-order difference operation is performed on the displacement time series to obtain the velocity time series. The formula for calculating the real-time velocity of the slider is as follows: ,in This represents the displacement signal of the grating ruler at the k-th sampling time. This represents the displacement signal of the grating ruler at the (k-1)th sampling time. The sampling period is [percentage missing]. A first-order difference operation is performed on the torque time series to obtain the torque change rate time series. The formula for calculating the torque change rate is [formula missing]. The product of the speed time series and the torque change rate time series is calculated using the following formula:

[0095]

[0096] in, This represents the product result at the k-th sampling time. The inflection point where the product result changes from negative to positive is identified. In the initial bending stage, before the upper die contacts the sheet metal, the slider moves downwards during idle travel. The servo motor torque only needs to overcome mechanical friction, and the torque change rate is close to 0. After the upper die contacts the sheet metal, it enters the elastic deformation stage. The elastic support of the sheet metal causes a brief decrease in slider speed; the speed is positive but the rate of increase is negative, and the torque change rate is low, resulting in a negative product result. When the sheet metal deformation enters the plastic deformation stage, the material's yield strength is exceeded, and the plastic deformation resistance rises sharply. The torque change rate increases rapidly, exceeding the speed decrease, and the product result changes from negative to positive. This inflection point is the critical switching point for the aluminum panel from the elastic deformation stage to the plastic deformation stage. Using this inflection point as the critical switching point, only the torque feedback signal and grating ruler displacement signal after the critical switching point are collected to calculate the real-time plastic deformation resistance, eliminating signal interference from the elastic deformation stage and ensuring that the calculated plastic deformation resistance accurately reflects the true plastic deformation state of the sheet metal.

[0097] refer to Figure 5Based on the grating ruler displacement signal after the critical switching point, the real-time downward displacement of the slider relative to the critical switching point position is calculated. Based on the torque feedback signal after the critical switching point, the real-time bending force output by the hydraulic cylinder of the bending machine is calculated. Combining the geometric parameters of the aluminum panel, such as bending span, bending length, panel thickness, and bending fillet radius, a mechanical equilibrium equation for bending force and plastic deformation resistance is constructed based on the principle of virtual work. Substituting the real-time bending force and real-time downward displacement into the mechanical equilibrium equation, the real-time plastic deformation resistance of the current bending zone is obtained. The real-time plastic deformation resistance is input into a pre-constructed dynamic differential equation to obtain the transient springback angle change rate at the current moment. The transient springback angle change rate is integrated over the remaining downward compression time to obtain the online compensation correction amount. The remaining unexecuted trajectory points of the multi-axis interpolation algorithm in the current interpolation cycle are obtained. The online compensation correction amount is distributed to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points, achieving smooth superposition of the compensation amount.

[0098] refer to Figure 6 When distributing the online compensation correction to the position coordinates of each remaining trajectory point according to the displacement ratio, the maximum allowable tensile strain threshold corresponding to the aluminum panel material is obtained. The maximum allowable tensile strain threshold is the ultimate tensile strain of the aluminum panel material before fracture, determined by the material grade. Based on the maximum allowable tensile strain threshold, the maximum allowable downward displacement boundary of the remaining trajectory points is calculated using the following formula:

[0099]

[0100] in, This is the maximum allowable downward displacement boundary. The width of the V-groove in the lower die. The limiting bending angle corresponding to the maximum allowable tensile strain. The radius of the upper die tip fillet. Limit bending angle. It is calculated using the maximum permissible tensile strain threshold, and the calculation formula is as follows: ,in The maximum allowable tensile strain threshold, For the thickness of the sheet metal, The radius of the neutral layer during bending is used. The system determines whether the position coordinates of the remaining trajectory points after the online compensation correction exceed the maximum allowable downward displacement boundary. If the compensated downward displacement of a certain remaining trajectory point exceeds the maximum allowable downward displacement boundary, the excess compensation is truncated, making the downward displacement of that trajectory point equal to the maximum allowable downward displacement boundary. Simultaneously, the truncated compensation is transferred to the pressure parameter adjustment during the holding pressure stage. The holding pressure stage is the stage where the slider maintains a downward pressure state after reaching the bottom dead center. Increasing the holding pressure can further increase the degree of plastic deformation of the sheet material, reduce the springback, achieve the compensation effect of the truncated compensation, and simultaneously avoid tearing caused by the tensile strain of the outer layer of the sheet material exceeding the threshold.

[0101] This embodiment eliminates the interference of mechanical vibration and transmission clearance on the acquired signal through sliding mean filtering. The critical switching point from elastic to plastic deformation is determined by the inflection point of the product of the rate of change of velocity and torque, ensuring the accuracy of the calculation of plastic deformation resistance. A precise online compensation correction amount is obtained through dynamic differential equations and integral operations. The smooth superposition of the compensation amount in the multi-axis interpolation trajectory is realized through displacement ratio distribution. By using the boundary constraint of the maximum allowable tensile strain threshold and the truncation transfer of the compensation amount, tearing of the sheet metal caused by excessive pressure is avoided, while ensuring the effect of springback compensation, further improving the yield and bending angle accuracy of bending processing.

[0102] Specifically, the compensation amount allocation and boundary verification results of the remaining trajectory points of multi-axis interpolation in this embodiment are shown in Table 4. This table shows the allocation process of online compensation correction amount, boundary verification results, and adjustment method of compensation amount exceeding the boundary, ensuring that the compensation process meets the needs of springback compensation without causing the sheet metal to tear.

[0103] Table 4. Results of Multi-Axis Interpolation Residual Trajectory Point Compensation Allocation and Boundary Verification

[0104]

[0105] In Table 4, the total online compensation correction is 0.30mm. It is distributed to the 5 remaining trajectory points according to the displacement ratio of the remaining trajectory points. The downward displacement of trajectory point 5 after compensation is 13.34mm, which exceeds the maximum allowable downward displacement of 13.2mm. Therefore, the compensation amount of this trajectory point is adjusted to 0.00mm, and the downward displacement of this trajectory point is further cut off to 13.2mm. The cut-off compensation amount of 0.14mm is transferred to the pressure parameter adjustment in the pressure holding stage. The pressure holding pressure is adjusted from the preset 10MPa to 12MPa to achieve springback compensation while avoiding tearing of the plate.

Claims

1. A multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation, characterized in that, include: Historical bending process data is collected, and the plate thickness, bending radius, lower die V-groove width and feed speed are used as input features. The process feature subspace is divided by clustering algorithm, and a bending angle springback mapping matrix is ​​fitted and established in each process feature subspace. During the actual bending process, the current aluminum panel parameters and target bending angle are read, and the initial pressing depth compensation value is obtained by looking up the table to execute feedforward control; In the multi-axis linkage stage, the torque feedback signal of the servo motor and the displacement signal of the grating ruler are collected in real time to calculate the real-time plastic deformation resistance of the current bending zone. The online compensation correction amount is obtained by using the established dynamic differential equation of deformation resistance and springback angle. The online compensation correction amount is then superimposed on the remaining trajectory planning of the multi-axis interpolation algorithm.

2. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 1, characterized in that, The process feature subspace is divided by clustering algorithm, including: standardizing the input features and calculating the Mahalanobis distance between each input feature to eliminate the correlation interference between different physical dimensions; A clustering algorithm based on density peaks is adopted, and local decision values ​​are constructed according to the Mahalanobis distance. Input features whose local decision values ​​satisfy the preset density conditions are clustered into the same process feature subspace, so that the bending conditions in the same process feature subspace have similar stress and strain distribution states. For input features with sparse edge distribution, a forced assignment determination is made based on the distribution variance of adjacent process feature subspaces.

3. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 1, characterized in that, The step of fitting and establishing a bending angle springback mapping matrix in each process feature subspace includes: in the process feature subspace, taking the target bending angle as the dependent variable and the difference between the initial pressing depth and the measured springback angle as the independent variable, using partial least squares regression to establish a mapping matrix reflecting the nonlinear relationship between pressing depth and springback. The step of obtaining the initial pressure depth compensation value by looking up a table includes: calculating the interpolation node coordinates of the current plate parameters and the target bending angle in the mapping matrix, and outputting the corresponding initial pressure depth compensation value using a bilinear interpolation algorithm.

4. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 1, characterized in that, The real-time acquisition of the torque feedback signal of the servo motor and the displacement signal of the grating ruler during the multi-axis linkage phase includes: during the pressing phase of the multi-axis linkage, synchronously reading the current feedback value of the servo driver and the position pulse value of the grating ruler at a fixed sampling period. The current feedback value is converted into a torque feedback signal, and the torque feedback signal and the grating ruler displacement signal are respectively subjected to sliding mean filtering to remove high-frequency glitch signals caused by mechanical transmission chain gaps and external vibrations, so as to obtain smooth torque time series and displacement time series.

5. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 1, characterized in that, The calculation of the real-time plastic deformation resistance of the current bending zone includes: calculating the real-time downward displacement of the slider based on the displacement signal of the grating ruler, and calculating the real-time bending force output by the hydraulic cylinder of the bending machine based on the torque feedback signal. Combining the bending span and real-time downward displacement of the aluminum single panel, a mechanical equilibrium equation for bending force and plastic deformation resistance is constructed based on the principle of virtual work. The real-time bending force and the real-time downward displacement of the slider are substituted into the mechanical equilibrium equation to solve for the real-time plastic deformation resistance of the current bending zone.

6. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 1, characterized in that, The method of solving the online compensation correction amount using the established dynamic differential equation of deformation resistance and rebound angle, and superimposing the online compensation correction amount into the remaining trajectory planning of the multi-axis interpolation algorithm, includes: inputting the real-time plastic deformation resistance into the pre-constructed dynamic differential equation, solving for the transient rebound angle change rate at the current moment, and performing an integral operation on the transient rebound angle change rate over the remaining compression time to obtain the online compensation correction amount; Obtain the remaining unexecuted trajectory points of the multi-axis interpolation algorithm in the current interpolation cycle, and allocate the online compensation correction amount to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points.

7. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 2, characterized in that, After clustering the input features whose local decision values ​​meet the preset density conditions into the same process feature subspace, the method also includes: real-time monitoring of the distribution density changes of newly added historical bending process data in each process feature subspace; When the distribution density of a certain process feature subspace exceeds the preset capacity threshold, a splitting operation is triggered. Based on the principal component direction of the new data in the Mahalanobis distance space, the original process feature subspace is divided into two subspaces, and the bending angle springback mapping matrix corresponding to the two subspaces is recalculated.

8. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 3, characterized in that, Before calculating the interpolation node coordinates of the current sheet parameters and the target bending angle in the mapping matrix, the method further includes: obtaining the measured yield strength value of the current aluminum single sheet, and comparing the measured yield strength value with the standard yield strength value in the historical bending process data; If the difference between the two exceeds the allowable fluctuation range, then based on the positive correlation between yield strength and springback, the plate thickness feature in the current plate parameters is equivalently converted, and the converted equivalent plate thickness is used as a new input feature to participate in the calculation of interpolation node coordinates.

9. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 4, characterized in that, After obtaining the smooth torque time series and displacement time series, the method further includes: performing a first-order difference operation on the displacement time series to obtain a velocity time series, and performing a first-order difference operation on the torque time series to obtain a torque change rate time series. The speed time series and the torque change rate time series are multiplied together, and the inflection point when the product result turns from negative to positive is identified. The inflection point is taken as the critical switching point for the aluminum panel to enter the plastic deformation stage from the elastic deformation stage. Only the torque feedback signal and the grating ruler displacement signal after the critical switching point are collected to calculate the real-time plastic deformation resistance.

10. The multi-axis linkage CNC bending method for aluminum single-panel based on springback compensation according to claim 6, characterized in that, When distributing the online compensation correction amount to the position coordinates of each remaining trajectory point according to the displacement ratio of the remaining trajectory points, the method further includes: obtaining the maximum allowable tensile strain threshold corresponding to the aluminum single-panel material; Calculate the maximum permissible downward displacement boundary of the remaining trajectory points based on the maximum permissible tensile strain threshold; Determine whether the position coordinates of the remaining trajectory points after allocating the online compensation correction amount exceed the maximum allowable downward displacement boundary; If the amount exceeds the limit, the excess compensation will be truncated and transferred to the pressure parameter adjustment during the pressure holding stage.

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