System error compensation method in batch processing of thin-walled blades

Abstract

The application discloses a system error compensation method in batch processing of thin-wall blades, comprising the following steps: step 1, obtaining profile error; step 2, obtaining system profile error; step 3, obtaining three-dimensional coordinates of measured correction points after removing random error, fitting to obtain a measured correction curve, and grouping the measured correction curve; step 4, obtaining intersection points and profile error compensation values of a single blade; step 5, obtaining the final profile error compensation value of the blade at the position; obtaining profile error compensation point coordinates, obtaining final compensation point cloud coordinates, and then obtaining compensation curves of each section; by collecting measurement data of multiple blades, the application adopts adaptive kernel density estimation to establish a probability density model of processing system error, and calculates system error compensation based on mathematical expectation, so that the problem of large accidental error and poor consistency caused by traditional methods which only rely on a small amount of blade data is effectively overcome.

Description

Technical Field

[0001] This invention belongs to the field of blade processing, and particularly relates to a method for compensating for systematic errors in the batch processing of thin-walled blades. Background Technology

[0002] As the power source for aircraft flight, the structure and performance of aero engines directly determine the overall efficiency of the aircraft. Due to the urgent need for weight reduction and efficiency improvement, modern aero engines extensively utilize complex thin-walled structures in their fans and compressors, such as large composite material blades, titanium alloy / high-temperature alloy compressor blades, and integral bladed disks. The manufacturing quality of these components largely determines the overall performance of the engine. In recent years, despite significant progress in aero engine manufacturing technologies such as intelligent manufacturing and adaptive machining, there is still considerable room for improvement in the processing quality and precision of key components.

[0003] Taking high-pressure compressor blades as an example, domestically produced new high-performance engines generally adopt integral bladed disk structures. Integral bladed disks eliminate tenon joints, thus eliminating airflow losses, significantly reducing structural weight and the number of parts; simultaneously, their wide chord, swept blades and narrow flow channel design greatly improve aerodynamic efficiency. However, open integral bladed disk blades are typical cantilever beam structures, with thin and extended blades, placing extremely high demands on machining accuracy and surface integrity. In actual production, integral bladed disks have complex structures and poor openness, with thin-walled airfoil surfaces on both sides of the channel, and the materials are mostly difficult-to-machine materials such as titanium alloys and high-temperature alloys, resulting in high thermal hardness and strength. Furthermore, aerodynamic performance requirements lead to increasingly distorted blade profiles and continuously thinner thicknesses, with the leading edge, trailing edge, and blade tip even below 0.1 mm, making it extremely difficult to guarantee machining accuracy. More importantly, thin-walled blade machining is a multi-source, multi-process manufacturing system; its final quality is not only affected by the current process but also constrained by related processes, resulting in significant error transmission and accumulation effects between processes. The aforementioned problems severely restrict the machining accuracy of integral bladed disk blades, and there is an urgent need to develop new processes and compensation strategies.

[0004] The existing technology has two main problems: Firstly, in actual inspection processes, coordinate measuring machines (CMMs) are typically used to digitally measure the machined thin-walled blades to obtain geometric error data. However, due to the drastic curvature changes in the leading and trailing edge regions of thin-walled blades, the measuring probe is prone to random jitter during inspection, introducing significant random error components. Most compensation methods directly construct error models based on the measurement data without filtering the data, resulting in the failure to effectively remove the random error components introduced during machining and inspection. Therefore, when compensation machining is performed based on such models, poor consistency in machining accuracy or even exceeding tolerances is likely to occur.

[0005] Secondly, existing error compensation methods mostly rely on measurement data from only a small number of blades (usually around two), failing to fully consider the random factors present in the machining of individual thin-walled blades. The test data used is therefore insufficient to accurately reflect the systematic errors of the machining system. This results in the actual machining accuracy remaining low even when machining based on the compensated model. Summary of the Invention

[0006] The purpose of this invention is to provide a systematic error compensation method in the batch processing of thin-walled blades, so as to solve the problems of existing error compensation technology, such as failure to eliminate random measurement errors, insufficient sample data, and poor compensation effect.

[0007] This invention adopts the following technical solution: a method for compensating for systematic errors in the batch processing of thin-walled blades, comprising: Step 1: Use the iterative verification method to determine the number of cross-sectional curves required for blade inspection and the corresponding cross-sectional height of each cross-section; based on the determined number of cross-sectional curves and cross-sectional height, register the measured point cloud data with the theoretical cross-sectional curves of the thin-walled blade to obtain the profile error; Step 2: For each detection section of the blade, sequentially number the contour error along the contour detection path of each section, then convert the ordered contour error data into contour error signals for each section, and perform sequence expansion and decomposition processing on the contour error signals of each section to obtain the system contour error; Step 3: Calculate the three-dimensional coordinates of the measured correction points after removing random errors based on the system contour error, fit the measured correction curves, and group the measured correction curves. Step 4: Discretize the theoretical profile of each section to generate a series of discrete points with equal chord height constraints; draw a normal line segment through each discrete point and make it intersect with the measured correction curve in the group to obtain the intersection point; the Euclidean distance between the intersection point and the corresponding discrete point is the profile error compensation value of the blade at the position of the section. Step 5: Estimate the final profile error compensation value of the blade at the same theoretical position based on the profile error compensation values ​​of multiple blades at the same theoretical position; offset each discrete point along the opposite direction of the actual deformation of the blade profile to obtain the corresponding final profile error compensation value to obtain the profile error compensation point coordinates; perform torsion and offset compensation on the profile error compensation point coordinates to obtain the final compensation point cloud coordinates, and then obtain the compensation curve of each section.

[0008] The beneficial effects of this invention are: This invention collects measurement data from multiple blades, establishes a probability density model of the machining system error using adaptive kernel density estimation, and calculates the system error compensation based on mathematical expectation. This effectively overcomes the problems of large random errors and poor consistency caused by traditional methods that rely on only a small amount of blade data, and significantly improves the overall consistency of the accuracy of batch-processed blades. In processing single blade profile error, this invention employs Integrated Empirical Mode Decomposition (EEMD) combined with a boundary data extension strategy, which can effectively suppress endpoint effects and accurately separate systematic error components from random error components. Compared with directly using the original measurement data, this method significantly improves the reliability of systematic error modeling and avoids compensation failure caused by random error interference.

[0009] This invention optimizes the number of cross-sectional curves required to construct a machining error compensation model through an iterative verification method. While ensuring that the geometric accuracy of the reconstructed model meets the preset tolerance (±0.005 mm), the number of cross-sections is reduced as much as possible, thereby reducing model data redundancy and improving the reconstruction efficiency of the compensation model.

[0010] This invention addresses profile error, positional error (X and Y directions), and torsional angle error by employing a mathematical expectation method to calculate compensation amounts cross-section and point-by-point, and then using the principle of inverse deformation for geometric correction. This method can simultaneously compensate for blade shape deviations, positional offsets, and torsional deformation, significantly improving the overall machining quality of the blade profile. This invention employs adaptive kernel density estimation to fit the systematic error distribution of multiple blade machining processes. It does not require assumptions that the errors follow a specific distribution and can adaptively characterize the error fluctuation patterns of the actual machining system. The compensation calculation based on mathematical expectation exhibits statistical optimality, reflecting the average systematic error of the machining system and demonstrating good robustness to normal process fluctuations in batch production. This significantly improves the consistency of batch machining accuracy and process stability.

[0011] In the Integrated Empirical Mode Decomposition (EEMD) process of a single thin-walled blade profile error signal, this invention employs a boundary data extension strategy. This strategy concatenates 30 profile error values ​​before and after each cross-section to both ends of the original signal sequence, effectively avoiding the "endpoint divergence" or "boundary distortion" phenomena that occur at the signal ends in traditional EEMD. This extension method ensures that the resulting system error component curves remain smooth and continuous globally, avoiding local distortion caused by endpoint effects. This provides high-quality, high-fidelity system error input for subsequent error compensation calculations based on multi-blade statistical modeling, significantly improving the robustness and reliability of the compensation model.

[0012] At the engineering application level, this invention can reliably calculate the system error of thin-walled blade processing under limited sample conditions (n≥30), and its calculation accuracy is significantly better than that of traditional empirical methods. In contrast, empirical rules based on sample statistics require the collection of a large amount of sample data (n≥300) to achieve comparable prediction accuracy. Attached Figure Description

[0013] Figure 1 This is a denoising effect diagram of the contour error signal without using boundary data expansion processing in this invention; Figure 2 This is a diagram showing the denoising effect of the contour error signal processed by boundary data extension in this invention. Figure 3 This is a calculation diagram of the X-direction position error compensation amount of the thin-walled blade based on mathematical expectation in this invention. Detailed Implementation

[0014] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0015] This invention discloses an error compensation method for blade processing systems based on error decomposition and Kalman filtering, comprising five steps.

[0016] Step 1: Use an iterative verification method to determine the number of cross-sectional curves required for blade inspection and the corresponding cross-sectional height of each cross-section; based on the determined number of cross-sectional curves and cross-sectional height, register the measured point cloud data with the theoretical cross-sectional curves of the thin-walled blade to obtain the profile error; Step 1 specifically involves: High-precision thin-walled blade inspection data is a prerequisite for building a reliable compensation model. Therefore, it is necessary to scientifically determine the number of key cross sections required to characterize the blade geometry, and then carry out compensation modeling based on accurate data. Determining the number of cross-sectional curves required for model reconstruction is a critical engineering decision that requires a balance between reconstruction accuracy and computational efficiency: too many cross sections will lead to model redundancy and increased computational burden; too few cross sections will fail to accurately capture the blade's geometric features, resulting in serious distortion of the compensation model.

[0017] Therefore, firstly, the original theoretical model of the thin-walled blade is extracted using a small number of reference planes to obtain theoretical cross-sectional curves, and preliminary model reconstruction is carried out accordingly. Secondly, the geometric deviation of the preliminary reconstructed model and the original theoretical model is compared and analyzed to quantitatively assess the differences between them. Then, the region with the largest deviation is identified through deviation cloud map. If the deviation exceeds the preset tolerance range (usually set to [-0.005 mm, +0.005 mm]), a new cross-sectional curve is inserted in the region with significant deviation. Finally, the model is reconstructed again using the updated cross-sectional set, and deviation analysis is performed again. The above iterative process is repeated until the geometric deviation of all regions meets the preset tolerance requirements, thereby finally determining the number of cross-sectional curves required for testing and the corresponding cross-sectional height of each cross-section.

[0018] Based on the determined number of cross-sectional curves and cross-sectional height, the machining accuracy of the blade is tested. The iterative nearest point algorithm is used to register the measured point cloud data with the theoretical cross-sectional curve of the thin-walled blade, thereby obtaining the profile error, position error and torsion angle error.

[0019] Step 2: For each detection section of the blade, sequentially number the contour error along the contour detection path of each section, then convert the ordered contour error data into contour error signals for each section, and perform sequence expansion and decomposition processing on the contour error signals of each section to obtain the system contour error.

[0020] The method for sequence expansion in step 2 is as follows: The error data corresponding to the first 30 sets of numbers in the contour error signal are concatenated to the end of the error signal, and the error data corresponding to the last 30 sets of numbers in the contour error signal are concatenated to the beginning of the error signal, thus completing the signal sequence expansion.

[0021] In step 2, the decomposition process is performed by using an integrated empirical mode decomposition algorithm to decompose the expanded cross-sectional profile error signal to obtain the system profile error.

[0022] Therefore, step 2 specifically involves: The profile error of the blade at each cross-section is numbered sequentially according to the detection path, and the point cloud data is converted into a profile error signal, i.e., the detection point number is used as the abscissa and the corresponding profile error value is used as the ordinate in a Cartesian coordinate system. Then, the original profile error signal sequence is subjected to boundary data expansion processing: if there are 'a' detection point clouds at a certain cross-section, the error data corresponding to the first 30 sets of numbers are concatenated to the end of the error signal, and the error data corresponding to the last 30 sets of numbers in the profile error signal are concatenated to the beginning of the error signal, thus forming an expanded profile error signal with a length of 30+a+30. This boundary expansion strategy can effectively suppress the endpoint effect in the filtering process, ensure the continuity between the end and the beginning of the signal, and achieve a smooth transition at the beginning and end, thereby ensuring that the extracted system profile error curve remains smooth and continuous in the global range, further improving the reliability of subsequent error compensation modeling. Finally, the integrated empirical mode decomposition algorithm is used to decompose the expanded profile error signal to obtain the system profile error, and based on this, the system profile error of each cross-section of all thin-walled blades is calculated.

[0023] Finally, the extended contour error signal is decomposed using an integrated empirical mode decomposition algorithm to obtain the system contour error. The specific process is as follows: (1) Arrange the measured profile error on the individual cross-section line of the thin-walled blade in sequence, and perform data expansion processing on the original sequence before error decomposition.

[0024] (2) A random Gaussian white noise sequence is superimposed on the measured profile error signal δ to construct a signal with added white noise, the expression of which is shown in equation (1), where k represents the amplitude coefficient of the white noise, l m It is Gaussian white noise.

[0025] (1) (3) Perform Empirical Mode Decomposition (EMD) on the signal with added white noise, solve for the upper and lower envelopes of the noisy signal by cubic spline interpolation, and calculate the average envelope a. m .

[0026] (4)h m =x m -a m If signal h m If the difference between the number of extreme points and the number of zero-crossing points is no greater than 1, and the mean value of the envelope at any point is 0, then it is considered an IMF sequence c obtained from empirical mode decomposition. q,m Conversely, return to step three for further processing.

[0027] (5) Subtract c from the noise signal q,m The remaining term r is obtained. q,mRepeat steps (3) and (4) for the remaining terms until the remaining terms are monotonic functions, and obtain a set of intrinsic mode functions (IMFs).

[0028] (6) Repeat steps (2)-(5), each time introducing a different white noise sequence to suppress the mode aliasing phenomenon that may be caused by a single noise. (7) The mean value of each IMF component obtained from multiple EMD decompositions is calculated and used as the final decomposition result of EEMD. The calculation method is shown in Equation (2).

[0029] (2) In the formula, N is the number of integrations of EMD, and c q,m This is the q-th IMF generated by the m-th EMD.

[0030] (8) The IMF set {c1, c2, ..., c} obtained in the previous steps is... n} and r n,m The EEMD decomposition result is used as the original contour signal. To further select the most representative systematic error components, the c of each IMF component is calculated using equations (3) and (4). q The energy and energy ratio.

[0031] (3) (4) n is the total number of IMF components, and p is the signal length.

[0032] (9) Retain β q IMF components >0.1 and r n,m As an effective systematic error component, it can be reconstructed to obtain the systematic profile error of a single blade. This method effectively removes redundant modes through noise-assisted decomposition and correlation screening, thereby improving the reliability and accuracy of systematic error extraction.

[0033] Step 3: Calculate the three-dimensional coordinates of the measured correction points after removing random errors based on the system contour error, fit the measured correction curves, and group the measured correction curves.

[0034] In step 3, when calculating the three-dimensional coordinates of the measured correction point after removing random errors, the three-dimensional coordinates of the measured correction point after removing random errors are calculated based on the system profile error, the theoretical measurement point, and the actual measurement point.

[0035] In step 3, when grouping the measured correction curves, the measured correction curves are grouped according to the cross-sectional height in step 1 to ensure that the measured correction curves in the same group correspond to the same theoretical cross-sectional line.

[0036] Therefore, step 3 specifically involves: First, obtain the theoretical measurement point p for each thin-walled blade. t(i) (x i ,y i ,z i ) and the actual measurement point p a(i) (x i ,y i ,z i Combined with the calculated system profile error δ s(i) It is possible to calculate the three-dimensional coordinates p of the actual correction point after removing random errors from a single leaf. s(i) (x i ,y i ,z i ), and calculate the three-dimensional coordinates p s(i) (x i ,y i ,z i Fitting a closed curve p s(i) (x i ,y i ,z i ), which is the measured correction curve.

[0037] (5) Secondly, the fitted closed curves are grouped according to the cross-sectional height to ensure that the closed curves in the same group correspond to the same theoretical cross-sectional line.

[0038] Step 4: Discretize the theoretical profile of each cross-section to generate a series of discrete points with equal chord height constraints; draw a normal line segment through each discrete point, and intersect it with the measured correction curve within the group to obtain the intersection point; the Euclidean distance between the intersection point and the corresponding discrete point is the profile error compensation value of the blade at the position of the cross-section. In Step 4, the equal chord height sampling method is used to discretize the theoretical profile of each cross-section. Therefore, Step 4 specifically involves: The theoretical contour lines of each section are discretized using the equal chord height sampling method, generating a series of discrete points with equal chord height constraints. The number of discrete points has a decisive impact on the reconstruction quality: too many points lead to data redundancy and reduced computational efficiency; too few points make it difficult to capture regions with drastic curvature changes, resulting in feature loss and affecting reconstruction accuracy and reliability. To achieve a reasonable balance between geometric fidelity and data simplicity, an appropriate chord height error tolerance (ℎ) needs to be set. max By iteratively adjusting hmax To optimize a discrete point set: First, set an initial h max The value is used to obtain discrete points and reconstruct the B-spline curve; the geometric deviation between the reconstructed curve and the original theoretical curve is calculated. If the maximum deviation exceeds ±0.0005 mm, the current h value is adjusted. max Halve the sample size, resample and reconstruct until the maximum deviation meets the tolerance requirement. At this point, h... max This is the optimal chord height tolerance. Based on this, a normal line segment is drawn through each discrete point, intersecting with the closed curves of each blade in the group to obtain the intersection point; the Euclidean distance between the intersection point and the corresponding discrete point is the profile error of the blade at that cross-section position.

[0039] Then, an adaptive kernel density estimation function is used to estimate the profile error X=[x1, x2,…,x] of n blades at the same theoretical position. n We fit the data to establish its probability density distribution function f(x).

[0040] The fixed-bandwidth kernel density estimation function is: (6) In the formula, x i The profile error of the i-th blade at the same theoretical position after removing random errors; n is the number of blades; K(·) is the Gaussian kernel function; h MISE It is a fixed bandwidth.

[0041] (7) In the formula, σ is the standard deviation of the profile error data of n blades at the same theoretical position after removing random errors.

[0042] The Adaptive Bandwidth Kernel Density Estimation Function (AKDE) is obtained by modifying the bandwidth parameter based on the Fixed Bandwidth Kernel Density Estimation Function, and its bandwidth is: (8) In the formula, h i Let λ be the bandwidth at the i-th estimation point. i f(x) is the local bandwidth factor. i ) represents the kernel density estimate at the i-th estimation point obtained in the fixed bandwidth kernel density estimation, and 0 ≤ β ≤ 1 is the sensitivity factor.

[0043] An adaptive bandwidth kernel density estimation function is used to model the probability density of the profile error of n blades at the same theoretical position, specifically: (9) Finally, an adaptive kernel density estimation function is used to establish the X-direction position error Y=[y1, y2,…, y] for n thin-walled blades at the same cross-sectional height. n The probability density model g(y) is used to establish the positional error Z=[z1, z2,…, z] of n thin-walled blades at the same cross-sectional height using an adaptive kernel density estimation function. n The probability density model h(z) is used to establish the torsional angle error W=[w1, w2,…,w] of n thin-walled blades at the same cross-sectional height using an adaptive kernel density estimation function. n The probability density model v(w) is given.

[0044] From a statistical modeling perspective, the systematic error probability distribution can be constructed by using an adaptive kernel density estimation function for batch processing of n blades. This can accurately characterize the multimodal, asymmetric, and thick-tailed characteristics of actual processing errors without the need for a preset parameter model. In contrast, empirical methods can only provide statistics for a limited number of samples and cannot characterize potential unobserved error values.

[0045] Step 5: Estimate the final profile error compensation value of the blade at the same theoretical position based on the profile error compensation values ​​of multiple blades at the same theoretical position; offset each discrete point along the opposite direction of the actual deformation of the blade profile to obtain the corresponding final profile error compensation value to obtain the profile error compensation point coordinates; perform torsion and offset compensation on the profile error compensation point coordinates to obtain the final compensation point cloud coordinates, and then obtain the compensation curve of each section.

[0046] In step 5, when estimating the final profile error compensation value of the blade at that position, an adaptive kernel density estimation function and a mathematical expectation method are used.

[0047] The method for torsional and offset compensation in step 5 is as follows: Based on the number of cross-sectional curves and the cross-sectional height in step 1, the measured point cloud data is registered with the theoretical cross-sectional curve of the thin-walled blade to obtain the positional error and torsion angle error. The positional error compensation value and torsion angle error compensation value are estimated based on the positional error and torsion angle error of multiple blades at the same cross-sectional height. Then, the coordinates of each profile error compensation point are translated and rotated in the opposite direction of the actual deformation of the blade cross-section to obtain the corresponding positional error compensation value and torsion angle error compensation value to obtain the final compensation point cloud coordinates.

[0048] Therefore, step 5 specifically involves: First, based on the calculated profile error X=[x1, x2,…,x] of n blades at the same theoretical position... nGiven the probability density distribution function f(x), calculate the expected value E[X] of the profile error at the same theoretical location, which is used as the compensation amount for the profile error at that location. Complete the calculation of the profile error compensation amount for all cross sections and all sampling points.

[0049] (10) Secondly, based on the calculated positional error Y=[y1, y2,…,y] of the n blades at the same cross-sectional height in the X direction, n Using the probability density model g(y), calculate the expected value E[Y] of the X-direction position error at the same cross-sectional height, which serves as the compensation amount for the X-direction position error at that location. Complete the calculation of the X-direction position error compensation amount for all cross-sections.

[0050] (11) Then, based on the calculated positional error Z = [z1, z2, ..., z] of the n blades at the same cross-sectional height in the Y direction,... n Using the probability density model h(z), calculate the expected value E[Z] of the Y-direction position error at the same cross-sectional height, which serves as the compensation for the Y-direction position error at that location. Complete the calculation of the compensation for the Y-direction position error for all cross-sections.

[0051] (12) Finally, based on the calculated torsion angle error W=[w1, w2,…,w] of the n blades at the same cross-sectional height, n The probability density model v(w) is used. The expected value E[W] of the torsional angle error at the same cross-sectional height is calculated as the compensation amount for the torsional angle error at that location. The compensation amount for the torsional angle error of all cross-sections is calculated.

[0052] (13) For discrete points on the theoretical profile lines of each cross-section obtained using the equal chord height method, a compensation amount is offset along the normal direction in the direction opposite to the machining deformation. This compensation amount is the expected value of the profile error E[X] calculated in step 4. This process is based on the principle of inverse deformation, by applying a geometric correction equal in magnitude and opposite in direction to the system profile error on the theoretical surface in advance to offset the system profile error generated during machining. Next, the point set obtained after profile error compensation for each cross-section is regarded as a whole and rotated. The rotation angle is equal to E[W], and the rotation direction is opposite to the direction of the actual torsional deformation of the blade cross-section. Through the above rotation operation, the overall torsional deviation generated by the blade during machining can be effectively compensated. Subsequently, the rotated point set is translated. The translation amount of each cross-section in the X direction is equal in magnitude to E[Y], and the translation direction is opposite to the direction of the actual position offset of the blade cross-section in the X direction; the translation amount in the Y direction is equal in magnitude to E[Z], and the translation direction is opposite to the direction of the actual position offset of the blade cross-section in the Y direction. This translation transformation aims to eliminate systematic positional errors of the blades at each cross-section. Finally, non-uniform rational B-splines (NURBS) are used to fit curves to the point sets of each translated cross-section, generating a compensation curve for each cross-section. Based on this, a lofting operation is used to construct a continuous NURBS surface for each cross-section curve, thereby obtaining the compensated geometric model.

[0053] Example The blade material is GH4169G. The machine tool used in the experiment was a Kede KMC800S U five-axis vertical machining center, with climb milling and coolant cooling. First, a flat-end milling cutter with a diameter of 8 mm was used for channel milling, followed by rough milling of the blade profile with an 8 mm diameter ball end mill to mill the remaining material to a uniform state. After milling, heat treatment was performed to effectively release the internal stress caused by material removal, cutting force, and temperature changes, thereby reducing deformation during machining. After heat treatment, finish machining was performed, which included machining of three cutting layers, with cutting layers two and three being machined using a simultaneous milling method. The cutting tool is Φ6×20×Φ8×100×2°-Z4, and the specific machining parameters are set as follows: Cutting depth of cut for cutting layer one is 0.375 mm, feed per tooth is 0.056 mm / z, and spindle speed is 6887 r / min; cutting depth of cut for cutting layer two is 0.22 mm, feed per tooth is 0.040 mm / z, and spindle speed is 8000 r / min; cutting depth of cut for cutting layer three is 0.08 mm, feed per tooth is 0.026 mm / z, and spindle speed is 8000 r / min. A total of 83 blades are machined.

[0054] First, three representative theoretical cross-sectional curves were extracted at equal intervals along the blade axis using the equal Z-axis section method as initial modeling benchmarks. Table 1 records the statistical results of the deviation between the reconstructed surface and the theoretical model surface during each iteration. Data analysis shows that when the number of cross-sectional curves increases to nine, the maximum geometric deviation between the reconstructed surface and the theoretical model surface decreases to 0.0036 mm, significantly better than the preset accuracy threshold, meeting the requirements of engineering applications. Based on this convergence result, the optimal number of cross-sectional curves required for compressor blade inspection and model reconstruction was finally determined to be nine, and coordinate measuring machines were used to measure the machining error of 83 blades after processing.

[0055] Table 1. Deviation between the reconstructed surface and the theoretical model surface Secondly, based on the integrated empirical mode decomposition method for calculating the profile error of a single thin-walled blade system, the profile error of all cross sections of 83 blades was calculated. Figure 1 The image shows the denoising effect of the contour error signal without boundary data expansion processing. Figure 2 The image shows the denoising effect of using boundary data expansion processing on the contour error signal. It can be seen that boundary data expansion processing ensures smooth continuity between the signal's beginning and end. Then, the ℎ... max When the radius of curvature is 0.00005 mm, the maximum deviation between the reconstructed curve and the original curve is only 0.0005 mm, meeting the accuracy requirements. After discretizing all cross-sectional curves, the profile error, X-direction positional error, Y-direction positional error, and torsion angle error for each of the 83 blades with theoretical positional accuracy were obtained. Adaptive kernel density estimation was then used to model the probability density of the machining system errors for multiple thin-walled blades. Next, the compensation amount for the batch machining system errors of thin-walled blades was calculated based on mathematical expectation. Figure 3 The first image shows the calculation results of the X-direction position error compensation for the thin-walled blade based on mathematical expectation. The calculation results for the profile error, Y-direction position error, and torsion angle error compensation are roughly the same. Finally, the machining error compensation model is reconstructed based on the systematic error compensation.

[0056] To verify the effectiveness of the established compressor blade machining error compensation model in actual machining, corresponding milling verification experiments were conducted. The experiments used a GH4169G high-temperature alloy rectangular blank with dimensions of 200mm × 80mm × 35mm. Experimental results showed that after compensation, the maximum values ​​of the blade's profile error, positional error, and torsion angle error were significantly reduced. The maximum profile error decreased by 28.39%, the maximum positional error by 57.84%, and the maximum torsion angle error by 42.98%. These results demonstrate that the proposed error compensation method for thin-walled blade displacement machining can effectively reduce the deformation of thin-walled blades during finishing, significantly improving the machining accuracy of the profile, positional error, and torsion angle.

Claims

1. A method for compensating for systematic errors in the batch processing of thin-walled blades, characterized in that, include: Step 1: Use the iterative verification method to determine the number of cross-sectional curves required for blade inspection and the corresponding cross-sectional height of each cross-section; Based on the determined number of cross-sectional curves and cross-sectional height, the measured point cloud data is registered with the theoretical cross-sectional curves of the thin-walled blade to obtain the profile error. Step 2: For each detection section of the blade, sequentially number the contour error along the contour detection path of each section, then convert the ordered contour error data into contour error signals for each section, and perform sequence expansion and decomposition processing on the contour error signals of each section to obtain the system contour error; Step 3: Calculate the three-dimensional coordinates of the measured correction points after removing random errors based on the system contour error, fit the measured correction curves, and group the measured correction curves. Step 4: Discretize the theoretical contour lines of each section to generate a series of discrete points with equal chord height constraints; draw a normal line segment through each discrete point and make it intersect with the measured correction curve within the group to obtain the intersection point; The Euclidean distance between the intersection point and the corresponding discrete point is the profile error compensation value of the blade at the cross-sectional position. Step 5: Estimate the final profile error compensation value of the blade at that position based on the profile error compensation values ​​of multiple blades at the same theoretical position; The coordinates of the profile error compensation point are obtained by shifting each discrete point in the opposite direction of the actual deformation of the blade profile along the normal vector. The coordinates of the profile error compensation point are then subjected to torsion and offset compensation to obtain the final compensation point cloud coordinates, and thus the compensation curves of each section are obtained.

2. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, The method for torsional and offset compensation in step 5 is as follows: Based on the number of cross-sectional curves and the cross-sectional height in step 1, the measured point cloud data is registered with the theoretical cross-sectional curve of the thin-walled blade to obtain the positional error and torsion angle error. The positional error compensation value and torsion angle error compensation value are estimated based on the positional error and torsion angle error of multiple blades at the same cross-sectional height. Then, the coordinates of each profile error compensation point are translated and rotated in the opposite direction of the actual deformation of the blade cross-section to obtain the corresponding positional error compensation value and torsion angle error compensation value to obtain the final compensation point cloud coordinates.

3. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, The method for sequence expansion in step 2 is as follows: The error data corresponding to the first 30 sets of numbers in the contour error signal are concatenated to the end of the error signal, and the error data corresponding to the last 30 sets of numbers in the contour error signal are concatenated to the beginning of the error signal, thus completing the signal sequence expansion.

4. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 3, characterized in that, The decomposition process in step 2 is as follows: the integrated empirical mode decomposition algorithm is used to decompose the expanded cross-sectional profile error signal to obtain the system profile error.

5. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, In step 3, when calculating the three-dimensional coordinates of the measured correction point after removing random errors: the three-dimensional coordinates of the measured correction point after removing random errors are calculated based on the system profile error, the theoretical measurement point, and the actual measurement point.

6. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, In step 3, when grouping the measured correction curves, the measured correction curves are grouped according to the cross-sectional height in step 1 to ensure that the measured correction curves in the same group correspond to the same theoretical cross-sectional line.

7. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, In step 4, the theoretical contour lines of each section are discretized using the equal chord height sampling method.

8. The method for compensating for systematic errors in the batch processing of thin-walled blades according to claim 1, characterized in that, In step 5, an adaptive kernel density estimation function and a mathematical expectation method are used to estimate the final profile error compensation value of the blade at that position.

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