A method for optimizing key tolerances of aero-engine compressor blades

Abstract

The present invention relates to the technical field of optimized design of low-pressure compressor blades for aircraft engines, and more specifically, to a method for optimizing the critical tolerances of aircraft engine compressor blades. The method comprises the following steps: obtaining the maximum tolerance offset coefficient corresponding to each tolerance; obtaining the total pressure loss coefficient value of the error blade profile; obtaining a proxy model for the aerodynamic performance of the critical machining errors; constructing a fitness function; and obtaining the final tolerance range for each critical machining error. The present invention is applicable to the optimization of critical tolerances for compressor blades of different types and sizes. The established proxy model exhibits excellent generalization performance and high fitting accuracy, while the optimization method is highly efficient, providing an effective means for reducing the blade machining error rate and improving blade machining production efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of optimization design of low-pressure compressor blades of aircraft engines, and in particular to a method for optimizing key tolerances of aircraft engine compressor blades. Background Art

[0002] Blades are the fundamental unit of a compressor, and their final geometric shape is a physical reflection of the compressor's aerodynamic and structural design. To meet the requirements of gas flow and structural strength, new-generation aeroengine compressor blades are typically designed as ultra-thin, free-form surfaces with three-dimensional twisting, forward curvature, and backward sweep. These blades are constructed from difficult-to-machine materials such as titanium alloys and high-temperature alloys, and they demand extremely high precision. The conflict between the structural and process characteristics of these difficult-to-machine materials and complex, thin-walled curved surfaces, and the ultra-high precision requirements, leads to low machining yields, high machining costs, and long machining cycles for compressor blades in the aeroengine industry. The fundamental reasons for this situation lie, on the one hand, inaccurate blade machining process control, and on the other hand, inappropriate blade tolerance design. Extensive research has been conducted on blade machining process control, primarily focusing on cutting force modeling, fixture optimization, machining deformation prediction, machining parameter optimization, tool path and tool axis vector optimization, tool wear prediction, and deformation compensation. The root cause of unreasonable blade tolerance design lies in a lack of understanding of the impact of blade machining errors on compressor aerodynamic performance. This results in existing blade tolerance design methods relying heavily on experience, leading to overly tight tolerances for some key features. To address this issue, a new compressor blade tolerance optimization method should be proposed based on the distribution of blade machining errors within existing process capabilities and their impact on aerodynamic performance, thereby improving blade machining qualification rates and efficiency.

[0003] Currently, research on compressor blade tolerance optimization methods is limited. Most tolerance research focuses on dimensional chain design between different parts in the assembly process, joint optimization of part product tolerance design and process solutions under cost constraints, and tolerance design for relatively simple free-form surface parts. For complex, thin-walled curved parts like compressor blades, profile tolerances include characteristic parameter tolerances (chord length, maximum thickness, leading and trailing edge radius, etc.) and form and position tolerances (position tolerance, torsion tolerance, and profile tolerance). Not only are the tolerance types numerous, but two-dimensional cross-sectional tolerances are intertwined with three-dimensional free-form surface tolerances. Existing methods struggle to meet the requirements for blade tolerance optimization for compressor service performance. Despite the complex internal correlations among compressor blade machining errors, previous research has shown that, among the 13 compressor blade machining errors, maximum thickness error, maximum leading edge profile error, minimum leading edge profile error, and torsion angle error are critical machining errors. Accordingly, three tolerances associated with these four errors are identified as critical tolerances: maximum thickness tolerance, leading edge profile tolerance, and torsion angle tolerance. While the identification of critical errors and key tolerance types has greatly reduced the difficulty of research, no applicable method has yet emerged.

[0004] Therefore, it is necessary to provide a method for optimizing the critical tolerances of aero-engine compressor blades to solve the above problems. Summary of the Invention

[0005] The present invention provides a method for optimizing the key tolerances of aero-engine compressor blades to solve the problem that existing methods are difficult to meet the blade tolerance optimization requirements for compressor service performance, which profoundly affects the qualification rate and efficiency of blade production and processing.

[0006] The present invention provides a method for optimizing the critical tolerances of aero-engine compressor blades using the following technical solutions, including:

[0007] Obtaining machining error data of key machining errors of the compressor blade, and obtaining a maximum tolerance deviation coefficient corresponding to each tolerance based on a distribution range of the machining error data of each key machining error and a corresponding original tolerance range;

[0008] Based on the full factor method, all machining error combinations at specific sampling points for all key machining error types are designed and error blade profiles corresponding to the error combinations are constructed. Then, CFD numerical simulations are performed to obtain the total pressure loss coefficient values ​​of the error blade profiles for all key machining error types at each machining error sampling point combination.

[0009] A neural network is constructed, each combination of all key machining errors is used as the input of the neural network, and the total pressure loss coefficient value of the error blade corresponding to each machining error combination is used as the output of the neural network. The neural network is trained to obtain a trained machining error-aerodynamic performance proxy model;

[0010] The out-of-tolerance range is obtained based on the distribution range and tolerance range of the machining error data of each key machining error, a target data is randomly selected from each out-of-tolerance range to form the target input data, and the target input data is input into the proxy model to obtain the target aerodynamic loss coefficient value; each data is selected from the original tolerance range of each key machining error to form a group of original data, and the proxy model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data; the constraint violation function is obtained based on the target aerodynamic loss coefficient value and the maximum aerodynamic loss coefficient value, and the fitness function is constructed based on the constraint violation function, the maximum tolerance offset coefficient corresponding to each tolerance, and the target input data;

[0011] Taking the target input data as the optimization target, the target input data is optimized based on the fitness function and the sparrow search algorithm until the fitness function value is minimized. The final tolerance range of each key machining error is obtained according to the target input data corresponding to the minimum fitness function value.

[0012] Preferably, the key processing errors include: maximum thickness error, maximum leading edge profile error, minimum leading edge profile error and torsion angle error.

[0013] Preferably, the steps of obtaining the maximum tolerance deviation coefficient corresponding to each tolerance are:

[0014] The ratio of the maximum limit value of the distribution range of the machining error data of each key machining error to the maximum limit value of the corresponding tolerance range is used as a first ratio;

[0015] The ratio of the minimum limit value of the distribution range of the machining error data of each key machining error to the minimum limit value of the corresponding tolerance range is used as a second ratio;

[0016] The maximum value of the absolute value of the first ratio and the absolute value of the second ratio is taken as the maximum tolerance deviation coefficient.

[0017] Preferably, all machining error combinations of all key machining errors are designed based on the full factor method, and error blade profiles corresponding to the machining error combinations are constructed for CFD numerical simulation. The steps for obtaining the total pressure loss coefficient value of the error blade profile under each machining error combination for all key machining error types are as follows:

[0018] Setting error sampling values ​​for different types of key machining errors according to the distribution range of error data;

[0019] The original design blade profile is constructed using the NURBS method, and the error sampling values ​​corresponding to each type of key machining error are inserted into the original design blade profile to fit the error blade profile;

[0020] By performing CFD numerical simulation on the error blade profile, the total pressure loss coefficient of the error blade profile under different error sampling value combinations of all key machining error types is obtained.

[0021] Preferably, the step of inserting the error sampling value corresponding to each type of key machining error into the original design blade profile to fit the error blade profile is:

[0022] Discretize the contour curves of the maximum thickness area and the leading edge area of ​​the original design blade to obtain discrete points;

[0023] Determine the error value at the maximum thickness position, use the Hanning window function as a weighting function to weight the error value, and insert the weighted error value into the discrete points on both sides of the maximum thickness position in the maximum thickness area;

[0024] The distribution range of the error data of the leading edge profile is from the minimum value of the leading edge profile to the maximum value of the leading edge profile;

[0025] Generate random error data that obeys normal distribution within the distribution range of error data of leading edge profile according to the number of discrete points in the leading edge profile area;

[0026] The generated random error data are sequentially added to the discrete point positions corresponding to the leading edge contour area;

[0027] After inserting the maximum thickness error and leading edge profile error at discrete points in the corresponding area, the insertion of the torsion angle error can be achieved by changing the angle of attack of the blade, and the contour curve of the error blade is obtained by fitting the NURBS method.

[0028] Preferably, the chord length regions of the front 5% and the rear 5% of the maximum thickness position are taken as the maximum thickness regions.

[0029] Preferably, the step of obtaining the out-of-tolerance range according to the error range and tolerance range of the machining error data of each key machining error is:

[0030] The maximum limit value of the tolerance range to the maximum limit value of the error range is taken as the maximum limit value deviation range;

[0031] The minimum limit value of the error range to the minimum limit value of the tolerance range is taken as the minimum limit value deviation range.

[0032] Preferably, the constraint violation function is expressed as:

[0033]

[0034] Where, Represents the constraint violation function value; Indicates that the target input data is The target aerodynamic loss coefficient value output by the proxy model when ; It means that one data set is selected from the original tolerance range of each key processing error to form a group of original data, and the agent model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data.

[0035] Preferably, the fitness function is expressed as:

[0036]

[0037] Where, represents the fitness function value; The maximum tolerance deviation factor indicating the maximum thickness error; Indicates the maximum tolerance deviation factor of the leading edge profile error; Indicates the maximum tolerance deviation factor of the torsion angle error; Indicates the target data selected within the tolerance range of the maximum thickness error; Indicates target data selected within the tolerance range of leading edge profile error; Indicates target data selected within the tolerance range of the torsion angle error; Expressed as a penalty factor; represents the constraint violation function value, Indicates taking the absolute value.

[0038] Preferably, the step of obtaining the final tolerance range according to the target input data corresponding to the minimum fitness function value is:

[0039] According to the target data corresponding to the maximum thickness error tolerance range in the target input data corresponding to the minimum fitness function value, the final tolerance range of the maximum thickness tolerance is obtained;

[0040] The target data corresponding to the tolerance range of the leading edge profile error in the target input data corresponding to the minimum fitness function value is used to obtain the final tolerance range of the leading edge profile tolerance;

[0041] The target data corresponding to the excess range of the torsion angle error in the target input data corresponding to the minimum fitness function value is used to obtain the final tolerance range of the torsion angle tolerance.

[0042] The beneficial effects of the present invention are:

[0043] The method of the present invention can optimize critical tolerances without compromising aerodynamic performance, reducing blade machining error rates. This method is applicable to critical tolerance optimization research for compressor blades of different types and sizes. The established proxy model exhibits excellent generalization performance and high fitting accuracy, while the optimization method is highly efficient, providing an effective means for reducing blade machining error rates and improving blade machining production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0045] Figure 1 A schematic flow chart of a method for optimizing key tolerances of aero-engine compressor blades according to the present invention;

[0046] Figure 2 Schematic diagram of the distribution of maximum thickness error in an embodiment of the present invention;

[0047] Figure 3 Schematic diagram of the distribution of the maximum error of the leading edge profile in an embodiment of the present invention;

[0048] Figure 4 Schematic diagram of the distribution of the minimum error of the leading edge profile in an embodiment of the present invention;

[0049] Figure 5 Schematic diagram of the distribution of torsion angle error in an embodiment of the present invention;

[0050] Figure 6 Schematic diagram of a two-dimensional profile curve of a blade cross section in an embodiment of the present invention;

[0051] Figure 7 A schematic diagram of the division of different regions of a blade in an embodiment of the present invention;

[0052] Figure 8 A curve diagram showing the change of the Hanning window weight function value with the sample points in an embodiment of the present invention;

[0053] Figure 9 Schematic diagram of torsion angle error in an embodiment of the present invention;

[0054] Figure 10 A schematic diagram of error blade profiles with all types of critical machining errors added to the embodiment of the present invention;

[0055] Figure 11This is a diagram illustrating CFD numerical simulation conditions in an embodiment of the present invention;

[0056] Figure 12 Schematic diagram of the topological structure of the BP neural network in an embodiment of the present invention;

[0057] Figure 13 This is a flow chart of optimizing blade key tolerances based on the sparrow search algorithm in an embodiment of the present invention;

[0058] Figure 14 Schematic diagram showing the comparison between the predicted values ​​and the true values ​​of the sample points in the test set in an embodiment of the present invention;

[0059] Figure 15 is a frequency distribution histogram of relative errors of test set sample points in an embodiment of the present invention;

[0060] Figure 16 Schematic diagram comparing the original tolerance range and the optimized tolerance range of maximum thickness in an embodiment of the present invention;

[0061] Figure 17 Schematic diagram comparing the original tolerance range and the optimized tolerance range of the maximum value of the leading edge profile in an embodiment of the present invention;

[0062] Figure 18 Schematic diagram comparing the original tolerance range and the optimized tolerance range of the minimum value of the leading edge profile in an embodiment of the present invention;

[0063] Figure 19 Schematic diagram comparing the original tolerance range and the optimized tolerance range of the torsion angle in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0065] An embodiment of a method for optimizing key tolerances of an aero-engine compressor blade according to the present invention is as follows: Figure 1 As shown, including:

[0066] S1. Obtain the maximum tolerance deviation coefficient corresponding to each tolerance;

[0067] Specifically, machining error data of key machining errors of the compressor blades are obtained, and the maximum tolerance deviation coefficient corresponding to each tolerance is obtained according to the distribution range of the machining error data of each key machining error and the corresponding original tolerance range.

[0068] In this embodiment, the steps for obtaining the maximum tolerance offset coefficient corresponding to each tolerance are: taking the ratio of the maximum limit value of the distribution range of the machining error data of each key machining error to the maximum limit value of the corresponding tolerance range as the first ratio; taking the ratio of the minimum limit value of the distribution range of the machining error data of each key machining error to the minimum limit value of the corresponding tolerance range as the second ratio; and taking the maximum value of the absolute value of the first ratio and the absolute value of the second ratio as the maximum tolerance offset coefficient.

[0069] Step 11: Determine the maximum tolerance deviation factor for the maximum thickness tolerance:

[0070] In this embodiment, the tolerance range of the maximum thickness error of the two-dimensional cross-sectional profile is determined to be (-0.150mm, +0.150mm) based on the blade design drawing, that is, the upper limit deviation is +0.150mm and the lower limit deviation is -0.150mm. The distribution of the machining error data of the maximum thickness error of the two-dimensional cross-sectional profile of 38 blades at the same height is shown in the figure below. Figure 2 As shown, Figure 2 The horizontal axis represents the blade number, and the vertical axis represents the processing error value of the maximum thickness error. Figure 2 It can be seen that there are a total of 10 data points outside the tolerance range of the maximum thickness error, of which 6 data points exceed the upper limit deviation and 4 data points exceed the lower limit deviation. This phenomenon shows that under the existing process capabilities, the maximum thickness error has a relatively obvious out-of-tolerance situation. Figure 2 It can also be found that the distribution range of all processing error data is between [-0.230mm, 0.240mm]. Therefore, the maximum value of the tolerance offset coefficient of the maximum thickness tolerance is set to 1.60 in this example. That is, this example will explore the impact of the maximum thickness error on the aerodynamic performance of the blade within the range of [-0.240mm, +0.240mm] and obtain the total pressure loss coefficient value.

[0071] Step 12: Determine the maximum tolerance deviation coefficient of the leading edge profile tolerance:

[0072] For the maximum and minimum leading edge profile errors, the tolerance range marked on the blade design drawing is [-0.030mm, +0.030mm], that is, the upper limit deviation is +0.030mm and the lower limit deviation is -0.030mm. The distribution of the sample data of the maximum leading edge profile error of 38 blade cross-section two-dimensional profiles in this example is as follows: Figure 3 As shown in the figure, the distribution of the minimum error sample data of the leading edge profile of the 38 blade cross-section two-dimensional profiles in this example is as follows: Figure 4 As shown, from Figure 3 and Figure 4It can be seen that both the maximum and minimum leading edge profile errors are severely out of tolerance. Not only are there a large number of data points outside the tolerance range, but the data points also deviate significantly from the upper and lower limit deviation lines. The maximum leading edge profile error data exceeds the upper limit deviation by up to three times, with a maximum of 0.095mm. Meanwhile, the minimum leading edge profile error data deviates from the lower limit deviation by as much as -0.053mm.

[0073] Combine Figure 3 The maximum error data of the leading edge profile shown and Figure 4 The distribution range of the minimum leading edge profile error data points is shown. Considering that both the maximum leading edge profile error and the minimum leading edge profile error are leading edge profile errors, and that they together reflect the machining level of the blade's leading edge, this example sets the maximum leading edge profile tolerance offset coefficient to 2.50. This setting indicates that this example will study the impact of leading edge profile error on aerodynamic performance parameters within the leading edge profile error distribution range of [-0.075mm, 0.075mm]. Although this maximum tolerance offset coefficient value does not include all data points, it does include 80% of the data points. Furthermore, since the leading edge has a significant impact on aerodynamic performance, the setting of the leading edge profile tolerance offset coefficient should be more cautious.

[0074] Step 13: Determine the maximum tolerance deviation factor of the torsion angle tolerance:

[0075] The design drawing requires the lower limit deviation of the torsion angle of the blade cross section with a span height of 352.742mm to be -0.250° and the upper limit deviation to be +0.250°. The torsion angle error data of the 38 blades measured in this example are as follows: Figure 5 As shown, the horizontal axis is the blade number and the vertical axis is the error value. Figure 5 It can be seen that while the deviation from the torsion angle is not as severe as the deviation from the leading edge profile, it is still not negligible. The data points in the figure are distributed within the range of [-0.450°, +0.480°]. Based on this range, this example sets the maximum deviation factor for the torsion angle tolerance to 1.92. In other words, this example will study the mapping relationship between torsion angle error and aerodynamic performance within the range of [-0.480°, 0.480°] to find the maximum torsion angle tolerance that meets the aerodynamic performance requirements.

[0076] S2. Obtain the total pressure loss coefficient value of the error blade profile;

[0077] Specifically, all machining error combinations for all key machining error types are designed based on the full factor method, and error blade profiles for the corresponding error combinations are constructed. CFD numerical simulations are then performed to obtain the total pressure loss coefficient values ​​for the error blade profiles for all key machining error types under each machining error combination. That is, error sampling values ​​for different types of key machining errors are set according to the distribution range of the error data. The original design blade profile is constructed using the NURBS method, and the blade profile curve is discretized to obtain discrete points. The error values ​​corresponding to each type of key machining error are inserted into the corresponding discrete points, and the error blade profile is then fitted using the NURBS method. CFD numerical simulations of the error blade profile are then performed to obtain the total pressure loss coefficients for the error blade profiles under different error sampling value combinations for all key machining error types.

[0078] Step 21: The steps of setting error sampling values ​​of different types of key processing errors according to the distribution range of error data are as follows:

[0079] Taking into account the different values ​​of the maximum tolerance deviation coefficient for different types of tolerances, this example sets sampling points (-0.240, -0.160, -0.008, 0, 0.008, 0.160, 0.240) for the maximum thickness error. That is, the aerodynamic performance of the two-dimensional blade profile when the maximum thickness error values ​​are -0.240 mm, -0.160 mm, -0.008 mm, 0 mm, 0.008 mm, 0.160 mm, and 0.240 mm are studied respectively. Sampling points (-0.480, -0.360, -0.240, -0.120, 0, 0.120, 0.240, 0.360, 0.480) were set for the torsion angle error. This means the aerodynamic performance of the two-dimensional blade profile is studied when the torsion angle errors are -0.480°, -0.360°, -0.240°, -0.120°, 0°, 0.120°, 0.240°, 0.360°, and 0.480°, respectively. Because the leading edge profile error is at the starting point of the airflow, it has a significant impact on the blade's aerodynamic performance. Furthermore, because the maximum tolerance offset coefficient of the leading edge profile tolerance is the largest among these key tolerances, the error sampling point intervals must be set more precisely to ensure the accuracy of the subsequent proxy model. In this example, the leading edge profile error sampling points are set to (0, ±0.0075, ±0.015, ±0.0225, ±0.030, ±0.0375, ±0.045, ±0.0525, ±0.060, ±0.0675, ±0.075) mm. The positive and negative signs indicate the error range. For example, ±0.045 mm indicates that the leading edge profile error is between (-0.045 mm, 0.045 mm). Using this sampling point setting for the leading edge profile error range ensures that the maximum and minimum leading edge profile error values ​​are both within the same range and are opposite to each other. Furthermore, it covers most of the maximum and minimum leading edge profile error data. At this point, since 7 sampling points have been set for the maximum thickness error, 9 sampling points have been set for the torsion angle error, and 11 sampling points have been set for the leading edge profile error, based on the full factorial method, this example needs to construct 7*9*11=693 combinations of error sampling values ​​of different levels for different types of errors, corresponding to 693 different error blade profiles. This also means that a total of 7*9*11=693 CFD numerical simulations of error blade profiles will be required in the future.

[0080] Step 22: Use the NURBS method to construct the original design blade profile, and insert the error sampling values ​​corresponding to each type of key processing error into the original design blade profile to fit the error blade profile. The steps are as follows:

[0081] In actual engineering applications, the description of the blade profile curve is usually achieved by fitting the coordinate points of the discrete curve. This requires the use of a parametric method to describe the blade profile curve to ensure that the blade profile curve has continuity and smoothness without distortion. The blade profile curve of this case study is as follows: Figure 6 shown.

[0082] Step 221: Parameterization of the original blade design:

[0083] In this example, the NURBS method is used to fit the two-dimensional contour curve of the original blade design, thus laying the foundation for constructing the blade profile curve with error based on the original blade profile curve. NURBS (Non-uniform rationalB-Spline) is the full name of non-uniform rational B-spline curve, which is developed based on non-rational Bezier curves and non-rational B-spline curves. It is a parametric method that can flexibly describe and control the shape of the blade profile curve. k The expressions of the sub-NURBS equations and rational basis functions are:

[0084] (1)

[0085] in, is the weight factor, which represents the influence of the control point on the blade curve and satisfies ; As control point, by controlling Ability to connect points in sequence to form polygons; for k The subnormal B-spline basis function can be represented by the knot vector Determined by the DeBoer-Cox formula; is the mathematical expression of the NURBS curve; for k Rational basis functions for sub-NURBS (Non-Uniform Rational B-Splines) equations.

[0086] Node Vector It can be determined by parameterizing the cumulative chord length. The specific calculation formula is as follows:

[0087] (2)

[0088] in, is the chord length vector, is called the forward difference vector.

[0089] Step 222: Error leaf profile modeling:

[0090] Based on the key blade machining error types identified by previous research—namely, maximum thickness error, leading edge profile error (including maximum and minimum leading edge profile errors), and torsion angle error—this section divides the blade's two-dimensional contour into regions based on these four key machining error types. Different error types are then added to the corresponding discrete points in the region. The NURBS method is then used to construct a blade profile curve with errors (i.e., construct an error blade profile).

[0091] It should be noted that, to simulate the actual machined leading edge profile, the error addition method employed is to first add random errors to the discrete data points of the leading edge profile, followed by curve fitting using the NURBS method. Unlike the method for adding leading edge profile errors, the method for adding maximum thickness errors to the blade's 2D profile is to first add a target error value at the maximum thickness location, then use a Hanning window function as a weighting function to further add errors on both sides of the maximum thickness location, and finally perform curve fitting using the NURBS method. This approach is motivated by the fact that the maximum and minimum leading edge profile errors are profile errors, while the maximum thickness error and torsion angle error are characteristic parameter errors. Another important reason is that this example aims to simulate the actual machined leading edge profile. Using the NURBS method to curve fit the discrete data points with added random errors preserves the peaks and troughs characteristic of the actual blade leading edge profile while avoiding cusps, which are typically absent in the milled and polished blade leading edge profile.

[0092] Some scholars have pointed out that the first 15% of the chord length of the blade profile curve contains the entire leading edge of the blade, and this area has a more significant impact on the blade performance. Based on this view, this section first normalizes the chord length so that the chord length remains parallel to the horizontal axis. Then, as Figure 7 As shown in the figure, the first 15% of the chord length of the blade profile curve is defined as the leading edge region, the last 15% of the chord length is defined as the trailing edge region, and the 16%-85% chord length region is divided into the blade basin and blade back regions. Since the maximum thickness is usually located in the blade basin and blade back region, there is overlap between the maximum thickness region and the blade basin and blade back region. To reduce the impact of adding the maximum thickness error to the maximum thickness region on the blade basin and blade back regions, only the first 5% and last 5% of the chord length of the maximum thickness location are divided into the maximum thickness region.

[0093] Step 2221: Construct the maximum thickness contour curve of the error blade profile:

[0094] Since the maximum thickness error is a parameter error, in order to ensure that the blade curve remains smooth after adding the maximum thickness error in the maximum thickness area, this example uses the Hanning window function as the weight function to perform weighted processing on the errors added to each discrete point in the maximum thickness area. The definition of the Hanning window function is as follows:

[0095] (3)

[0096] Where, n is the sequence number of the sample points in the window, starting from 0. N Represents the length of the window function or the total number of sample points. Also, because the maximum thickness error is a parameter error, when adding the error to the maximum thickness area of ​​the blade's 2D profile, half of the error value is added to the suction side and half to the pressure side.

[0097] The number of sample points of the weight function is set according to the number of discrete points in the maximum thickness area, so that the weight function value increases from 0 to 1 and then slowly decreases to 0. The weight function value changes with the sample points as shown in the following example: Figure 8 This change causes the error value to gradually increase and then decrease within the maximum thickness region, ensuring the smoothness of the curve within this region. After adding the generated error value to the corresponding discrete points, the maximum thickness region contour curve of the error blade profile can be fitted using the NURBS method.

[0098] Step 2222: construct a leading edge profile curve of the error blade profile;

[0099] Leading edge profile error is a type of profile error, so the method for adding leading edge profile error to the 2D blade profile curve is different from the maximum thickness error. When adding leading edge profile error, the leading edge profile error range, namely the maximum and minimum leading edge profile values, must be determined. Then, based on the number of discrete points in the leading edge, random error data that follows a normal distribution within the error range is generated. Next, the generated random error data is sequentially added to the corresponding discrete points in the leading edge. Finally, the known discrete points are fitted using the NURBS method to construct the 2D blade leading edge profile curve with error (i.e., the leading edge profile curve of the error blade). This error addition method simulates the actual leading edge profile curve after milling and polishing, preserving the peaks and troughs of the actual profile. The decision to add a normally distributed error to the blade leading edge profile is based on the conclusions of previous researchers who conducted statistical analysis of measured compressor blade profile errors.

[0100] Step 2223: Determine the twist angle of the error blade profile;

[0101] Torsion angle error is a type of form and position error in blade processing quality inspection. In actual inspection, in order to correspond to the blade design, the contour method is usually used to measure the two-dimensional cross-sectional profile of the blade. The torsion angle is an important design parameter of the compressor element blade grid, which determines the installation direction of the blade profile in the blade grid. Although the processing accuracy of compressor blades has improved with the development of current CNC machine tools and the continuous improvement of manufacturing processes, the compressor blades are typical "cantilever beam" structures. In addition, the material stress release of the blades after three-dimensional distortion and the action of the normal force during high-speed tool cutting will cause the element blade grid to deflect around its center of gravity, resulting in "over-deflection" or "under-deflection". This leads to the actual installation angle of each element blade grid of the blade. Deviation from the design installation angle , thus forming a torsion angle error , actual installation angle , design installation angle , torsion angle error The specific relationship between them is: . Figure 9 Installation angle for design , actual installation angle and torsion angle error When using CFD method for numerical calculation, the addition of torsion angle error can be achieved by changing the angle of attack:

[0102] At this point, based on the contour curve of the original design blade, the maximum thickness error and the leading edge profile error are added to the discrete points of the maximum thickness area and the leading edge area of ​​the original design blade respectively. The contour curves of all error blades are constructed by fitting all discrete points using the NURBS method. Figure 10 The addition of the torsion angle error can be achieved by changing the angle of attack.

[0103] Step 223: CFD numerical simulation of the error blade profile;

[0104] This embodiment uses the total pressure loss coefficient as the aerodynamic performance evaluation index, and the specific calculation formula is:

[0105] (4)

[0106] Where, is the total inlet pressure; is the total outlet pressure; is the inlet static pressure.

[0107] The NUMECA FINE / Turbo module was used to perform CFD numerical simulations of the two-dimensional error blade profile, setting the incoming flow Mach number to 0.7. The aerodynamic performance was solved using the Reynolds-Averaged Navier-Stokes (RANS) method, and the Spalart-Allmaras (SA) turbulence model was selected to close the RANS governing equations. Figure 11 The computational mesh and computational domain for the error blade are presented. The O4H mesh in the blade passage domain was generated using the NUMECA Autogrid.5 module, with a total grid size of approximately 9.83×10⁴. To meet the SA turbulence model's requirements for meshing near the wall, the first grid layer was set to 10⁶, ensuring that y+ is less than 3. The first three layers of y+, or mesh size, are located in the viscous substratum. The computational domain inlet boundary conditions for the CFD simulation include total pressure, total temperature (300.0K), and flow angle; a static pressure of 101300 Pa is applied at the outlet boundary. The computational domain inlet is 1.0 chord lengths from the leading edge, and the trailing edge extension is 2.5 chord lengths to ensure adequate mixing of the outlet airflow. This example uses a two-dimensional error blade, so periodic boundary conditions are applied along the pitch direction, with all solid walls set as no-slip boundaries. The total pressure loss coefficient for all error blades is obtained through numerical simulations corresponding to the number of error blades.

[0108] S3, obtain the proxy model of key machining error-aerodynamic performance;

[0109] Specifically, a neural network is constructed, each combination of all key machining errors is used as the input of the neural network, and the total pressure loss coefficient value of the error blade corresponding to each machining error combination is used as the output of the neural network. The neural network is trained to obtain a trained machining error-aerodynamic performance proxy model.

[0110] Step 31: Build the dataset:

[0111] The total pressure loss coefficient of each error blade profile and the corresponding error sampling value are combined as a set of sample data, thereby obtaining multiple sets of sample data corresponding to different error blade profiles, thereby forming a data set of the key processing error of the blade - the total pressure loss coefficient.

[0112] Step 32: Build a neural network:

[0113] In this embodiment, a BP neural network with a topological structure of 4-5-5-1 is constructed, each group of error sampling values ​​in the data set is used as the input of the BP neural network, and the total pressure loss coefficient of the error blade corresponding to the group of error sampling values ​​is used as the output of the BP neural network. The BP neural network is trained to obtain a trained processing error-aerodynamic performance proxy model.

[0114] Step 321: Network initialization:

[0115] There are 4 inputs to the neural network, namely the maximum thickness error, the maximum leading edge profile error, the minimum leading edge profile error and the torsion angle error. For each set of sample data, the maximum leading edge profile error and the minimum leading edge profile error should be in a positive and negative relationship, and the two together represent the range of the leading edge profile error. Therefore, the number of nodes in the neural network input layer is 4. The aerodynamic performance parameter selected by the present invention is the total pressure loss coefficient, so the output layer of the neural network contains only one node. The performance of different combinations of hidden layers and nodes is evaluated through cross-validation, and it is finally determined to set 2 hidden layers for the neural network structure, and each hidden layer contains 5 nodes. After such a setting, you can get a Figure 12 The 4-5-5-1 BP neural network topology shown. Figure 12 middle, represents the weight from the input layer to the first hidden layer, represents the weight from the first hidden layer to the second hidden layer, represents the weights from the second hidden layer to the output layer. represents the bias from the input layer to the first hidden layer, represents the bias from the first hidden layer to the second hidden layer, Represents the bias from the second hidden layer to the output layer. For other hyperparameters of the BP neural network, set the learning rate η =0.001, select is the activation function.

[0116] Step 322, input layer:

[0117] The input data is a combination of the sampling points of the four key errors at all levels. Since the dimensions of different types of error data vary greatly and their distribution ranges are different, in order to eliminate the adverse effects of the dimensions and ranges of different error data on the model, and to improve numerical stability and model performance, the error data needs to be normalized before input into the neural network. In this example, Z-score normalization is used to normalize the error data. The calculation formula is as follows:

[0118] (5)

[0119] in: Indicates the i Error data, Represents the normalized i Error data is the mean of the error data; is the standard deviation of the error data.

[0120] The error sampling value sample data matrix of the processing error input into the network after normalization is as follows:

[0121] (6)

[0122] in: is the total number of types of key blade machining errors entered and N =4, is the number of samples of each type of key processing error, Indicates the m The first group of samples n Sample data of error types, m The value of is [1, M ], n The value of is [1, N ].

[0123] Step 323, hidden layer:

[0124] According to the data forward propagation principle of BP neural network, the output of the first hidden layer for

[0125] (9)

[0126] represents the weight from the input layer to the first hidden layer, represents the bias from the input layer to the first hidden layer, Represents the first sample of each group after normalization i Error data.

[0127] The output of the second hidden layer for

[0128] (10)

[0129] represents the weight from the first hidden layer to the second hidden layer, represents the bias from the first hidden layer to the second hidden layer.

[0130] The weight matrix and bias matrix from the input layer to the first hidden layer are:

[0131] (11)

[0132] The weight matrix and bias matrix from the first hidden layer to the second hidden layer are:

[0133] (12)

[0134] Step 324, output layer:

[0135] Output of the output layer for:

[0136] (13)

[0137] represents the weight from the second hidden layer to the output layer, Represents the bias from the second hidden layer to the output layer.

[0138] The weight matrix from the second hidden layer to the output layer is:

[0139] (14)

[0140] Step 325: BP neural network training mean square error and determination coefficient:

[0141] The mean square error formula for neural network training is:

[0142] (15)

[0143] in, is the expected output, that is, the true value. Predicted value for the neural network. M is the number of all predicted values. is the error between the expected output and the output of the output layer, and .

[0144] Determination coefficient of neural network regression fitting The calculation formula is as follows:

[0145] (16)

[0146] in is the mean of the true values ​​of the samples. R 2 It can be used to measure the degree to which the model explains the target variable during the training process, and its value range is 0 to 1. R 2 The closer it is to 1, the better the explanatory power of the constructed BP neural network is for the target variable and the better the regression performance is.

[0147] Step 326: Weight and bias update:

[0148] This example uses the mean square error (MSE) as the loss function and updates the weights and biases of each layer based on the gradient descent method.

[0149] Step 327, iterative update end criteria:

[0150] During three consecutive training sessions MSE The difference is less than a certain threshold When the threshold is set too low, the model performance is considered stable and the iterative update can be terminated. At the same time, in order to avoid setting the threshold too low, which will increase the training time and cause overfitting, the maximum number of iterations is set to 1000.

[0151] At this point, the trained processing error-aerodynamic performance proxy model can be obtained.

[0152] S4, construct fitness function;

[0153] Specifically, an out-of-tolerance range is obtained based on the error range and tolerance range of the machining error data of each key machining error, a target data is randomly selected from each out-of-tolerance range to form the target input data, and the target input data is input into the proxy model to obtain the target aerodynamic loss coefficient value; one data is selected from the original tolerance range of each key machining error to form a group of original data, and the proxy model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data; a constraint violation function is obtained based on the target aerodynamic loss coefficient value and the maximum aerodynamic loss coefficient value, and a fitness function is constructed based on the constraint violation function, the maximum tolerance offset coefficient corresponding to each tolerance, and the target input data.

[0154] Among them, the expression of the fitness function is

[0155]

[0156] Where, represents the fitness function value; The maximum tolerance deviation factor indicating the maximum thickness error; Indicates the maximum tolerance deviation factor of the leading edge profile error; Indicates the maximum tolerance deviation factor of the torsion angle error; Indicates the target data selected within the tolerance range of the maximum thickness error; Indicates target data selected within the tolerance range of leading edge profile error; Indicates target data selected within the tolerance range of the torsion angle error; Expressed as a penalty factor; represents the constraint violation function value, Indicates taking the absolute value.

[0157] Step 41: The corresponding fitness function for upper limit deviation optimization is:

[0158] In this implementation, due to the different sensitivities of the total pressure loss coefficient of the two-dimensional blade profile to the four key processing errors, the blade total pressure loss coefficient has different trends in change with the error within different error ranges (referring to the two ranges of 0 to the lower limit deviation and 0 to the upper limit deviation). In this engineering context, the blade tolerance range optimization problem is decomposed into upper limit deviation optimization and lower limit deviation optimization. Different fitness functions are used for the two decomposed optimization problems. For the upper limit deviation optimization problem, the following function is used as its fitness function, and the specific expression is:

[0159] (17)

[0160] Where, Represents the fitness function value during upper limit deviation optimization; K 1 represents the maximum tolerance deviation factor of the maximum thickness tolerance, which is 1.6; Indicates the target maximum thickness upper limit deviation value selected within the maximum thickness upper limit deviation tolerance range [0.150, 0.240]; K 2 represents the maximum tolerance deviation coefficient of the leading edge profile tolerance, and its value is 2.5. Indicates the upper limit deviation value of the target leading edge profile selected within the tolerance range of [0.030, 0.075], K 3 represents the maximum tolerance deviation coefficient of the torsion angle tolerance, and its value is 1.92. Indicates the target torsion angle upper limit deviation value selected within the torsion angle upper limit deviation tolerance range [0.250, 0.480]. It is expressed as a penalty factor, which is 1000 here; g is the constraint violation function.

[0161] The expression of the constraint violation function is:

[0162] (18)

[0163] Where, Indicates that , , , Substitute the aerodynamic loss coefficient value calculated by the trained proxy model. This example has only 3 optimization variables, while the input variables of the established BP proxy model are 4. The main reason for this is that the four input variables of the BP proxy model are the maximum thickness error, the maximum leading edge profile error, the minimum leading edge profile error, and the torsion angle error. When optimizing the tolerance in this example, the upper and lower limits of the tolerance are optimized separately, and the maximum leading edge profile error and the minimum leading edge profile error represent the upper and lower limits of the leading edge profile tolerance respectively, and together represent the leading edge profile tolerance range. Since the upper and lower limits of the tolerance range are generally positive and negative numbers, here we set = - ,Right now When the BP proxy model is used for calculation, the minimum value of the leading edge profile error and the maximum value of the leading edge profile error have an opposite numerical relationship. It means that one data set is selected from the original tolerance range of each key processing error to form a group of original data, and the proxy model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data, that is, the maximum value of the total pressure loss coefficient of the blade that can be calculated within the original maximum thickness tolerance range [-0.150, +0.150], the original leading edge profile tolerance range [-0.030, +0.030], and the original torsion angle tolerance range [-0.250, +0.250].

[0164] A careful observation of the constraint violation function and fitness function reveals that if , , The corresponding total pressure loss coefficient is [0, ] range, then the fitness function value will be a smaller value, only affected by , , However, if , , The corresponding total pressure loss coefficient exceeds , then due to the penalty factor If the value is set to a large value, the resulting fitness will be large. These sparrows with large fitness values ​​will tend to move towards the current optimal position when updating their positions. In light of the engineering background of the fitness function setting in this example, this movement towards the current optimal position can be seen as the sparrow population moving towards a position that satisfies both the constraint conditions (i.e., the total pressure loss coefficient satisfies [0, ]), and then iteratively updates towards a position with a smaller fitness function value. Overall, the fitness function setting in this example has the following three advantages: 1. It reflects the urgency of optimizing each of the three key errors (i.e., the larger the tolerance offset, the more critical the tolerance range needs to be optimized); 2. It reflects the error types most likely to exceed tolerances under existing process conditions (i.e., the larger the tolerance offset, the more pronounced the deviation of this type of error); and 3. This fitness function ensures that the blade's aerodynamic performance is not compromised during tolerance optimization.

[0165] For the lower limit deviation optimization problem, the following function is used as its fitness function, and the specific expression is:

[0166] (20)

[0167] Where, Represents the fitness function value during lower limit deviation optimization; K 1 represents the maximum tolerance deviation factor of the maximum thickness tolerance, which is 1.6; Indicates the target maximum thickness lower limit deviation value selected within the maximum thickness lower limit deviation tolerance range [-0.150, -0.240]; K 2 represents the maximum tolerance deviation coefficient of the leading edge profile tolerance, and its value is 2.5. Indicates the target leading edge profile lower limit deviation value selected within the tolerance range of the leading edge profile lower limit deviation [-0.030, -0.075], K 3 represents the maximum tolerance deviation coefficient of the torsion angle tolerance, and its value is 1.92. Indicates the target torsion angle lower limit deviation value selected within the torsion angle lower limit deviation tolerance range [-0.250, -0.480]. It is expressed as a penalty factor, which is 1000 here; g is the constraint violation function.

[0168] S5. Obtain the final tolerance range of each key processing error;

[0169] Specifically, the target input data is used as the optimization target, and the target input data is optimized based on the fitness function and the sparrow search algorithm until the fitness function value is maximized. The final tolerance range of each key processing error is obtained according to the target input data corresponding to the minimum fitness function value.

[0170] Sparrow Search Algorithm (SSA) is a new intelligent swarm optimization algorithm first proposed in 2020 based on the foraging behavior of sparrows and their response to natural enemies. Some scholars have compared the performance of various swarm intelligence optimization algorithms through experiments and found that SSA has higher search accuracy, shorter optimization time and faster convergence speed. Figure 14 The following describes the process of blade tolerance optimization using the sparrow search algorithm in this embodiment:

[0171] Step 51: Population initialization:

[0172] In the experiment simulating predation on sparrow populations, n The available matrix form for a population of sparrows is:

[0173] (twenty one)

[0174] Where, n is the number of sparrows in the population; d Indicates the dimension of the variable to be optimized. Combined with the optimization goal of this example, we can determine d =3; In the technical context of the present invention, the physical meaning of the sparrow is the combination of the maximum thickness error, the leading edge profile error and the torsion angle error within their respective tolerance ranges. Different value combinations represent different sparrow individuals. n Individual sparrows constitute a population.

[0175] Step 52, fitness function:

[0176] The fitness function is set according to step S4.

[0177] Step 53: Update the discoverer's location:

[0178] In the entire population, the finder is responsible for finding food and providing the foraging area and direction for the entire sparrow population. Its position update formula is:

[0179] (twenty two)

[0180] Where, t Indicates the current iteration number; is the maximum number of iterations, which is a constant; For the i A sparrow in the j The location information in the dimension and j =1, 2, 3; is a random number with a value range of ∈(0,1]; R 2 is the warning value, R 2∈[0,1]; ST is a safe value, ST ∈[0.5, 1]; B is a random number that obeys the normal distribution; L is a 1× d A matrix in which all elements are 1. R 2< ST When , it indicates that there are no natural enemies around the sparrow population, the entire population is in a safe environment, and the sparrows can forage safely; when R 2≥ ST When the sparrows are bitten, it indicates that natural enemies have been found around the sparrow population. The sparrows are in danger and need to fly to a safe area immediately to search for new food.

[0181] Step 54: Follower location update:

[0182] Throughout the population, followers closely monitor the behavior of the discoverer. Once the discoverer finds a food source, the followers will immediately follow the discoverer to grab the food. In the sparrow search algorithm, followers correspond to individuals with relatively low fitness values. They update their positions by following the discoverer to find a better solution. In addition, some followers may continuously monitor the discoverer to compete for food resources. This is reflected in the algorithm as a competitive and cooperative relationship between individuals. The formula for followers to update their positions based on the information from the discoverer is:

[0183] (twenty three)

[0184] Where: Indicates the current global optimal position; is a random number that follows a normal distribution; Indicates the current global worst position; A + =A T (AA T ) -1 , where A is a 1× d The elements in the matrix are randomly assigned 1 or -1; when i > n / 2, indicating the i The follower is now in the worst foraging area and is facing starvation. It needs to find other areas to forage for food to replenish energy.

[0185] Step 55: Update the scout's position:

[0186] Within a population, scouts monitor the area surrounding their foraging area. When a predator (or danger) appears near the foraging area, they immediately issue an alert. In the algorithm, scouts represent individuals with specific responsibilities. They monitor for anomalies during the search process, such as falling into a local optimal solution or encountering an infeasible solution. When a scout issues an alert, the entire sparrow population adjusts its search strategy to avoid difficulties or seek new search directions. The mathematical expression for the scout's position update is:

[0187] (twenty four)

[0188] Where: Indicates the optimal position in the current group; The moving step length control parameter for controlling the global optimal position is a random parameter that conforms to the normal distribution and has a value range of [0, 1]; K It is also a random number and its value range is [-1, 1]. In order to avoid the denominator being 0, a minimum constant is added. ; Represents the fitness function value of the current sparrow individual; and The values ​​represent the best and worst fitness function values ​​in the current population, respectively. In this example, when using the sparrow search algorithm to optimize leaf tolerance, the population is set to 20 sparrows, with 70% being discoverers, 30% being followers, and 20% being discoverers. The warning value is set to 0.6, and the maximum number of iterations is set to 50.

[0189] At this point, the target input data is used as the optimization target, and the target input data is optimized based on the fitness function during the upper limit deviation optimization and the sparrow search algorithm until the fitness function value during the upper limit deviation optimization is maximized. The final upper limit tolerance of the final tolerance range of each key machining error is obtained according to the target input data corresponding to the minimum fitness function value during the upper limit deviation optimization, that is, the final upper limit tolerance corresponding to the maximum thickness tolerance, leading edge profile tolerance, and torsion angle tolerance is obtained; the target input data is used as the optimization target, and the target input data is optimized based on the fitness function during the lower limit deviation optimization and the sparrow search algorithm. The optimization is performed until the fitness function value during the lower limit deviation optimization is maximized. According to the target input data corresponding to the minimum fitness function value during the lower limit deviation optimization, the final lower limit tolerance of the final tolerance range of each key machining error is obtained, that is, the final upper limit tolerance corresponding to the maximum thickness tolerance, leading edge profile tolerance and torsion angle tolerance is obtained; the final upper limit tolerance corresponding to the maximum thickness tolerance, leading edge profile tolerance and torsion angle tolerance; the final upper limit tolerance corresponding to the maximum thickness tolerance, leading edge profile tolerance and torsion angle tolerance; the final tolerance range corresponding to the maximum thickness tolerance, leading edge profile tolerance and torsion angle tolerance is obtained.

[0190] The following is a simulation verification of this embodiment:

[0191] This example illustrates the method of the present invention based on the optimization of the maximum thickness tolerance, leading edge profile tolerance, and twist angle tolerance of a blade cross section at a spanwise height of 352.742 mm for a certain type of low-pressure compressor.

[0192] In this example, the BP neural network model is constructed using MATLAB software based on the BP neural network hyperparameter settings and topology structure established in step S3. All 693 groups of sample data are randomly shuffled, and then 90% of the sample data are divided into the training set and 10% into the test set. The constructed neural network is trained with the training set data, and the fitting effect and prediction accuracy of the trained neural network model are tested with the test set. According to the grouping method of the original sample data set, the number of samples for each type of key processing error in step S3 can be determined. M =616. The constructed neural network is iteratively trained with the training set data. After 513 iterations of training, the iterative update termination condition is reached. At this point, the training set MSE 6.5×10 -6 , R 2 The trained BP neural network is used to predict the total pressure loss coefficient of the error sample data in the test set. MSE and R 2 9.7×10 -6 By comparison, we can find that the two indicators of the training set and the test set are not much different, indicating that the trained BP neural network shows good performance on the test set, indicating that the model has good generalization ability.

[0193] like Figure 14 As shown, Figure 14 The predicted values ​​and true values ​​of the sample points in the test set are compared, and a relative error band of ±5% is given. Figure 14 A ±5% error band is also given to show the relative error and error distribution characteristics of the prediction. Figure 14 There are 77 data points in total. The horizontal coordinates of these points are the true values, and the vertical coordinates are the predicted values ​​of the constructed neural network model. Ideally, if the true value and predicted value of each data point are equal, then all data points should fall within y = x On this straight line. Figure 14 It can be clearly seen that these data points are scattered across y = xOn both sides of this line, most data points fall within the ±5% error band, while a small number fall on the error band boundary or outside the error band. This indicates that the prediction accuracy of the dual-hidden-layer BP neural network proxy model established in this example can reach 95%, which basically meets the requirements of engineering applications.

[0194] Figure 15 The relative error frequency distribution histogram of all sample data points in the test set is given. The horizontal axis of the graph represents the error of the predicted value relative to the true value, and the vertical axis represents the error distribution density. The curve in the figure is the normal distribution fitting curve of the relative error data. Figure 15 It can be seen that the absolute value of the relative error of about 15% of the sample data in the test set exceeds 5%. This indicator seems very high, but in fact, combined with Figure 15 The scattering of sample points within the ±5% relative error band reveals that for those data points with relative errors exceeding 5%, their relative errors only slightly exceed 5%, not significantly. Although there are a few sample points with absolute relative errors exceeding 5%, these absolute values ​​are generally small, around 5%, and not exceeding 6%, making this situation completely acceptable. The frequency distribution histogram also clearly shows that the number of sample points with relative errors less than -5% is approximately twice the number of sample points with relative errors greater than +5%. Another intuitive observation is that the number of sample points with relative errors within the range of (-2.5%, 2.5%) accounts for approximately 55% of the test set sample points, while the number of sample points with relative errors within the range of (-5%, 5%) is as high as 85%. These findings further demonstrate that the prediction accuracy of the surrogate model established using the BP neural network in this example fully meets the requirements and effectively characterizes the quantitative relationship between key blade errors and the total pressure loss coefficient.

[0195] Based on the constructed proxy model, the maximum thickness tolerance, leading edge profile tolerance, and torsion angle tolerance are optimized according to the methods from steps S4 to S5. The optimization results are compared with the original tolerance bands as shown in Table 1. The left column of Table 1 shows the optimization results of the sparrow search algorithm under the condition that the total pressure loss coefficient does not increase, the middle column shows the original tolerance ranges of the three errors, and the right column shows the optimization results under the condition that the total pressure loss coefficient of the blade increases by 0.005. As can be seen from Table 1, under the condition that the total pressure loss coefficient does not increase, the optimization result of the lower limit deviation of the maximum thickness is -0.215mm, which is 0.065mm smaller than the original lower limit deviation; the optimization result of the upper limit deviation is +0.183mm, which is 0.033mm larger than the original upper limit deviation. Under the condition that the total pressure loss coefficient does not increase, the optimization result of the lower limit deviation of the leading edge profile tolerance is -0.046mm, which is 0.016mm smaller than the original lower limit deviation, and the optimization result of the upper limit deviation is 0.043mm, which is 0.013mm larger than the original upper limit deviation. Under the condition that the total pressure loss coefficient does not increase, the optimization result of the lower limit deviation of the torsion angle is -0.272°, which is 0.022° smaller than the original lower limit deviation, and the optimization result of the upper limit deviation of the torsion angle is 0.419°, which is 0.169° larger than the original upper limit deviation. In this embodiment, when establishing a proxy model for the key machining error of the blade - aerodynamic performance, since the leading edge profile error is a profile error, and the maximum thickness error and the torsion angle error are characteristic parameter errors, the inputs related to the leading edge profile error in the proxy model are the upper and lower limit deviations of the leading edge profile, which represent the profile error range of the leading edge of the blade's two-dimensional profile. When optimizing blade tolerances, we previously discussed the relationship between the three optimization variables and the four inputs of the surrogate model for the upper and lower limit deviations. Therefore, for the leading edge profile tolerance, the optimization result should be the smaller of the upper and lower limit deviations. Therefore, assuming the total pressure loss coefficient remains constant, the tolerance optimization result for the leading edge profile error should be [-0.043mm, +0.043mm].

[0196] Table 1

[0197]

[0198] In order to more intuitively compare the optimization effects of the three tolerance ranges, Figure 16-Figure 18 The comparison results of the original tolerance range and the optimized tolerance range are given. Figure 16It can be seen that in the maximum thickness error data of the cross section of the 38 blades measured in this paper with a spanwise blade height of 352.742 mm, 10 data points fell outside the original tolerance range, of which 6 exceeded the original upper limit deviation and 4 exceeded the lower limit deviation. If the maximum thickness tolerance optimization results of this paper without losing aerodynamic performance are used as a reference, then only 4 data points fall outside the optimization tolerance range, that is, only 4 blades will fail due to the maximum thickness error exceeding the tolerance, and the tolerance rate of the maximum thickness error of the blade has decreased by 15.77%. In addition, it can be seen intuitively that the optimization effect of the lower limit deviation of the maximum thickness is better than that of the upper limit deviation. After further investigation, this embodiment believes that it is still related to the trend of the influence of the maximum thickness error on the total pressure loss coefficient of the blade. Combined with the optimization results under the condition of a total pressure loss coefficient increase of 0.005 given in the rightmost column of Table 1 and Figure 16 Judging from the distribution of the sample data points, if an increase of 0.005 in the total pressure loss coefficient is acceptable, then at least 80% of the maximum thickness error out-of-tolerance problem can be solved. That is, among all 10 out-of-tolerance data points, at least 8 blades will be transformed from unqualified to qualified due to the relaxation of the maximum thickness tolerance range.

[0199] Analyze the optimization results of the leading edge profile tolerance from the same perspective. Figure 17 It can be seen that when the original leading edge profile tolerance range is used to constrain the 38 leading edge profile error maximum measurement data points, 21 leading edge profile error maximum measurement data points fall outside the original tolerance range. Figure 18 It can be seen that when the original leading edge profile tolerance range is used to constrain the 38 minimum leading edge profile error data points, 16 of the minimum leading edge profile error data points fall outside the original tolerance range. The resulting deviation rates are 55.26% and 42.11%, respectively. If the optimization results of the leading edge profile tolerance [-0.043mm, +0.043mm] in this paper, without increasing the total pressure loss coefficient, are used as the evaluation criteria, the deviation rates are 23.68% and 15.79%, respectively, which are decreases of 31.58% and 26.32%, respectively. Figure 17 and 18 It can also be seen that, using the optimized tolerance range as the evaluation index, among the data points with the maximum value of the leading edge profile error, only one data point is smaller than the lower limit deviation of the leading edge profile, and among the data points with the minimum value of the leading edge profile error, only one data point is larger than the lower limit deviation of the leading edge profile.

[0200] Figure 19 The optimization results of the torsion angle tolerance without loss of aerodynamic performance are given in this paper. Figure 19It can be clearly seen that among the 38 torsion angle error data points, 13 data points are scattered outside the original torsion angle tolerance range, of which 7 data points exceed the original upper limit deviation, and 6 exceed the original lower limit deviation. Taking the optimized tolerance range as the upper and lower constraint limits, there are only 7 error data points that are out of tolerance, of which two exceed the optimized upper limit deviation and 5 are lower than the lower limit deviation. This shows that the optimization result of this embodiment is more effective in solving the problem of upper limit deviation out of tolerance. The reason for this phenomenon may be related to the trend of the blade total pressure loss coefficient decreasing with the increase of the torsion angle error. Overall, the optimized torsion angle tolerance range under the condition that the total pressure loss coefficient does not increase can reduce the out-of-tolerance rate from 34.21% to 18.42%, and the out-of-tolerance rate has decreased by 15.79%. Combined with the optimization results of the torsion angle tolerance under the condition that the total pressure loss coefficient increases by 0.005 given in Table 1 and Figure 19 Judging from the distribution of the mean error data, if an increase of 0.005 in the total pressure loss coefficient is acceptable, the deviation rate can be reduced to 7.89%.

[0201] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for optimizing the critical tolerances of aero-engine compressor blades, characterized in that: include: Obtaining machining error data of key machining errors of the compressor blade, and obtaining a maximum tolerance deviation coefficient corresponding to each tolerance based on a distribution range of the machining error data of each key machining error and a corresponding original tolerance range; Based on the full factor method, all machining error combinations of all key machining error types are designed and error blade profiles corresponding to the error combinations are constructed. At the same time, CFD numerical simulation is performed to obtain the total pressure loss coefficient value of the error blade profile under each machining error combination for all key machining error types. A neural network is constructed, each combination of all key machining errors is used as the input of the neural network, and the total pressure loss coefficient value of the error blade corresponding to each machining error combination is used as the output of the neural network. The neural network is trained to obtain a trained machining error-aerodynamic performance proxy model; The out-of-tolerance range is obtained based on the error range and tolerance range of the machining error number of each key machining error, a target data is randomly selected from each out-of-tolerance range to form the target input data, and the target input data is input into the proxy model to obtain the target aerodynamic loss coefficient value; each data is selected from the original tolerance range of each key machining error to form a group of original data, and the proxy model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data; the constraint violation function is obtained based on the target aerodynamic loss coefficient value and the maximum aerodynamic loss coefficient value, and the fitness function is constructed based on the constraint violation function, the maximum tolerance offset coefficient corresponding to each tolerance, and the target input data; Taking the target input data as the optimization target, the target input data is optimized based on the fitness function and the sparrow search algorithm until the fitness function value is minimized. The final tolerance range of each key machining error is obtained according to the target input data corresponding to the minimum fitness function value.

2. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 1, characterized in that: The key processing errors include: maximum thickness error, maximum leading edge profile error, minimum leading edge profile error and torsion angle error.

3. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 1, characterized in that: The steps to obtain the maximum tolerance deviation coefficient corresponding to each tolerance are: The ratio of the maximum limit value of the distribution range of the machining error data of each key machining error to the maximum limit value of the corresponding tolerance range is used as a first ratio; The ratio of the minimum limit value of the distribution range of the machining error data of each key machining error to the minimum limit value of the corresponding tolerance range is used as a second ratio; The maximum value of the absolute value of the first ratio and the absolute value of the second ratio is taken as the maximum tolerance deviation coefficient.

4. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 2, characterized in that: Based on the full factor method, all machining error combinations of all key machining errors are designed and the error blade profiles of the corresponding error combinations are constructed. At the same time, CFD numerical simulation is performed to obtain the total pressure loss coefficient value of the error blade profile under each machining error combination for all key machining error types. The steps are as follows: Setting error sampling values ​​for different types of key machining errors according to the distribution range of error data; The original design blade profile is constructed using the NURBS method and the contour curve is discretized. The error value of each type of key processing error is inserted into the discrete points of the corresponding area. The discrete points are then fitted using the NURBS method to obtain the error blade profile. By performing CFD numerical simulation on the error blade profile, the total pressure loss coefficient of the error blade profile under different error sampling value combinations of all key machining error types is obtained.

5. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 4, characterized in that: The steps for inserting the error sampling values ​​corresponding to each type of key machining error into the original design blade profile to fit the error blade profile are as follows: Discretize the contour curve of the maximum thickness area of ​​the original designed blade to obtain discrete points; Determine the error value at the maximum thickness position, use the Hanning window function as a weighting function to weight the error value, and insert the weighted error value into the discrete points on both sides of the maximum thickness position in the maximum thickness area; The distribution range of the error data of the leading edge profile is from the minimum value of the leading edge profile to the maximum value of the leading edge profile; Generate random error data that obeys normal distribution within the distribution range of error data of leading edge profile according to the number of discrete points in the leading edge profile area; The generated random error data are sequentially added to the discrete point positions corresponding to the leading edge contour area; After inserting the maximum thickness error and leading edge profile error at discrete points in the corresponding area, the insertion of the torsion angle error can be achieved by changing the angle of attack of the blade, and the contour curve of the error blade is obtained by fitting the NURBS method.

6. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 5, characterized in that: The chord length areas before and after the maximum thickness position are taken as the maximum thickness area.

7. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 1, characterized in that: The steps for obtaining the out-of-tolerance range based on the error range and tolerance range of the machining error number of each key machining error are as follows: The maximum limit value of the tolerance range to the maximum limit value of the error range is taken as the maximum limit value deviation range; The minimum limit value of the error range to the minimum limit value of the tolerance range is taken as the minimum limit value deviation range.

8. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 1, characterized in that: The expression of the constraint violation function is: Where, Represents the constraint violation function value; Indicates that the target input data is The target aerodynamic loss coefficient value output by the proxy model when ; It means that one data set is selected from the original tolerance range of each key processing error to form a group of original data, and the agent model is used to obtain the maximum aerodynamic loss coefficient value among the aerodynamic loss coefficient values ​​corresponding to all groups of original data.

9. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 1, characterized in that: The expression of the fitness function is: Where, represents the fitness function value; The maximum tolerance deviation factor indicating the maximum thickness error; Indicates the maximum tolerance deviation factor of the leading edge profile error; Indicates the maximum tolerance deviation factor of the torsion angle error; Target data indicating the maximum thickness error range selection; Target data representing the selected tolerance range of the leading edge profile error; Indicates target data for selecting the tolerance range of the torsion angle error; Expressed as a penalty factor; represents the constraint violation function value, Indicates taking the absolute value.

10. The method for optimizing critical tolerances of aero-engine compressor blades according to claim 9, characterized in that: The steps to obtain the final tolerance range based on the target input data corresponding to the minimum fitness function value are: According to the target data corresponding to the maximum thickness error tolerance range in the target input data corresponding to the minimum fitness function value, the final tolerance range of the maximum thickness tolerance is obtained; The target data corresponding to the tolerance range of the leading edge profile error in the target input data corresponding to the minimum fitness function value is used to obtain the final tolerance range of the leading edge profile tolerance; The target data corresponding to the tolerance range of the torsion angle error in the target input data corresponding to the minimum fitness function value is used to obtain the final tolerance range of the torsion angle tolerance.

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