Collaborative Optimization Method for Machining Parameters of Aeroengine Compressor Blades in Multiple Processes

Abstract

The present invention discloses a method for collaborative optimization of multi-process machining parameters of aero-engine compressor blades, including: Step 1: Calculate the upper 0.01 quantile of the maximum value distribution of the rough machining profile error; Step 2: Establish an optimization model; Step 3: Use the multi-objective dung beetle optimization algorithm to solve the optimization model to obtain a Pareto solution set; Step 4: Screen out a candidate set of machining parameters from the Pareto solution set according to the selection conditions; Step 5: Calculate the relative closeness of the candidate set to the ideal solution, and select the machining parameters corresponding to the maximum value of the relative closeness as the multi-process machining parameters of the compressor blade; The present invention not only reasonably optimizes the machining error and efficiency of finish machining, but also can reasonably optimize the machining error and efficiency of semi-finish machining, reduce the error transmission and accumulation amount, and improve the machining efficiency under the condition of ensuring the finish machining accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of blade processing, and particularly relates to a method for collaborative optimization of multi-process machining parameters of aero-engine compressor blades. Background Art

[0002] With the rapid development of the aviation industry towards high thrust-to-weight ratio, long life, and low emissions, the design complexity of compressor blades has been significantly improved. High-temperature alloys, titanium alloys and other difficult-to-machine materials are commonly used, and they show structural characteristics of large twist angles, thin walls, and asymmetric curved surfaces. In addition, the accuracy requirements for compressor blades are more stringent. Such characteristics lead to particularly prominent problems of error accumulation caused by process parameter mismatch in multi-process collaborative machining. By collaboratively optimizing the machining parameters of the semi-finishing process and the finishing process of the compressor blade, the error transmission can be significantly reduced, and the accuracy and consistency of the final product can be improved. Therefore, in the case of the increasing demand for high-performance and high-reliability components, how to shorten the production cycle and reduce the production cost while ensuring the machining accuracy has become an urgent problem to be solved in the manufacturing field.

[0003] Although there are already various methods and technologies to control the machining errors and improve the machining efficiency of compressor blades from the aspect of optimizing machining parameters, there are still the following deficiencies:

[0004] (1) The traditional methods for optimizing machining parameters mainly rely on empirical methods and professional knowledge, lacking systematic mathematical models and optimization methods, resulting in insufficient scientificity and accuracy of parameter optimization, which limits the optimization scope and may hinder the best machining performance.

[0005] (2) The existing machining parameter optimization mainly adopts a phased and independent optimization method, and most of them focus on the local parameter adjustment of a single process of the compressor blade, especially the finishing process, ignoring the mutual influence between the machining parameters of multiple processes. In the actual production process, multiple machining stages often work together, and the parameters between different processes influence each other. The above deficiencies directly lead to problems such as low machining accuracy, long machining cycle, and low efficiency of compressor blades. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for collaborative optimization of multi-process machining parameters of aero-engine compressor blades to solve the problems of low machining accuracy, long machining cycle, and low efficiency of compressor blades.

[0007] The present invention adopts the following technical solutions: A method for collaborative optimization of multi-process machining parameters of aero-engine compressor blades, including:

[0008] Step 1: Under the same rough machining parameters, count the maximum value of the rough machining profile errors of multiple compressor blades, and calculate the upper 0.01 quantile of the distribution of the maximum value of the rough machining profile errors;

[0009] Step 2: Establish an optimization model with the minimum value of the total processing time of semi-finishing and finishing, the profile error of finishing, the leaf profile position error of finishing, and the leaf profile twist angle error of finishing as the objective function, the maximum profile error of rough machining being equal to the upper 0.01 quantile of Step 1 as the constraint, and the value range of the processing parameters of semi-finishing and finishing as the constraint;

[0010] Step 3: Solve the optimization model using the multi-objective dung beetle optimization algorithm to obtain the Pareto solution set;

[0011] Step 4: Screen out the candidate set of processing parameters from the Pareto solution set according to the selection conditions;

[0012] Step 5: Calculate the relative closeness of the candidate set to the ideal solution, and select the processing parameters corresponding to the maximum relative closeness as the multi-process processing parameters of the compressor blade.

[0013] Furthermore, the optimization model in Step 2 is:

[0014] ;

[0015] In the formula, δ c is the profile error of the compressor blade finishing, δ p is the leaf profile position error of the compressor blade finishing, δ t is the leaf profile twist angle error of the compressor blade finishing; t is the total processing time of semi-finishing and finishing; δ r is the profile error of the compressor blade rough machining, is the cutting depth of semi-finishing, is the minimum allowable value of the cutting depth of semi-finishing, is the maximum allowable value of the cutting depth of semi-finishing, is the feed per tooth of semi-finishing, is the minimum allowable value of the feed per tooth of semi-finishing, is the maximum allowable value of the feed per tooth of semi-finishing, n s is the spindle speed of semi-finishing, n s(min) is the minimum allowable value of the spindle speed of semi-finishing, n s(max) is the maximum allowable value of the spindle speed of semi-finishing; is the cutting depth of finishing, The minimum value allowed for the cutting depth of finish machining, The maximum value allowed for the cutting depth of finish machining, The feed per tooth of finish machining, The minimum value allowed for the feed per tooth of finish machining, The maximum value allowed for the feed per tooth of finish machining, The spindle speed of finish machining, The minimum value allowed for the spindle speed of finish machining, The maximum value allowed for the spindle speed of finish machining; The upper 0.01 quantile of the maximum value distribution of the rough machining profile error of the compressor blade.

[0016] Furthermore, the selection conditions in step 4 include:

[0017] δ c ∈[0.8×T c-min , 0.8×T c-max ;

[0018] δ p ∈[0.8×T p-min , 0.8×T p-max ;

[0019] δ t ∈[0.8×T t-min , 0.8×T t-max ;

[0020] where, [T c-min , T c-max is the profile tolerance range of the compressor blade finish machining, [T p-min , T p-max is the position tolerance range of the compressor blade finish machining, [T t-min , T t-max is the twist angle tolerance range of the compressor blade finish machining.

[0021] Furthermore, the selection conditions in step 4 also include:

[0022] t ≤ t q ; where, t q is the total machining time of semi-finish machining and finish machining in empirical parameter machining.

[0023] Furthermore, the formula for calculating the upper 0.01 quantile of the maximum value distribution of the rough machining profile error in step 1 is:

[0024] ,

[0025] wherein, F (·) is the cumulative distribution function; is the value of the maximum of the rough machining profile error of the compressor blade; is the adaptive bandwidth kernel density estimation function; α = 0.01.

[0026] The beneficial effects of the present invention are:

[0027] The present invention not only reasonably optimizes the machining error and efficiency of finish machining, but also can reasonably optimize the machining error and efficiency of semi-finish machining, reduce the error transmission and accumulation amount, and improve the machining efficiency under the condition of ensuring the finish machining accuracy;

[0028] When the maximum error of the rough machining profile is equal to the 0.01 quantile of the above in step 1, the present invention optimizes the process parameters of semi-finish machining and finish machining, which can improve the robustness of the subsequent semi-finish machining and finish machining processes; even if the actual rough machining error fluctuates, the optimized machining parameters can still ensure the stability and reliability of the subsequent machining processes, neither affecting the production efficiency nor obtaining better finish machining accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a statistical analysis diagram of the maximum of the rough machining profile errors of 44 compressor blades in the embodiment of the present invention;

[0030] Figure 2 is a three-dimensional Pareto front diagram in the embodiment of the present invention ( δ p - δ c - t );

[0031] Figure 3 is a three-dimensional Pareto front diagram in the embodiment of the present invention ( δ t - δ c - t );

[0032] Figure 4 is a projection diagram of the collaborative optimization result of the machining parameters in the embodiment of the present invention on the δ c - t plane;

[0033] Figure 5 is a projection diagram of the collaborative optimization result of the machining parameters in the embodiment of the present invention on the δ p - tProjection diagram on a plane;

[0034] Figure 6 For the collaborative optimization result of the machining parameters in the embodiment of the present invention in δ t - t Projection diagram on a plane. Specific implementation manner

[0035] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0036] The present invention discloses a method for collaborative optimization of multi-process machining parameters of aero-engine compressor blades, including:

[0037] Step 1: Under the same rough machining parameters, statistically calculate the maximum value of the rough machining profile error of multiple compressor blades, and calculate the upper 0.01 quantile of the distribution of the maximum value of the rough machining profile error.

[0038] First, conduct a multi-axis milling experiment on superalloy compressor blades under the same rough machining parameters, and obtain the maximum value of the rough machining profile error of each blade through a coordinate measuring instrument.

[0039] Secondly, use the Gaussian kernel as the kernel function and adopt an adaptive bandwidth kernel density estimation function to perform probability density modeling on the rough machining profile error of the compressor blades.

[0040] Among them, the fixed bandwidth kernel density estimation function is:

[0041]

[0042] In the formula, is the maximum value of the rough machining profile error of the th compressor blade; n is the number of compressor blades; K (·) is the Gaussian kernel function; h MISE is the fixed bandwidth.

[0043]

[0044] In the formula, σ is the standard deviation of the rough machining profile error data of the compressor blades.

[0045] The adaptive bandwidth kernel density estimation function (AKDE) is obtained by modifying the bandwidth parameter on the basis of the fixed bandwidth kernel density estimation function, and its bandwidth is:

[0046]

[0047] In the formula, is the bandwidth at the th estimation point, is the local bandwidth factor, is the kernel density estimate value at the -th estimated point obtained from the fixed bandwidth kernel density estimation, and 0 ≤ β ≤ 1 is the sensitivity factor.

[0048] Then, using the Gaussian kernel as the kernel function, an adaptive bandwidth kernel density estimation function is adopted to perform probability density modeling on the rough machining profile error of the compressor blade, specifically as follows:

[0049]

[0050] Finally, according to the principle of small probability events (α = 0.01), the upper 0.01 quantile of the maximum value distribution of the rough machining profile error of the compressor blade is calculated according to the following formula, denoted as ; then the maximum error of the rough machining profile of the compressor blade is taken to be equal to .

[0051]

[0052] In the formula, is the value of the maximum value of the rough machining profile error of the compressor blade, F (·) is the cumulative distribution function.

[0053] In the prior art, although the empirical method based on sample statistics can also obtain the maximum value of the rough machining profile error of the compressor blade, it has significant limitations, that is, the finite samples cannot exhaust the extreme working conditions in actual production, resulting in an unreasonable maximum value of the obtained rough machining profile error. Compared with the traditional empirical method based on sample statistics, the prediction method of the maximum value of the rough machining profile error based on the combination of the adaptive kernel density estimation function and the principle of small probability events has significant theoretical and practical advantages.

[0054] From the perspective of statistical modeling, by constructing the error probability distribution through non-parametric kernel density estimation, the multi-modal, asymmetric and heavy-tailed characteristics of the actual machining error can be accurately characterized without presetting a parameter model, while the empirical method can only provide the extreme value statistics of finite samples and cannot represent potential unobserved error values.

[0055] In terms of maximum value prediction, based on the principle of small probability events, the upper limit of the error under a given confidence level (such as 99.9%) is calculated. Its mathematical essence is to solve the tail integral equation of the probability density function, which has a strict probability interpretation; while the empirical method can only obtain the maximum value of historical samples, which can neither quantify the confidence level nor reflect the statistical distribution characteristics of the process system, and the maximum value of the statistically obtained rough machining profile error will change with the samples. When the number of samples increases, the maximum value obtained by the empirical method will change.

[0056] At the engineering application level, it is possible to reliably predict the maximum value of the contour error of the rough machined compressor blade under the condition of limited samples (n≥30), and its prediction accuracy is significantly better than that of traditional empirical methods; in contrast, empirical rules based on sample statistics require a large amount of sample data (n≥300) to achieve comparable prediction accuracy.

[0057] Step 2: Taking the total machining time of semi-finishing and finishing, the minimum values of the contour error, the profile position error, and the profile twist angle error of the finishing as the objective function, taking the maximum contour error of the rough machining equal to the 0.01 quantile of the upper limit in Step 1 as the constraint, and taking the value ranges of the machining parameters of semi-finishing and finishing as the constraints to establish an optimization model.

[0058] First, conduct milling experiments on the semi-finishing and finishing of compressor blades, and establish a prediction model for the semi-finishing error of compressor blades using the single-output Gaussian process regression method, specifically:

[0059]

[0060] In the formula, δ s is the contour error of the semi-finishing of the compressor blade, δ r is the contour error of the rough machining of the compressor blade, is the cutting depth of the semi-finishing, is the feed per tooth of the semi-finishing, n s is the spindle speed of the semi-finishing.

[0061] Secondly, establish a prediction model for the finishing error of compressor blades using the multi-output Gaussian process regression method, specifically:

[0062]

[0063] In the formula, δ n are the contour error, the profile position error, and the profile twist angle error of the finishing; δ c is the contour error of the finishing of the compressor blade, δ p is the profile position error of the finishing of the compressor blade, δ t is the profile twist angle error of the finishing of the compressor blade, δ s is the contour error of the semi-finishing of the compressor blade, is the cutting depth of the finishing, is the feed per tooth of the finishing, The spindle speed for finish machining.

[0064] The total machining time for semi-finish machining and finish machining of the compressor blade is specifically expressed as:

[0065]

[0066] In the formula, z is the number of teeth of the cutting tool, is the cutting width for semi-finish machining, is the cutting width for finish machining, H is the height of the compressor blade airfoil, S is the perimeter of the two-dimensional cross-section of the compressor blade.

[0067] Finally, an optimization model is established according to the constraint conditions and the objective function:

[0068]

[0069] In the formula, δ c is the profile error of the compressor blade during finish machining, δ p is the profile position error of the compressor blade during finish machining, δ t is the profile twist angle error of the compressor blade during finish machining; t is the total machining time for semi-finish machining and finish machining; δ r is the profile error of the compressor blade during rough machining, is the cutting depth for semi-finish machining, is the minimum value allowed for the cutting depth of semi-finish machining, is the maximum value allowed for the cutting depth of semi-finish machining, is the feed per tooth for semi-finish machining, is the minimum value allowed for the feed per tooth of semi-finish machining, is the maximum value allowed for the feed per tooth of semi-finish machining, n s is the spindle speed for semi-finish machining, n s(min) is the minimum value allowed for the spindle speed of semi-finish machining, n s(max) is the maximum value allowed for the spindle speed of semi-finish machining; is the cutting depth for finish machining, is the minimum value allowed for the cutting depth of finish machining, is the maximum value allowed for the cutting depth of finish machining, is the feed per tooth for finish machining, is the minimum value allowed for the feed per tooth of finish machining, The maximum value allowed for the feed per tooth in finish machining, The spindle speed in finish machining, The minimum value allowed for the spindle speed in finish machining, The maximum value allowed for the spindle speed in finish machining; x 0.01 The upper 0.01 quantile of the maximum distribution of the profile error in rough machining of compressor blades.

[0070] Step 3: Use the multi-objective dung beetle optimization algorithm to solve the optimization model to obtain the Pareto solution set.

[0071] The solution steps are as follows:

[0072] (1) Set the maximum number of iterations T. At the same time, initialize the dung beetle population, determine the number N of dung beetles in the population and their initial positions. A larger population size helps to improve the global search ability of the algorithm and avoid falling into local optimal solutions. In addition, set the maximum capacity A of the external archive to manage non-dominated solutions. The external archive is used to store the currently found non-dominated solutions (Pareto front solutions);

[0073] (2) Evaluate the current position information of the dung beetles according to the given objective function and calculate the fitness value of each dung beetle;

[0074] (3) Perform non-dominated sorting on the dung beetle population to determine the non-dominated rank and crowding distance;

[0075] (4) Update the positions of all dung beetles according to the position update formula of the dung beetle optimization algorithm;

[0076] (5) Update the fitness value of the entire population to reflect the performance change brought by the new position;

[0077] (6) For the updated dung beetle population, obtain new non-dominated solutions and store them in the external archive. Replace some old solutions in the archive to keep the archive updated and diverse, ensuring that the high-quality non-dominated solutions are stored;

[0078] (7) Judge whether the maximum number of iterations has been reached. If so, perform step (8), otherwise return to step (4);

[0079] (8) Output the non-dominated solution set in the external archive as the final result of the algorithm.

[0080] Step 4: Screen out the candidate set of machining parameters from the Pareto solution set according to the selection conditions.

[0081] The profile tolerance for finish machining of compressor blades is [T c-min , T c-max, the profile position tolerance for the finish machining of the compressor blade is [T p-min , T p-max , and the profile twist angle tolerance for the finish machining of the compressor blade is [T t-min , T t-max . To ensure that the final machining accuracy of the compressor blade meets the design requirements, it is necessary to exclude those machining parameters whose machining errors exceed the design tolerances. Considering the possible uncertainties in the machining process, a safety factor of 0.8 is introduced.

[0082] Therefore, the selection conditions are: δ c ∈ [0.8×T c-min , 0.8×T c-max , δ p ∈ [0.8×T p-min , 0.8×T p-max , δ t ∈ [0.8×T t-min , 0.8×T t-max . t ≤ t q ; where, t q is the total machining time for semi-finish machining and finish machining in the empirical parameter machining.

[0083] Step 5: Calculate the relative closeness degree between the candidate set and the ideal solution, and select the machining parameters corresponding to the maximum relative closeness degree as the multi-process machining parameters for the compressor blade.

[0084] Calculate the weights of the blade profile error, blade profile position error, blade profile twist angle error, and machining time respectively using the Entropy Weight Method and the Criteria Importance Through Intercriteria Correlation method; then, obtain the combined weight based on the principle of minimum discrimination information; finally, use the Technique for Order Preference by Similarity to Ideal Solution method to calculate the relative closeness degree between each candidate set and the ideal solution, and select the machining parameters corresponding to the maximum relative closeness degree as the multi-process machining parameters for the compressor blade.

[0085] Example 1: Taking a specific compressor blade of an aero-engine as an example, a cuboid block is used as the blank of the blade, and the material is GH4169G. 44 groups of experiments are carried out for rough machining and semi-finishing machining, and 35 groups of experiments are carried out for finishing machining. After rough machining of the compressor blade, a coordinate measuring machine is used for measurement to obtain its rough machining profile error. Then semi-finishing machining is carried out. The process parameters of semi-finishing machining (one cutting layer) are shown in Table 1. After semi-finishing machining, a coordinate measuring machine is used for measurement to obtain its semi-finishing machining error. Finally, finishing machining is carried out. The process parameters of finishing machining (two cutting layers) are shown in Table 1. After finishing machining, a coordinate measuring machine is used for measurement to obtain its finishing machining error. The milling parameters of semi-finishing machining and finishing machining are shown in Table 1. The machining errors of the blade are statistically analyzed at the position where the blade deformation is the largest, and the experimental data are shown in Tables 2 and 3.

[0086] Table 1 Milling parameters of semi-finishing machining and finishing machining

[0087]

[0088] Table 2 Machining errors of rough machining and semi-finishing machining

[0089]

[0090] Table 3 Machining errors of semi-finishing machining and finishing machining

[0091]

[0092] Based on the rough machining profile errors of 44 groups of compressor blades, is calculated, as shown in Figure 1 . In the figure, the AKDE curve represents the adaptive bandwidth kernel density estimation function curve of the rough machining profile error of the compressor blade. .

[0093] First, taking the rough machining profile error and semi-finishing machining parameters as inputs and the semi-finishing machining profile error as the output, a semi-finishing machining error transfer model is established. Then, taking the semi-finishing machining error and finishing machining parameters as inputs and the finishing machining profile error, position error and twist angle error as the outputs, a finishing machining error transfer model is established. The evaluation indexes of the multi-process machining error prediction model of the compressor blade are shown in Table 4.

[0094] Table 4 Evaluation indexes of the multi-process machining error prediction model

[0095]

[0096] The circumference of the compressor blade is 68.3822 mm, and the overall height of the blade profile is 35.5603 mm. The tools for semi-finishing (one cutting layer) and finishing (two cutting layers) are both 6 mm taper ball end mills. The residual height of semi-finishing is 0.01 mm, the residual height of the first layer of finishing is 0.01 mm, and the residual height of the second layer of finishing is 0.005 mm. Therefore, the cutting width of each cutting layer in semi-finishing and finishing can be calculated. The calculated cutting width of the semi-finishing cutting layer is 0.4895 mm, the cutting width of the first finishing cutting layer is 0.4895 mm, and the cutting width of the second finishing cutting layer is 0.3463 mm. Therefore, the number of cutting rows for semi-finishing is 73, the number of cutting rows for the first layer of finishing is 73, and the number of cutting rows for the second layer of finishing is 103. The cutting length of semi-finishing is 4991.9006 mm, the cutting length of the first layer of finishing is 4991.9006 mm, and the cutting length of the second layer of finishing is 7043.3666 mm. Therefore, the processing time for semi-finishing is:

[0097]

[0098] The processing time for finishing is:

[0099]

[0100] Taking the minimum values of the total processing time of semi-finishing and finishing, the profile error of finishing, the leaf profile position error of finishing, and the leaf profile twist angle error of finishing as the objective function, with the maximum error of rough machining profile equal to the upper 0.01 quantile as the constraint, and the value ranges of the processing parameters of semi-finishing and finishing as the constraints, an optimization model is established:

[0101]

[0102] Set the population size to 100 and the maximum capacity of the external archive to 60. In addition, the maximum number of iterations is set to 200 to fully explore the solution space and improve the convergence of the algorithm. The objective function to be solved contains four, and the dimension of each objective function is 5. By running the program multiple times, a Pareto solution set is generated, as shown in Figure 2 and Figure 3 Some of the solution sets are shown in Table 5.

[0103] Table 5 Partial Pareto front solution sets

[0104]

[0105] The profile tolerance range for the finish machining of the compressor blade is [-0.03 mm, +0.05 mm], the position tolerance range for the finish machining of the compressor blade is [-0.15 mm, +0.15 mm], and the twist angle tolerance range for the finish machining of the compressor blade is [-0.33°, +0.33°]. Therefore, the selection conditions are as follows: δ c Between -0.024 mm and +0.040 mm, δ p Within ±0.12 mm, δ t Within ±0.264°, and t≤ 16.54 min. Therefore, considering both machining accuracy and machining efficiency, three optional machining schemes are determined according to the Pareto front.

[0106] Scheme Ⅰ: δ c Is 0.0358 mm, δ p Is 0.111 mm, δ t Is -0.117°, t Is 16.54 min.

[0107] Scheme Ⅱ: δ c Is 0.0362 mm, δ p Is 0.109 mm, δ t Is -0.115°, t Is 15.54 min.

[0108] Scheme Ⅲ: δ c Is 0.0388 mm, δ p Is 0.112 mm, δ t Is -0.117°, t Is 14.65 min.

[0109] Table 6 lists the relative closeness degrees of the three schemes to the ideal solution. The results show that the relative closeness degree of Scheme Ⅱ to the ideal solution is the highest, indicating that Scheme Ⅱ is the optimal solution. The optimization results are as Figures 4 - 6 shown.

[0110] Table 6 Relative Closeness Degrees of Different Schemes to the Ideal Solution

[0111]

[0112] Table 7 Empirically optimized processing parameters, independently optimized processing parameters, and the processing parameters synergistically optimized in this embodiment

[0113]

[0114] The empirical parameters in Table 7 refer to the processing parameters determined depending on empirical methods and professional knowledge, and the independent optimization refers to the processing parameters determined by an independent optimization method in stages.

[0115] It can be seen from Table 7 that compared with the empirical parameters, the optimization method of this embodiment can make δ c decrease by 28.88%, δ p decrease by 28.29%, δ t decrease by 7.26%, t decrease by 6.05%.

[0116] It can also be seen from Table 7 that compared with the independent optimization, the optimization method of this embodiment can make δ c reduce by 8.12%, δ p decrease by 2.68%, δ t decrease by 0.86%, t decrease by 6.39%.

[0117] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for collaborative optimization of multi-process machining parameters of a compressor blade of an aero-engine, characterized in that, Including: Step 1: Under the same rough machining parameters, count the maximum value of the rough machining profile error of multiple compressor blades, and calculate the upper 0.01 quantile of the distribution of the maximum value of the rough machining profile error; Step 2: Taking the total machining time of semi-finishing and finishing, the profile error of finishing, the profile position error of the blade profile in finishing, and the minimum value of the blade profile twist angle error in finishing as the objective function, with the maximum rough machining profile error equal to the upper 0.01 quantile of Step 1 as the constraint, and with the value range of the machining parameters of semi-finishing and finishing as the constraints, establish an optimization model; Step 3: Use the multi-objective dung beetle optimization algorithm to solve the optimization model to obtain a Pareto solution set; Step 4: Screen out the candidate set of machining parameters from the Pareto solution set according to the selection conditions; Step 5: Calculate the relative closeness of the candidate set to the ideal solution, and select the machining parameters corresponding to the maximum relative closeness as the multi-process machining parameters of the compressor blade.

2. The collaborative optimization method for multi-process machining parameters of an aero-engine compressor blade according to claim 1, characterized in that The optimization model in Step 2 is: ， In the formula, δ c is the profile error of the compressor blade during finish machining, δ p is the profile position error of the compressor blade during finish machining, δ t is the profile twist angle error of the compressor blade during finish machining; t is the total machining time of semi-finish machining and finish machining; δ r is the profile error of the compressor blade during rough machining, is the cutting depth of semi-finish machining, is the minimum allowable value of the cutting depth of semi-finish machining, is the maximum allowable value of the cutting depth of semi-finish machining, is the feed per tooth of semi-finish machining, is the minimum allowable value of the feed per tooth of semi-finish machining, is the maximum allowable value of the feed per tooth of semi-finish machining, n s is the spindle speed of semi-finish machining, n s(min) is the minimum allowable value of the spindle speed of semi-finish machining, n s(max) is the maximum allowable value of the spindle speed of semi-finish machining; is the cutting depth of finish machining, is the minimum allowable value of the cutting depth of finish machining, is the maximum allowable value of the cutting depth of finish machining, is the feed per tooth of finish machining, is the minimum allowable value of the feed per tooth of finish machining, is the maximum allowable value of the feed per tooth of finish machining, is the spindle speed of finish machining, is the minimum allowable value of the spindle speed of finish machining, is the maximum allowable value of the spindle speed of finish machining; is the upper 0.01 quantile of the maximum value distribution of the profile error of the compressor blade during rough machining.

3. The collaborative optimization method for multi-process machining parameters of an aero-engine compressor blade according to claim 2, wherein, The selection conditions in Step 4 include: δ c ∈[0.8×T c-min , 0.8×T c-max ; δ p ∈ [0.8×T p-min , 0.8×T p-max ; δ t ∈ [0.8×T t-min , 0.8×T t-max ; Among them, [T c-min , T c-max is the profile tolerance range for the finish machining of the compressor blade, [T p-min , T p-max is the position tolerance range for the finish machining of the compressor blade, and [T t-min , T t-max is the twist angle tolerance range for the finish machining of the compressor blade.

4. The collaborative optimization method for multi-process machining parameters of an aero-engine compressor blade according to claim 3, wherein, The selection conditions in Step 4 also include: t ≤ t q ; wherein, t q is the total processing time for semi-finishing and finishing in the empirical parameter processing.

5. The collaborative optimization method for multi-process machining parameters of an aero-engine compressor blade according to claim 1, wherein The formula for calculating the upper 0.01 quantile of the distribution of the maximum value of the rough machining profile error in Step 1 is: ， In the formula, F (·) is the cumulative distribution function; is the value of the maximum of the rough machining profile error of the compressor blade; is the adaptive bandwidth kernel density estimation function; α = 0.01.

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