Three-dimensional sorting method and system for aero-engine blades with high aspect ratio

Abstract

The invention discloses a high-aspect-ratio aero-engine blade three-dimensional sorting method and system, and relates to the technical field of aero-engine vibration optimization, and the method comprises the steps: collecting the measurement data of aero-engine blades; establishing a Cartesian coordinate system according to the measurement data, mapping engine axis and engine blade distribution on the coordinate system, and determining a vector direction; establishing a multi-objective function of the unbalanced state of the aero-engine blade; the multi-objective function is solved through multiple heuristic algorithms, and aero-engine blades are sequenced; and screening to obtain a final sorting result. According to the method, a multi-objective optimization function is adopted, multiple objectives are taken as optimization directions, and multiple heuristic algorithms are combined to sort the aero-engine blades, so that reasonable blade sorting and mass distribution are realized, unbalanced moments in all directions are effectively counteracted or reduced, and the quality of the aero-engine blades is improved. Therefore, the vibration and the load generated in the operation process of the engine are kept within an acceptable range, and the stability and the performance of the engine are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of aeroengine vibration optimization, and more particularly to a three-dimensional sorting method and system for aeroengine blades with a large aspect ratio. Background Technique

[0002] During the high-speed rotation of the blades, they are affected by strong centrifugal forces. Since there is always unbalanced mass in the engine rotor, it will cause vibrations during the operation of the engine. The greater the unbalanced mass, the greater the vibration. If the vibration is too large, it will cause a rapid decline in the performance of the engine in the lightest case, and in the most serious case, it can cause damage to the engine bearings and blade fracture, thus affecting aviation safety. In order to improve the stability and efficiency of the engine, the magnitude of the unbalanced force can be reduced by reasonably distributing the blade arrangement, optimizing its dynamic performance, and thus reducing the engine vibration. With the progress of computing technology and the development of optimization algorithms, multi-objective optimization methods have gradually become an important tool for solving the blade sorting problem. By comprehensively considering multiple objectives, an optimal or approximate optimal blade sorting scheme can be found under complex constraint conditions, thereby improving the performance and stability of the engine.

[0003] Balance adjustment and blade sorting are two main methods for effectively reducing the unbalanced force of aeroengine blades. They ensure that the engine reaches balance as much as possible during operation by optimizing the mass and position distribution of the blades or adding or subtracting appropriate counterweights at special parts of the rotor, thereby reducing vibration and improving stability and efficiency. Dynamic balance adjustment refers to measuring the unbalance amount of the blades or rotor during rotation by dynamic testing (such as using a dynamic balance instrument or vibration sensor). At this time, the centrifugal force and vibration data caused by uneven mass are recorded, the position and magnitude of the unbalance are determined, and according to the test results, a small amount of mass is added or removed to adjust the mass distribution of the rotating system and reduce the magnitude of the unbalance of the entire rotor, achieving the purpose of reducing vibration. For example, a counterweight can be added to a certain part of the rotor, or the counterweight can be reduced at other positions, and this process is repeated until all blades reach the expected balanced state during rotation. This method is accurate and effective, but its applicable scenarios are limited. Especially for engines in the installed state, the process of changing the balance state by adding or subtracting counterweights is relatively complex. Therefore, this method is mainly applicable to the case of single blade or less blade unbalance.

[0004] Blade sorting refers to arranging the positions of blades reasonably so that the mass unbalance forces between the blades cancel each other out, thereby reducing the magnitude of the unbalance force acting on the engine during operation. This method first analyzes the mass of all blades in a certain stage in detail, measures the mass, mass center, radial mass-radius product, axial mass moment, and tangential mass moment of each blade, and then calculates the arrangement order that meets the criteria of the objective function based on the mass distribution and mass moment of each blade through a mathematical model or optimization algorithm. This method is usually applicable to scenarios where the masses of multiple blades in a certain stage of the engine are uneven due to manufacturing and processing. However, blade sorting involves a large amount of calculations. Especially when dealing with complex mass distributions, advanced optimization algorithms such as genetic algorithms and ant colony algorithms, which are heuristic algorithms, need to be used. However, the blade sorting algorithms also have the problem that the dependent constraint conditions (i.e., the objective function) are relatively single. For example, the blade sorting method based only on the magnitude of the radial mass-radius product has poor adaptability to wide blades, and the calculation results cannot minimize the unbalance caused by unreasonable blade distribution as much as possible.

[0005] Therefore, how to propose a three-dimensional sorting method and system for blades of a high aspect ratio aeroengine, through a multi-objective optimization algorithm, comprehensively considering multiple factors such as the mass distribution of the blades, moment balance, and vibration minimization, optimizing the sorting order of the blades, so as to effectively reduce the total unbalance of the blades and ensure that the engine vibration remains within an acceptable range is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a three-dimensional sorting method and system for blades of a high aspect ratio aeroengine. Through a multi-objective optimization algorithm, comprehensively considering multiple factors such as the mass distribution of the blades, moment balance, and vibration minimization, optimizing the sorting order of the blades, so as to effectively reduce the total unbalance of the blades and ensure that the engine vibration remains within an acceptable range. To achieve the above object, the present invention adopts the following technical solutions:

[0007] A three-dimensional sorting method for blades of a high aspect ratio aeroengine includes:

[0008] Collect measurement data of the blades of the aeroengine;

[0009] Establish a Cartesian coordinate system according to the measurement data, map the engine axis and the blade distribution of the engine on the coordinate system, and determine the vector direction;

[0010] After determining the vector direction, establish a multi-objective function for the unbalanced state of the blades of the aeroengine;

[0011] Solve the multi-objective function through a variety of heuristic algorithms to sort the blades of the aeroengine;

[0012] Screen the sorting results of multiple aero-engine blades to obtain the final sorting results.

[0013] Optionally, the measurement data of the aero-engine blades include: obtaining and recording the radial mass-radius product R, tangential mass moment T, and axial mass moment A of each aero-engine blade through measurement, looking up and recording the calculated axial distance of the aero-engine blade, measuring and recording the angle θ between adjacent blades centered on the rotation axis, and the number n of aero-engine blades.

[0014] Optionally, establish a Cartesian coordinate system based on the measurement data, map the engine axis and the distribution of engine blades on the coordinate system, and determine the vector direction as follows: establish a Cartesian coordinate system, make the engine axis coincide with the Z-axis, and the engine blades are distributed on the OXY plane. Determine the direction of the centroid of the blade relative to the rotation axis as the direction of the radial mass-radius product vector; the direction tangent to the circumference as the vector direction of the tangential mass moment; and define the direction along the engine axis from the compressor end to the turbine end as the positive axial direction with the engine axis as the reference to obtain the direction of the axial mass moment.

[0015] Optionally, the multi-objective function for establishing the unbalanced state of the aero-engine blades includes: the radial unbalance, the radial unbalance caused by the axial torque, the unbalance considering the combination of the radial mass-radius product and the tangential mass moment, and the maximum value among the differences in the radial mass-radius products of each pair of blades.

[0016] Optionally, the radial unbalance includes:

[0017] Decompose the radial mass-radius product into x and y direction components and sum them:

[0018]

[0019] Calculate the vector sum of the radial mass-radius product:

[0020]

[0021] Optionally, the radial unbalance caused by the axial torque includes:

[0022]

[0023] Calculate the radial unbalance C2 caused by the axial torque;

[0024]

[0025] In the formula, Ar is the axial distance, A x is the component of the blade axial mass moment on the X-axis, and A y is the component of the blade axial mass moment on the Y-axis.

[0026] Optionally, the unbalance quantity considering the combination of the radial mass-radius product and the tangential mass moment includes:

[0027] Decompose the tangential mass moment into x and y direction components and sum them:

[0028]

[0029] Sum the components on the x-axis and y-axis respectively:

[0030]

[0031] Calculate the magnitude of the resultant vector, that is, the unbalance quantity C3, S of the radial and tangential interaction x is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the X-axis, S y is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the Y-axis;

[0032]

[0033] Optionally, the maximum value among the differences in the radial mass-radius products of each pair of blades includes:

[0034] Find the maximum value among the differences in the radial mass-radius products between each pair of blades, and make the maximum value less than the standard, that is, the differences in the radial mass-radius products of each pair of blades will meet the standard conditions:

[0035]

[0036] C4 = max[ΔR i ;

[0037] where C4 is the maximum value of the differences in the radial mass-radius products of each pair of blades, R i is the radial mass-radius product of the blade at the i-th position, is for the position of the blade's radial mass-radius product, the difference in the radial mass-radius products between the blade at the i-th position and the blade at the -th position is as small as possible.

[0038] Optionally, solving the multi-objective function through multiple heuristic algorithms and performing aero-engine blade sorting includes: solving the blade sorting problem through genetic algorithms, ant colony algorithms, and particle swarm optimization algorithms respectively, and screening the optimal algorithm.

[0039] Optionally, a three-dimensional sorting system for aero-engine blades with a large aspect ratio includes:

[0040] Acquisition module: used to acquire the measurement data of aero-engine blades;

[0041] Calibration module: used to establish a Cartesian coordinate system based on the measurement data, map the engine axis and the distribution of engine blades on the coordinate system, and determine the vector direction;

[0042] Multi-objective function determination module: used to establish a multi-objective function for the unbalanced state of aero-engine blades after determining the vector direction;

[0043] Solution module: used to solve the multi-objective function through various heuristic algorithms and perform sorting of aero-engine blades;

[0044] Sorting module: used to screen the sorting results of various aero-engine blades to obtain the final sorting result.

[0045] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a three-dimensional sorting method and system for aero-engine blades with a large aspect ratio, having the following beneficial effects:

[0046] The present invention proposes a three-dimensional sorting method for aero-engine blades with a large aspect ratio, including: collecting measurement data of aero-engine blades; establishing a Cartesian coordinate system according to the measurement data, mapping the engine axis and the distribution of engine blades on the coordinate system, and determining the vector direction; after determining the vector direction, establishing a multi-objective function for the unbalanced state of aero-engine blades; solving the multi-objective function through various heuristic algorithms and performing sorting of aero-engine blades; screening the sorting results of various aero-engine blades to obtain the final sorting result. The present invention adopts a multi-objective optimization function, with multiple objectives as the optimization directions, and combines various heuristic algorithms to sort aero-engine blades. For engines of different models, this method sets corresponding numerical standard ranges (i.e., sorting constraint conditions) for each objective function, and controls the values of the four objective functions within the specified ranges through heuristic algorithms. In this way, reasonable blade sorting and mass distribution can be achieved, effectively offsetting or reducing the unbalanced moments in each direction, thereby ensuring that the vibration and load generated during the operation of the engine are kept within an acceptable range and improving the stability and performance of the engine. Description of the Drawings

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on the provided drawings.

[0048] Figure 1 It is a schematic diagram of the imbalance of the tangential mass moment caused by the centroid offset provided by the present invention.

[0049] Figure 2 Schematic diagram of the vector sum of the radial mass-radius products provided by the present invention.

[0050] Figure 3 Schematic diagram of the radial imbalance caused by the axial torque provided by the present invention.

[0051] Figure 4 Schematic diagram of the vector sum of the radial mass-radius products and the tangential mass moments provided by the present invention.

[0052] Figure 5 Schematic diagram of the difference in the radial mass-radius products of each pair of blades provided by the present invention.

[0053] Figure 6 Schematic diagram of the single-point crossover principle provided by the present invention.

[0054] Figure 7 Schematic diagram of various local search methods provided by the present invention.

[0055] Figure 8 Comparison chart of the convergence performance of three algorithms for the first sorting provided by the present invention.

[0056] Figure 9 Comparison chart of the convergence performance of three algorithms for the second sorting provided by the present invention.

[0057] Figure 10 Comparison chart of the convergence performance of three algorithms for the third sorting provided by the present invention.

[0058] Figure 11 Comparison chart of the average convergence performance of three algorithms provided by the present invention.

[0059] Figure 12 Schematic diagram of the flow of a three-dimensional sorting method for aero-engine blades with a large aspect ratio provided by the present invention. Detailed implementation manners

[0060] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0061] The embodiments of the present invention disclose a three-dimensional sorting method for aero-engine blades with a large aspect ratio, as Figure 12 shown, including:

[0062] Collect measurement data of aero-engine blades;

[0063] Establish a Cartesian coordinate system based on the measured data, map the engine axis and the distribution of engine blades onto the coordinate system, and determine the vector direction;

[0064] After determining the vector direction, establish a multi-objective function for the unbalanced state of aero-engine blades;

[0065] Solve the multi-objective function through various heuristic algorithms to perform the sorting of aero-engine blades;

[0066] Screen the sorting results of various aero-engine blades to obtain the final sorting result.

[0067] Furthermore, the measured data of the aero-engine blades include: the radial mass-radius product R, the tangential mass moment T, and the axial mass moment A of each aero-engine blade obtained and recorded through measurement, search and record the calculated axial distance of the aero-engine blade, measure and record the angle θ between adjacent blades with the rotation axis as the center, and the number n of aero-engine blades.

[0068] Furthermore, the step of establishing a Cartesian coordinate system based on the measured data, mapping the engine axis and the distribution of engine blades onto the coordinate system, and determining the vector direction includes: establishing a Cartesian coordinate system, making the engine axis coincide with the Z-axis, the engine blades are distributed on the OXY plane, determining the direction of the blade centroid relative to the rotation axis as the direction of the radial mass-radius product vector; the direction tangent to the circumference as the vector direction of the tangential mass moment; with the engine axis as the reference, the direction from the compressor end to the turbine end along the engine axis is defined as the positive axial direction to obtain the direction of the axial mass moment.

[0069] Furthermore, the establishment of the multi-objective function for the unbalanced state of aero-engine blades includes: the maximum value among the radial unbalance, the radial unbalance caused by the axial torque, the unbalance considering the combination of the radial mass-radius product and the tangential mass moment, and the difference in the radial mass-radius products of each pair of blades.

[0070] Furthermore, the radial unbalance includes:

[0071] Decompose the radial mass-radius product into x and y direction components and sum them:

[0072]

[0073] Calculate the vector sum of the radial mass-radius products:

[0074]

[0075] Furthermore, the radial unbalance caused by the axial torque includes:

[0076]

[0077] Calculate the radial unbalance C2 caused by the axial torque;

[0078]

[0079] Wherein, Ar is the axial distance, A x is the component of the axial mass moment of the blade on the X-axis, A y is the component of the axial mass moment of the blade on the Y-axis.

[0080] Furthermore, the unbalance amount considering the combination of the radial mass-radius product and the tangential mass moment includes:

[0081] Decompose the tangential mass moment into x and y direction components and sum them:

[0082]

[0083] Sum the components on the x-axis and y-axis respectively:

[0084]

[0085] Calculate the magnitude of the resultant vector, that is, the unbalance C3 of the radial and tangential interaction. Sx is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the X-axis, and Sy is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the Y-axis;

[0086]

[0087] Furthermore, the maximum value among the differences of the radial mass-radius products of each pair of blades includes:

[0088] Find the maximum value among the differences of the radial mass-radius products between each pair of blades, and make the maximum value less than the standard, that is, the differences of the radial mass-radius products of each pair of blades will meet the standard conditions:

[0089]

[0090] C4 = max[ΔR i ;

[0091] Wherein, C4 is the maximum value of the differences of the radial mass-radius products of each pair of blades, R i is the radial mass-radius product of the blade at the i-th position, is the radial mass-radius product of the blade at the position of , and the difference of the radial mass-radius products between the blade at the i-th position and the blade at the -th position is as small as possible.

[0092] Furthermore, the method of solving the multi-objective function by using a plurality of heuristic algorithms to sort the blades of an aero-engine includes: solving the blade sorting problem by using a genetic algorithm, an ant colony algorithm and a particle swarm optimization algorithm respectively, and screening the optimal algorithm.

[0093] In a specific embodiment, a three-dimensional sorting system for large aspect ratio aero-engine blades includes:

[0094] Acquisition module: used to collect measurement data of aircraft engine blades;

[0095] Calibration module: used to establish a Cartesian coordinate system according to the measurement data, map the engine axis and the engine blade distribution on the coordinate system, and determine the vector direction;

[0096] Multi-objective function determination module: used to establish a multi-objective function of the imbalance state of the aero-engine blade after determining the vector direction;

[0097] Solution module: used to solve multi-objective functions through a variety of heuristic algorithms and sort aircraft engine blades;

[0098] Sorting module: used to screen the sorting results of various aircraft engine blades to obtain the final sorting results.

[0099] In a specific implementation, a three-dimensional sorting method for large aspect ratio aircraft engine blades optimizes the circumferential distribution of engine blades, minimizes the imbalance caused by unreasonable distribution of engine blades, reduces the vibration of the engine during operation, and improves the life, stability and safety of the engine. First, it is necessary to conduct a detailed analysis of the mass, center of mass (CoG), radial mass-diameter product, axial mass moment and tangential mass moment of each blade. By calculating the torque of each blade and the blade pairing position relationship, the influence of each blade on the engine rotor is determined. The heuristic algorithm uses an iterative process to continuously adjust the arrangement order of the blades to find a sorting scheme that meets the objective function standard, avoid falling into a local optimal solution, and comprehensively consider the optimization of multiple objectives, including the mass distribution of the blades, torque balance, vibration minimization and other factors, so as to ensure the final optimization effect of the blade sorting, so that the torque and mass moment generated by the rotor system during the rotation process can offset each other as much as possible in multiple directions to reduce the unbalanced force. The specific steps include:

[0100] S1. Propose to consider the unbalanced state of aero-engine blades using four different objective functions, namely the radial unbalance, the radial unbalance caused by the axial torque, the unbalance considering the combination of the radial mass-radius product and the tangential mass moment, and the maximum value among the differences in the radial mass-radius products of each pair of blades. In the past, only the radial mass moment and mass distribution were considered, and this method was only applicable to short compressor blades because their tangential and axial mass moment components were small, and the error had little impact on the balancing scheme. However, with the increase in the size of high-bypass ratio fan blades, the tangential and axial mass moments have a significant impact on the balance of the fan rotor and cannot be ignored. As Figure 1 shown, CoG represents the ideal design centroid of the blade, while CoG’ represents the actual centroid of the blade. t i represents the deviation between the ideal centroid and the actual centroid. For the sake of simplicity in explanation, only two blades are taken as an example in the figure to show that due to problems such as asymmetric blade geometry, non-uniform materials, or machining accuracy in the actual manufacturing process, the masses of individual blades are different, and there are differences between the actual centroid and the ideal centroid of the blades. Due to these deviations, additional tangential torques (i.e., tangential mass moments) will be generated during the rotation of the blades. This unbalanced tangential torque will cause unbalanced forces during the rotation of the blades, thereby triggering engine vibration and possibly affecting its stability.

[0101] The technical solutions for calculating each unbalance are as follows:

[0102] S11. Data collection: Obtain and record three values of the radial mass-radius product R, the tangential mass moment T, and the axial mass moment A of each blade through measurement, and look up and record the axial distance of the calculated engine blade. Taking the rotation axis as the center, measure and record the angle θ between adjacent blades, and the number of engine blades n.

[0103] S12. Determine the vector direction; establish a Cartesian coordinate system, making the engine axis coincide with the Z-axis, and the engine blades are distributed on the OXY plane. As Figure 2 shown, the red arrow represents the direction of the blade centroid relative to the rotation axis, which is the direction of the radial mass-radius product vector. As Figure 3 shown, the green arrow represents the direction tangent to the circumference, that is, the vector direction of the tangential mass moment. Taking the engine axis as the reference, the direction from the compressor end to the turbine end along the engine axis is defined as the positive axial direction, which is also the direction of the axial mass moment.

[0104] S13. Establish four objective functions

[0105] (1) The sum of the radial mass-radius product vectors C1

[0106] The dynamic balance of the engine rotor has a great impact on its performance and service life. However, in the actual manufacturing process of engine blades, due to processing errors, it is very difficult to make the mass and center of gravity position of each blade the same. The radial mass-radius product of the blade is the product of the vector radius from the center of gravity of the blade to the rotating shaft and the mass. The error of the radial mass-radius product will cause a certain initial unbalance in the synthesized rotor. Decompose the radial mass-radius product into x and y direction components and sum them up:

[0107]

[0108] Calculate the vector sum of the radial mass-radius products:

[0109]

[0110] (2) The radial unbalance C2 caused by the axial torque

[0111]

[0112]

[0113] Among them, Ar is the axial distance (Axialradius), and for engines of different models, the value of the axial distance will also be different. A x is the component of the axial mass moment of the blade on the X-axis, and A y is the component of the axial mass moment of the blade on the Y-axis.

[0114] (3) The vector sum C3 of the mass-radius products combining radial and tangential directions

[0115] As Figure 4 shown, only two blades are used for illustration. On the basis of Figure 2 , introduce the tangential mass moment. The red arrow represents the radial mass-radius product, denoted by the letter R; the green arrow represents the tangential mass moment, denoted by the letter T; the blue arrow represents the resultant vector S of the radial mass-radius product R and the tangential mass moment T of a single blade. Since the magnitudes of the radial mass-radius products and the tangential mass moments of each blade are not necessarily the same, the magnitudes of their resultant vectors are not necessarily the same. Decompose the tangential mass moment into x and y direction components and sum them up:

[0116]

[0117] Sum up the components on the x-axis and y-axis respectively:

[0118]

[0119] Calculate the magnitude of the resultant vector, that is, the unbalance C3 of the interaction between radial and tangential directions:

[0120]

[0121] Among them, S x is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the X-axis, and S y is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this group of blades on the Y-axis.

[0122] (4) The maximum value C4 of the difference in the radial mass-radius products of each pair of blades

[0123] Such as Figure 5 shown, during actual use, in order to facilitate maintenance personnel to quickly replace fan blades and balance them on the route, it is required that the difference in the radial mass moments of each pair of fan blades on the diameter of the fan disk be as small as possible. Find the maximum value among the differences in the radial mass-radius products between each pair of blades, and make the maximum value less than the standard, that is, the differences in the radial mass-radius products of each pair of blades will meet the standard conditions.

[0124]

[0125] C4 = max[ΔR i ;

[0126] Among them, R i is the radial mass-radius product of the blade at the i-th position, is the blade at the position of , that is, the radial mass-radius product of the blade opposite to it. The difference in the radial mass-radius products between the blade at the i-th position and the blade at the -th position is as small as possible.

[0127] S2: Most of the current domestic and foreign research on blade sequencing focuses on static balance optimization. The blade is simplified into a mass point, and only the radial mass moment component and mass distribution of the blade are considered. This method is only applicable to the short compressor blades in the past. The tangential and axial mass moment components are very small, and their errors will not significantly affect the balance state of the engine. However, nowadays, the length and chord width of the high-bypass ratio fan blades are very large, and the tangential and axial mass moments of the blades also significantly affect the balance state of the entire fan rotor and cannot be ignored. In contrast, there is less research on the blade sequencing method using constraint conditions, mainly focusing on using various heuristic algorithms to optimize the blade sequencing with a small amount of unbalance function as the goal. The present invention uses a multi-objective optimization function, takes multiple objectives as the optimization directions, and combines multiple heuristic algorithms to sequence the aeroengine blades. For different types of engines, the present invention sets corresponding numerical standard ranges (i.e., sequencing constraint conditions) for each objective function, and controls the values of the four objective functions within the specified ranges through heuristic algorithms. In this way, reasonable blade sequencing and mass distribution can be achieved, effectively offsetting or reducing the unbalanced torques in each direction, thereby ensuring that the vibration and load generated during the operation of the engine are kept within an acceptable range, improving the stability and performance of the engine. The specific steps are as follows:

[0128] When solving the blade sequencing problem, heuristic algorithms are a very effective choice. The main reason is that they can handle complex multi-objective optimization problems, especially when weighing multiple factors such as the unbalanced force of the blade, vibration minimization, and torque balance. Traditional physical model optimization methods often ignore the complexity of the working conditions when facing complex non-linear and highly constrained practical problems, and perform poorly. Heuristic algorithms have strong global search capabilities, can avoid being troubled by local optimal solutions, and find relatively good blade sequencing schemes.

[0129] There is a set of mass moment data of a large aspect ratio fan blade available, which is summarized in Table 1 below. This table data will also be used for blade sequencing and comparing the advantages and disadvantages of algorithms later.

[0130] Table 1 Mass moment data of a set of large aspect ratio fan blades

[0131]

[0132] S21. Solving the blade sequencing problem with genetic algorithms

[0133] When using genetic algorithms to solve this blade sequencing problem, each engine blade can be regarded as an individual, and the characteristics of each engine blade are used as its genes. A random set of blade arrangements is generated as the initial population, and then genetic crossover and mutation are carried out to gradually optimize the blade arrangement order until the standard effect is achieved.

[0134] The steps to solve using the genetic algorithm are as follows:

[0135] (1) Sequential coding.

[0136] (2) Fitness function. The criterion for evaluating the quality of each permutation scheme is the magnitude of the four objective function values. The smaller the value, the better the permutation scheme.

[0137] (3) Selection. There are many methods to implement selection, including roulette wheel method, elitist preservation method, expected value method, ranking selection method, tournament selection method, and crowding algorithm, etc. In this embodiment, the most commonly used roulette wheel selection method is adopted. The better the fitness of the blade individual, the greater the probability of being selected. Just like a roulette wheel, the individuals with good fitness occupy a larger sector.

[0138] (4) Crossover. Selection only optimizes within the population and cannot generate individuals different from the parent generation. Each time for crossover, two individuals are randomly selected from the mating pool to generate two different offspring individuals. They are generally different from their parent individuals but contain the genetic material of both parents. As Figure 6 shown, in this embodiment, single-point crossover is adopted, that is, the first half of parent 1 is directly copied to the offspring, and then the order of the blades in parent 2 is used to fill the remaining positions, ensuring that the blades are not reused.

[0139] (5) Mutation. Selection and crossover can only optimize within the existing permutations of genotypes and cannot generate new genotypes, which may lead to falling into a local optimal solution. The mutation operator changes one or more bits of an individual according to the mutation probability to generate new genotypes, expanding the scope of optimization, thus making it possible to search for the global optimal solution. The mutation probability in this embodiment is set to 0.1 to prevent premature convergence to the local optimum. The simplest mutation strategy is used, that is, randomly select two positions of the blades for exchange to increase the population diversity.

[0140] (6) Other parameters. The population size is set to 50. A smaller population size can accelerate the convergence speed. The elite retention ratio is 30%, ensuring that good solutions will not be lost during the evolution process and at the same time accelerating the convergence speed.

[0141] S22. Solving the blade sorting problem using the ant colony algorithm

[0142] In using the ant colony algorithm to solve this blade sorting problem, ants simulate blade sorting. When each ant selects a blade, it considers both historical pheromone and current heuristic information. The steps are as follows:

[0143] (1) Set key parameters. Each iteration has 20 ants trying to find the optimal solution. The maximum number of iterations is 200. The pheromone evaporation rate is set to 0.15 to avoid premature convergence to a local optimum. The importance factor α of pheromone is set to 1, and the importance factor β of heuristic information is set to 2, that is, the ratio of α to β is 1:2 to balance the algorithm between using historical experience and exploring new paths. The pheromone increase intensity coefficient is set to 100, that is, the intensity of pheromone increase when each ant finds a solution.

[0144] (2) Initialize the pheromone matrix τ ij and the heuristic matrix η ij . τ ij represents the pheromone value of placing blade i at position j, and the initial value is set to 0.15. η ij represents the heuristic information value of placing blade i at position j, which is calculated based on the difference in the radial mass-radius product of the blade. The smaller the value, the higher the fitness of the blade at this position.

[0145] (3) Construct the blade sorting solution. Randomly select a blade and place it at position 1 to avoid too low diversity of solutions. Select the remaining blades and positions through the roulette wheel method to ensure that all blades are placed. Calculate the probability P of all unused blades. Blades with high pheromone and high heuristic values are more likely to be selected.

[0146] P = (τ ij ) α ·(η ij ) β ·rand(0.9, 1.1);

[0147] (4) Pheromone update, the contribution of the better solution is greater, accelerating convergence.

[0148] Decay of old pheromone: τ ij ← (1 - ρ) · τ ij ;

[0149] Contribution of new solution to pheromone:

[0150] Pheromone evaporation rate ρ (0 < ρ < 1), constant Q represents the amount of pheromone release, and f k represents the fitness value corresponding to the k-th ant.

[0151] (5) Evaluation of the solution. Calculate the values of four objective functions. The smaller the value, the better the corresponding arrangement scheme.

[0152] S23, Particle Swarm Optimization Algorithm for Solving Blade Sorting Problem

[0153] In using the particle swarm optimization algorithm to solve this blade sorting problem, the arrangement order of the blades serves as the movement of particles in the search space, guided by the individual best and the global best. The steps are as follows:

[0154] (1) Set key parameters. Set the particle swarm size to 50. The maximum number of iterations is 300, which controls the number of loops for the algorithm to execute. Set the initial value of the inertia weight w to 0.9 and the final value to 0.4 to control the inertia when the particles move. Set both the individual learning factor C1 and the social learning factor C2 to 2.5, which are used to control the degree to which the particles approach their own historical best solutions and the global best solution respectively. V MAX Set it to 6.0 to prevent the particles from moving too fast and causing instability in the solution.

[0155] (2) Initialize the particle swarm. For each particle, use three strategies (greedy strategy, random strategy, hybrid strategy) to generate different initial solutions. Generate an initial solution using the greedy strategy. First, select the blade with the maximum radial mass-radius product as the first blade, and then select the unused blades one by one, and select the optimal blade according to the quality of the current solution (through the evaluation score). Generate a random initial solution by randomly sorting the blades. For the hybrid strategy, use the greedy strategy with a 70% probability and the random strategy with a 30% probability. At the same time, perform a certain amount of random swapping to increase the diversity of the solutions.

[0156] (3) Enter the main loop. Enter the loop with the maximum number of iterations MAX_ITERATIONS. Update the velocity and position of the particles in each iteration. Perform dynamic adjustment of parameters, particle update, local search, and diversity maintenance in sequence.

[0157] 1) Dynamic adjustment: As the iteration progresses, iter represents the current loop, denoted by progress. The inertia weight w, the individual learning factor C1, and the social learning factor C2 will be dynamically adjusted, gradually reducing the randomness of exploration and increasing the utilization of the optimal solution. The dynamic adjustment process is shown by the following formula.

[0158] represents the iteration progress;

[0159] 2) Position update: The new position is obtained by adding the updated velocity to the old position, and it is ensured that it does not exceed the search space. The formula is as follows:

[0160] x i = x i + v i ;

[0161] 3) Particle update: The position of the particle represents the layout of the blades. When updating, it will determine how to exchange the order of the blades according to its current velocity. v i represents the velocity of particle i in the current iteration, x iThe current position of particle i represents the current solution, pBest represents the best position found by particle i in historical iterations, gBest represents the global best position found by the entire population so far, r1 and r2 are random numbers between [0,1], which are used to increase the randomness of the search.

[0162] v i =w·v i +C1·r1·(pBest-x i )+C2·r2·(gBest-x i ).

[0163] 4) Local search: Each particle has the opportunity to conduct local search to further optimize the current solution. The local search strategy includes basic local search and enhanced local search. The basic local search strategy is to find a better solution by exchanging leaf positions and evaluating the quality of the new solution. The enhanced local search strategy is as follows: Figure 7 As shown, try a variety of local search methods (such as exchange, inversion, and three-point circular movement) to further optimize the solution;

[0164] 5) Diversity maintenance: Maintain the diversity of the population by generating new mixed solutions or mutating existing particles to avoid falling into local optimality.

[0165] (4) Return the optimized solution. Return the historical optimal solution, that is, the global optimal solution in the whole process.

[0166] In a specific implementation, using the mass moment data of a set of large aspect ratio fan blades in the above table, the four objective function optimization values, namely C1, C2, C3, and C4, are limited to 400, 800, 400, and 600 respectively, and three heuristic algorithms are used to sort the blades. The objective function calculation results are shown in Table 2.

[0167] Table 2 Objective function calculation results

[0168] Algorithm <![CDATA[C1]]> <![CDATA[C2]]> <![CDATA[C3]]> <![CDATA[C4]]> Genetic Algorithm 128.09 362.56 319.94 394.00 Ant Colony Algorithm 128.64 473.08 348.02 394.00 Particle Swarm Algorithm 262.32 90.60 341.47 417.00

[0169] pass Figure 8 , Figure 9 , Figure 10 It can be seen that the results of the three runs are very different. This is because the initial conditions of the algorithm are usually randomly generated, and the various random operations during the operation make the search path and results of each run different. This randomness is one of the core characteristics of the heuristic algorithm, which aims to avoid falling into the local optimal solution. Through random exploration, the algorithm can conduct a wider search in the solution space, thereby increasing the chance of finding the global optimal solution, but this also brings diversity and uncertainty to the results. In order to compare the advantages and disadvantages of the three algorithms, the algorithm was run 10 times and the best result was selected. The comparison chart and results are shown in the figure below. Figure 11As shown, the best fitness results of the three algorithms are shown in Table 3.

[0170] Table 3 Best Fitness Results of Three Algorithms

[0171] Algorithm Best Fitness Improved Ant Colony Algorithm 603.96 Improved Genetic Algorithm 332.58 Improved Particle Swarm Algorithm 990.01

[0172] As can be seen from Table 3 above, in solving the problem of blade arrangement, the genetic algorithm exhibits the best convergence performance, with the lowest average fitness value of 332.58. This indicates that the genetic algorithm has significant advantages in exploring the solution space and finding the global optimal solution. The ant colony algorithm comes second, with a fitness value of 603.96, showing good convergence ability but slightly inferior to the genetic algorithm. The fitness value of the particle swarm algorithm is 990.01, which is relatively high, indicating that its performance in this problem is not as good as the other two algorithms. From Figure 11 it can be seen that all algorithms have a relatively fast convergence speed in the initial stage and then gradually tend to be stable. The shaded area of the genetic algorithm is the narrowest, indicating higher stability and consistency of its results. The results of the ant colony algorithm and the particle swarm algorithm fluctuate more, showing higher result uncertainty. In summary, the genetic algorithm performs best in solving the blade distribution problem, with higher efficiency and stability. The ant colony algorithm also shows certain competitiveness, while the particle swarm algorithm has relatively weak effects in this problem.

[0173] The various embodiments in this specification are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[0174] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A three-dimensional sorting method for aeroengine blades with a large aspect ratio, characterized in that Including: Collecting measurement data of aero-engine blades; Establishing a Cartesian coordinate system according to the measurement data, mapping the engine axis and the distribution of aero-engine blades on the coordinate system, and determining the vector direction; After determining the vector direction, establishing a multi-objective function for the unbalanced state of aero-engine blades; Solving the multi-objective function through various heuristic algorithms to sort the aero-engine blades; Screening the sorting results of various aero-engine blades to obtain the final sorting result.

2. A three-dimensional sorting method for aeroengine blades with a large aspect ratio according to claim 1, characterized in that The measurement data of the aero-engine blades includes: radially obtaining and recording the radius-mass product R, tangential mass moment T, and axial mass moment A of each aero-engine blade through measurement, looking up and recording the axial distance of the calculated aero-engine blade, measuring and recording the angle θ between adjacent blades with the rotation axis as the center, and the number n of aero-engine blades.

3. A three-dimensional sorting method for aeroengine blades with a large aspect ratio according to claim 1, characterized in that, The establishing a Cartesian coordinate system according to the measurement data, mapping the engine axis and the distribution of aero-engine blades on the coordinate system, and determining the vector direction includes: establishing a Cartesian coordinate system, making the engine axis coincide with the Z-axis, distributing the aero-engine blades on the OXY plane, and determining the direction of the centroid of the blade relative to the rotation axis as the direction of the radially radius-mass product vector; the direction tangent to the circumference as the vector direction of the tangential mass moment; taking the engine axis as the reference, and defining the direction from the compressor end to the turbine end along the engine axis as the positive axial direction to obtain the direction of the axial mass moment.

4. A three-dimensional sorting method for an aero-engine blade with a large aspect ratio according to claim 1, characterized in that, The establishing a multi-objective function for the unbalanced state of aero-engine blades includes: the maximum value among the radial unbalance, the radial unbalance caused by the axial torque, the unbalance considering the combination of the radially radius-mass product and the tangential mass moment, and the difference between the radially radius-mass products of each pair of blades.

5. A three-dimensional sorting method for aero-engine blades with a large aspect ratio according to claim 4, characterized in that, The radial unbalance includes: Decomposing the radially radius-mass product into x and y direction components and summing them: Calculating the vector sum of the radially radius-mass product:

6. A three-dimensional sorting method for aeroengine blades with a large aspect ratio according to claim 4, characterized in that, The radial unbalance caused by the axial torque includes: Calculating the radial unbalance C2 caused by the axial torque; where Ar is the axial distance, A x is the component of the axial mass moment of the blade on the X-axis, A y is the component of the axial mass moment of the blade on the Y-axis.

7. A three-dimensional sorting method for aero-engine blades with a large aspect ratio according to claim 4, characterized in that The unbalance considering the combination of the radially radius-mass product and the tangential mass moment includes: Decomposing the tangential mass moment into x and y direction components and summing them: Respectively summing the components on the x-axis and y-axis: Calculate the magnitude of the resultant vector, i.e., the imbalance C3, S of the radial and tangential interactions x is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this set of blades on the X-axis, S y is the component of the resultant vector of the radial mass-radius product R and the tangential mass moment T of this set of blades on the Y-axis; 8. A three-dimensional sorting method for aero-engine blades with a large aspect ratio according to claim 4, characterized in that The maximum value among the differences between the radially radius-mass products of each pair of blades includes: Finding the maximum value among the differences between the radially radius-mass products of each pair of blades, and making the maximum value less than the standard, that is, the differences between the radially radius-mass products of each pair of blades will meet the standard conditions: C4 = max[ΔR i ; Among them, C4 is the maximum value of the difference in the radial mass-radius products of each pair of blades, and R i is the radial mass-radius product of the blade at the i-th position, is the radial mass-radius product of the blade at the position of , and the difference in the radial mass-radius products between the blade at the i-th position and the blade at the -th position is as small as possible.

9. A three-dimensional sorting method for an aero-engine blade with a large aspect ratio according to claim 1, characterized in that, The solving the multi-objective function through various heuristic algorithms to sort the aero-engine blades includes: respectively solving the blade sorting problem through genetic algorithms, ant colony algorithms, and particle swarm optimization algorithms, and screening the optimal algorithm.

10. A three-dimensional sorting system for aero-engine blades with a large aspect ratio, characterized in that Including: Acquisition module: used to collect measurement data of aero-engine blades; Calibration module: used to establish a Cartesian coordinate system according to the measurement data, map the engine axis and the distribution of aero-engine blades on the coordinate system, and determine the vector direction; Multi-objective function determination module: used to establish a multi-objective function for the unbalanced state of aero-engine blades after determining the vector direction; Solving module: used to solve the multi-objective function through various heuristic algorithms to sort the aero-engine blades; Sorting module: used to screen the sorting results of various aeroengine blades to obtain the final sorting result.

Images