Stator blade shape-following frequency modulation design method based on bending vibration mode and application

Abstract

The invention discloses a stator blade shape-following frequency modulation design method based on a bending vibration mode and application, belongs to the field of vibration design of stator blades of aero-engines and gas turbines, and is suitable for vibration frequency modulation design of non-cantilever type stator structure blades (such as fans and gas compressor stators) with inner rings and outer rings in the aero-engines or the gas turbines. According to the method, firstly, static frequency and dynamic frequency modal analysis is carried out through finite element modeling, and dangerous resonance points and corresponding vibration modes in a working rotating speed range are recognized by combining a Campbell diagram; based on a vibration mode amplitude normalization result, setting a vibration degree parameter and a scale factor, selecting a high response node and carrying out directed disturbance, and updating a structure model to improve a target vibration mode frequency; and through frequency amplification verification and iterative optimization, geometric reconstruction and frequency modulation confirmation are finally completed in combination with aerodynamic performance and processing requirements. The method can realize rapid and accurate frequency modulation of a specific bending vibration mode, avoids introduction of new resonance, and has the advantages of high efficiency, strong adaptability and the like.

Description

Technical Field

[0001] The present invention belongs to the field of vibration design of stator blades of aircraft engines and gas turbines, and relates to a stator blade frequency modulation design method, specifically to a stator blade conformal frequency modulation design method based on bending vibration mode and its application, which can effectively avoid dangerous resonance points, greatly increase the frequency of one or two bends, broaden the frequency modulation range of the stator blade vibration design, and improve the frequency modulation design efficiency of the stator blade. Background Art

[0002] To improve efficiency and thrust-to-weight ratio, modern high-performance aircraft engine blades are designed to be thinner and longer. Coupled with the requirement for wide operating conditions, the blades have dense vibration modes within the operating speed range. In particular, the increase in aerodynamic loads on trans-supersonic blades has greatly increased the risk of blade vibration failure. Multiple-order resonances often exist within a wide speed range and need to be avoided simultaneously, posing a huge challenge to frequency modulation design.

[0003] Depending on the excitation force, blade vibration can be categorized as free vibration without an excitation force, forced vibration under periodic alternating external excitation forces, self-excited vibration under self-excitation forces, and random vibration under the combined action of multiple excitations. Among these types of blade vibration, the most common vibration fault is forced resonance, where the blade vibration frequency is equal to the excitation force frequency.

[0004] It's often difficult to avoid all resonances within the entire engine's operating speed range. During the design phase, it's typically important to ensure that dangerous resonances within the critical operating speed margin are avoided. Methods for avoiding dangerous resonances include changing the excitation force, modifying the blade's natural vibration frequency, increasing resistance, and adding damping. The latter two methods cannot fundamentally avoid resonance and can only serve as supplementary measures when dangerous resonances are difficult to avoid. The former two methods can fundamentally prevent resonance. Changing the excitation force is only suitable during the preliminary design phase, where the excitation force is caused by front and rear structural blades / struts / nozzles, and where changing the number of front and rear blades / struts / nozzles has little impact on performance and structure. When the excitation force is an unchangeable low-frequency excitation, when the number of front and rear blades / struts / nozzles cannot be changed or is difficult to change to the desired value due to performance and structural constraints, and during the detailed design and troubleshooting stages, the only option is to modify the blade's natural frequency, or to employ blade frequency modulation, to avoid resonance.

[0005] Blade frequency modulation design is usually achieved by changing the blade material, changing the blade shape and changing the support stiffness. The frequency modulation method of changing the material achieves frequency change by changing the specific stiffness, but the frequency modulation amplitude is limited and the frequency modulation direction is the same for multiple frequencies, and differentiated regulation cannot be achieved. The frequency modulation method of changing the support stiffness generally has a large application space in the frequency modulation design of stator blades. For vibration modes with weak support stiffness and support structure participating in vibration, increasing the support stiffness will greatly increase certain frequencies, and reducing the support stiffness will reduce certain frequencies, but strength and processing requirements must be guaranteed. The method of changing the blade shape has a large frequency modulation space due to the large number of blade parameters, but is limited by the large influence of blade parameters on aerodynamic performance. There is an obvious coupling effect between parameters, and it is difficult to distinguish the influence of a single parameter on vibration or aerodynamics. Usually, simple frequency modulation of thickening or thinning the blade body is adopted based on experience, but it is limited by aerodynamic performance and the small adjustable thickness range, which limits the frequency modulation effect.

[0006] In recent years, some studies have shown that radial stacking of curved blades can increase the bending frequency of stator blades to a certain extent, with minimal or even beneficial effects on aerodynamic performance within a certain range. However, determining which parts and how much to bend to achieve the desired frequency modulation remains a time-consuming, iterative design process. Other existing methods for frequency modulation have been proposed, such as rounding the blade profile and shroud junction (CN116341124A), adjusting the blade-to-disk fit (CN116085304A), and parameterizing and optimizing the blade profile (CN117759576A, CN117236190A). However, these methods suffer from limitations such as a limited frequency modulation range, significant impact on aerodynamic performance, high computational complexity, or reliance on empirical evidence, making them difficult to meet the requirements for efficient and precise frequency modulation of high-performance aircraft engine stator blades.

[0007] In summary, existing design methods for stator blade frequency modulation generally suffer from limited adjustment space, difficult to control frequency modulation effects, complex vibration response coupling, and low design efficiency. Therefore, how to achieve rapid and effective frequency modulation of specific bending vibration modes of stator blades without significantly affecting aerodynamic performance and structural strength is a technical challenge that needs to be addressed in the field of engine blade vibration design. Summary of the Invention

[0008] (1) Purpose of the invention In response to the above-mentioned defects and shortcomings in the prior art, the present invention aims to solve the technical problem that the existing aircraft engine and gas turbine stator designs often cannot meet the frequency modulation requirements by thickening / thinning and other means under the premise of meeting aerodynamic performance. A stator blade conformal frequency modulation design method and application based on bending vibration mode is provided. By extracting the amplitude distribution of specific dangerous bending vibration modes (such as one bend on the leading edge, two bends on the trailing edge, etc.), the stator blade structural nodes are subjected to targeted geometric perturbations by normalization and proportional factor control, and an iterative finite element model is constructed to achieve rapid improvement and precise regulation of specific modal frequencies. At the same time, changes in other modal responses are controlled to avoid introducing new resonance risks. This effectively solves the problem of difficult frequency modulation of the bending vibration modes of engine stator blades, can greatly accelerate the frequency modulation design efficiency while maintaining aerodynamic and structural performance, and has obvious frequency modulation effects.

[0009] (2) Technical solution In order to achieve the purpose of the invention and solve the technical problems, the present invention adopts the following technical solutions: The first object of the present invention is to provide a method for designing stator blade conformal frequency modulation based on bending vibration mode, which is used for the vibration frequency modulation design of stator blades containing inner and outer rings in aircraft engines or gas turbines under the premise of meeting aerodynamic performance and structural constraints, so as to avoid dangerous resonance areas within the operating speed range. The method includes at least the following steps: SS1. Initial structural modeling and finite element partitioning: Based on the initial three-dimensional stator geometry model of inner ring-blade-outer ring, the finite element mesh is divided according to the mesh density suitable for vibration analysis to construct the vibration finite element model of the initial stator structure; SS2. Static frequency analysis of each order of the initial structure: Based on the vibration finite element model of the initial stator structure, displacement boundary conditions are applied according to the actual positioning of the stopper, and the material properties of the stator structure at ambient temperature are input to obtain the static frequency finite element model of the initial stator structure. The static frequency modal analysis of the initial stator blade is completed to obtain the static frequencies of each order and their vibration modes. SS3. Dynamic frequency analysis of initial structure: Based on the vibration finite element model of the initial stator structure, displacement boundary conditions are applied according to the actual positioning stop deformation under the working state. Load boundary conditions are applied according to the aerodynamic pressure, cavity pressure and temperature under the working state. The material properties that vary with temperature are input to obtain the dynamic frequency finite element model of the initial stator structure. The prestress analysis of the initial stator structure under the working state is completed. The dynamic frequency modal analysis of the initial stator blade is further completed to obtain the dynamic frequencies and vibration modes of each order. SS4. Initial Structural Resonance Analysis: Based on the static frequency and dynamic frequency analysis results, the dynamic frequency coefficients of each order frequency are calculated to obtain the dynamic frequencies of each order within the full speed range. The main excitation frequency harmonics are input, and the Campbell diagram is drawn to perform resonance analysis. SS5. Identification of dangerous resonances and target setting: Identify the dangerous resonance points and corresponding dangerous bending modes within the main operating speed range in the Campbell diagram, calculate the dangerous resonance speed of the initial stator blades and determine the expected frequency increase after frequency modulation design; SS6. Dangerous Mode Normalization and Node Selection: Normalize the amplitude of the dangerous vibration mode obtained from the static frequency modal analysis of the initial stator structure and define the vibration degree parameter λ And give the initial value 0, select the normalized dangerous vibration amplitude greater than λ The stator structure vibration finite element model node is used as the node for conformal frequency modulation design; SS7. Node disturbance calculation and structure update: Given a scale factor k , multiply the scale factor by the normalized dangerous vibration mode amplitude to obtain the offset of the node of the conformal frequency modulation design of the stator blade finite element model, and update the node coordinates of the conformal frequency modulation design accordingly to obtain the static frequency finite element model of the stator structure after conformal frequency modulation design; SS8. Frequency Modulation Effect Verification and Iterative Optimization: Repeat the modal analysis on the updated model to determine whether the dangerous vibration frequency meets the target frequency increase and does not introduce new dangerous resonance points. If not, adjust λ or k , iterative steps SS5~SS7; SS9. Geometry Reconstruction and FM Design Verification: Combining aerodynamic performance and processing requirements, the blade profile of the stator blade's conformal frequency modulation design is improved and the three-dimensional geometric model is reconstructed to verify the frequency modulation effect and determine the final structure.

[0010] The second object of the present invention is to provide an engine stator blade, the design of which adopts the above-mentioned stator blade conformal frequency modulation design method based on bending vibration mode of the present invention.

[0011] (3) Technical effects Compared with the prior art, the stator blade conformal frequency modulation design method based on bending vibration mode and its application of the present invention have at least the following significant technical effects: (1) The present invention is aimed at stator blades with inner and outer rings, and takes into account the influence of blade profile changes with vibration mode on blade frequency. The stator blade profile is designed with a small amplitude according to the bending vibration mode (including the vibration mode dominated by bending), which can effectively increase the frequency of the blade bending vibration mode.

[0012] (2) The present invention broadens the frequency modulation range of the stator blade vibration design, and can achieve a frequency-increasing effect that cannot be achieved by adjusting the blade thickness, chord length, and other conventional frequency modulation methods while meeting aerodynamic performance. For multi-order bending vibration modes whose main amplitude regions do not overlap, the present invention can increase the frequency of a certain order bending vibration mode while keeping the frequencies of the other order vibration modes basically unchanged, thereby achieving the desired frequency modulation effect. For multi-order bending vibration modes whose main amplitude regions do not overlap, the present invention can achieve a comprehensive frequency modulation design, and achieve the desired frequency modulation effect by simultaneously superimposing multiple vibration modes to perform blade-adaptive frequency modulation design.

[0013] (3) The design method of the present invention is simple and effective. It can achieve rapid frequency modulation iteration only through the initial design of the finite element model and its vibration mode results, thereby quickly designing the stator blades that meet the vibration requirements. It is very suitable for engineering design and application, and has a wide range of applications. It can be used for the vibration design of non-cantilevered stator blades with inner and outer rings of aircraft engines and gas turbines, including but not limited to fan stator blades, compressor stator blades, diffuser blades, turbine guide vanes and casing support plates. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings, which constitute part of the present invention, are provided to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are provided to explain the present invention and do not constitute undue limitations thereon. The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein: Figure 1 This is a flow chart of a method for designing stator blade conformal frequency modulation based on bending vibration mode according to an embodiment of the present invention; Figure 2 The initial three-dimensional stator sector geometric model and positioning diagram for the embodiment of the present invention; Figure 3 This is the initial stator blade Campbell diagram targeted by the embodiment of the present invention; Figure 4 This is a contour line diagram of the normalized amplitude of the two bending modes of the leading edge of the initial stator structure targeted by the embodiment of the present invention; Figure 5 This is a contour line diagram of the normalized amplitude of the second bending mode of the trailing edge of the initial stator structure targeted by the embodiment of the present invention; Figure 6 This is a Campbell diagram of the stator blade after the frequency modulation design targeted by the embodiment of the present invention; Figure 7 This is a schematic diagram of the three-dimensional stator sector geometric model after frequency modulation design according to an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The present invention proposes a design method and application of stator blade frequency modulation based on bending vibration mode. In order to make the purpose, technical solution, characteristics and engineering practicality of the implementation of the present invention clearer, the technical solution in the embodiment of the present invention will be described in more detail with reference to the drawings in the embodiment of the present invention. The described embodiment is a part of the embodiment of the present invention, not all of the embodiments. The embodiment described below with reference to the drawings is exemplary and is intended to be used to explain the present invention, and cannot be understood as a limitation of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0016] As a specific example, the stator blade conformal frequency modulation design method based on bending vibration mode of the present invention is as follows: Figure 1 The implementation process shown in the figure realizes the frequency modulation design of the second bend of the leading edge and the second bend of the trailing edge of a certain compressor integral blade ring, which specifically includes the following steps: SS1. Initial structural modeling and finite element partitioning: The initial three-dimensional stator blade ring geometric model based on the inner ring-blade-outer ring is as follows: Figure 2 As shown in the figure, the sector units are divided according to the periodic symmetry. According to the structural complexity and vibration modal accuracy requirements, the grid density and unit type suitable for vibration analysis are selected to perform finite element division on the stator structure, and the initial vibration finite element model of the stator structure is established.

[0017] SS2. Static frequency analysis of each order of the initial structure: Based on the vibration finite element model of the initial stator structure and according to the actual positioning of the spigot, such as Figure 2 As shown, displacement boundary conditions are applied, the front end face of the outer ring is the axial positioning face, an axial zero displacement constraint is applied, zero displacement constraints are applied to the front and rear radial positioning faces of the outer ring, a circumferential zero displacement constraint is applied to the circumferential positioning position, the inner ring is free, and the material properties of the stator structure at ambient temperature are input to obtain the static frequency finite element model of the initial stator structure, complete the static frequency modal analysis of the initial stator blades, and obtain the first five static frequencies and their vibration modes. The fifth-order static frequency of the structure has exceeded the maximum excitation frequency.

[0018] SS3. Dynamic frequency analysis of the initial structure: Based on the vibration finite element model of the initial stator structure, displacement boundary conditions are applied according to the actual positioning stop deformation under the working state. The front end face of the outer ring is the axial positioning surface, and an axial zero displacement constraint is applied. The front and rear radial positioning surfaces of the outer ring are respectively imposed with radial displacements of 1.69mm and 1.67mm. A circumferential zero displacement constraint is imposed on the circumferential positioning position. The inner ring is free. According to the aerodynamic pressure, cavity pressure and temperature under the design state, load boundary conditions are applied, and the material properties that change with temperature are input to obtain the dynamic frequency finite element model of the initial stator structure. The prestress analysis of the initial stator structure under the working state is completed, and the dynamic frequency modal analysis of the initial stator blade is further completed to obtain the first five dynamic frequencies and their vibration shapes. The fifth-order dynamic frequency of the structure has exceeded the maximum excitation frequency.

[0019] SS4. Initial Structural Resonance Analysis: Enter the static frequencies of the first five vibration modes f 0,i and the dynamic frequency under design status f nd,i , according to the empirical formula, calculate the dynamic frequency coefficient of each order frequency, obtain the dynamic frequency of each order in the full speed range, input the main excitation frequency multiplication 1 to 6, the number of front and rear rotors 63 and 83, and draw the Campbell diagram as shown Figure 3 As shown, resonance analysis was performed.

[0020] Specifically, the empirical formula for calculating the dynamic frequency coefficient is: , where f 0,i For the i Order static frequency, n is the rotation speed, f d,i is the speed n The corresponding i Step frequency, B i For the i The order frequency coefficient and , n d The dynamic frequency under specific working conditions f nd,i The corresponding speed, i is the order and i =1,2,3,… In the Campbell diagram, the frequency line represents the change of each order frequency of the stator blade with the speed, the radial line is the frequency-doubled excitation force line; the vertical solid line is the working speed line of each working condition, and the resonance speed margin and the resonance point where the frequency margin is insufficient are calculated respectively; the frequency margin Δ f and speed margin Δ n Press Calculate, where f w is the operating frequency, fe is the excitation frequency, n r is the resonance speed, n w is the working speed.

[0021] SS5. Identification of dangerous resonances and target setting: Identify the dangerous resonance points in the main operating speed range of the Campbell diagram as follows: Figure 3 The frequency orders of points Y3 and Y4 are third and fourth respectively, and the corresponding dangerous bending vibration modes are the second bending of the leading edge and the second bending of the trailing edge. The dangerous resonance speeds of the initial stator blades are calculated to be 20723r / min and 21193r / min respectively, which are insufficient to meet the takeoff and design speed margins. The expected frequency modulation direction is to increase the frequencies of Y3 and Y4 to above the maximum operating speed (design speed), and the frequency margin from the maximum operating speed is not less than 5%. Therefore, the expected frequency increases of the third-order frequency and the fourth-order frequency after the frequency modulation design are determined to be 、 , set different expected frequency increases Δ for different dangerous vibration modes fg oi , precise vibration avoidance is achieved through vibration mode classification and control.

[0022] It is worth noting that wide-chord stator blades are prone to chord-bending resonance within the operating speed range, and chord-bending is often a dangerous vibration mode that needs to be avoided. However, the proposed conformal frequency modulation design method is not very suitable for chord-bending vibration modes. This is because the maximum chord-bending amplitude position is often close to the maximum amplitude position of the first bend. Therefore, when the chord-bending frequency is increased, it is often accompanied by a significant or even doubling increase in the first bend frequency, which may increase the first bend resonance speed, which was originally lower than the operating speed, to within the operating speed range. In addition, the chord-bending vibration mode is bent along the chord direction. If a conformal design is adopted along the chord direction, it will have an adverse effect on aerodynamic performance and processing.

[0023] SS6. Dangerous Mode Normalization and Node Selection: The amplitudes of dangerous vibration modes obtained from the static frequency modal analysis of the initial stator structure are normalized. The amplitudes of the two bending vibration modes of the leading edge and the two bending vibration modes of the trailing edge are normalized as follows: Figure 4 and Figure 5 As shown, define the vibration degree parameters , select the normalized dangerous vibration amplitude greater than and The static structure vibration finite element model node, when the initial When , all nodes are used as nodes of the adaptive frequency modulation design.

[0024] Specifically, the formula for normalizing the amplitude of dangerous vibration mode is: In the formula: node( j ) is the node number, j =1,2,3,… N max , N max is the total number of nodes in the finite element model, U i (node( j )) is the first i The amplitude of the order mode, U i,max For the i The maximum amplitude of the order vibration mode, D i (node( j )) is the first i The normalized amplitude of the order mode, i =1,2,3,…, and when Di (node( j ))≥ λ i When , the node is selected as the FM area, λ i For the i The vibration degree parameter corresponding to the dangerous vibration mode of the first order is .

[0025] SS7. Node disturbance calculation and structure update: Given a scale factor and , initial settings , the scale factor and Multiplying by the normalized dangerous vibration mode amplitude, the offset of each node of the stator blade finite element model is obtained. Based on this, the node coordinates of the conformal frequency modulation design are updated to obtain the vibration finite element model of the stator structure after conformal frequency modulation design.

[0026] It is worth noting that the scaling factor k Used to adjust the disturbance effect of the normalized vibration amplitude in the spatial structure, and set different proportional factors for different vibration modes k i ( i =1,2,3,...), adjust each scale factor simultaneously or individually according to needs k i , realizing the superposition of multiple dangerous vibration modes and frequency modulation design or the separate frequency modulation design of specific vibration modes.

[0027] SS8. Frequency Modulation Effect Verification and Iterative Optimization: Repeat the calculation in step SS2 to obtain the static frequencies and vibration modes of each order after the stator structure is designed with frequency modulation, calculate the frequency increase of the dangerous vibration mode, and pay attention to the frequency changes of the other vibration modes. If the frequency changes of the other vibration modes lead to the introduction of new dangerous resonance points within the operating speed range, then increase the frequency of the dangerous vibration mode. λ Then continue to execute steps SS6 to SS8. If the frequency change of the remaining vibration modes is not enough to introduce a new dangerous resonance point within the operating speed range but the frequency increase is less than the expected frequency increase, then further increase the proportional factor. k , and continue to execute SS7 and SS8. If the frequency change of the remaining vibration modes is not enough to introduce a new dangerous resonance point within the operating speed range and the frequency increase is not less than the expected frequency increase, execute the next step SS9.

[0028] In this embodiment, by repeating the calculation of step SS2, the static frequencies and vibration modes of each order after the stator structure is designed with frequency modulation are obtained, and the frequency increase of the dangerous vibration mode is calculated. 、 The frequency changes of the other vibration modes are the first-order frequency (leading edge one bend) and the increase , second-order frequency (trailing edge bend) amplification , fifth-order frequency (composite vibration mode) amplification , the frequency increase of the dangerous vibration mode meets the expected requirements, and the frequency changes of the other vibration modes do not introduce new dangerous resonance points within the operating speed range, so the next step is directly executed.

[0029] SS9. Geometry Reconstruction and FM Design Verification: Based on the finite element model of the stator structure after the conformal frequency modulation design, the bending and sweeping stacking lines of each blade section are adjusted. Combined with the aerodynamic performance and processing requirements, the blade profile of the conformal frequency modulation design of the stator blade is further improved and the three-dimensional geometric model is reconstructed. SS1 to SS4 are performed on the reconstructed geometric model. The optimized Campbell diagram is shown in Figure 6. The Y3 and Y4 resonant speeds exceed the maximum operating speed and the frequency margin is greater than 5%. After optimization, the compressor stator meets the aerodynamic, vibration and processing requirements, the frequency modulation design is completed, and the final structure is determined. Figure 7 It is worth noting that there may be a situation where the aerodynamic performance and processing requirements are not met. In this case, the expected frequency increase in step SS5 needs to be reduced. , and at the same time take the approach of combining it with other FM methods to complete the final FM design.

[0030] In summary, the present invention proposes a method for designing stator blade frequency modulation based on bending vibration mode, which updates the vibration finite element model based on the amplitude of the dangerous bending vibration mode with an adjustable ratio, thereby realizing the rapid frequency modulation design of the bending vibration mode, so that the frequency of the specific bending vibration mode of the blade is increased to the desired level, while controlling the remaining bending vibration modes to remain almost unchanged or even decrease. It solves the problem that the compressor blades cannot meet the frequency modulation requirements through conventional means such as thickening / thinning while meeting the aerodynamic performance. On the basis of basically maintaining the original design scheme, it can quickly iterate and optimize the design of a blade shape that meets both vibration and aerodynamic performance. It is very suitable for engineering design applications and has a wide range of applications. It can be used for the frequency modulation design of aircraft engines and gas turbine compressor blades.

[0031] The above embodiments fully and effectively achieve the objectives of the present invention. Those skilled in the art will appreciate that the present invention includes, but is not limited to, the contents described in the accompanying drawings and the above specific embodiments. Although the present invention has been described with reference to the embodiments currently considered to be the most practical and preferred, it should be understood that the present invention is not limited to the disclosed embodiments, and any modifications that do not deviate from the functional and structural principles of the present invention are intended to be included within the scope of the claims.

Claims

1. A stator blade conformal frequency modulation design method based on bending vibration mode, characterized in that: include: SS1. Based on the initial 3D stator geometry model of inner ring, blades, and outer ring, create a finite element mesh with a density suitable for vibration analysis and construct a vibration finite element model of the initial stator structure. SS2. Apply displacement boundary conditions based on the actual stopper positioning and input the stator structural material properties at ambient temperature to complete the initial stator blade static frequency modal analysis and obtain the various static frequencies and their vibration modes. SS3. Based on the actual positioning flange deformation, aerodynamic pressure, cavity pressure, and temperature under operating conditions, boundary conditions are applied. Temperature-dependent material properties are input to perform prestressed and dynamic frequency modal analysis of the initial stator structure under operating conditions, and the dynamic frequencies and vibration modes of each order are determined. SS4. Based on the static and dynamic frequency analysis results, calculate the dynamic frequency coefficients for each frequency order, obtain the dynamic frequencies for each order within the full speed range, input the main excitation frequency harmonics, and plot the Campbell plot. SS5. Identify the dangerous resonance points and corresponding dangerous bending modes within the main operating speed range of the Campbell diagram, calculate the initial dangerous resonant speed of the stator blades, and determine the expected frequency increase after frequency modulation design; SS6. Normalize the amplitude of the dangerous vibration mode obtained from the static frequency modal analysis of the initial stator structure and define the vibration degree parameter λ And give the initial value 0, select the normalized dangerous vibration amplitude greater than λ The stator structure vibration finite element model node is used as the node for conformal frequency modulation design; SS7. Given scale factor k , multiplied by the normalized dangerous vibration amplitude value to obtain the offset of the conformal frequency modulation design node, update the node coordinates, and obtain the static frequency finite element model after conformal frequency modulation design; SS8. Repeat the modal analysis on the updated model to determine whether the dangerous vibration frequency meets the target frequency increase and does not introduce new dangerous resonance points. If not, adjust λ or k , iterative steps SS5~SS7; SS9. Integrate aerodynamic performance and machining requirements to refine the stator blade profile for conformal frequency modulation and complete 3D geometric model reconstruction. Verify the frequency modulation effect and determine the final structure.

2. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1 is characterized in that: In step SS2, displacement boundary conditions are applied according to the actual stop positioning conditions, including: the front end face of the outer ring is used as the axial positioning surface to impose an axial zero displacement constraint, the front and rear radial positioning surfaces of the outer ring are both imposed with zero displacement constraints, the circumferential zero displacement constraint is imposed on the circumferential positioning position of the outer ring, and the inner ring is a free boundary.

3. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1 is characterized in that: In step SS3, the actual positioning stop deformation is the deformation after the deformation of various components of the entire stator is coordinated in the working state, including: the front end face of the outer ring is used as the axial positioning surface to impose an axial zero displacement constraint, the front and rear radial positioning surfaces of the outer ring are respectively imposed with radial displacement constraints of preset deformation amounts, the circumferential positioning position of the outer ring is imposed with a circumferential zero displacement constraint, and the inner ring is a free boundary condition.

4. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1, characterized in that: In step SS4, the empirical formula for calculating the dynamic frequency coefficient is: Where: f 0,i For the i Order static frequency, n is the rotation speed, f d,i is the speed n The corresponding i Step frequency, B i For the i The order frequency coefficient and , n d The dynamic frequency under specific working conditions f nd,i The corresponding speed, i is the order and i =1,2,3,….

5. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 4 is characterized in that: In the Campbell diagram drawn in step SS4, the frequency line represents the change of each order frequency of the stator blade with the speed, and the radial line is the frequency-doubled excitation force line; the vertical solid line is the working speed line of each working condition, and the resonance speed margin and the resonance point where the frequency margin is insufficient are calculated respectively; the frequency margin Δ f and speed margin Δ n Calculate according to the following formula: Where: f w is the operating frequency, f e is the excitation frequency, n r is the resonance speed, n w is the working speed.

6. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1, characterized in that: In step SS5, the dangerous bending vibration mode includes at least one bend and two bends. When identifying, it is necessary to comprehensively consider the modal energy concentration area, the corresponding excitation frequency multiplication, and the margin between the resonant frequency and the operating speed, and set different expected frequency increases Δ for different dangerous vibration modes. fg oi .

7. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 6, characterized in that: In step SS6, the formula for normalizing the amplitude of the dangerous vibration mode is: In the formula: node( j ) is the node number, j =1,2,3,… N max , N max is the total number of nodes in the finite element model, U i (node( j )) is the first i The amplitude of the order mode, U i,max For the i The maximum amplitude of the order vibration mode, D i (node( j )) is the first i The normalized amplitude of the order mode, i =1,2,3,…, and when Di (node( j ))≥ λ i When , the node is selected as the FM area, λ i For the i The vibration degree parameter corresponding to the dangerous vibration mode of the first order is .

8. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1, characterized in that: In step SS7, the scaling factor k Used to adjust the disturbance effect of the normalized vibration amplitude in the spatial structure, and set different proportional factors for different vibration modes k i ( i =1,2,3,...), adjust each scale factor simultaneously or individually according to needs k i , realizing the superposition of multiple dangerous vibration modes and frequency modulation design or the separate frequency modulation design of specific vibration modes.

9. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1, characterized in that: In step SS8, when implemented, it includes: repeating the calculation of step SS2 to obtain the static frequencies and vibration modes of each order after the stator structure is designed with frequency modulation, calculating the frequency increase of the dangerous vibration mode, and paying attention to the frequency changes of the remaining vibration modes. If the frequency changes of the remaining vibration modes lead to the introduction of new dangerous resonance points within the operating speed range, then increase the frequency increase of the dangerous vibration mode. λ Then continue to execute steps SS6 to SS8. If the frequency change of the remaining vibration modes is not enough to introduce a new dangerous resonance point within the operating speed range but the frequency increase is less than the expected frequency increase, then further increase the proportional factor. k , and continue to execute SS7 and SS8. If the frequency change of the remaining vibration modes is not enough to introduce a new dangerous resonance point within the operating speed range and the frequency increase is not less than the expected frequency increase, execute the next step SS9.

10. The stator blade conformal frequency modulation design method based on bending vibration mode according to claim 1, characterized in that: In step SS9, its implementation includes: based on the finite element model of the stator structure after the conformal frequency modulation design, combined with aerodynamic performance and processing requirements, improving the blade profile of the conformal frequency modulation design of the stator blade and completing the three-dimensional geometric model reconstruction, executing steps SS1 to SS4 on the reconstructed geometric model, completing the frequency modulation design, and determining the final structure.

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