A turbine blade frequency modulation method and system based on parameterized design

Abstract

The application provides a turbine blade frequency modulation method and system based on parameterized design, belonging to the technical field of aero-engines. The method comprises: parameterizing a turbine blade two-dimensional profile, selecting parameters affecting mass distribution; designing a three-dimensional stacking mode, determining the axial and circumferential stacking positions of the cross-sectional profile; parameterizing the blade rim plate, root extension and tenon, selecting key parameters as the input of a proxy model; obtaining modeling data in combination with cooling structure parameters, optimizing parameter input into the proxy model; performing three-dimensional entity modeling and frequency evaluation; constructing a proxy model through initial sample collection and cross-validation for frequency evaluation; using a data mining algorithm for rapid sampling to identify key influencing factors and rules of each order frequency, and adjusting design parameters. The method reduces workload, shortens the design cycle, standardizes data transmission, realizes efficient frequency modulation of turbine blades and avoids dangerous frequency intervals based on the parameterized process.

Description

Technical Field

[0001] This application relates to the field of aero-engine technology, and more specifically, to a method and system for frequency modulation of turbine blades based on parametric design. Background Technology

[0002] Turbine blades, as core hot-end components of aero-engines, operate in extreme environments of high temperature, high pressure, and high speed, and are subjected to complex aerodynamic excitation forces. If the blade's natural frequency coincides with or approaches the primary excitation frequency, resonance will occur, leading to high-cycle fatigue damage. In severe cases, this can cause catastrophic accidents such as blade fracture. Therefore, turbine blade frequency tuning is a crucial factor in ensuring the reliable operation of aero-engines. The natural frequency of turbine blades is mainly affected by the following factors: 1) Turbine blade material properties The natural frequency of turbine blades is closely related to the material properties. However, in order to withstand more complex turbine inlet conditions, the materials selected for aero-engine turbine blades need to have high heat resistance, oxidation resistance, corrosion resistance and other properties. The selection conditions for turbine blade materials are very demanding. Therefore, the material properties are generally not changed for turbine frequency tuning.

[0003] 2) Turbine blade mass distribution During the turbine blade design phase, the turbine inlet temperature is far higher than the temperature that the blade material can withstand, therefore the blades often have very complex cooling structures. In this type of blade, many design parameters, such as mass distribution, blade profile design, blade wall thickness, number, position, and thickness of ribs, all affect the blade's natural frequency. Therefore, by changing the mass distribution of the turbine blade, the natural frequency of the turbine blade can be adjusted.

[0004] Based on the above considerations, patent application CN116186943A proposes a turbine blade frequency tuning method based on adjusting the blade root structural parameters. This method achieves turbine blade frequency tuning during the design phase by adjusting specific design parameters of the blade root, while minimizing impact on aerodynamic and heat transfer / cooling characteristics. The main problem with this method is its limited adjustable range and its focus only on the first-order frequency of the turbine blade, failing to clarify the complex coupling relationship between higher-order and first-order frequencies. Patent application CN119514056A focuses on addressing frequency issues after an accident, rather than conducting frequency assessment during the design phase to prevent accidents. The method in patent application CN117236190A focuses on optimization, neglecting the specific impact mechanism of design variables on turbine blade frequency, thus hindering the development of general empirical methods applicable to turbine frequency tuning. Patent application CN120509239A discloses a stator blade conformal frequency tuning design method based on bending mode shape. It uses finite element modeling to conduct static and dynamic frequency modal analysis, and combines Campbell diagrams to identify dangerous resonance points and corresponding mode shapes within the operating speed range. Based on the normalized mode shape amplitude results, relevant parameters are set and high-response nodes are directionally perturbed to update the structural model to raise the target mode shape frequency. Finally, the frequency is verified and iteratively optimized through frequency amplification. However, it focuses on stator blade frequency tuning, only applies directional perturbation to nodes based on mode shape amplitude, and cannot quantify the influence of structural features such as cooling channels and special surfaces on the frequency based on mode shape node offset. Summary of the Invention

[0005] To address or mitigate the problems mentioned in the background art, this application provides a turbine blade frequency tuning method based on parametric design. It analyzes typical turbine blade structural characteristics, parametrically characterizes complex turbine blade profiles and cooling structures, and obtains turbine blade geometry and cooling structure modeling data. Computer-aided modeling techniques are then used to rapidly generate the geometric model. Finally, turbine blade frequency evaluation software is employed to quickly evaluate the frequencies of each blade order. Based on this, optimal parameters are selected from the complex turbine blade profile / cooling structure parameters. The aforementioned rapid frequency calculation process is used for sampling, and a surrogate model is constructed using the obtained frequencies as the objective function to achieve rapid frequency evaluation of turbine blades based on parametric design. Then, advanced data mining algorithms are combined to perform turbine blade frequency tuning. Given a fixed turbine material, the turbine blade frequency is primarily influenced by the turbine blade mass distribution; therefore, factors with a significant impact on the turbine blade mass distribution are prioritized when selecting key parameters.

[0006] To achieve the above objectives, firstly, this application provides a turbine blade frequency modulation method based on parametric design, comprising the following steps: The complex profile of the turbine blade is parametrically characterized, and the structural modeling data of the turbine blade profile is obtained by solving the parametric characterization. Based on the degree of influence on the mass distribution of the turbine blade, parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning. Parametric design of turbine blade cooling structure is performed to obtain cooling structure shape data; parameters in the cooling structure design parameters are selected based on their influence on turbine blade mass distribution for turbine blade frequency modulation. Based on the turbine blade profile structure modeling data, a turbine blade shape solid model is established in computer-aided modeling software. Combined with the obtained cooling structure modeling data, a cooling structure solid model is obtained. Boolean operations are performed on the cooling structure solid model and the blade shape solid model to realize the three-dimensional solid modeling of the turbine blade. The frequency evaluation software is used to evaluate the turbine blade frequency and obtain the natural frequencies of each order of the turbine blade. Using the selected two-dimensional blade profile parameters, three-dimensional stacking parameters, tenon parameters, cooling structure design parameters, and natural frequencies of the turbine blades as inputs, a surrogate model is constructed and its accuracy is verified to meet the requirements. By sampling through a surrogate model, the influencing factors and their laws of influence of each order frequency of the turbine blade are identified. The design parameters of the turbine are then adjusted according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

[0007] Furthermore, the complex profile of the turbine blade is parametrically characterized. The turbine blade profile structure data obtained from the parametric characterization includes: using a hybrid parametric method of overall geometric parameter setting and local parameter correction, the key two-dimensional profiles of the turbine blade are mathematically defined, and the profiles are decomposed into two parts for control: one part is controlled by a set of overall parameters with clear aerodynamic and structural significance, including leading edge radius, trailing edge radius, axial chord length, center-to-center angle, inlet geometric angle, inlet upper wedge angle, lower wedge angle, effective exhaust angle, outlet deflection angle, and outlet wedge angle; the other part is adjusted by B-spline curve control points to adjust the complex curvature of the pressure surface and suction surface. The B-spline curve control points are composed of two B-spline control points on the pressure surface and four B-spline control points on the suction surface.

[0008] Furthermore, based on the degree of influence on the turbine blade mass distribution, parameters from the two-dimensional blade profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning, including: Parametric design of the two-dimensional profile of the turbine blade is carried out, and the two-dimensional profile parameters are selected according to their influence on the mass distribution of the turbine blade. Two-dimensional profiles are stacked in three dimensions, and the three-dimensional stacking method of turbine two-dimensional profiles is designed to determine the axial and circumferential stacking positions of different cross-sectional profiles. Parametric design was performed on the turbine blade rim plate, extension root, and tenon respectively, and the tenon parameters were selected based on their influence on the mass distribution of the turbine blade.

[0009] Furthermore, the three-dimensional stacking of the two-dimensional profiles includes: adjusting the axial and circumferential stacking parameters of the stacking center of each two-dimensional profile to achieve four different forms of stacking lines: straight lines, curves, end curves, and free curves, in order to control the relative axial and circumferential positions of the stacking centers of each profile. By adjusting the three-dimensional stacking relationship of the blade profiles, a three-dimensional blade surface is obtained.

[0010] Furthermore, parametric design was performed on the turbine blade rim, extensor, and tenon. Tenon parameters were selected based on their impact on turbine blade mass distribution. The parametric scope was expanded from the blade aerodynamic profile to the key load-bearing structures connected to the turbine disk. These key load-bearing structures included the rim, extensor, and tenon. Key parameters for the rim included the blade's forward / backward offset, rim thickness, and the rim angle relative to the axial direction. Key parameters for the extensor included the length and connection method of the transition section, and the design parameters of the near-rim end profile and the near-tenon end profile. Key parameters for the tenon included the number of teeth, pressure angle, tooth profile angle, tooth root fillet radius, tooth tip fillet radius, overall tenon height, and the increase in tenon width relative to the extensor. Simultaneously, the overall tenon height, pressure angle, tooth profile angle, and rim thickness were selected as design parameters for blade frequency tuning.

[0011] Furthermore, the cooling structure design parameters are selected based on the influence of the turbine blade mass distribution. These parameters include: evaluating all parameters affecting the turbine blade mass based on the influence law of mass distribution on turbine blade frequency, and selecting parameters that play a decisive role in the overall mass distribution and cross-sectional moment of inertia of the turbine blade. The key B-spline control points on the axial chord length, leading edge radius, trailing edge radius, pressure surface, and suction surface are used as design parameters to participate in blade frequency tuning.

[0012] Furthermore, based on the generated blade solid model, the design of the internal cooling structure is introduced, the dimensionless processing of the turbine blade geometry is carried out, and the complex cooling structure of the turbine blade, including wall thickness distribution, ribs, double wall, impact holes / film cooling holes, is obtained through parametric design. The cooling structure parameters that have a significant impact on the blade mass distribution are included in the final design parameter set for constructing a proxy model.

[0013] Furthermore, using the selected two-dimensional blade profile parameters, three-dimensional stacking parameters, tenon parameters, cooling structure design parameters, and the natural frequencies of each turbine blade as inputs, a surrogate model is constructed and its accuracy is verified to meet the requirements, including: Using selected blade 2D profile parameters, 3D stacking parameters, tenon parameters, cooling structure design parameters, and turbine blade natural frequencies as inputs, an initial input variable set is obtained using a Latin hypercube sampling strategy. The initial samples are evaluated to obtain the natural frequency values ​​corresponding to each sample point, and these natural frequency values ​​are added to the sample set as output variables. A surrogate model is constructed based on the sample set after adding sample points, and the accuracy of the surrogate model is evaluated through cross-validation. If the surrogate model does not meet the accuracy requirements, additional sampling is performed and added to the sample set before reconstructing the surrogate model. This process continues until the surrogate model's prediction accuracy meets the requirements, ultimately resulting in a surrogate model that meets the accuracy requirements for subsequent blade frequency evaluation.

[0014] Furthermore, by sampling through a surrogate model, the influencing factors and patterns of each order frequency of the turbine blade are identified. Based on the requirements, the turbine design parameters are adjusted to obtain the target natural frequency of the turbine blade and its corresponding parameters. This includes: combining total variation analysis or SHAP analysis data mining algorithms, using the constructed surrogate model as a basis, performing Latin hypercube sampling and data mining, and combining global sensitivity analysis to obtain the weight ratio and coupling influence relationship of each design parameter on the frequency changes of each order of the blade. This clarifies the complex relationship between each order frequency of the turbine blade and the design parameters, as well as the influence mechanism between each order frequency. Based on the target natural frequency requirement of the turbine blade and the obtained mechanism of action of the design parameters, the corresponding design parameters are adjusted to obtain the target natural frequency of the turbine blade and its corresponding parameters.

[0015] Secondly, this application provides a turbine blade frequency modulation system based on parametric design, including a parameter acquisition module, a natural frequency acquisition module, a surrogate model optimization module, and a sampling adjustment module; The parameter acquisition module is used to parametrically characterize the complex profile of the turbine blade, and obtain the turbine blade profile structure data based on the parametric characterization. Based on the degree of influence on the turbine blade mass distribution, parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning. The turbine blade cooling structure is parametrically designed to obtain cooling structure shape data, and parameters from the cooling structure design parameters are selected based on the influence on the turbine blade mass distribution for turbine blade frequency tuning. The natural frequency acquisition module establishes a turbine blade shape solid model in computer-aided modeling software based on turbine blade profile structure modeling data, and obtains a cooling structure solid model by combining the obtained cooling structure modeling data. Boolean operation is performed between the cooling structure solid model and the blade shape solid model to realize three-dimensional solid modeling of the turbine blade. The frequency evaluation software is used to evaluate the turbine blade frequency and obtain the natural frequencies of each order of the turbine blade. The surrogate model optimization module takes the selected blade 2D profile parameters, 3D stacking parameters, tenon parameters, cooling structure design parameters, and turbine blade natural frequencies as inputs to construct a surrogate model and verify that its accuracy meets the requirements. The sampling and adjustment module is used to sample through a surrogate model, identify the influencing factors and influence laws of each order frequency of the turbine blade, and adjust the design parameters of the turbine according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

[0016] Thirdly, this application also provides a computer device, including a processor and a memory. The memory is used to store a computer-executable program. The processor reads part or all of the computer-executable program from the memory and executes it. When the processor executes part or all of the computer-executable program, it can realize the above-mentioned turbine blade frequency modulation method based on parametric design.

[0017] A computer-readable storage medium is also provided, in which a computer program is stored. When the computer program is executed by a processor, it can implement the above-described method for frequency modulation of turbine blades based on parametric design.

[0018] Compared with existing turbine blade frequency tuning methods, this application has at least the following advantages: Traditional frequency tuning methods are essentially empirical local adjustments to a specific design scheme, relying on the engineer's intuition and experience. This method, however, constructs a fully parametric design framework: through parametric design, it achieves rapid modal analysis and frequency calculation of the turbine blade, constructing a high-precision proxy model from design parameters to various frequencies of the turbine blade. The advantage of this method lies in reducing manual workload and shortening the design cycle based on the parametric process, while making the data transmission throughout the process more standardized. Furthermore, relying on the influence mechanism of design parameters obtained through data mining, it ensures the globality and accuracy of the frequency tuning direction, enabling efficient frequency tuning of the turbine blade during the turbine blade design stage, avoiding dangerous frequency ranges. Attached Figure Description

[0019] To provide a more detailed and intuitive explanation of the specific implementation methods of this application, the accompanying drawings provide an implementation example applied to a specific turbine blade, intended as a typical example of the solution in this application. Those skilled in the art can refer to the methods and implementation steps in the drawings to apply the invention and steps to frequency regulation tasks of other types of air-cooled turbine blades.

[0020] Figure 1 This application presents a technical approach for the rapid frequency evaluation method of turbine blades based on parametric design. Figure 2 This application adopts the parametric design method to implement the overall technical approach for turbine blade frequency modulation. Figure 3 These are the preferred parameters in the airfoil parametric design method selected in this application; Figure 4 This is a schematic diagram of the preferred parameters for the tenon in the example selected in this application; Figure 5 This is a schematic diagram of the wall thickness distribution parameters in the example selected in this application; Figure 6 This is a schematic diagram of the rib design parameters in the example selected in this application.

[0021] Explanation of reference numerals in the attached figures: P1 is the first control point on the pressure side, P2 is the second control point on the pressure side; SLE1 is the first control point on the leading edge of the suction side; SLE2 is the second control point on the leading edge of the suction side; STE1 is the first control point on the trailing edge of the suction side, STE2 is the second control point on the trailing edge of the suction side; γ is the tenon tooth angle; β is the tenon pressure angle; hs is the height of the tenon-extended root connection section; Ws is the tenon width increment relative to the extended root; Rs is the rounding radius of the tenon-extended root connection section; t0 is the leading edge wall thickness; t1 is the trailing edge wall thickness; ti and i take values ​​of 0-1, representing the wall thickness at position i (arc length percentage); r is the rounding radius of the trailing end of the inner wall surface; x1 is the percentage of the rib pressure side; θ is the angle between the rib and the axial direction. Detailed Implementation

[0022] To clarify the specific implementation path of the method described in this application, a complete demonstration case is provided, using a specific turbine blade as the research object. This case aims to fully illustrate the entire process from parametric modeling, automated simulation, surrogate model construction to final data-driven analysis and mining.

[0023] This application proposes a turbine blade frequency tuning method based on parametric design. The specific implementation measures of this application are described below with reference to the examples provided in the accompanying drawings. Its core content consists of two parts: First, it achieves parametric characterization of the complex surface and cooling structure of the turbine blade, and integrates computer-aided modeling and frequency analysis tools to construct a fully automated process from geometry generation to performance evaluation, thereby significantly reducing time and labor costs, standardizing the evaluation process, and laying a technical foundation for subsequent efficient prediction. Second, based on this parametric system, it constructs a surrogate model that meets the accuracy requirements through system sampling, and conducts large-scale numerical experiments on this basis. Furthermore, it uses data mining techniques to deeply analyze and clarify the influence mechanism and laws of each design parameter on the vibration frequencies of each order of the turbine blade.

[0024] For ease of understanding, the following explains some key terms in this embodiment: Turbine blade frequency tuning: refers to the design process of adjusting the structural or material parameters of turbine blades to make their natural frequency deviate from the excitation frequency that may be encountered during engine operation, thereby avoiding resonance and ensuring the safe operation of the blades.

[0025] 3D solid modeling, performed in computer-aided design software, involves constructing a 3D model of a turbine blade with realistic geometry and volume based on surface and cooling structure modeling data. Frequency evaluation software is specialized software used for modal analysis of the 3D solid model. Through the finite element method, it predicts the natural frequencies of the turbine blade under different vibration modes. A surrogate model is a mathematical model built based on a small amount of sample data, used to approximate the relationship between the input and output of a complex system. This model can quickly predict the system response with lower computational cost, thus replacing time-consuming high-precision simulation calculations. The natural frequencies of a turbine blade are specific vibration frequencies exhibited by the turbine blade under free vibration conditions in different vibration modes (such as first-order bending, second-order bending, first-order torsion, etc.).

[0026] This application provides a turbine blade frequency tuning method based on parametric design, which solves the problems of limited adjustment range, inability to fully consider high-order frequency coupling relationships, and lack of in-depth understanding of the influence mechanism of design parameters in existing turbine blade frequency tuning methods. The method includes the following steps: The complex profile of the turbine blade is parametrically characterized, and the structural modeling data of the turbine blade profile is obtained based on this parametric characterization. A method based on key section profile control points can be used for parametric characterization.

[0027] The parameters selected from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are used for turbine blade frequency tuning based on their degree of influence on the turbine blade mass distribution. Parameters with a significant impact on the blade mass distribution can be manually selected based on experience or preliminary sensitivity analysis.

[0028] Parametric design of the turbine blade cooling structure is performed to obtain cooling structure shape data. Based on the impact on the turbine blade mass distribution, parameters from the cooling structure design parameters are selected for turbine blade frequency modulation. A pre-defined cooling structure template can be used for parametric design.

[0029] Based on the turbine blade profile structure data, a solid model of the turbine blade's external shape is established in computer-aided modeling software. Using the obtained cooling structure modeling data, a solid model of the cooling structure is obtained. Boolean operations are then performed between the cooling structure solid model and the blade external shape solid model to achieve 3D solid modeling of the turbine blade. Frequency evaluation software is then used to evaluate the turbine blade's frequency, obtaining its natural frequencies. Scripts, macros, and API calls can be used to automate the data import and modeling and Boolean operation processes, improving modeling efficiency. During frequency evaluation, standard finite element analysis methods can be employed to perform modal analysis on the constructed 3D solid model, thereby obtaining the blade's natural frequencies.

[0030] Using the selected two-dimensional blade profile parameters, three-dimensional stacking parameters, tenon parameters, cooling structure design parameters, and natural frequencies of the turbine blades as inputs, a surrogate model is constructed and its accuracy is verified to meet the requirements.

[0031] By sampling through a surrogate model, the influencing factors and their laws of influence of each order frequency of the turbine blade are identified. The design parameters of the turbine are then adjusted according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

[0032] This application achieves refined control of blade geometry by parametrically characterizing and designing the complex profile and cooling structure of turbine blades. Compared with existing frequency tuning methods that only focus on local structures (such as root extension structures), it offers a broader design space and stronger adjustment capabilities. By comprehensively incorporating the blade's two-dimensional profile parameters, three-dimensional stacking parameters, tenon parameters, and cooling structure design parameters into the frequency tuning considerations, it can more comprehensively reflect the influence of blade mass distribution on the natural frequency, overcoming the limitations of existing technologies that only target a single influencing factor for frequency tuning. Furthermore, this embodiment utilizes a surrogate model for rapid sampling and analysis, enabling efficient identification of the influencing factors and patterns of each order frequency of the turbine blade. Compared with existing methods that use finite element analysis for iterative optimization but lack a deep understanding of the influence mechanism of design parameters, this improves frequency tuning efficiency and helps clarify the complex relationship between each order frequency and design parameters, as well as the influence mechanism between different orders of frequencies.

[0033] This application further proposes a parametric characterization of the complex profile of turbine blades. The turbine blade profile structure data obtained by solving the parametric characterization includes: using a hybrid parametric method of overall geometric parameter setting and local parameter correction, the key two-dimensional profiles of the turbine blade are mathematically defined, and the profiles are decomposed into two parts for control: one part is a set of overall parameter controls with clear aerodynamic and structural significance, including leading edge radius, trailing edge radius, axial chord length, center-to-center angle, inlet geometric angle, inlet upper wedge angle, lower wedge angle, effective exhaust angle, outlet deflection angle, and outlet wedge angle; the other part is the adjustment of the complex curvature of the pressure surface and suction surface by B-spline curve control points, which are composed of two B-spline control points on the pressure surface and four B-spline control points on the suction surface.

[0034] One approach employs a hybrid parameterization method that combines global geometric parameter setting with local parameter correction. This method aims to integrate two different parameterization strategies to achieve both macroscopic control and microscopic refinement of complex turbine blade profiles. One implementation involves first defining the basic shape and dimensions of the blade using a set of global parameters, and then fine-tuning specific regions based on these global parameters. Another approach is to divide the blade profile into several regions and apply different parameterization strategies to each region. The key two-dimensional profiles of the turbine blade are mathematically defined, transforming the physical geometry of the blade cross-section into a computable mathematical expression. The geometric characteristics of the profiles can be described using polynomial functions and spline curves (such as B-splines and NURBS curves), or the profiles can be defined using discrete point coordinates combined with interpolation algorithms (such as Lagrange interpolation and cubic spline interpolation). The profile shape can then be altered by adjusting control points or interpolation functions.

[0035] Decomposing the blade profile into two parts for control facilitates hierarchical management and independent adjustment of the blade profile. One approach is to decompose the profile into macroscopic feature control and microscopic detail control, each managed by different parameter sets. Another approach is to decompose it according to its functional regions, for example, separating the aerodynamic performance-related parts from the structural strength-related parts for control. A set of overall parameters with clear aerodynamic and structural significance, including leading-edge radius, trailing-edge radius, axial chord length, center-to-center angle, inlet geometry angle, upper inlet wedge angle, lower inlet wedge angle, effective outlet angle, outlet deflection angle, and outlet wedge angle, are key macroscopic geometric features in turbine blade design, determining the blade's aerodynamic performance (such as airflow deflection and losses) and structural characteristics (such as strength and stiffness). For example, the leading-edge and trailing-edge radii affect the inlet and outlet characteristics of the airflow; the axial chord length determines the blade size; and various angular parameters control the guidance and deflection of the airflow. By adjusting these parameters, the overall performance of the blade can be initially optimized. The complex curvature of the pressure and suction surfaces is adjusted using B-spline control points. These control points consist of two B-spline control points on the pressure surface and four on the suction surface. B-spline curves are powerful mathematical tools that allow for flexible modification of the curve's shape by adjusting its control points. In this application, precise adjustment of the pressure and suction surfaces using B-spline control points enables fine-grained control of the complex curvature of the blade surface.

[0036] A hybrid parametric method employing both global geometric parameter setting and local parameter correction effectively addresses the shortcomings of single parametric methods in representing complex turbine blade profiles, such as insufficient accuracy and inconvenient adjustment. This method rapidly defines the macroscopic shape of the blade through global parameters, while simultaneously using B-spline control points to finely adjust the complex curvatures of the pressure and suction surfaces. This allows for high-precision and highly flexible characterization of the blade profile structure data. This not only improves the accuracy of the parametric model and ensures geometric fidelity in subsequent 3D solid modeling, but also provides more precise and controllable design parameters for turbine blade frequency tuning, thereby significantly enhancing the accuracy of turbine blade frequency evaluation and the efficiency of the tuning process.

[0037] This application proposes a parametric design of the two-dimensional profile of turbine blades, selecting the two-dimensional profile parameters based on their influence on the turbine blade mass distribution. It also designs a three-dimensional stacking method for the turbine's two-dimensional profiles, determining the axial and circumferential stacking positions of different cross-section profiles to form a complete blade entity. However, in actual turbine blade design, simply determining the stacking positions may be insufficient to address the complex and varied blade geometry requirements, especially when fine adjustments to the blade mass distribution are needed to achieve frequency modulation targets. The lack of flexible control over the stacking line form may prevent the generation of a three-dimensional blade profile that meets specific frequency requirements.

[0038] This application further proposes to perform three-dimensional stacking of two-dimensional profiles. This process includes adjusting the axial and circumferential stacking parameters of the stacking center of each two-dimensional profile to achieve four different forms of stacking lines: straight lines, curves, end curves, and free curves. This controls the relative axial and circumferential positions of the stacking centers of each profile. By adjusting the three-dimensional stacking relationship of the blade profiles, a three-dimensional blade surface is obtained.

[0039] This application's solution addresses the problem of insufficient control over the three-dimensional morphology of turbine blades during frequency tuning by refining the three-dimensional stacking method of the two-dimensional profiles. Specifically, firstly, by adjusting the axial and circumferential stacking parameters of the stacking centers of the two-dimensional profiles at each cross-section, precise control of the blade's torsion and bending in three-dimensional space is achieved. Furthermore, by supporting four different stacking line forms—straight lines, curves, tip bends, and free curves—the design space for the blade's three-dimensional morphology is expanded, allowing designers to flexibly select the most suitable stacking line form according to complex frequency tuning requirements. This diverse stacking line form, combined with precise axial and circumferential stacking parameters, effectively controls the relative axial and circumferential positions of the stacking centers of each cross-section profile, thereby precisely shaping the blade's mass distribution and stiffness characteristics. Finally, by adjusting the three-dimensional stacking relationship of the blade profiles, these two-dimensional profiles are connected according to the preset stacking line form and relative position, resulting in a three-dimensional blade profile with specific geometric features and mass distribution. This holistic stacking control mechanism enables the generation of diverse three-dimensional solid models of the blades according to the target frequency requirements during turbine blade frequency tuning.

[0040] Furthermore, this application proposes to introduce the design of an internal cooling structure based on the generated blade solid model, perform dimensionless processing on the turbine blade geometry, and obtain a complex cooling structure for the turbine blade, including wall thickness distribution, ribs, double walls, impact holes / film cooling holes, etc., through parametric design. Cooling structure parameters that significantly affect the blade mass distribution are included in the final design parameter set to construct a proxy model. By systematically introducing the design of the internal cooling structure based on the generated blade solid model and performing dimensionless processing on the turbine blade geometry, the design parameters of the cooling structure are made more universal and controllable.

[0041] Furthermore, this application selects cooling structure design parameters based on the influence of turbine blade mass distribution, including: evaluating all parameters affecting blade mass based on the influence law of mass distribution on turbine blade frequency, and screening out parameters that play a decisive role in the overall blade mass distribution and cross-sectional moment of inertia. The axial chord length, leading edge radius, trailing edge radius, and key B-spline control points on the pressure and suction surfaces are used as design parameters for blade frequency tuning. By comprehensively evaluating all parameters that may affect blade mass based on the influence law of mass distribution on turbine blade frequency when selecting cooling structure design parameters, this evaluation allows for a systematic understanding of the contribution of each parameter to the blade mass distribution. This further screens out parameters that play a decisive role in the overall blade mass distribution and cross-sectional moment of inertia. This ensures that the selected parameters are truly key factors affecting blade vibration characteristics, avoiding the inclusion of non-critical parameters in the frequency tuning process, thereby improving the targeting and efficiency of frequency tuning. The axial chord length, leading edge radius, trailing edge radius, and key B-spline control points on the pressure and suction surfaces, as core design parameters, directly determine the macroscopic geometry and local curvature of the blade, significantly influencing its mass distribution and stiffness characteristics. In this way, it is ensured that subsequent proxy model construction and parameter adjustment can focus on the most critical cooling structure design parameters.

[0042] Furthermore, this application uses a surrogate model for sampling to identify the influencing factors and patterns of each order frequency of the turbine blade. The steps for adjusting the turbine's design parameters according to requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters include: combining total variation analysis or SHAP analysis data mining algorithms, based on the constructed surrogate model, performing Latin hypercube sampling and data mining; combining global sensitivity analysis to obtain the weight ratio and coupling influence relationship of each design parameter on the frequency changes of each order of the blade; clarifying the complex relationship between each order frequency of the turbine blade and the design parameters, as well as the influence mechanism between each order frequency; and adjusting the corresponding design parameters according to design requirements and the obtained mechanism of action of the design parameters to obtain the target natural frequency of the turbine blade and its corresponding parameters. This overcomes the problem of insufficient understanding of the complex relationship between design parameters and natural frequency in traditional frequency modulation methods. By combining total variation analysis or SHAP analysis data mining algorithms, and supplemented by Latin hypercube sampling and global sensitivity analysis, this application can deeply explore and quantify the weight ratio and coupling influence of each design parameter on the frequency changes of each order of turbine blades. This enables designers to clearly understand the complex relationship between the frequency of each order of turbine blades and the design parameters, as well as the influence mechanism between the frequencies of each order. This transforms the frequency tuning process from experience-based trial and error to precise adjustment based on scientific insight, avoiding the problems of excessive iterations or failure to reach the target frequency due to blind parameter adjustments.

[0043] To further clarify the turbine blade frequency modulation method based on parametric design proposed in this application, a preferred embodiment will be used to provide a detailed explanation of the method provided in this application, and the relevant research work will be carried out in a logical order. Taking a certain type of turbine blade as an example, this application first realizes the rapid calculation of turbine blade frequency assisted by the parametric modeling method, and the technical process is shown in the attached figure. Figure 1 As shown, the specific implementation steps are described below: Step 1: Parametrically characterize the complex profile of the turbine blade, and obtain the turbine blade profile structure data based on the parametric characterization; select parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters of the blade for turbine blade frequency tuning based on the degree of influence on the mass distribution of the turbine blade.

[0044] In the turbine blade design process, aerodynamic profile design often takes precedence over turbine blade frequency tuning. Therefore, during the adjustment of the turbine blade profile, it is essential to maintain the aerodynamic performance as much as possible to avoid problems such as turbine performance degradation caused by frequency adjustments. Thus, the two-dimensional blade profile design selected in this example is achieved through a method of determining overall parameters and then fine-tuning them locally.

[0045] Furthermore, to avoid changes in turbine blade performance during frequency modulation, it is necessary to control aerodynamic design parameters as directly as possible. The two-dimensional profile of the turbine blade is parametrically characterized by leading-edge radius, trailing-edge radius, axial chord length, angle between the centers, inlet geometric angle, upper inlet wedge angle, lower inlet wedge angle, effective outlet angle, outlet deflection angle, and outlet wedge angle. During turbine frequency modulation, these parameters are kept constant to maintain turbine performance.

[0046] Furthermore, while keeping the aforementioned parameters unchanged, the two-dimensional profile of the turbine blades is locally adjusted by adding two control points on the pressure side (the first pressure surface control point P1 and the second pressure surface control point P2) and four control points on the suction side (the first control point SLE1 on the suction side leading edge, the second control point SLE2 on the suction side leading edge, the first control point STE1 on the suction side trailing edge, and the second control point STE2 on the suction side trailing edge). Specific control point parameters are as follows: Figure 2 As shown. Since the suction-side blade profile has a significant impact on the aerodynamic performance of turbine blades, the parameters of the first pressure-side control point P1 and the second pressure-side control point P2 are selected as the frequency modulation input variables in this specific embodiment.

[0047] Furthermore, the three-dimensional shape of the turbine blade profile is achieved through the design of axial and circumferential stacking parameters. Considering the limitation on the number of design parameters and their impact on turbine blade performance, the three-dimensional stacking parameters of the turbine blade remain unchanged.

[0048] Furthermore, since the tenon is located outside the blade's main flow path, and changes to the tenon's geometry do not affect the blade's aerodynamic performance, the turbine blade frequency can be adjusted independently and efficiently by adjusting the blade tenon. In this application's implementation example, a set of core design parameters for the tenon is determined, and their geometric definitions are as follows: Figure 3 As shown, the main parameters include: the width increment Ws of the tenon relative to the blade root section, the height hs of the connection section between the tenon and the root, the rounding radius Rs of the connection section between the root and the tenon, and the tenon pressure angle β and tenon tooth profile angle γ that constitute the geometric shape of the fir tree-shaped tenon teeth. By adjusting the above tenon design parameters, efficient frequency regulation of turbine blades can be achieved without sacrificing aerodynamic efficiency.

[0049] Furthermore, using the aforementioned two-dimensional blade profile parameters, three-dimensional stacking parameters, and tenon parameters as input parameters, the turbine blade surface structure modeling data is obtained, providing data support for the cooling structure modeling in subsequent steps.

[0050] Step 2: Perform parametric design on the turbine blade cooling structure and select appropriate parameters for turbine blade frequency modulation.

[0051] Specifically, the turbine blades are first parametrically characterized by selecting key cooling structure parameters. Adjustments to these parameters are then made to adjust the turbine blade cooling structure design data. Blade wall thickness and internal rib structure have a significant impact on the overall blade mass; therefore, these parameters are prioritized for frequency tuning and finely adjusted. Film cooling holes and impact holes have relatively minor impacts on mass distribution and are therefore simplified during model building and excluded from the parameter considerations for this frequency tuning process.

[0052] Furthermore, in specific implementations, the parameterized model for blade wall thickness is as follows: Figure 4 As shown, variable wall thickness distribution is achieved by setting the wall thickness at different locations, specifically including the leading edge thickness t0, the trailing edge thickness t1, and the thickness at the blade profile interpolation point. By adjusting the values ​​of each control point, the blade mass distribution can be flexibly adjusted. Similarly, the blade tuning parameters for the internal ribs are shown in the attached figure. Figure 5 As shown, the percentage of the pressure side (i.e., the relative position of the rib between the pressure surface and the suction surface), the angle between the geometric axis of the rib and the reference axis, and the rib thickness have a significant impact on the quality, and are also preferably the design parameters for blade frequency tuning.

[0053] Step 3: Combining computer-aided modeling software with the obtained surface structure modeling data and cooling structure modeling data, the three-dimensional model of the turbine blade is quickly generated, and the natural frequency is calculated.

[0054] In the specific implementation described in this application, UG / NX is selected as the modeling tool, and its C++ API is used for secondary development. First, functions for importing curves, passing curve groups, Boolean operations, and rotation are implemented. Second, the import curve function is used to complete the turbine blade outline data and cooling structure modeling data obtained in steps 1 and 2. Third, the passing curve group function is used to construct the turbine blade, inner cavity, ribs, and tenon shapes. Next, the rotation function is used to construct the flow channel's rotating body. Finally, Boolean operations are used to sum the constructed turbine blade and cooling structure entities, and intersection is performed through the flow channel to obtain the turbine blade structure within the flow channel. This process encapsulates the tedious manual modeling process into a programmable automated script, ensuring the standardization and repeatability of the modeling process. In practical applications, those skilled in the art can select computer-aided modeling software that can automatically and quickly generate the 3D geometric model of the turbine blade.

[0055] Furthermore, the automated program executes according to a preset process, generating solid surfaces from the blade profile data, constructing the inner cavity based on the inner wall profile generated in step 2 and performing Boolean operations to calculate the difference, and solidifying the solved rib profile inside the blade. After merging with the blade body, a complex cooling channel is formed inside the blade. Finally, the edge plate, extension root, and tenon structure are integrated to form a complete three-dimensional solid model of the turbine blade that can be used for engineering analysis.

[0056] Furthermore, using the 3D solid model of the turbine blade as input, ANSYS Workbench was used for mesh generation, and boundary conditions were set on the tenon bearing surface before calculating the natural frequencies of each order of the turbine blade. The initial manual setup served as a template, and subsequent processes were automated through a program.

[0057] Step 4: Using the selected parameters as input variables, follow the instructions in the appendix. Figure 6 Data mining was conducted during the process to explore the mechanism by which design parameters affect turbine blade frequency, as detailed below: To construct a high-precision surrogate model capable of characterizing the mapping relationship between design parameters and turbine blade frequencies (such as the Kriging model used in the specific implementation case provided in this application), initial sample collection is first performed using Latin hypercube sampling, and model accuracy is evaluated using cross-validation. Samples are supplemented through parametric modeling, automated mesh generation, and turbine blade frequency calculation until the prediction error of the surrogate model meets the accuracy requirements.

[0058] Furthermore, leveraging the computational advantages of this high-precision surrogate model, data mining is performed to reveal the intrinsic influence mechanism of design parameters on turbine blade frequency. In a specific embodiment of this application, total variation analysis is employed to quantify the contribution rate of each design parameter and its interaction effects to a specified order frequency, identifying key influencing factors on turbine blade frequency. Subsequently, by constructing variance contribution rate diagrams and two-dimensional interaction diagrams of variables, the coupling influence mechanism between single and two variables is presented in a visual manner. This accurately depicts the non-monotonic, highly nonlinear frequency change patterns and trends caused by changes in key design parameters, revealing the intrinsic physical mechanism by which each variable affects blade frequency, thereby achieving precise frequency tuning of the turbine blade.

[0059] Based on the above-mentioned methodological concept, this application can also provide a turbine blade frequency modulation system based on parametric design, including a parameter acquisition module, a natural frequency acquisition module, a surrogate model optimization module, and a sampling adjustment module; The parameter acquisition module is used to parametrically characterize the complex profile of the turbine blade, and obtain the turbine blade profile structure data based on the parametric characterization. Based on the degree of influence on the turbine blade mass distribution, parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning. The turbine blade cooling structure is parametrically designed to obtain cooling structure shape data, and parameters from the cooling structure design parameters are selected based on the influence on the turbine blade mass distribution for turbine blade frequency tuning. The natural frequency acquisition module is based on the turbine blade profile structure modeling data. It establishes a turbine blade shape solid model in computer-aided modeling software and combines it with the obtained cooling structure modeling data to obtain a cooling structure solid model. Boolean operations are performed between the cooling structure solid model and the blade shape solid model to realize the three-dimensional solid modeling of the turbine blade. The frequency evaluation software is used to evaluate the turbine blade frequency and obtain the natural frequencies of each order of the turbine blade. The surrogate model optimization module takes the selected blade 2D profile parameters, 3D stacking parameters, tenon parameters, cooling structure design parameters, and turbine blade natural frequencies as inputs to construct a surrogate model and verify that its accuracy meets the requirements. The sampling and adjustment module is used to sample through a surrogate model, identify the influencing factors and influence laws of each order frequency of the turbine blade, and adjust the design parameters of the turbine according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

[0060] On the other hand, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the turbine blade frequency modulation method based on parametric design described in this application.

[0061] This application may also provide a computer device, including a processor and a memory, wherein the memory is used to store a computer executable program, the processor reads the computer executable program from the memory and executes it, and the processor can implement the turbine blade frequency modulation method based on parametric design described in this application when executing the computer executable program.

[0062] The computer device may be a laptop, a desktop computer, or a workstation.

[0063] The processor can be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), or an off-the-shelf programmable gate array (FPGA).

[0064] The memory described in this application can be an internal storage unit of a laptop, desktop computer, or workstation, such as memory or hard disk; or it can be an external storage unit, such as a portable hard disk or flash memory card.

[0065] Computer-readable storage media can include computer storage media and communication media. Computer storage media includes volatile and non-volatile, removable and non-removable media implemented using any method or technology for storing information such as computer-readable instructions, data structures, program modules, or other data. Computer-readable storage media can include: read-only memory (ROM), random access memory (RAM), solid-state drives (SSDs), or optical discs, etc. Random access memory can include resistive random access memory (ReRAM) and dynamic random access memory (DRAM).

[0066] This specific embodiment is merely illustrative and should not be construed as limiting the scope of protection of this application in any way. Any obvious modifications, equivalent substitutions, or adaptive adjustments made by those skilled in the art based on the core principles of this application do not exceed the spirit and scope of this application and are covered by the appended claims.

Claims

1. A method for frequency modulation of turbine blades based on parametric design, characterized in that, Includes the following steps: The complex profile of the turbine blade is parametrically characterized, and the structural modeling data of the turbine blade profile is obtained by solving the parametric characterization. Based on the degree of influence on the mass distribution of the turbine blade, parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning. Parametric design of turbine blade cooling structure is performed to obtain cooling structure shape data; parameters in the cooling structure design parameters are selected based on their influence on turbine blade mass distribution for turbine blade frequency modulation. Based on the turbine blade profile structure modeling data, a turbine blade shape solid model is established in computer-aided modeling software. Combined with the obtained cooling structure modeling data, a cooling structure solid model is obtained. Boolean operations are performed on the cooling structure solid model and the blade shape solid model to realize the three-dimensional solid modeling of the turbine blade. The frequency evaluation software is used to evaluate the turbine blade frequency and obtain the natural frequencies of each order of the turbine blade. Using the selected two-dimensional blade profile parameters, three-dimensional stacking parameters, tenon parameters, cooling structure design parameters, and natural frequencies of the turbine blades as inputs, a surrogate model is constructed and its accuracy is verified to meet the requirements. By sampling through a surrogate model, the influencing factors and their laws of influence of each order frequency of the turbine blade are identified. The design parameters of the turbine are then adjusted according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

2. The frequency modulation method for turbine blades based on parametric design according to claim 1, characterized in that, The complex profile of the turbine blade is parametrically characterized. The turbine blade profile structure data obtained from the parametric characterization includes: using a hybrid parametric method of giving global geometric parameters and correcting local parameters, the key two-dimensional profiles of the turbine blade are mathematically defined, and the profiles are decomposed into two parts for control: one part is controlled by a set of global parameters with clear aerodynamic and structural significance, including leading edge radius, trailing edge radius, axial chord length, center-to-center angle, inlet geometric angle, inlet upper wedge angle, lower wedge angle, effective exhaust angle, outlet deflection angle, and outlet wedge angle; the other part is adjusted by B-spline curve control points to adjust the complex curvature of the pressure surface and suction surface. The B-spline curve control points are composed of two B-spline control points on the pressure surface and four B-spline control points on the suction surface.

3. The frequency modulation method for turbine blades based on parametric design according to claim 1, characterized in that, Based on the degree of influence on the turbine blade mass distribution, parameters from the two-dimensional blade profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency modulation, including: Parametric design of the two-dimensional profile of the turbine blade is carried out, and the two-dimensional profile parameters are selected according to their influence on the mass distribution of the turbine blade. Two-dimensional profiles are stacked in three dimensions, and the three-dimensional stacking method of turbine two-dimensional profiles is designed to determine the axial and circumferential stacking positions of different cross-sectional profiles. Parametric design was performed on the turbine blade rim plate, extension root, and tenon respectively, and the tenon parameters were selected based on their influence on the mass distribution of the turbine blade.

4. The frequency modulation method for turbine blades based on parametric design according to claim 3, characterized in that, The process of stacking two-dimensional profiles into three dimensions involves adjusting the axial and circumferential stacking parameters of the stacking center of each two-dimensional profile to achieve four different forms of stacking lines: straight lines, curves, end curves, and free curves. This controls the relative position of the axial and circumferential stacking centers of each profile. By adjusting the three-dimensional stacking relationship of the blade profiles, a three-dimensional blade surface is obtained.

5. The frequency modulation method for turbine blades based on parametric design according to claim 3, characterized in that, Parametric design was performed on the turbine blade rim, extension root, and tenon. Tenon parameters were selected based on their impact on turbine blade mass distribution. The parametric scope was expanded from the blade aerodynamic profile to the key load-bearing structures connected to the turbine disk. These key load-bearing structures included the rim, extension root, and tenon. Key parameters for the rim included the blade's forward / backward offset, rim thickness, and the rim angle relative to the axial direction. Key parameters for the extension root included the length and connection method of the transition section, and the design parameters of the near-rim end profile and the near-tenon end profile. Key parameters for the tenon included the number of teeth, pressure angle, tooth profile angle, tooth root fillet radius, tooth tip fillet radius, overall tenon height, and the increase in tenon width relative to the extension root. Simultaneously, the overall tenon height, pressure angle, tooth profile angle, and rim thickness were selected as design parameters for blade frequency tuning.

6. The frequency modulation method for turbine blades based on parametric design according to claim 1, characterized in that, Using the selected two-dimensional blade profile parameters, three-dimensional stacking parameters, tenon parameters, cooling structure design parameters, and the natural frequencies of each turbine blade as inputs, a surrogate model is constructed and its accuracy is verified to meet the requirements, including: Using selected blade 2D profile parameters, 3D stacking parameters, tenon parameters, cooling structure design parameters, and turbine blade natural frequencies as inputs, an initial input variable set is obtained using a Latin hypercube sampling strategy. The initial samples are evaluated to obtain the natural frequency values ​​corresponding to each sample point, and these natural frequency values ​​are added to the sample set as output variables. A surrogate model is constructed based on the sample set after adding sample points, and the accuracy of the surrogate model is evaluated through cross-validation. If the surrogate model does not meet the accuracy requirements, additional sampling is performed and added to the sample set before reconstructing the surrogate model. This process continues until the surrogate model's prediction accuracy meets the requirements, ultimately resulting in a surrogate model that meets the accuracy requirements for subsequent blade frequency evaluation.

7. The frequency modulation method for turbine blades based on parametric design according to claim 1, characterized in that, By sampling using a surrogate model, the influencing factors and patterns of each order frequency of the turbine blade are identified. Based on the requirements, the turbine design parameters are adjusted to obtain the target natural frequency of the turbine blade and its corresponding parameters. This includes: combining total variation analysis or SHAP analysis data mining algorithms, using the constructed surrogate model as a basis, performing Latin hypercube sampling and data mining, and combining global sensitivity analysis to obtain the weight ratio and coupling influence relationship of each design parameter on the frequency changes of each order of the blade. This clarifies the complex relationship between each order frequency of the turbine blade and the design parameters, as well as the mutual influence mechanism of each order frequency. Based on the target natural frequency requirement of the turbine blade and combined with the obtained mechanism of action of the design parameters, the corresponding design parameters are adjusted to obtain the target natural frequency of the turbine blade and its corresponding parameters.

8. A turbine blade frequency modulation system based on parametric design, characterized in that, It includes a parameter acquisition module, a natural frequency acquisition module, a surrogate model optimization module, and a sampling adjustment module; The parameter acquisition module is used to parametrically characterize the complex profile of the turbine blade, and obtain the turbine blade profile structure data based on the parametric characterization. Based on the degree of influence on the turbine blade mass distribution, parameters from the two-dimensional profile parameters, three-dimensional stacking parameters, and tenon parameters are selected for turbine blade frequency tuning. The turbine blade cooling structure is parametrically designed to obtain cooling structure shape data, and parameters from the cooling structure design parameters are selected based on the influence on the turbine blade mass distribution for turbine blade frequency tuning. The natural frequency acquisition module establishes a turbine blade shape solid model in computer-aided modeling software based on turbine blade profile structure modeling data, and obtains a cooling structure solid model by combining the obtained cooling structure modeling data. Boolean operation is performed between the cooling structure solid model and the blade shape solid model to realize three-dimensional solid modeling of the turbine blade. The frequency evaluation software is used to evaluate the turbine blade frequency and obtain the natural frequencies of each order of the turbine blade. The surrogate model optimization module takes the selected blade 2D profile parameters, 3D stacking parameters, tenon parameters, cooling structure design parameters, and turbine blade natural frequencies as inputs to construct a surrogate model and verify that its accuracy meets the requirements. The sampling and adjustment module is used to sample through a surrogate model, identify the influencing factors and influence laws of each order frequency of the turbine blade, and adjust the design parameters of the turbine according to the requirements to obtain the target natural frequency of the turbine blade and its corresponding parameters.

9. A computer device, characterized in that, It includes a processor and a memory, the memory being used to store a computer-executable program, the processor reading part or all of the computer-executable program from the memory and executing it, and the processor executing part or all of the computer-executable program is able to implement the turbine blade frequency modulation method based on parametric design as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, A computer-readable storage medium stores a computer program that, when executed by a processor, enables the implementation of a turbine blade frequency modulation method based on parametric design as described in any one of claims 1-7.

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