Parameterization calculation method for modal and pitch diameter of top cover of water turbine

Abstract

The invention provides a parameterization calculation method for a top cover modal and a pitch diameter of a water turbine, and belongs to the technical field of hydraulic mechanical structure dynamics and simulation automation. The method comprises the steps of parameter input, parametric modeling, automatic simulation control, pitch diameter identification and analysis and result output: after a parameter set is input, constructing a parametric modeling module based on Python and ANSYS Spaceclaim, and automatically generating a three-dimensional geometric model containing a basic panel, a rib plate and a connecting hole; an automatic simulation control module is constructed based on Python and ANSYS Workbench, and full-process automatic simulation is completed to obtain a modal analysis result; pitch diameter characteristic parameters are automatically recognized through a least square discrete Fourier transform algorithm of non-equiangular sampling and confidence degree judgment; and outputting results to form a standardized database. According to the method, automation and quantification of the whole process are achieved, modeling and simulation efficiency is improved, manual misjudgment is avoided, the method is suitable for different types of water turbine top covers, and reliable data support is provided for structural optimization and resonance risk assessment.

Description

Technical Field

[0001] This invention relates to the field of hydropower unit structural dynamics and simulation automation technology, and in particular to a parametric calculation method for the top cover mode and section diameter of a hydropower turbine. Background Technology

[0002] The turbine top cover is a crucial load-bearing component that withstands water pressure and transmits shaft loads. Its geometry, stiffener arrangement, and reinforcement methods significantly impact the structure's stiffness, natural frequencies, and resonance safety. Existing modal analysis methods primarily rely on manual modification of geometric dimensions and boundary conditions within CAD / CAE software, followed by manual import of the finite element model for calculation. This process is cumbersome, inefficient, and prone to errors, making it difficult to achieve rapid simulation and data consistency under multi-parameter conditions.

[0003] Furthermore, the nodal diameter characteristic in modal results, i.e., the number of lobes in the mode shape along the circumferential direction, is a key indicator for conducting dynamic and static interference analysis and resonance risk assessment. However, traditional methods mostly rely on manual observation of mode shape diagrams for judgment, lacking quantitative identification and automatic classification methods, making it difficult to extract nodal diameter patterns in batch calculations. Existing technologies have not yet established an automated system capable of uniformly controlling modeling, simulation solutions, and nodal diameter identification, and cannot systematically characterize the mapping relationship between roof structure parameters and modal responses and nodal diameter characteristics, nor can they support data-driven analysis needs for optimization design or dynamic and static interference prediction.

[0004] Existing technologies for parametric modeling and modal analysis of turbine top cover structures suffer from the following main drawbacks: low modeling efficiency, complex top cover geometry, and difficulty in ensuring geometric consistency and modeling accuracy through manual adjustments; fragmented simulation processes, with geometric modeling, mesh generation, load setting, and modal analysis being independent of each other, lacking a unified automated control mechanism; lack of standardized data output, making it impossible to extract modal results and nodal diameter data in batches, and data traceability and comparison difficult; and isolated modal analysis results, lacking a systematic mapping relationship between parameters, modes, and nodal diameter, which limits the digital and intelligent improvement of turbine top cover structure performance. Summary of the Invention

[0005] This invention provides a parameterized calculation method for the mode and diameter of a turbine top cover. It addresses the problems in existing technologies, such as complex modeling of turbine top covers, fragmented simulation processes, difficulties in data extraction, and reliance on manual judgment for diameter identification. The method automates the entire process, establishes a quantitative mapping relationship, and supports structural optimization and risk assessment.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A parametric calculation method for the top cover mode and nodal diameter of a water turbine includes the following steps: Step 1, Parameter Input: Input the parameter set P of the turbine top cover. The parameter set P includes the feature parameter points of the sketch.p i Angular characteristic parameters θ j and structural characteristic parameters d k Among them, sketch feature parameter points p i This includes the rotation section points of the base panel, the tensile section points of the long and short stiffeners, etc.; angular characteristic parameters. θ j Including rotation angle, stiffener arrangement angle, and connection hole distribution angle; structural characteristic parameters. d k This includes the number of parameters such as the number of stiffeners, their thickness, and the radius of the connecting holes. i , j , k It can be flexibly expanded according to design requirements.

[0007] Step 2, Parametric Modeling: A parametric modeling module is built based on the joint interface of Python and ANSYS Spaceclaim. This module automatically generates a 3D geometric model of the turbine top cover based on the parameter set P. The modeling process is abstracted as mapping M = ... T (P), where P is the set of input parameters and M is the automatically generated 3D geometric model, ensuring that each set of parameters corresponds to a unique model. The specific steps are as follows: 1. Basic panel generation: Based on the outline point set of the top cover, establish the cross-sectional curve in the ZX plane, and generate a rotating solid by 360° to form the basic panel of the top cover. At the same time, reserve the connection part between the center hole and the outer edge to determine the overall shape and thickness of the top cover.

[0008] 2. Radial long stiffener construction: Multiple radial long stiffeners are arranged in a circumferential array on the foundation panel. A single stiffener is formed by symmetrical stretching, and then a complete ring reinforcement system is generated by rotating the array. Its parameters include cross-sectional sketch points, number of stiffeners, fillet radius and thickness.

[0009] 3. Radial short stiffener construction: Short stiffeners are arranged between long stiffeners and stretched to form a short stiffener solid, thereby achieving local stiffness enhancement and stress concentration suppression. Its parameters include section sketch points, number of stiffeners, thickness, and start and end angle range, etc.

[0010] 4. Connection hole array construction: Automatically arrange connection holes on the outer edge of the top cover according to the input parameters for the assembly of guide vanes, seals or seat rings. The input parameters include the position of the hole reference plane, the arrangement radius, the hole diameter and the coordinates of the hole center point.

[0011] 5. Geometric Fusion: After each feature is modeled, Boolean operations are automatically performed to fuse all substructures, and a micro-rotation alignment algorithm is used to eliminate duplicate geometry. The geometry file is automatically saved to the specified path by the Python interface.

[0012] Step 3: Automated Simulation Control: An automated simulation control module is built based on Python and ANSYS Workbench to achieve fully automated management of the entire process, including geometry import, system setup, mesh generation, modal solving, and result export. The specific steps are as follows: 1. System Setup and Geometric Import: The background system automatically calls ANSYS Workbench to create a dual system of "statics-modal". Data sharing enables the inheritance of the two-stage mechanical fields. The modal system uses the prestressed field obtained from the statics solution as the initial condition, satisfying the relationship f= W ( σ 0, P,M,B), where σ 0 represents the prestress distribution obtained from static analysis, M represents the set of material parameters, B represents the boundary and load conditions, and f represents the modal frequency vector.

[0013] 2. Material, Boundary Conditions, and Load Settings: After importing geometry, material parameters are automatically set, including Young's modulus, density, Poisson's ratio, etc. The geometric centroid coordinates of each face are calculated by traversing the model face set. , where Ω i Let A be the area of ​​the region, and r = ( x , y , z Based on the target coordinates c of the typical stress and constraint area of ​​the top cover. t =( x t , y t , z t ) and allowable error (Δ x Δ y Δ z Perform tolerance envelope judgment on candidate surfaces to ensure they meet the requirements. The target surface is determined by the person. F j It automatically creates naming options and binds them with physical meaning, thus automatically applying forces and constraints.

[0014] 3. Automatic Mesh Generation: Automatically calls the Workbench mesh generator to perform global mesh generation, setting the element size to... l e The grid density control condition is: ,in V model The total volume of the model is κ, which is a scaling factor related to the element type. N e Automatically adjust to the expected number of units. le To ensure N min ≤ N e ≤ N max ,in, N min and N max These are the lower and upper thresholds for the expected number of elements, respectively. Tetrahedral elements are used, and the ribbed ends and hole edges are locally densified.

[0015] 4. Simulation Solution and Data Extraction: Modal problems satisfy the characteristic equation Where K is the global stiffness matrix and M is the mass matrix. ω i and φ i These represent the i-th angular frequency and mode shape, respectively. After the solution is completed, the displacement results of each frequency and the specified node / surface are automatically extracted and written to a CSV file through the "TabularData" interface. A file verification mechanism is set up: "done.flag" is generated upon successful export, and "err.flag" is generated and the subsequent process is stopped if an error occurs.

[0016] 5. Batch computation: Based on the combination of values ​​of parameter space P and a predetermined sampling strategy, a sample sequence is generated. For each sample, a closed loop of "modeling-mesh-boundary-modal-derivation" is automatically executed to obtain the frequency vector f. k And establish mapping P k →f k The scheduler allocates tasks in a serial or parallel manner and monitors the status of the flag file. The results are archived into a standardized database using a parameterized naming rule.

[0017] Step 4, Nodal Diameter Identification and Analysis: Construct a nodal diameter identification and analysis module based on modal simulation results to automatically identify the nodal displacement patterns, segmentation characteristics, and number of nodal diameters along the circumferential direction in the central hole region of the turbine top cover. The specific steps are as follows: 1. Data Extraction and Node Filtering: Extract the spatial coordinates of sampling nodes at the circumferential feature lines of the top cover, and extract the displacement response values ​​of the sampling nodes in preset directions under each target mode. Calculate the circumferential angle position corresponding to each sampling node. θ i This forms a sampling dataset, retaining only the nodes located on the upper surface of the hole edge to ensure that the data constitutes a complete closed circular curve.

[0018] 2. Non-equiangular sampling curve reconstruction: The least squares discrete Fourier transform (LS-DFT) algorithm is used to fit the non-equiangular sampling points to an equiangular continuous function, given... NFor each sample point, minimize the weighted objective function. Find the optimal Fourier coefficients A 0, A m , B m and reconstruct the continuous curve ,in It is a periodic trapezoidal weight used to eliminate pseudo-frequency interference.

[0019] 3. Spectral Energy Decomposition: Perform spectral energy decomposition on the reconstructed curve and define the energy weights for each order. The wave number corresponding to the one with the highest energy m This refers to the dominant nodal diameter number K of the mode. When K=0, it is the overall rigid body mode; when K=1, it is the single-lobe warping mode; and when K=2, 3, 4..., it corresponds to the double-lobe, triple-lobe and higher-order nodal diameter modes, respectively.

[0020] 4. Confidence Assessment: Based on the inverse reconstruction curve of the dominant wavenumber component, a confidence index is defined by comparing the error between the original curve and the reconstructed curve. ;in For the first i The circumferential angle position corresponding to each sampling point For the original curve in The displacement value at that location. The reverse reconstruction curve is constructed to retain only the harmonic components corresponding to the dominant nodal diameter number K. For its in The displacement value at that location. The sample mean and confidence level are given. η The closer it is to 100%, the higher the modal energy concentration and the more reliable the nodal diameter determination.

[0021] 5. Output Results: Automatically outputs nodal diameter recognition results, including modal order, nodal diameter number K, and confidence level. η The maximum displacement amplitude, pitch angle (angle difference between adjacent peaks), and curve reconstruction data are exported in a unified format and batch-summarized to form a database, while generating modal energy spectra.

[0022] Step 5, Output Results: Output the modal analysis results and nodal diameter characteristic parameters to form a standardized database, supporting subsequent statistical analysis, sensitivity assessment, design optimization, and machine learning modeling.

[0023] Compared with the prior art, the present invention has the following beneficial effects: 1. Intelligent modeling process and traceable parameters: Fully parametric modeling is achieved through Python and the ANSYS Spaceclaim interface. Users only need to input key geometric parameters to automatically generate a complete 3D model. All geometric features correspond one-to-one with the parameter set, ensuring geometric consistency and repeatability of results, significantly improving modeling efficiency, and parameter modification is intuitive and convenient.

[0024] 2. Automated simulation process and significantly improved computational efficiency: An automated simulation control system based on Python and ANSYS Workbench is established to achieve a fully automated closed loop from parameter input to modal output without manual intervention, significantly shortening the simulation cycle, ensuring computational consistency and data reliability between different parameter models, and providing a unified technical framework for large-scale parametric calculations.

[0025] 3. Quantitative and reliable nodal diameter identification: The proposed nodal diameter identification module uses the LS-DFT algorithm and confidence level discrimination method to perform harmonic energy analysis on the displacement data of the hole edge nodes, automatically identify the number of modal lobes and symmetry characteristics and output confidence level index, avoiding human misjudgment and improving the scientificity, objectivity and repeatability of modal analysis.

[0026] 4. Strong engineering adaptability and scalability: It does not depend on a specific geometric form and can be flexibly applied to the top cover of turbines of different models, sizes and reinforcement structures. It can also be extended to other axisymmetric components such as guide vane rings and upper crowns. Each functional module adopts an independent interface design, which can be embedded into existing enterprise simulation platforms and supports single-machine and distributed batch calculations, providing reliable digital support for the safe and stable operation of hydropower units. Attached Figure Description

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 A schematic diagram of the overall process for the parameterized calculation method of turbine top cover modes and nodal diameter based on Python and ANSYS platform established in this invention; Figure 2 This is a schematic diagram of the specific process of the parameterized calculation system for the turbine top cover mode and nodal diameter of the present invention; Figure 3 This is a schematic diagram of the parametric modeling of the turbine top cover according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the boundary conditions, load settings, and mesh generation for the automated simulation of the turbine top cover according to an embodiment of the present invention; Figure 5 A schematic diagram illustrating the variation and relative differences of the modal frequencies of the top cover under different parameter design spaces in an embodiment of the present invention; Figure 6 This is a schematic diagram of the top cover modal diameter identification results according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the inherent frequency distribution of the top cover under different section diameters (K values) according to an embodiment of the present invention. Detailed Implementation

[0028] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0029] The proposed system for parameterized calculation of turbine top cover modal characteristics and nodal diameter consists of three main modules: a parameterized modeling module, an automatic simulation control module, and a nodal diameter identification and analysis module. Through a unified parameter interface and file rules, the system achieves an integrated automated process from geometric modeling and simulation solving to modal characteristic and nodal diameter identification, and features data traceability, scalability, and reproducibility.

[0030] In terms of the overall process (see) Figure 1 The system first generates a 3D geometric model of the roof using the ANSYS Spaceclaim parametric modeling module. Then, the automatic simulation control module calls ANSYS Workbench to complete static and modal analyses, automatically establishing the system, applying loads, meshing, and extracting the calculation results. Finally, the nodal diameter identification and analysis module reads the modal result file, performs harmonic analysis and nodal diameter identification on the displacement distribution of the borehole edge nodes, and outputs the dominant nodal diameter number, confidence level, and pitch for each mode, forming a complete parameter-modal-nodal diameter database. The development and running environment of this system is Python 3.11 + ANSYS Spaceclaim + ANSYS Workbench 2023R1. The script uses a TCP interface to achieve bidirectional communication between Python and Workbench, enabling automatic execution of batch tasks in the background.

[0031] Specifically, the following steps are included: Step 1: Parametric Modeling Module.

[0032] The first step is to generate the basic panel. In the unit's coordinate system, with Z as the rotation axis and X–Y as the horizontal plane, all sectional sketches are drawn on the ZX plane, using mm and ° as the units of measurement. Based on... Figure 3 As shown in the rules, the system reads the panel rotation section parameters (see Appendix Table 1(a)) to automatically generate a closed profile and performs a 360° rotation to obtain an axisymmetric panel solid. At the same time, a central hole and an outer edge connection area are reserved to meet assembly and stress requirements. This process is automatically completed by a Python script in ANSYS Spaceclaim, and the geometric files are saved according to the parameter naming convention for subsequent automatic simulation calls and batch retrieval.

[0033] The second step involves defining the cross-section of the long stiffener plate in the ZX plane based on the control points given in Appendix 1(b). The system first extrudes to generate a single long stiffener plate entity, and then rotates it into an array according to a set circumferential step (30° in this embodiment, corresponding to 12 long stiffeners, which can be expanded as needed). To ensure mechanical continuity and mesh quality, transition fillets and necessary chamfers are applied to the stiffener roots and ends before merging with the panel. The key geometric quantities in this step are directly controlled by the parameter set, and... Figure 3 This is presented intuitively in the text.

[0034] The third step is the construction of radial short ribs. The short rib profiles are defined in the ZX plane according to Table 1(c). The system is stretched to form short rib entities, and a circumferential arrangement with a half-step angle offset is performed with reference to the long rib array, so that the short ribs form staggered supports between adjacent long ribs. The number, thickness, and start / end angle range of the short ribs are specified by the parameter set; in the typical working case configured in this embodiment with the same number of long ribs (12) and a local thickness of 70 mm, the number and arrangement angle range of the short ribs can be directly adjusted in the parameter set.

[0035] The fourth step is to construct the connecting hole array. The hole array adopts a parameterized definition of the reference plane position, arrangement radius, hole diameter, and hole center point coordinates: the system completes the equal-angle hole arrangement on the specified Z plane and cuts through in the normal direction to realize the coexistence and independent control of multiple hole rings. This embodiment gives three types of typical hole ring parameters for reproduction: (1) guide vane hole ring: number of holes 24, distribution radius 4230 mm, hole radius 175; (2) seat ring high-density hole ring: number of holes 120, distribution radius 5115 mm, hole radius 40; (3) center hole ring: number of holes 60, distribution radius 2215 mm, hole radius 32. The above parameters can be listed in Appendix 1(d) and flexibly adjusted according to engineering needs.

[0036] Appendix Table 1 is a parameter table of the top cover according to an embodiment of the present invention.

[0037] The fifth step is geometric fusion and output. After the panels, long ribs, short ribs, and hole array are all generated, the system automatically performs overall Boolean fusion and micro-rotation alignment to eliminate possible duplicate geometry and minor tolerance deviations. Then, standardized geometric files are exported to a specified directory, with parameter summaries embedded in the filenames to achieve a one-to-one correspondence. This modeling chain can be rebuilt with a single click when parameters are updated, ensuring the traceability of "parameters-geometry" and providing a basis for subsequent automatic simulation systems (…). Figure 2 (As shown) provides a consistent input. Formally, this is denoted as a mapping M = T (P), where P is the set of input parameters and M is the automatically generated 3D geometric model; in this embodiment, this mapping is achieved through the parameters in the appendix table and... Figure 3 The rules are specified to facilitate reproduction by those skilled in the art.

[0038] Step 2: Automatic simulation control module.

[0039] The first step is system setup and geometry import. A Python script automatically calls ANSYS Workbench to create a "static-modal" cascade system, and inherits the two-stage mechanical fields through data sharing. The modal system uses the prestressed field obtained from the static solution as the initial condition, and its relationship can be expressed as f = W ( σ 0， P, M, B), where σ 0 represents the prestress distribution obtained from static analysis, M represents the set of material parameters, B represents the boundary and load conditions, and the output modal frequency vector f is given.

[0040] The second step involves setting the material, boundary conditions, and loads. The material parameters, including Young's modulus, are automatically set within the Mechanical environment. ,density Poisson's ratio (Can be replaced by the engineering material library). Then, iterate through the model face set and calculate the geometric centroid of each face. , where c i For the first i The centroid coordinates of each face, Ω i For its surface area, A For the area, r = ( x , y , z Based on the target coordinates c of the typical stress and constraint area of ​​the top cover. t =( x t , y t , z t ) and allowable error (Δ x Δ y Δ z The tolerance envelope is determined for the candidate surface using the formula (0.05 mm, 0.05 mm, 0.05 mm). Those that meet the conditions are judged as the target surface. F j After naming is completed, loads and constraints are automatically applied. In this embodiment: F 1 represents the pressure-bearing surface between the guide vane distribution circle and the runner inlet radius. F 2 represents the pressure-bearing surface between the impeller inlet radius and the upper sealing ring. F 3 is the pressure-bearing surface between the seal on the impeller and the main shaft seal. F 4 represents the connection constraint surface between the top cover and the seat ring. After naming, loads and constraints will be automatically applied. F 1. Apply pressure , F 2. Apply pressure , F 3. Apply pressure , F 4. Apply fixed constraints (displacement constraints). Load values ​​and boundary types can be retrieved from the load case library (and...). Figure 4 (Corresponding), and recorded in the project log and parameter snapshot for review.

[0041] The third step is automatic mesh generation. The Workbench mesher is invoked to perform global mesh generation and refinement of critical areas. The target element size is set. l e =0.2mm, mesh density control conditions are as follows ,in V model is the total volume of the model, and is the scaling factor related to the element type. N e This is the expected number of units. The system adjusts automatically. l e To ensure 10 5 ≤ N e ≤10 7 The system uses tetrahedral elements by default and locally refines the ribbed ends and hole edges to achieve a balance between computational load and accuracy.

[0042] The fourth step is simulation and data extraction. The modal problem satisfies the characteristic equation. Where K is the global stiffness matrix and M is the mass matrix. ω i and φ i The first i Angular frequencies and mode shapes. The script automatically schedules the first 10 frequencies for solving. After the solution is completed, the system automatically extracts the frequencies and displacements of specified nodes / faces through the "TabularData" interface and writes them to a CSV file. To ensure data integrity, a file verification mechanism is set up: when all... f i Upon successful export, "done.flag" is generated; if an error occurs, "err.flag" is generated and the subsequent process is stopped, thus achieving traceability and discriminability of the calculation.

[0043] The fifth step is batch computation and modal dataset generation. Building upon the single automated process, the system samples the given parameter space (using full factorization, equidistant grids, or Latin hypercubes) to form a parameter sequence. It automatically performs a closed-loop process of "modeling → meshing → boundary conditions → modal analysis → export" for each set of parameters to obtain the frequency vector f. k And establish mapping Pk →f k In this embodiment, the thickness range of the radial long / short stiffeners [20, 120] mm and the transition radius range of the long stiffener hole [10, 290] mm are selected as variables, while the remaining geometric and material parameters are fixed; the loads and constraints are as follows: Figure 4 The settings are configured to solve for the first 10 natural frequencies and archive them into a standardized database with parameterized names. The results are as follows: Figure 5 As shown, the natural frequencies of each modal order increase overall with increasing modal order; simultaneously, the frequency differences between different parameter combinations in the dataset span a large range (20.2%–41.4%), demonstrating significant adjustability and design margin. Therefore, the automatic simulation control module of this invention can stably complete batch modeling and solving under multi-parameter conditions, generating a consistent and traceable "parameter-modal" dataset, providing effective support for subsequent nodal diameter identification and design optimization.

[0044] Step 3: Nodal diameter identification and analysis module.

[0045] The first step is data extraction and node filtering. The system automatically reads the spatial coordinates of the nodes at the upper edge of the main shaft hole of the top cover and the parameters for each mode from the modal analysis results. Z Directional displacement forms a sampled dataset. Node angle θ i Calculated from its planar projection coordinates ,in( x i , y i Let be the position of the node in the local coordinate system. Only nodes located on the upper surface of the hole edge are retained to ensure that the data forms a complete closed circular curve, and the node displacement is... u i It reflects the vibration characteristics along the circumferential direction under this mode and is the basic data for pitch diameter identification.

[0046] The second step is the reconstruction of non-equiangular sampling curves. Since the nodes of the finite element mesh are not strictly equiangularly distributed on the circumference, direct spectral analysis will lead to phase errors and pseudo-frequency distortion. Therefore, this invention proposes a curve reconstruction algorithm based on least squares discrete Fourier transform (LS-DFT) to fit the non-equiangular sampling points to an equiangular continuous function. Given... N sample points By minimizing the weighted objective function: Find the optimal Fourier coefficients A 0, A m , B m and reconstruct the continuous curve .in The periodic trapezoidal weight is a correction factor that is directly related to the arrangement parameters of the top cover stiffener and the local mesh density. It is used to eliminate pseudo-frequency interference generated by complex structural topologies (such as stiffeners and openings) in local high-density mesh areas, thereby improving the robustness and accuracy of section diameter identification. A 0 indicates the axisymmetric (zeroth order) component. A m , B m For the first m The method can accurately recover the continuous displacement field in the circumferential direction under uneven node distribution, achieving high-precision modal waveform reconstruction.

[0047] The third step is to reconstruct the curve. Perform spectral energy decomposition, defining the energy weights for each order as follows: The wavenumber corresponding to the highest energy level is the dominant lobe number of that mode. Its physical meaning corresponds to the number of nodal diameters K of the dome: when K=0, it is a global rigid body mode; when K=1, it is a single-lobe warped mode; when K=2, 3, 4…, it corresponds to double-lobe, triple-lobe, and higher-order nodal diameter modes, respectively. This algorithm automatically identifies the dominant symmetry of the mode through harmonic energy, avoiding human error and possessing stability and scalability.

[0048] The fourth step is curve reconstruction and confidence assessment. To verify the reliability of the identified nodal diameter number K, the system reconstructs the curve in reverse based on the dominant wavenumber component. A confidence index is defined by comparing the errors between the original curve and the reconstructed curve. ;in For the first i The circumferential angle position corresponding to each sampling point For the original curve in The displacement value at that location. The reverse reconstruction curve is constructed to retain only the harmonic components corresponding to the dominant nodal diameter number K. For its in The displacement value at that location. The confidence level is the sample mean. The closer the confidence level is to 100%, the higher the modal energy concentration and the more reliable the nodal diameter determination. η A lower value indicates the presence of multi-wavenumber coupling or local asymmetry in that mode. This evaluation method can quantitatively determine modal purity, an innovative approach that traditional visual interpretation methods cannot achieve. Taking the structure in step 1 as an example, the LS-DFT reconstruction curve based on the hole edge node displacement matches the original curve well, and the waveform morphology is consistent (see...). Figure 6The identification confidence levels obtained from spectral energy decomposition were all 100%, indicating that the dominant energy was highly concentrated and the identification results were reliable. The determined nodal diameter K values ​​corresponded one-to-one with the lobe mode shapes: K=0 represented overall axial deformation, K=1 represented single-lobe warping, and K=2, 3, and 4 represented multi-lobe distribution. The visual mode shape and the main peak position of the spectral energy were consistent, verifying the identification effectiveness and robustness of the method under unequal angle sampling conditions, and realizing the automated and quantitative conversion from finite element modal data to nodal diameter parameters.

[0049] Step 5: Nodal diameter results output and statistical analysis. The module automatically outputs the nodal diameter identification results, including modal order, nodal diameter number K, and confidence level. η The data includes maximum displacement amplitude, pitch angle (angle difference between adjacent wave crests), and curve reconstruction data. The results are exported in a unified format and can be batch-summarized into a database. Simultaneously, modal energy spectra are generated, showing the distribution patterns of different modal energies across wavenumbers and revealing the evolutionary trends of structural modal characteristics. The sorting results are as follows: Figure 7 As shown, the natural frequencies corresponding to different K values ​​exhibit a clear and regular distinction. In this embodiment, the natural frequencies generally increase as K=1-4, and the frequency level at K=0 is higher than that at K=1, reflecting the consistency between the nodal diameter characteristics and the frequency response. This statistic shows that the identification method of the present invention can not only stably output the dominant K and confidence level, but also construct a "K-frequency" mapping and database in batch calculations, providing a quantitative and traceable basis for subsequent modal regulation, structural reinforcement layout, and dynamic and static interference assessment, demonstrating the innovation of this embodiment in terms of engineering usability and methodology.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A parametric calculation method for the top cover mode and nodal diameter of a water turbine, characterized in that, Includes the following steps: Step 1: Input the parameter set P={ for the turbine top cover p i , θ j , d k Define the key geometric features of the top cover, wherein the parameter set P includes sketch feature parameter points. p i Angular characteristic parameters θ j and structural characteristic parameters d k ; Step 2: Construct a parametric modeling module based on the joint interface of Python and ANSYS Spaceclaim, and automatically generate a three-dimensional geometric model of the turbine top cover according to the parameter set P. The three-dimensional geometric model includes a foundation panel, radial long stiffeners, radial short stiffeners and an array of connecting holes. Step 3: Build an automatic simulation control module based on Python and ANSYS Workbench to perform automatic simulation on the three-dimensional geometric model and obtain modal analysis results. The automatic simulation includes system establishment and geometry import, material boundary conditions and load setting, automatic mesh generation, simulation solution and data extraction. Step 4: Construct a nodule diameter identification and analysis module to process the modal analysis results and automatically identify nodule diameter characteristic parameters, including the nodule diameter number K and confidence level. η The maximum displacement amplitude and pitch angle; wherein, the number of pitch diameters K is determined by performing a weighted least squares discrete Fourier transform (LS-DFT) on the discrete circumferential sampling data and performing energy decomposition; Step 5: Output the modal analysis results and nodal diameter characteristic parameters to form a standardized database.

2. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 1, characterized in that, In step 2), the sketch feature parameter points p i This includes the rotational section points of the base panel and the tensile section points of the long and short stiffeners; the angular characteristic parameters θ j Including rotation angle, stiffener arrangement angle, and connecting hole distribution angle; the structural characteristic parameters d k This includes the number of stiffeners, their thickness, and the radius of the connecting holes.

3. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 2, characterized in that, The specific process of generating the base panel in step 2) is as follows: Based on the top cover outline point set, a cross-sectional curve is established in the ZX plane, and the cross-sectional curve is rotated 360° to generate a rotating solid, forming the top cover base panel, while reserving the connection part between the center hole and the outer edge.

4. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 2, characterized in that, The specific process for generating the radial long stiffeners and radial short stiffeners in step 2) is as follows: 1) Arrange radial long stiffeners in a circumferential array along the foundation panel, form a single long stiffener solid by symmetrical stretching, and then generate a complete ring reinforcement system by rotating array; 2) Arrange radial short stiffeners alternately between adjacent radial long stiffeners, and form short stiffener solids by stretching to achieve spatial stiffness balance.

5. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 2, characterized in that, The specific process of generating the connecting hole array in step 2) is as follows: Based on the input hole reference plane position, arrangement radius, hole diameter and hole center point coordinate parameters, connecting holes are automatically arranged on the outer edge of the top cover. The connecting holes include guide vane hole ring, seat ring high-density hole ring and center hole ring.

6. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 1, characterized in that, Step 3) involves the following process for system setup and geometry import: A joint calculation process for static and modal analysis is automatically created. Data sharing enables the inheritance of the two-stage mechanical fields. The modal system uses the prestressed field obtained from the static solution as initial conditions, satisfying the relationship f= W ( σ 0, P, M, B), where... σ 0 represents the prestress distribution obtained from static analysis, P represents the parameter set, M represents the material parameter set, B represents the boundary and load conditions, and f represents the output modal frequency vector.

7. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 1, characterized in that, The specific process of automatic mesh generation in step 3) is as follows: The Workbench mesh generator is called to perform global mesh generation, with the element size set to [value missing]. l e The grid density control condition is: ,in V model Where is the total volume of the model, and is a scaling factor related to the element type. N e The expected number of units; automatic adjustment. l e To ensure N min ≤ N e ≤ N max ,in, N min and N max These are the lower and upper thresholds for the expected number of elements, respectively. Tetrahedral elements are used, and the ribbed ends and hole edges are locally densified.

8. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 1, characterized in that, Step 3) also includes a batch calculation step: generating a sample sequence based on the combination of values ​​of parameter space P and a predetermined sampling strategy, and automatically performing a closed loop of "modeling-mesh-boundary-modal-derivation" for each sample to obtain the frequency vector f. k And establish mapping P k →f k The results are archived using a naming convention with parameters to form a standardized database.

9. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 1, characterized in that, The specific process of nodal diameter identification in step 4) is as follows: 1) Extract the spatial coordinates of the sampling nodes at the circumferential feature line of the top cover, and extract the displacement response values ​​of the sampling nodes in the preset direction under each target mode. Calculate the circumferential angle position corresponding to each sampling node. θ i This forms a sampled dataset; 2) The circular discrete sampling dataset is fitted and reconstructed using a weighted least squares discrete Fourier transform (LS-DFT) with non-equiangular sampling. The Fourier coefficients are obtained by minimizing the sum of squared weighted residuals. A 0, A m , B m The weighting coefficients are constructed as periodic trapezoidal weights based on the circumferential angle interval between adjacent sampling points, which are used to reduce the impact of spectral leakage or spurious peaks caused by unequal angle sampling on nodal diameter identification. The circumferential reconstruction function is constructed from the Fourier coefficients. 3) Perform spectral energy decomposition on the reconstructed curve and define the energy weights for each order. The order with the highest energy m The corresponding wave number is the dominant node diameter number K of that mode.

10. The parameterized calculation method for the top cover mode and nodal diameter of a water turbine as described in claim 9, characterized in that, Step 4) also includes a confidence assessment step: based on the inverse reconstruction curve of the dominant wavenumber component, a confidence index is defined by comparing the error between the original curve and the reconstructed curve. ;in For the first i The circumferential angle position corresponding to each sampling point For the original curve in The displacement value at that location. The reverse reconstruction curve is constructed to retain only the harmonic components corresponding to the dominant nodal diameter number K. For its in The displacement value at that location. The sample mean and confidence level are given. η The closer it is to 100%, the higher the modal energy concentration and the more reliable the nodal diameter determination.

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