Method for automatically completing missing data of a turbine blade profile front trailing edge and related device

Abstract

The application discloses a method for automatically completing missing data of a front trailing edge of a turbine blade profile and a related device, and relates to the field of turbine blade profile data processing.The method comprises the following steps: acquiring geometric data of two known segments of a to-be-completed aerodynamic profile; fitting two reference curves by using cubic B-spline; confirming whether the two reference curves have intersection points; calculating four equidistant lines of the front trailing edge corresponding to the two reference curves respectively on the basis of the reference curves; obtaining the center of a circle of the front trailing edge by finding intersection points of the two front equidistant lines and the two trailing equidistant lines; completing the circular arc segment of the front trailing edge and the trailing edge based on the center of the circle of the front trailing edge and the normal vector of the equidistant lines; and completing the remaining interval between the end point of the circular arc and the known segment by using the reference curve, so as to complete the automatic completion of the aerodynamic profile data.The application realizes the full-automatic repair of the missing aerodynamic profile of the front trailing edge, greatly reduces the working time compared with manual operation, has good reproducibility and stability, is convenient for batch processing, and can provide favorable support for the establishment of a reverse engineering database.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic shape design, and specifically relates to a method and related apparatus for automatically completing missing data of the leading and trailing edges of turbine blades. Background Technology

[0002] High-quality aerodynamic design of components such as airfoils and gas turbine blades is essential for obtaining excellent equipment. Excellent designs often rely on the accumulation of extensive experimental data, a process requiring a large number of aerodynamic profile samples. Besides in-house design, reverse engineering, as a tool for absorbing advanced designs from other sources, is widely used in the field of aerodynamic profile design.

[0003] Reverse engineering is the process of analyzing and deducing various design elements of an existing target product, ultimately resulting in a product that is not entirely identical but has similar functions. The reverse engineering process for aerodynamic profiles generally involves steps such as contour measurement, data processing, and geometric reconstruction. Among these, contour measurement is crucial for the accuracy of the profile and has seen significant advancements in recent years.

[0004] However, regardless of the advancements in profile measurement technology, accuracy issues inevitably arise at the leading and trailing edges. Airfoils and turbine blades, for example, have relatively sharp leading and trailing edges to improve aerodynamic efficiency. These regions are small in scale, have extremely high curvature, and are highly sensitive to flow fields, making it difficult to achieve sufficient measurement accuracy. In practical applications, measurement points at the leading and trailing edges are often omitted, and manual methods are used to complete the measurements, which requires improvement in both accuracy and efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a method and related apparatus for automatically completing missing data of the leading and trailing edges of turbine blades, so as to solve the problem that it is difficult to achieve sufficient measurement accuracy in the region where the leading or trailing edge is small in scale, has extremely large curvature, and the flow field is highly sensitive to the surface of this region.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] In a first aspect, the present invention provides a method for automatically completing missing data on the leading and trailing edges of turbine blades, comprising:

[0008] Obtain the geometric data of two known segments of the aerodynamic profile to be completed;

[0009] Using two known segments, two baseline curves are fitted using cubic B-splines.

[0010] Push the two reference curves outward in the direction of the front and tail edges to confirm whether the reference curves intersect.

[0011] Based on the specified leading and trailing radii, calculate a total of four equidistant lines corresponding to the leading and trailing edges of the two reference curves.

[0012] Find the intersection of the two equidistant lines of the leading edge and the two equidistant lines of the trailing edge to obtain the center of the circle of the leading edge and the trailing edge;

[0013] Based on the centers of the leading and trailing edges, and the normal vectors of the equidistant lines, complete the arc segments of the leading and trailing edges.

[0014] Using the baseline curve, the remaining interval between the endpoints of the arc and the known segments is completed, thus automatically completing the aerodynamic profile data.

[0015] Optionally, obtain the geometric data of two known segments of the aerodynamic profile to be completed:

[0016] Due to the lack of measurement points at the leading and trailing edges, the aerodynamic profile to be reconstructed is divided into two segments. The geometric data should be represented as two ordered sets of points (x, y), and the direction of each set of points should be processed from the leading edge to the trailing edge.

[0017] Optionally, two baseline curves can be fitted using cubic B-splines:

[0018] By calling the cubic B-spline fitting module, the two baseline curves r are fitted. ss (t),r ps Construction of (t); the first and last ends of the spline curve adopt non-node boundary conditions, that is, the polynomial expression of the first and second spline curves should be exactly the same, and the same applies to the second to last spline curve; the starting position of the origin corresponds to the spline curve parameter t=0, and the ending position corresponds to t=1.

[0019] Optionally, the two reference curves can be pushed outwards in the directions of the front and rear edges to confirm whether the reference curves intersect.

[0020] Extrapolating using the expressions for the first and last spline curves constructed in the previous step, the calculation of the intersection points of the baseline curves is described as an optimization problem:

[0021]

[0022]

[0023] Where: r ss (t) represents the suction surface reference curve; r ps (t) represents the pressure surface reference curve; t 10 ,t 20 The parameter value of the leading edge intersection point on the suction and pressure surface reference curve, t 11 ,t 21The parameter values ​​for the trailing edge intersection point on the suction and pressure surface reference curves are given. If an intersection point exists within an acceptable range of parameter variation, the objective function of the above optimization problem should be approximately zero. In this case, the intersection point can be taken as the average of the positions of the corresponding parameters on the two curves. If the optimal value of the objective function differs significantly from zero, it is assumed that the reference curves have no intersection point at the leading or trailing edge, and the algorithm is terminated.

[0024] Optionally, calculate a total of four equidistant lines corresponding to the leading and trailing edges of the two reference curves:

[0025] An equidistant line is defined as the curve formed by moving each point on a reference curve by the same distance along its normal vector direction; the mathematical form of an equidistant line is:

[0026]

[0027] Where: r(t) is the original curve; d is the offset; n′(t) is the normal vector at any point on the original curve. Utilizing the analytical form of the B-spline normal vector, the equidistant lines of the reference curve can be accurately calculated. Since the equidistant lines are parallel to the tangent vectors at corresponding points on the original curve, the intersection of equidistant lines with the same offset is equivalent to the center of the common tangent circle of the two curves with a given radius.

[0028] Optionally, find the intersection points of the two equidistant lines of the leading edge and the two equidistant lines of the trailing edge to obtain the centers of the leading and trailing edges:

[0029] The method for calculating the centers of the leading and trailing edges also adopts an optimization problem description, with the following problem form:

[0030]

[0031]

[0032] Where: R ss R represents the equidistant line corresponding to the suction surface. ps The equidistant lines corresponding to the pressure surface; t 12 ,t 22 The parameter value t represents the center of the leading edge circle lying on the equidistant lines of the suction and pressure surfaces. 13 ,t 23 The parameter value is the center of the trailing edge on the equidistant line of the suction and pressure surfaces.

[0033] Optionally, by using the parameter values ​​obtained from solving the optimization problem, the normal vectors of the two reference curves and the point of tangency of the circle can be obtained, thereby deriving the argument angle between the starting and ending points of the arc relative to the center of the circle; by using the parametric equation of the arc, the arc segments of the leading and trailing edges can be obtained.

[0034] Using the reference curve r ss In (t) 12 ,0)∪(1,t 13 The part of ) and the reference curve rps In (t) 22 ,0)∪(1,t 23 The section that connects the arc segment with the existing profile is completed, thus obtaining the aerodynamic profile.

[0035] Secondly, the present invention provides a system for automatically completing missing data on the leading and trailing edges of turbine blades, comprising:

[0036] The data acquisition module is used to acquire the geometric data of two known segments of the aerodynamic profile to be completed;

[0037] The benchmark curve acquisition module is used to fit two benchmark curves using cubic B-splines with two known segments.

[0038] The reference curve intersection confirmation module is used to push the two reference curves outward in the direction of the front edge and the tail edge to confirm whether there is an intersection point between the reference curves;

[0039] The equidistant line confirmation module is used to calculate a total of four equidistant lines corresponding to the front and rear edges of the two reference curves, based on the specified leading and trailing edge radii.

[0040] The module for confirming the center of the leading and trailing edges is used to find the intersection point of two equidistant lines of the leading edge and two equidistant lines of the trailing edge, and obtain the center of the leading and trailing edges.

[0041] The completion module is used to complete the arc segments of the leading and trailing edges based on the centers of the leading and trailing edges and the normal vectors of the equidistant lines; using the reference curve, it completes the remaining intervals between the endpoints of the arcs and the known segments, thus completing the automatic completion of the aerodynamic profile data.

[0042] Thirdly, the present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a method for automatically completing missing data of the leading and trailing edges of a turbine blade.

[0043] Fourthly, the present invention provides a computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, the steps of a method for automatically completing missing data on the leading and trailing edges of a turbine blade are implemented.

[0044] Compared with the prior art, the present invention has the following technical effects:

[0045] This invention enables fully automated repair of missing aerodynamic profiles at the leading and trailing edges, significantly reducing working time compared to manual operation. It also exhibits good reproducibility and stability, facilitates batch processing, and provides valuable support for the construction of reverse engineering databases.

[0046] This invention features simple input; it only requires inputting the coordinate point set directly obtained from contour measurement and adjusting the direction to run from the leading edge to the trailing edge. No prior affine transformations of the profile are necessary.

[0047] The automatic completion algorithm for missing aerodynamic profile data at the leading and trailing edges provided by this invention can be implemented using high-level programming languages ​​such as C++, Python, and MATLAB with the help of FORTRANFITPACK or similar spline curve toolkit interfaces, without relying on any modeling software. Attached Figure Description

[0048] Figure 1 A flowchart of the automatic aerodynamic profile completion algorithm for missing leading and trailing edges is provided for this invention.

[0049] Figure 2 This is a schematic diagram of the intermediate process of completing the leading edge portion according to the present invention.

[0050] Figure 3 This is a schematic diagram of the intermediate process of completing the trailing edge portion according to the present invention.

[0051] Figure 4 This is the final processing effect of the present invention on various types of missing leading and trailing edge profiles. Detailed Implementation

[0052] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0053] like Figure 1 As shown, the automatic completion algorithm for aerodynamic profile data with missing leading and trailing edges provided by this invention includes the following steps performed in sequence:

[0054] 1) Prepare the geometric data for the two known segments of the aerodynamic profile to be completed: In this example, the low-pressure turbine blade profile of the GE E3 engine is used. The data points for its leading and trailing edges are removed and used as an example, such as... Figure 2 As shown, the profile direction is adjusted to point from the leading edge to the trailing edge.

[0055] 2) Using two known segments, call the cubic B-spline fitting module to fit two baseline curves;

[0056] 3) Extrapolate the two reference curves outwards in the directions of the front and tail edges to confirm whether the reference curves intersect: The intersection point is calculated using the optimization problem solution described above, with the variable range set to -1. <t 10 ,t 20 <0,1 <t 11 ,t 21 <2.

[0057] 4) Based on the specified leading and trailing edge radii, calculate a total of four equidistant lines corresponding to the leading and trailing edges of the two reference curves. In this embodiment, the leading edge radius is specified as 0.5 mm, and the trailing edge radius is specified as 0.25 mm. The equidistant lines corresponding to the leading and trailing edges are as follows: Figure 2 and Figure 3 As shown by the dashed line in the image.

[0058] 5) Find the intersection point of the two equidistant leading edge lines and the two equidistant trailing edge lines to obtain the center of the leading edge and trailing edge: The specific optimization problem to be solved and the range of variables are the same as the corresponding content in the previous text.

[0059] 6) Based on the centers of the leading and trailing edges, and the normal vectors corresponding to the parameters at the intersection of the equidistant lines, use the parametric equation of the circle to complete the arc segments of the leading and trailing edges.

[0060] 7) Using the baseline curve, complete the remaining intervals between the endpoints of the circular arc and the known segments to automatically complete the aerodynamic profile data. Related parts include... Figure 2 and Figure 3 The light-colored solid line in the image shows the completed aerodynamic profile data. The completed aerodynamic profile data obtained above can be exported in plain text, CSV, PLT, and other formats, facilitating data exchange and post-processing. The overall processing effect of the algorithm on more examples is shown in the image. Figure 4 As shown.

[0061] In step 1), the aerodynamic profile to be reconstructed is divided into two segments due to the lack of measurement points at the leading and trailing edges. Taking a turbine blade as an example, these are the suction surface and the pressure surface. The geometric data should be represented as two ordered sets of points (x, y), and the direction of each set of points should be processed from the leading edge to the trailing edge.

[0062] In step 2), by calling the cubic B-spline fitting module, the two reference curves r can be fitted. ss (t),r ps Construction of (t). The first and last points of the spline curve use non-node boundary conditions, meaning the polynomial expressions of the first and second spline curves should be identical, and the same applies to the penultimate and penultimate spline curves. The starting position of the origin corresponds to the spline curve parameter t = 0, and the ending position corresponds to t = 1.

[0063] In step 3), the expression for the first and last spline curves constructed in the previous step is used for extrapolation. The calculation of the intersection points of the reference curves is described as an optimization problem:

[0064]

[0065]

[0066] Where: r ss (t) represents the suction surface reference curve; rps (t) represents the pressure surface reference curve; t 10 ,t 20 The parameter value of the leading edge intersection point on the suction and pressure surface reference curve, t 11 ,t 21 Let be the parameter value of the trailing edge intersection point on the suction and pressure surface reference curves. If an intersection point exists within an acceptable range of parameter variation, the objective function of the above optimization problem should be approximately zero. In this case, the intersection point can be taken as the average value of the corresponding parameter positions on the two curves. If the optimal value of the objective function differs significantly from zero, it is assumed that the reference curves have no intersection point at the leading or trailing edge, and the algorithm terminates.

[0067] In step 4), the leading and trailing edge radii can be specified according to manufacturing capabilities or fitted with existing rough data. An equidistant line is defined as the curve formed by moving each point of the reference curve the same distance along its normal direction. The mathematical form of an equidistant line is:

[0068]

[0069] Where: r(t) is the original curve; d is the offset; n′(t) is the normal vector at any point on the original curve. Utilizing the analytical form of the B-spline normal vector, the equidistant lines of the reference curve can be accurately calculated. Clearly, the equidistant lines are parallel to the tangent vectors at corresponding points on the original curve; therefore, the intersection of equidistant lines with the same offset is equivalent to the center of the common tangent circle of the two curves with a given radius.

[0070] In step 5), the method for calculating the centers of the leading and trailing edges also adopts the optimization problem description from step 3). Since the intersection point obtained in the previous problem is equivalent to the center of the common tangent circle of the two reference curves with a radius of 0, the parameter range corresponding to the actual center of the common tangent circle must be between the calculation result in step 3) and the endpoint parameter values. Therefore, the new problem form is as follows:

[0071]

[0072]

[0073] Where: R ss R represents the equidistant line corresponding to the suction surface. ps The equidistant lines corresponding to the pressure surface; t 12 ,t 22 The parameter value t represents the center of the leading edge circle lying on the equidistant lines of the suction and pressure surfaces. 13 ,t 23 The parameter value is the center of the trailing edge on the equidistant line of the suction and pressure surfaces.

[0074] In step 6), using the parameter values ​​obtained from solving the optimization problem, the normal vectors of the two reference curves and the point of tangency of the circle can be obtained, thus deriving the argument angle between the starting and ending points of the arc relative to the center of the circle. Using the parametric equation of the arc, the arc segments of the leading and trailing edges can be obtained.

[0075] In step 7), the reference curve r is used. ss In (t) 12 ,0)∪(1,t 13 The part of ) and the reference curve r ps In (t) 22 ,0)∪(1,t 23 The section that connects the arc segment with the existing profile is completed, thus obtaining the aerodynamic profile.

[0076] In one embodiment of the present invention, a system for automatically completing missing data of the leading and trailing edges of turbine blades is provided, which can be used to implement the above-mentioned method for automatically completing missing data of the leading and trailing edges of turbine blades. Specifically, the system for automatically completing missing data of the leading and trailing edges of turbine blades includes:

[0077] The data acquisition module is used to acquire the geometric data of two known segments of the aerodynamic profile to be completed;

[0078] The benchmark curve acquisition module is used to fit two benchmark curves using cubic B-splines with two known segments.

[0079] The reference curve intersection confirmation module is used to push the two reference curves outward in the direction of the front edge and the tail edge to confirm whether there is an intersection point between the reference curves;

[0080] The equidistant line confirmation module is used to calculate a total of four equidistant lines corresponding to the front and rear edges of the two reference curves, based on the specified leading and trailing edge radii.

[0081] The module for confirming the center of the leading and trailing edges is used to find the intersection point of two equidistant lines of the leading edge and two equidistant lines of the trailing edge, and obtain the center of the leading and trailing edges.

[0082] The completion module is used to complete the arc segments of the leading and trailing edges based on the centers of the leading and trailing edges and the normal vectors of the equidistant lines; using the reference curve, it completes the remaining intervals between the endpoints of the arcs and the known segments, thus completing the automatic completion of the aerodynamic profile data.

[0083] The module division in this embodiment of the invention is illustrative and represents only one logical functional division. In actual implementation, other division methods may be used. Furthermore, the functional modules in the various embodiments of the invention can be integrated into a single processor, exist as separate physical entities, or be integrated into a single module. The integrated modules described above can be implemented in hardware or as software functional modules.

[0084] In another embodiment of the present invention, a computer device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions in the computer storage medium to achieve a corresponding method flow or corresponding function. The processor described in this embodiment of the present invention can be used for the operation of a method for automatically completing missing data on the leading and trailing edges of turbine blades.

[0085] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory), which is a memory device in a computer device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the computer device and extended storage media supported by the computer device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory or a non-volatile memory, such as at least one disk storage device. The processor can load and execute one or more instructions stored in the computer-readable storage medium to implement the corresponding steps of the method for automatically completing missing data on the leading and trailing edges of turbine blades in the above embodiments.

[0086] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for automatically completing missing data on the leading and trailing edges of turbine blades, characterized in that, include: Obtain the geometric data of two known segments of the aerodynamic profile to be completed; Using two known segments, two baseline curves are fitted using cubic B-splines. Push the two reference curves outward in the direction of the front and tail edges to confirm whether the reference curves intersect. Based on the specified leading and trailing radii, calculate a total of four equidistant lines corresponding to the leading and trailing edges of the two reference curves. Find the intersection of the two equidistant lines of the leading edge and the two equidistant lines of the trailing edge to obtain the center of the circle of the leading edge and the trailing edge; Based on the centers of the leading and trailing edges, and the normal vectors of the equidistant lines, complete the arc segments of the leading and trailing edges. Using the baseline curve, the remaining interval between the endpoint of the arc and the known segment is completed, thus automatically completing the aerodynamic profile data.

2. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 1, characterized in that, Obtain the geometric data of two known segments of the aerodynamic profile to be completed: The aerodynamic profile to be reconstructed is divided into two segments due to the lack of measurement points at the leading and trailing edges. The geometric data should be represented as two ordered sets of points. The direction of the point array should be processed from the leading edge to the trailing edge.

3. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 1, characterized in that, Two baseline curves were obtained by fitting cubic B-splines: By calling the cubic B-spline fitting module, the two baseline curves can be fitted. The construction of the spline curve; the first and last ends of the spline curve use non-node boundary conditions, that is, the polynomial expression of the first and second segments of the spline curve should be exactly the same, and the same applies to the penultimate and penultimate segments; the origin points correspond to the spline curve parameters. The endpoint location corresponds to .

4. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 1, characterized in that, Push the two reference curves outwards in the directions of the front and rear edges to confirm whether the reference curves intersect: Extrapolating using the expressions for the first and last spline curves constructed in the previous step, the calculation of the intersection points of the baseline curves is described as an optimization problem: in: This is the reference curve for the suction surface; This is the pressure surface reference curve; These are the parameter values ​​of the leading edge intersection point on the suction and pressure surface reference curves. The parameter values ​​for the trailing edge intersection point on the suction and pressure surface reference curves are given. If an intersection point exists within an acceptable range of parameter variation, the objective function of the above optimization problem should be approximately zero. In this case, the intersection point can be taken as the average of the positions of the corresponding parameters on the two curves. If the optimal value of the objective function differs significantly from zero, it is assumed that the reference curves have no intersection point at the leading or trailing edge, and the algorithm is terminated.

5. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 1, characterized in that, Calculate a total of four equidistant lines corresponding to the leading and trailing edges of the two reference curves: An equidistant line is defined as the curve formed by moving each point on a reference curve by the same distance along its normal vector direction; the mathematical form of an equidistant line is: in: This is the original curve; This is the offset; Let be the normal vector at any point on the original curve; by utilizing the analytical form of the B-spline normal vector, the equidistant lines of the reference curve can be accurately calculated; the equidistant lines are parallel to the tangent vectors at corresponding points on the original curve, so the intersection of equidistant lines with the same offset is equivalent to the center of the common tangent circle of the two curves with a given radius.

6. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 4, characterized in that, Find the intersection points of the two equidistant lines of the leading edge and the two equidistant lines of the trailing edge to obtain the centers of the circles at the leading and trailing edges: The method for calculating the centers of the leading and trailing edges also adopts an optimization problem description, with the following problem form: in: These are the equidistant lines corresponding to the suction surface; These are the equidistant lines corresponding to the pressure surface; The parameter value represents the center of the leading edge on the equidistant lines of the suction and pressure surfaces. The parameter value is the center of the trailing edge on the equidistant line of the suction and pressure surfaces.

7. The method for automatically completing missing data of the leading and trailing edges of turbine blades according to claim 1, characterized in that, By using the parameter values ​​obtained from solving the optimization problem, the normal vectors of the two reference curves and the point of tangency of the circle are obtained, thereby deriving the argument angle between the starting and ending points of the arc relative to the center of the circle; Using the parametric equations of the circular arc, the arc segments of the leading and trailing edges are obtained; Using the baseline curve exist Part of the reference curve exist In this part, the arc segment is connected to the existing profile, thus completing the aerodynamic profile.

8. A system for automatically completing missing data on the leading and trailing edges of turbine blades, characterized in that, include: The data acquisition module is used to acquire the geometric data of two known segments of the aerodynamic profile to be completed; The baseline curve acquisition module is used to fit two baseline curves using cubic B-splines with two known segments. The reference curve intersection confirmation module is used to push the two reference curves outward in the direction of the front edge and the tail edge to confirm whether there is an intersection point between the reference curves; The equidistant line confirmation module is used to calculate a total of four equidistant lines corresponding to the front and rear edges of the two reference curves, based on the specified leading and trailing edge radii. The module for confirming the center of the leading and trailing edges is used to find the intersection point of two equidistant lines of the leading edge and two equidistant lines of the trailing edge, and obtain the center of the leading and trailing edges. The completion module is used to complete the arc segments of the leading and trailing edges based on the centers of the leading and trailing edges and the normal vectors of the equidistant lines. Using the baseline curve, the remaining interval between the endpoints of the arc and the known segments is completed, thus automatically completing the aerodynamic profile data.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method for automatically completing missing data on the leading and trailing edges of turbine blades as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for automatically completing missing data of the leading and trailing edges of turbine blades as described in any one of claims 1 to 7.

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