A method for reconstructing the surface of an aero-engine blade while preserving local properties

Abstract

This invention discloses a method for reconstructing the surface of an aero-engine blade while preserving local characteristics. First, after clamping the aero-engine blade blank, the actual surface shape is measured in-flight to obtain the coordinates of the measurement points. Then, using a pre-positioning optimization model, the blade surface to be reconstructed is rotated and translated in space to approximate the actual shape measurement points, generating a pre-positioning surface. Next, based on the measured coordinates of the actual shape measurement points and the pre-positioning surface, the anchor points required for mesh deformation are calculated. Finally, the Cartesian coordinates of each vertex on the deformed triangular mesh model are calculated using the Laplace coordinates of the pre-positioning surface and the deformation anchor points. The triangular mesh model formed by connecting the deformed vertices is considered a reconstructed surface model that preserves local characteristics. This invention can transfer the local characteristics of the actual blade surface to the reconstructed surface, enabling the reconstructed surface to more realistically reflect the actual shape of the blade and improving the processing efficiency and accuracy of aero-engine blades.

Description

Technical Field

[0001] This invention belongs to the field of mechanical manufacturing and processing, and specifically relates to a method for reconstructing the curved surface of an aero-engine blade while preserving local characteristics. Background Technology

[0002] Blades are critical components in aero-engines, and their machining quality directly affects the overall performance of the engine. Blade surfaces are freeform, and the machining process is complex, ultimately requiring grinding and polishing to ensure surface quality meets operational requirements. To achieve more accurate toolpath planning and precision measurement during grinding and polishing, it is often necessary to obtain the actual shape of the blade blank or the finished blade. Surface reconstruction technology can acquire the actual shape of a freeform surface during machining over a large area at once, and therefore this technology is commonly used for acquiring geometric information of aero-engine surfaces and for reverse engineering. However, traditional surface reconstruction techniques, after obtaining the coordinates of some points on the surface, often use the least squares method to fit the actual shape of the surface. This process does not consider the local characteristics of the surface, leading to potential local distortions in the final reconstructed surface shape, thus failing to accurately reflect the global true shape of the aero-engine blade surface. Therefore, developing a reconstruction method that can accurately reflect the local characteristics of aero-engine blade surfaces is of great significance. Summary of the Invention

[0003] To address the aforementioned technical challenges, a surface reconstruction method based on Laplace mesh deformation that preserves local characteristics is proposed. The method pre-positions the surface to be reconstructed to eliminate rotational distortion caused by Laplace mesh deformation. The anchor points required for Laplace mesh deformation are calculated based on the measured coordinates of spatial points on the blade surface. Finally, the pre-positioned surface is used to generate a reconstructed blank surface that closely approximates the actual blank surface through Laplace mesh deformation. This method can realistically and effectively reflect the local characteristics of aero-engine blade surfaces, while also improving blade manufacturing efficiency and accuracy.

[0004] The technical solution adopted by this invention to solve its technical problem is: a method for reconstructing the surface of an aero-engine blade while preserving local characteristics, characterized by the following steps:

[0005] Step 1: Data Acquisition and Surface Pre-positioning of Actual Blade Blank

[0006] First, the blade blank is measured to obtain the actual shape measurement points. Then, Laplace mesh deformation technology is used to reconstruct the actual blank surface of the blade using the designed blank surface and the actual shape measurement points. Finally, the reconstructed blank surface is obtained. However, Laplace mesh deformation is rotationally sensitive. If the deformation requires rotating the vertices on the triangular mesh model, distortion will occur, and the final reconstructed surface will not reflect the actual shape of the blade surface. Therefore, surface pre-positioning is required to eliminate rotational distortion. Here, surface pre-positioning is an optimization process that makes the surface to be reconstructed close to the actual shape measurement points of the blade blank. For clarity, the surface to be reconstructed is denoted as S. d The actual shape measurement point is denoted as m. Specifically, surface pre-positioning is achieved by changing the surface S to be reconstructed. d The coordinate position in space is used to obtain a surface that is closer to the actual shape measurement point m. Here, the surface that is closer is called the prepositioning surface S. p Mathematically, the pre-positioning of a curved surface can be optimized using the objective function s. dis The corresponding constraint condition st is described as follows:

[0007]

[0008] In the formula: the subscript i represents the i-th shape measurement point; S d (u i ,v i ) represents the surface S to be reconstructed d The coordinates of the i-th point closest to the actual shape measurement point, S p (u i ,v i ) indicates the use of S d (u i ,v i The pre-positioned surface S obtained by calculation p The coordinates of the point on, u i and v i For the prepositioned surface S p The parameters are in the range of [0,1]; N is the number of actual shape measurement points; R is the coordinate rotation matrix, and α, β and λ are the coordinates of the surface to be reconstructed, S. d Rotation angles about the X, Y, and Z axes; T is the coordinate translation matrix, and Δx, Δy, and Δz are the coordinates of the surface to be reconstructed, S. d Translational distances along the X, Y, and Z axes.

[0009] Step 2: Obtain the Laplace mesh deformation anchor points

[0010] First, the pre-positioning surface S of the blade p(u,v) is converted into a triangular mesh model, and its point set V, edge set E, and triangular facet set P are obtained. Then, the N actual shape measurement points m obtained in step one are... i Projecting onto the triangular mesh model, the projected points fall into the triangular facets. Finally, the spatial points obtained by moving the three vertices of the triangular facets into which the projected points fall along the projection direction by the projection length are used as anchor points for the Laplace mesh deformation. The anchor points corresponding to all projected points form the anchor point matrix U. Essentially, this provides the Laplace mesh deformation with some known information about the deformed state, allowing the entire Laplace mesh deformation to retain more of the local characteristics before deformation.

[0011] Step 3: Reconstruct the blade blank surface using Laplace mesh deformation

[0012] The Laplacian coordinates of each vertex on the prepositioned surface triangular mesh model can be calculated in matrix form as follows:

[0013] δ=LV (2)

[0014] In the formula: δ is the Laplace coordinate matrix of each vertex on the triangular mesh model, L is the Laplace transformation matrix, and V is the Cartesian coordinate matrix of the triangular mesh model containing all vertices.

[0015] Laplacian coordinates record the geometric and topological information of the vertices. Since the Laplacian coordinates of each vertex remain unchanged before and after deformation, the local properties of the surface are preserved. Furthermore, by combining the Laplacian coordinate matrix δ and the anchor point matrix U obtained in step two, the spatial coordinates of each vertex of the triangular mesh model after Laplacian mesh deformation can be obtained in reverse, which can be expressed in matrix form as follows:

[0016]

[0017] In the formula: F is the identifier matrix; U is the anchor matrix; D is the upper triangular matrix obtained by decomposing matrix A; V' is the Cartesian coordinate matrix containing all vertices after Laplace mesh deformation.

[0018] The calculated deformed spatial points are reconnected to obtain a new triangular mesh model, which is then regarded as a reconstruction of the blank surface.

[0019] Beneficial effects

[0020] The beneficial effects of this invention are as follows:

[0021] 1. With the coordinates of the actual surface shape measurement points of the blade obtained, the blade surface to be reconstructed is brought close to the shape measurement points by spatial rotation and translation using the optimization model, generating a pre-positioned surface, which can eliminate the rotational distortion phenomenon of Laplace mesh deformation.

[0022] 2. The local characteristics of the actual blade surface can be transferred to the reconstructed surface, so that the reconstructed surface can more realistically reflect the actual shape of the blade;

[0023] 3. It can promote the improvement of processing efficiency and precision of aero-engine blades.

[0024] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0025] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0026] Figure 1 Flowchart of the implementation of the method of the present invention;

[0027] Figure 2 Triangular mesh model;

[0028] Figure 3 Obtain the deformation anchor point;

[0029] Figure 4 Pre-positioning of the surface to be reconstructed before deformation;

[0030] Figure 5 Selection of the cotangent calculation angle;

[0031] Figure 6 The wide-chord hollow fan blade to be tested. Detailed Implementation

[0032] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0033] Step 1: Acquisition of actual blank data and pre-positioning of curved surface

[0034] The specific implementation method of step 1 above is as follows:

[0035] Step 1.1: Use a coordinate measuring machine to measure the blade blank and obtain the actual shape measurement point m. i ;

[0036] Step 1.2: Construct the optimization function model for the pre-positioning of the surface, i.e., the objective optimization function s. dis The corresponding constraint st is:

[0037]

[0038] In the formula: S d For the surface to be reconstructed, S d (u i ,v i ) represents the surface S to be reconstructed d The coordinates of the i-th point closest to the actual shape measurement point; S p For the prepositioned surface, S p (u i ,v i ) indicates the use of S d (u i ,v i The pre-positioned surface S obtained by calculation p The coordinates of the point on, u i and v i For the prepositioned surface S p The parameter above has a value range of [0,1]; m i Let be the coordinates of the i-th actual shape measurement point; N be the number of actual shape measurement points; R be the coordinate rotation matrix; and α, β, and λ be the coordinates of the surface S to be reconstructed. d Rotation angles about the X, Y, and Z axes; T is the coordinate translation matrix, and Δx, Δy, and Δz are the coordinates of the surface to be reconstructed, S. d Translational distances along the X, Y, and Z axes.

[0039] Step 2: Obtain the Laplacian mesh deformation anchor point matrix U

[0040] The specific implementation method of step 2 above is as follows:

[0041] Step 2.1: The pre-positioned surface S obtained in Step 1 p Input the data into UG software and convert it into a triangular mesh model, such as... Figure 2 As shown, the triangular mesh model is defined as R = (V, E, P), where V is the set of points, E is the set of edges, and P is the set of triangular facets.

[0042] Step 2.2: Measure the actual external shape at point m. i Projected onto the triangular mesh model, projection point m' i Falling into the triangular facet, as Figure 3 As shown.

[0043] Step 2.3: Assume that the three vertices of any triangular facet are A i B i C i The projection vector is Projection length is The resulting triangle has three new vertices, denoted as A'. i B' i C' iIts coordinates can be calculated as follows:

[0044]

[0045] Here, the new vertex A' i B' i C' i These are the anchor points for Laplace mesh deformation, such as... Figure 3 As shown.

[0046] Repeat step 2 to calculate the anchor points of the Laplacian mesh deformation corresponding to the actual shape measurement points, and form the anchor point matrix U together with these anchor points.

[0047] Step 3: Reconstruct the blade surface using Laplacian mesh deformation

[0048] The specific implementation method of step 3 above is as follows:

[0049] Step 3.1: The Laplace coordinates of each vertex in the triangular mesh model formed by the pre-positioning surface transformation are calculated as follows:

[0050]

[0051] In the formula: La is the Laplace coordinate operator, v i Let w be the Cartesian coordinate of the i-th vertex in the triangular mesh model, and N(i) be the set of adjacent vertices connected to the i-th vertex. i,j Calculate the weights for the Laplacian coordinates, v j Let be the Cartesian coordinates of the adjacent vertices connected to the i-th vertex.

[0052] Step 3.2: Equation (3) can be used to obtain the Laplacian coordinates of all vertices in matrix form, that is, the matrix form can be expressed as:

[0053] δ=LV (4)

[0054] In the formula: δ is the Laplace coordinate matrix of each vertex on the triangular mesh model; L is the Laplace transformation matrix, which can be further expressed as:

[0055]

[0056] In the formula: i is the row sequence in the Laplace matrix, j is the column sequence in the Laplace matrix, E is the edge set of the triangular mesh model, E I E represents the edge set inside the triangular mesh model. B Let d be the set of edges on the boundary of the triangular mesh model. i cotα is the number of adjacent vertices connected to the i-th vertex. i,j cotβ i,jLet α and β be the cotangent values ​​of the opposite angles of the two triangular faces corresponding to the edge formed by connecting the j-th adjacent vertex and the i-th vertex, respectively. The selection of α and β is as follows: Figure 5 As shown.

[0057] Step 3.3: Combine the Laplacian coordinate matrix δ obtained in Step 3.2 with the anchor point matrix U obtained in Step 2 to inversely calculate the spatial coordinates of each vertex of the triangular mesh model after the Laplacian mesh deformation. This can be expressed in matrix form as follows:

[0058]

[0059] In the formula: V′ is the matrix containing the Cartesian coordinates of the vertices after the triangular mesh model is deformed, F is the identifier matrix, and U is the anchor point matrix.

[0060] An example of a further implementation of step 3.3 above is as follows:

[0061] Suppose a mesh model consists of 5 points, and the Cartesian coordinates of the 1st and 5th points after deformation are known. Then the identification matrix F and the anchor matrix U can be represented as follows:

[0062]

[0063]

[0064] Equation (6) can be rewritten as a least squares system, which is:

[0065]

[0066] Multiply both sides of equation (9) by A T Then we can obtain its normal equation:

[0067] A T AV' = A T b (10)

[0068] In equation (10), A T A can be decomposed into the product of two triangular matrices, let D be the triangular matrix, then we can obtain:

[0069] D T DV'=A T b (11)

[0070] Multiply both sides of equation (11) by (D) T D) -1 The Cartesian coordinates of the vertices on the new triangular mesh model obtained after the Laplace mesh deformation can be represented in matrix form as follows:

[0071] V'=(D T D) -1 AT b (12)

[0072] Connect all the deformed vertices obtained by Equation (12) to form a new triangular mesh model, which is the reconstructed surface.

[0073] The following is an experiment on surface reconstruction based on Laplace mesh deformation on a certain type of blade:

[0074] The measurement system used in this embodiment is: an MTS 1600-500-6NC six-axis CNC belt grinder, a Siemens SINUMERIK 840D controller, and a Renishaw LP2 contact probe. The blade to be measured is as follows: Figure 6 As shown.

[0075] First, the blade shape measurement results were obtained, as shown in Table 1.

[0076] Table 1. Blade morphology measurement results

[0077]

[0078] The blades are pre-positioned, and then the pre-positioned surface is converted into a triangular mesh model, the vertex coordinates of which are shown in Table 2.

[0079] Table 2 Vertex coordinates of the triangular mesh model before deformation

[0080]

[0081] The prepositioned surface is subjected to Laplacian mesh deformation, and the vertex coordinates after deformation are shown in Table 3.

[0082] Table 3 Vertex coordinates of the deformed triangular mesh model

[0083]

[0084] To verify that the surface reconstruction method can ensure that local characteristics remain unchanged before and after deformation, the external normal vectors of 20 points on the surface obtained by the coordinate measuring machine are compared with the external normal vectors at the same positions on the triangular mesh model. If the difference between the external normal vectors obtained by the two methods is small, it indicates that the local features of the surface are preserved. The angular deviation between the two normal vectors is shown in Table 4.

[0085] Table 4. Comparison of normal vectors at wall thickness measurement points.

[0086]

[0087] As can be seen from the results of the above embodiments, the blade outer surface normal vector obtained by the present invention is relatively similar to that obtained by the coordinate measuring machine. At all detection positions, the maximum normal vector angle deviation is only 0.3680°, indicating that the blade surface reconstructed by the method of the present invention can ensure that most of the local features are preserved.

Claims

1. An aeroengine blade surface reconstruction method that preserves local properties, characterized by: The following steps are adopted: Step 1: Collecting actual blade blank data, and pre-positioning the surface according to the actual blade blank data; The surface pre-positioning is an optimization process of making the to-be-reconstructed surface close to the blade blank actual shape measurement points; By optimizing process, the coordinate position of the surface to be reconstructed in space is changed to obtain a surface closer to the actual profile measurement points of the blade blank, and the surface is pre-positioned, wherein the target optimization function s dis and the corresponding constraint conditions s.t. are described as: In the formula: S d For the surface to be reconstructed, For the surface S to be reconstructed d The coordinates of the i-th point closest to the actual shape measurement point; S p For the pre-positioned surface, Indicates use The calculated prepositioned surface S p The coordinates of the point on, u i and v i Pre-positioned surface The parameters above have a range of values. ; For the first Coordinates of the actual shape measurement points; R represents the number of actual shape measurement points, i = 1, 2, ..., N; R is the coordinate rotation matrix. , and The surfaces to be reconstructed are S d Around , and The rotation angle of the axis; T is the coordinate translation matrix. , and The surfaces to be reconstructed are S d along , and Translational distance of the axis; Step 2: Obtain the Laplace grid deformation anchor point matrix U, the specific process is: Step 2.1: Pre-positioning the blade surface Converting to a triangle mesh model where is a set of points, is a set of edges, is a set of triangles; Step 2.2: Any actual shape measurement point in step 1 is projected onto the triangle mesh model Projecting onto a triangle mesh model Above, the projected point falls into a triangle patch, where the vertices of the triangle patch are noted as A i , B i , C i ; Step 2.3: Set vertex A of the triangular facet. i B i C i Along the projection vector direction Moving projection length Afterwards, three new vertices A' are obtained. i B' i C' i for: These three new vertices A' i , B' i , C' i are anchor points for the Laplacian mesh deformation; Step 2.4: Repeat step 2.2 and step 2.3, calculate the N anchor points of the Laplace grid deformation corresponding to the N actual shape measurement points measured in step 1, and the N anchor points form the anchor point matrix U together; Step 3: Reconstruct the blank surface by Laplace grid deformation.

2. The method of claim 1, wherein the method further comprises: In step 3, the process of reconstructing the blank surface by Laplace grid deformation is: Step 3.1: Calculate the Laplace coordinates of each vertex on the pre-positioned surface triangular mesh model, which is expressed in matrix form as: where: δ Laplace coordinate matrix, is the Laplace transform matrix, is the matrix containing all the Cartesian coordinates of the vertices of the triangular mesh model; Step 3.2: Combine the Laplace coordinate matrix δ calculated in step 3.1 with the anchor point matrix U obtained in step 2 to inversely solve the spatial coordinates of each vertex of the triangular mesh model after Laplace grid deformation, which is expressed in matrix form as: wherein: is the identity matrix, is the anchor point matrix, is the upper triangular matrix resulting from the decomposition of the matrix is the upper triangular matrix resulting from the decomposition of the matrix is the matrix containing all the Cartesian coordinates of the vertices after the Laplacian mesh deformation; Step 3.3: Connect the deformed spatial points calculated in step 3.2 again to obtain a new triangular mesh model, which is regarded as the reconstructed blank surface.

3. The method of claim 2, wherein: In step 3.1, the calculation expression of each element in the Laplace transformation matrix L is: wherein: is a sequence of rows in the Laplacian matrix, is a sequence of columns in the Laplacian matrix, is a set of edges of the triangle mesh model, is a set of edges inside the triangle mesh model, is a set of edges on the boundary of the triangle mesh model, is the number of adjacent vertices connected to the th vertex, , are the cotangent values of the edges connecting the th adjacent vertex and the th vertex, respectively.

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