A blade airfoil modeling method based on T-spline local skinning

Abstract

The application discloses a kind of blade airfoil modeling methods based on T spline local skin.First, according to the input of each blade section line, the method of combining T spline local skin with the nearest refinement criterion of middle boundary is used to construct topological T network, and the initial blade airfoil surface model is obtained;Then, after uniform sampling and interpolation of each blade section line, a plurality of contour guide curves are obtained, and the comprehensive curvature of all surface guide points on each contour guide curve is calculated;Then, surface region division is carried out, and whether each surface region meets the preset accuracy is calculated and judged, if not, constantly modified and updated, and the control vertex in the surface model is locally interpolated and transformed, until each surface region meets the preset accuracy, and finally the overall smooth blade airfoil surface model is obtained.The application finally generates a periodic T spline surface that takes into account the key section interpolation and overall surface smoothness, with high-order continuity at the closed loop of the surface.

Description

Technical Field

[0001] This invention relates to a blade shaping method in the field of blade design, and more particularly to a blade shaping method based on T-spline partial skinning. Background Technology

[0002] Blades are key components in large turbine machinery such as gas turbines and expanders, enabling fluid energy conversion through high-speed rotation. The aerodynamic design of blades is closely related to the performance of these turbines. A common method for modeling 3D blade surfaces is to first obtain the profile curves of several key cross-sections using various parametric methods. Then, under certain stacking rules, these cross-sections are arranged in 3D space, and interpolation is performed using skinning / lofting to obtain the overall blade surface. Traditionally, both blade surfaces and cross-sections are described using NURBS. When the node vectors of different cross-sections differ, NURBS surfaces allow for refinement using a global control mesh to ensure consistent node vectors at each cross-section along the skin direction, satisfying the tensor product property. However, when there are too many input blade cross-sections or significant differences in node vectors among the cross-sections, the tensor product property of NURBS leads to a large number of redundant control vertices on the surface, severely impacting surface modeling efficiency and ease of modification.

[0003] In recent years, T-spline modeling techniques have been proposed, allowing the introduction of T-shaped anchor points into NURBS surfaces. This makes the topology more flexible while also achieving unstructured characteristics of local subdivision, making it highly likely to become the next industry standard for shape representation and data exchange. There has been some research on T-spline surface skinning methods in academia. Nasri et al. first proposed the T-spline local skinning method in their 2012 paper "Local T-spline surface skinning" in *The Visual Computer*. This method inserts an intermediate cross section between the input profile lines and uses a derived T-spline surface interpolation formula to locally adjust the control vertices, ultimately achieving the generation of T-spline skinned surfaces capable of interpolating the input profile lines. However, for scenarios where the vector differences between adjacent profile node nodes are too large, this method can fall into the problem of surface wobbling due to the insufficient number of control vertices in the intermediate cross section. Therefore, in their 2018 paper "Local T-spline surface skinning with shape preservation" published in *Computer-Aided Design*, Oh et al. further modified the topology stage by inserting two intermediate bisectors and introduced the Least Square Progressive Iterative Approximation method in the geometric adjustment stage to adjust the surface, alleviating the surface wobble problem and improving the surface's shape preservation ability. However, this method is not stable in its control over the size of vertices, which may lead to a situation where there are far more control vertices than NURBS surfaces. In addition, Zheng et al.'s 2015 paper "Surface skinning using periodic T-spline in semi-NURBS form" published in *Journal of Computational and Applied Mathematics* proposed a skinning method for closed periodic T-spline surfaces based on the Nasri method. However, the problem of excessive manual interaction also limits the efficiency of surface modeling and lacks an automatic skinning modeling criterion. Summary of the Invention

[0004] To address the problems mentioned in the background, this invention proposes a blade profile modeling method that combines T-spline local skinning with the Least Square Progressive Iterative Approximation (LSPIA) method. Utilizing the blade cross-sectional profile obtained from design calculations, a T-spline-described aerodynamic structure surface model of the blade is skinned using controlled vertices with limited scale, achieving the same quality requirements as NURBS surfaces. This method can meet the application requirements of various subsequent T-spline modeling modifications. This invention has the following advantages: ① Compared to current T-spline local skinning methods, the surface control mesh distribution and scale obtained by this invention are more reasonable and controllable; ② While ensuring interpolation of the input profile, it improves the wrinkling defect problem of the T-spline skinned surface, generating a blade surface that maintains an overall smooth shape; ③ The unidirectional periodicity of the surface allows for a smoother closed-loop effect, and the high-order continuity at the closed loops aligns with the characteristics and requirements of blade modeling scenarios.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] 1) Based on the input blade cross-sectional profiles, a topological T-network is constructed using a combination of T-spline local skinning and the nearest neighbor refinement criterion at the middle boundary. This yields the T-spline control mesh model of the blade surface and serves as the initial blade surface model.

[0007] 2) After uniformly sampling and interpolating the profile of each blade section, multiple shape guide curves are obtained, and then the comprehensive curvature of all surface guide points on each shape guide curve is calculated;

[0008] 3) Divide the surface region according to the current blade blade surface model to obtain multiple surface regions. Based on the comprehensive curvature of all surface guide points on multiple shape guide curves, calculate and determine whether each surface region meets the preset accuracy. If it does, the current blade blade surface model is used as the overall smooth blade blade surface model; otherwise, each surface region is continuously corrected and updated, and local interpolation transformation is performed on the control vertices in the surface model until each surface region meets the preset accuracy, and finally the overall smooth blade blade surface model is obtained.

[0009] Specifically, 1) refers to:

[0010] Based on the input blade section profiles, a topological T-network is constructed using T-spline local skinning to obtain the initial T-spline control mesh. Then, the initial T-spline control mesh is refined by inserting intermediate secants and refining the mesh using the nearest neighbor refinement criterion to obtain the T-spline control mesh model of the blade surface.

[0011] The steps for inserting the intermediate section line between two adjacent blade section profiles and refining the mesh in the initial T-spline control mesh are as follows:

[0012] S1: After interpolating the current two blade section profiles, obtain the intermediate cross-section (ICS) between the current two blade section profiles. r ;

[0013] S2: Select the current intermediate cutoff line ICS r Find the midpoint position t between the two nodes with the largest spacing along the cross-section direction of the current two blade profiles and these two nodes. mid The nearest point is denoted as the nearest control vertex. The blade section profile containing the nearest control vertex is denoted as the nearest profile C. x The other blade section profile is denoted as the opposite profile C. y ;

[0014] S3: First, adjust the opposite side profile C y Discretize and then use the nearest curve C x The same node vector interpolation reconstructs a dashed curve C. y2 Next, take the imaginary curve C. y2 Top and nearest control vertex Control vertices at positions corresponding to the same node value Then, the dashed curve C y2 Control vertex on As the opposite side profile C y The new control vertex on the corresponding T-grid vertical edge Control Vertex Insert into the opposite side profile C y On the corresponding T-mesh edge, then the nearest control vertex is selected. and the opposite side profile C y Control vertex on The midpoint of the spatial coordinates is used as the current intermediate intercept (ICC). r The coordinates of the control vertex at the node value corresponding to the vertical edge are used as the new control vertex of the surface control mesh, thereby realizing the control of this intermediate intercept line ICS in the T mesh. r The longitudinal edges of the grid corresponding to the cross-sectional profiles of the blades on both sides are refined and updated;

[0015] S4: Repeat S2-S3 until the current intermediate cutoff ICC. r If the number of control vertices is greater than the preset number, the resulting intermediate cutoff line (ICC) will be... r The distribution of control vertices is used as the longitudinal edge distribution between the current two blade section profiles in the initial T-spline control mesh, and the longitudinal edges corresponding to the current two blade section profiles are updated to achieve the refinement of the control mesh.

[0016] In step S1, a four-point interpolation subdivision method is used to interpolate the current two blade section profiles. The interpolation formula is as follows:

[0017]

[0018] Among them, V mid This indicates the interpolation point between the current two blade profiles. This indicates the control vertices that have the same node values ​​in the current two blade profiles. These represent the distances from the interpolation point V on the left and right sides, respectively. mid The two more distant control vertices, α is the distance from the interpolation point V. mid Two more distant control vertices The influence weighting coefficient.

[0019] Specifically, 2) refers to:

[0020] 2.1) Uniformly sample each blade section profile in the direction of parameter t at the first sampling frequency to obtain the sampling point set corresponding to each blade section profile; interpolate and fit the sampling point set of each blade section profile into multiple third-order B-spline curves in the direction of parameter s and use them as shape guidance curves.

[0021] 2.2) Each shape guide curve is sampled and discretized at the second sampling frequency to obtain multiple sampling points on each shape guide curve. The sampling points whose distance from the blade section profile is less than the preset distance are offset to make the sampling points between different input profiles, thereby obtaining the set of curved surface guide points.

[0022] 2.3) For the guiding points of the surface with the same s-parameters, interpolate them into third-order B-spline curves in the t-direction using periodic boundary conditions to obtain the corresponding auxiliary curves;

[0023] 2.4) Calculate the combined curvature of each surface guide point using the shape guide curve where the surface guide point is located and the corresponding auxiliary curve.

[0024] For the overall curvature of each of the surface guide points, calculate the curvature value k of the shape guide curve in the s-direction at that surface guide point. s The curvature value k of the parameter t in the guide direction of the auxiliary curve at the guide point of the surface. t Calculate the curvature value k in the s direction. s and the curvature value k in the t direction t The mean value is used as the composite curvature k of the guiding point of the surface. s,t .

[0025] Specifically, 3) refers to:

[0026] 3.1) Divide the surface region according to the current blade blade surface model. The longitudinal edge of the T-grid generated by the two blade cross section profiles is recorded as the boundary. The area between these two longitudinal edges is a surface sub-interval. The adaptive local fitting threshold of all surface sub-intervals in each surface region is calculated based on the average comprehensive curvature of each surface guide point in the surface sub-interval.

[0027] 3.2) Calculate the deviation vector between each surface guide point in each surface sub-interval of each surface region and the corresponding spatial position point of the current blade surface model. The L2 norm of the deviation vector is recorded as the fitting error of each surface guide point. Then, calculate the average fitting error of the current surface sub-interval. When the average fitting error of each surface sub-interval is greater than or equal to the corresponding adaptive local fitting threshold, the preset accuracy is not met. The current surface sub-interval is recorded as the region to be fitted, and all surface guide points of the current surface sub-interval are added to the set of guide points to be approximated.

[0028] 3.3) Select the control vertices of the surface in the current blade blade surface model that meet the adjustment conditions. Add it to the set of adjusted vertices, and determine the adjustment region based on the surface control vertices in the set of adjusted vertices. The adjustment condition is: for the surface control vertex V in the k-th iteration process... l (k) If there exists a surface guide point Q in the set of guide points to be approximated i,j Its corresponding parameter value (s) i,j ,t i,j Located at the control vertex of the surface Within the local support range of the basis functions, the control vertex of the surface satisfies the adjustment conditions;

[0029] 3.4) Based on the local support of the surface blending function, add the surface guide points that satisfy the affected conditions from the set of surface guide points to the set of affected points, and then determine the affected region based on the control vertex boundary of the affected point set; the affected condition is: for surface guide points Q in the set of surface guide points... i,j If a certain control vertex V exists in the set of control vertices of the surface to be adjusted l (k) Its mixing function is at the guide point Q on the surface. i,j If the value at the corresponding parameter location is non-zero, then the guide point Q of the surface... i,j The affected conditions are met;

[0030] 3.5) Calculate the surface deviation vector based on the surface control vertices in the affected point set, calculate the adjustment vector of each surface control vertex in the adjustment area using the least squares asymptotic iterative approximation method, and then update the surface control vertices sequentially by superimposing the adjustment vectors, so as to finally realize the correction and update of each surface control vertex in the current surface sub-interval of the current surface region.

[0031] 3.6) Perform interpolation update transformation on the surface control vertices in the corrected and updated blade blade surface model to obtain the interpolated surface control vertices, and then update the blade blade surface model.

[0032] 3.7) Repeat steps 3.1)-3.6) until the average fitting error of all surface sub-intervals in each surface region is less than the corresponding adaptive local fitting threshold or the number of iterations of each surface sub-interval reaches the maximum iteration value. Then, the overall smooth blade surface model is obtained.

[0033] In section 3.1), when the difference in average composite curvature between each surface sub-interval is significantly different or greater than a preset difference, the average composite curvature of each surface sub-interval is smoothed to obtain the corresponding smoothed average curvature, and the average curvature of each surface guide point is updated. Then, the adaptive local fitting threshold of each surface sub-interval is calculated using the following formula based on the updated average curvature; otherwise, the adaptive local fitting threshold of each surface sub-interval is directly calculated using the following formula:

[0034]

[0035]

[0036] in, h represents the adaptive local fitting threshold for each surface sub-interval. r This represents the curvature correction factor for each surface sub-interval. Indicates the local fitting threshold of the interval. Here, η represents the maximum and minimum average curvature of the guiding points of the surface in each sub-interval, η is a coefficient used to balance the differences in average curvature between intervals, and max() represents taking the maximum value.

[0037] Compared to the conventional least squares asymptotic iterative approximation fitting method, this invention transforms the global fitting strategy into local fitting in the process, and adaptively adjusts the fitting accuracy for different regions according to the richness of geometric features. In the process of blade skin modeling with multiple cross-sectional profiles, it can effectively balance fitting accuracy and fitting efficiency.

[0038] The beneficial effects of this invention are:

[0039] 1) The skinning process utilizes the nearest neighbor refinement criterion at the middle boundary, resulting in a simplified surface control mesh with controllable vertex size, which is beneficial for improving blade shape and optimizing computational efficiency.

[0040] 2) While ensuring interpolation at the input key section profile, the T-spline skin surface can effectively improve the wobble defect problem by introducing a more uniform distribution of control vertices in the intermediate section, thus generating an overall smooth blade surface.

[0041] 3) It has the characteristics of a unidirectional periodic surface, and the high-order continuity at the closed loop of the surface facilitates the airflow structure design of the blade.

[0042] In summary, this invention achieves the goal of modeling a smooth T-spline skin surface from a periodically described blade cross-sectional profile, thereby enabling convenient design adjustments and surface optimization calculations. Attached Figure Description

[0043] Figure 1 This is an overall framework diagram of the present invention.

[0044] Figure 2 This is a detailed process for the leaf shaping method using T-spline partial skinning.

[0045] Figure 3 This is a flowchart of the nearest neighbor refinement criterion for the middle boundary.

[0046] Figure 4 This is a schematic diagram illustrating the use of the nearest neighbor refinement criterion in the middle boundary.

[0047] Figure 5 This is a schematic diagram of the region division in the local fitting strategy.

[0048] Figure 6 This is an example of the T-spline curved surface skin modeling process of the present invention for a certain type of blade structure. Detailed Implementation

[0049] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0050] The embodiments and processes of the present invention are as follows:

[0051] Figure 1 The diagram illustrates the overall algorithm flow, which can be mainly divided into three parts: establishing the T-grid topology connection relationship, extracting the ideal surface shape features, and adjusting the surface smoothing under curvature constraints.

[0052] like Figure 2 As shown, the present invention includes the following steps:

[0053] 1) Based on the input blade cross-sectional profiles, each blade cross-sectional profile is described by a periodic basis function. The topological T-network is constructed by combining T-spline local skinning with the nearest neighbor refinement criterion at the middle boundary, and the T-spline control mesh model of the blade surface is obtained and used as the initial blade surface model.

[0054] 1) Specifically:

[0055] Based on the input blade section profiles, a topological T-network is constructed using T-spline local skinning to obtain the initial T-spline control mesh, as shown below. Figure 4 As shown in (a).

[0056] Specifically: First, the input periodic basis function description lines (cross-sectional curves) are parameterized in the skin direction (assumed to be represented by the parameter s direction) using chord length parameterization, and the parameter values ​​are used as the C values ​​for each curve. r The isoparametric value s of the T-spline surface r The obtained parameters are normalized to the range of 0 to 1. The control polygons of each input profile are directly used as the longitudinal edges of the T-grid, which are used as the initial T-grid of the blade surface. It is assumed that the corresponding directions of the control polygons of each profile are used as the parameter t direction.

[0057] When the difference between the node vectors of adjacent input profiles is too large, it will result in too few control vertices at the intermediate section of the surface, and the surface will wobble. Therefore, this invention introduces a middle-bound nearest neighbor refinement criterion for the refinement of control vertices at the intermediate section of the T-spline skin surface. That is, after using the middle-bound nearest neighbor refinement criterion to insert intermediate sections and refine the mesh of the initial T-spline control mesh, the T-spline control mesh model of the blade surface is obtained.

[0058] like Figure 3 As shown, the steps for inserting the intermediate section line between two adjacent blade section profiles and refining the mesh in the initial T-spline control mesh are as follows:

[0059] S1: After interpolating the current two blade section profiles, obtain the intermediate cross-section (ICS) between the current two blade section profiles. r ;

[0060] S2: Select the current intermediate cutoff line ICS r Find the midpoint position t between the two nodes with the largest spacing along the cross-section direction of the current two blade profiles and these two nodes. mid The nearest point is denoted as the nearest control vertex. The blade section profile containing the nearest control vertex is denoted as the nearest profile C. x The other blade section profile is denoted as the opposite profile C. y ,like Figure 4As shown in (b);

[0061] S3: First, adjust the opposite side profile C y Discretize and then use the nearest curve C x The same node vector interpolation reconstructs a dashed curve C. y2 Next, take the imaginary curve C. y2 Top and nearest control vertex Control vertices at positions corresponding to the same node value Then, the dashed curve C y2 Control vertex on As the opposite side profile C y The new control vertex on the corresponding T-grid vertical edge Control Vertex Insert into the opposite side profile C y On the corresponding T-mesh edge, then the nearest control vertex is selected. and the opposite side profile C y Control vertex on The midpoint of the spatial coordinates is used as the current intermediate intercept (ICS). r The coordinates of the control vertex at the node value corresponding to the vertical edge are used as the new control vertex of the surface control mesh, thereby realizing the control of this intermediate intercept line ICS in the T mesh. r The longitudinal edges of the grid corresponding to the cross-sectional profiles of the blades on both sides are refined and updated;

[0062] S4: Repeat S2-S3 until the current intermediate cutoff line ICS. r The number of control vertices is greater than the preset number. In specific implementation, the preset number is 60% of the total number of control vertices for any one of the two current blade section profiles in S1. For example... Figure 4 As shown in (c), this is a schematic diagram of the T-mesh structure after two refinements. The final obtained intermediate cross-section ICS... r The distribution of control vertices is used as the longitudinal edge distribution between the current two blade section profiles in the initial T-spline control mesh, and the longitudinal edges corresponding to the current two blade section profiles are updated to achieve the refinement of the control mesh.

[0063] Under the nearest-neighbor refinement criterion, refinement is performed each time in the interval with the maximum spacing in the middle section of the surface, maximizing the filling of sparse mesh regions and effectively improving the rationality of the control vertex distribution. The T-mesh structure established in this way has only one middle section between each input profile. Its control vertex distribution is more reasonable than the method proposed by Nasri et al. in the paper "Local T-spline surface skinning," dispersing sparse vertex regions. At the same time, compared with the skinning method of Oh Minjae et al. in the paper "Local T-spline surface skinning with shapepreservation" which inserts two middle sections, it effectively controls the mesh vertex scale, which is conducive to improving the efficiency of blade surface design optimization.

[0064] Furthermore, under the periodic basis function description form adopted in this invention, the T-grid established in the above manner has its longitudinal edges all passing through the t direction. That is, for any vertex in the generated T-grid, there must be an upper and lower neighboring point with a connection relationship in the t direction. Compared with the conventional T-grid structure, the vertices on the same longitudinal edge have the same horizontal node vector. Therefore, it is more regular in terms of data storage. It can use the global s-direction node vector to replace the node vector of each vertex for storage, effectively compressing the amount of surface storage data and improving the data storage and transmission efficiency of T-spline blade surface.

[0065] In S1, to achieve a smoother surface effect, the four-point interpolation subdivision method considers more control vertex information compared to linear interpolation. Therefore, the four-point interpolation subdivision method is used for the current two blade section profiles C. r C r+1 Interpolation is performed using the following formula:

[0066]

[0067] Among them, V mid This indicates the interpolation point between the current two blade profiles. This indicates that the current two blade section profiles C r C r+1 The nodes with the same value t j The control vertex, Indicate C r Left side section profile C r-1 The corresponding control vertex at the top Indicate C r+1 Right side section profile C r-1 The corresponding control vertex is α, which is the distance from the interpolation point V. mid Two more distant control vertices The influence weighting coefficient can usually be set to 0.2.

[0068] 2) After uniformly sampling and interpolating the profile of each blade section, multiple shape guide curves are obtained, and then the comprehensive curvature of all surface guide points on each shape guide curve is calculated;

[0069] 2) Specifically:

[0070] 2.1) Uniformly sample each blade section profile in the direction of parameter t at the first sampling frequency. Obtain n+1 profile points for each blade section profile. Considering the periodic closed curve characteristics, make the first and last sampling points coincide to obtain the sampling point set corresponding to each blade section profile. With the boundary condition that the second derivative at the end is 0, interpolate and fit the sampling point set of each blade section profile into multiple (n in the specific implementation) third-order B-spline curves in the direction of parameter s and use them as shape guidance curves.

[0071] The interpolation fitting formula is as follows:

[0072]

[0073] Where V0, V1, and V2 represent the first three control vertices at the beginning of an interpolation curve, s0, s1, and s2 represent the S-parameter values ​​of the first three model points of the curve to be interpolated, and Q0 represents the spatial coordinates of the first model point to be interpolated. j ,s j Let C(s) represent the spatial coordinates of the j-th type value point and the corresponding s-direction parameter value, respectively. j ) indicates that the interpolation curve is at s j Spatial coordinates of the curve point at V i N represents the i-th control point of the interpolation curve. i,3 (s j ) indicates that the third-order B-spline basis function corresponding to the control point has parameters s at the model value point. j The function value at point V n V n+1 V n+2 The three control vertices at the very end of the interpolation curve are represented sequentially by Q. n This represents the coordinates of the last control point of the model value to be interpolated. These n+1 skin direction guide curves can be considered to reflect the design shape characteristics of the blade surface.

[0074] 2.2) Each shape guide curve is sampled and discretized using the second sampling frequency, and multiple sampling points on each shape guide curve are obtained as surface guide points (m sampling points in the specific implementation), thus a total of n*m shape guide points. To ensure the interpolation property of the surface on the blade section profile, the sampling points whose distance from the blade section profile is less than a preset distance (i.e., when the guide curve sampling point and the profile position are close to coincide) are offset so that the sampling points are located away from the blade section profile between different input profiles, thereby obtaining the set of surface guide points;

[0075] 2.3) To facilitate the calculation of surface curvature, the guiding points of surfaces with the same s-parameter are interpolated into third-order B-spline curves in the t-direction using periodic boundary conditions to obtain the corresponding auxiliary curves.

[0076] 2.4) Calculate the combined curvature of each surface guide point using the shape guide curve where the surface guide point is located and the corresponding auxiliary curve.

[0077] For the overall curvature of each surface guide point, calculate the curvature value k of the shape guide curve in the s-direction at that surface guide point. s The curvature value k of the parameter t in the guide direction of the auxiliary curve at the guide point of the surface. t and the curvature value k in the s direction. s and the curvature value k in the t direction t The mean value is used as the composite curvature k of the guiding point of the surface. s,t The average curvature of the guide point of the surface serves as a measure of the surface's curvature at that location, characterizing the surface's shape information at various points. The calculation formula is as follows:

[0078]

[0079] Among them, s i,j ,t i,j The guide points Q of the surface are respectively j In the parameter values ​​corresponding to the s and t directions, C′ t (t i,j ),C″ t (t i,j C' and C' represent the first and second derivatives of the auxiliary curve at the guiding point, respectively. s (s i,j ),C″ s (s i,j ) represent the first and second derivatives of the shape guide curve at the guide point, respectively, and || represents taking the absolute value.

[0080] 3) Divide the surface region according to the current blade blade surface model to obtain multiple surface regions. Based on the comprehensive curvature of all surface guide points on multiple shape guide curves, calculate and determine whether each surface region meets the preset accuracy. If it does, the current blade blade surface model is used as the overall smooth blade blade surface model; otherwise, each surface region is continuously corrected and updated, and local interpolation transformation is performed on the control vertices in the surface model until each surface region meets the preset accuracy. Finally, a blade blade surface model with both overall smoothness and key section interpolation is obtained. The blade blade surface model is used for subsequent isogeometric analysis and other related performance analysis processes.

[0081] 3) Specifically:

[0082] 3.1) Divide the surface region according to the current blade blade surface model. The longitudinal edge of the T-grid generated by the two blade cross section profiles is recorded as the boundary. The area between these two longitudinal edges is a surface sub-interval. The adaptive local fitting threshold of all surface sub-intervals in each surface region is calculated based on the average comprehensive curvature of each surface guide point in the surface sub-interval.

[0083] In section 3.1), the comprehensive curvature of the guide points within each surface sub-interval is statistically analyzed, and the average comprehensive curvature value of the guide points within each surface sub-interval is calculated. The average comprehensive curvature of each surface sub-interval is compared. If there is a difference in magnitude between the average comprehensive curvature values, or if the difference in average comprehensive curvature between surface sub-intervals exceeds a preset difference, then the average comprehensive curvature of each surface sub-interval is smoothed to facilitate calculation. The smoothing formula is as follows: Let be the average composite curvature of the guiding points of the surface within the sub-interval. The average composite curvature after smoothing is used as the basis for subsequent surface smoothing adjustments. The corresponding average composite curvature after smoothing is then used as a substitute, and the adaptive local fitting threshold for each surface sub-interval is calculated using the following formula; otherwise, the adaptive local fitting threshold for each surface sub-interval is directly calculated using the following formula:

[0084]

[0085]

[0086] in, h represents the adaptive local fitting threshold for each surface sub-interval. r This represents the curvature correction factor for each surface sub-interval. Indicates the local fitting threshold of the interval. The maximum and minimum average curvature of the surface guide points in each surface sub-interval are given by η, which is a coefficient used to balance the differences in average curvature between intervals. It is usually taken as 0.05, and max() indicates taking the maximum value.

[0087] 3.2) Calculate the deviation vector between each guide point of each surface sub-interval in each surface region and the corresponding spatial position point of the current blade surface model. The L2 norm of the deviation vector is denoted as the fitting error of each guide point. The calculation formula is as follows:

[0088] δ i,j =Q i,j -S(s i,j ,t i,j )

[0089] ε i,j =||δ i,j ||

[0090] Wherein, S(s) represents i,j ,t i,j ) represents the guide point Q of the surface. i,j At the spatial location point corresponding to the current blade surface model, δ i,j Let ε denote the bias vector, ||| denotes the L2 norm operation, and ε i,j This represents the fitting error; then, the average fitting error of the current surface sub-interval is calculated. When the average fitting error of each surface sub-interval is greater than or equal to the corresponding adaptive local fitting threshold, the preset accuracy is not met, and the surface sub-interval is marked as an interval that has not yet reached the accuracy requirement. The current surface sub-interval is also recorded as the region to be fitted, and all surface guide points of the current surface sub-interval are added to the set of guide points to be approximated. In the figure, k is the number of iterations for surface adjustment;

[0091] 3.3) Select the control vertices V of the surface that meet the adjustment conditions in the current blade blade surface model. l (k) Add to the set of vertices to be adjusted (cp) (k) In the process of adjusting the vertex set, the adjustment area is determined based on the surface control vertices in the set. Specifically, the clamped interval is defined by the vertical edge containing the surface control vertices in the set and used as the adjustment area. The adjustment condition is: for the surface control vertex V in the k-th iteration... l (k) If the set is located at the guide point to be approached There exists a surface guide point Q. i,j Its corresponding parameter value (s) i,j ,t i,j Located at the control vertex V of the surface l (k)Within the local support range of the basis functions, i.e., at the position of the parameter, the value of the mixture function is not equal to zero, and we have B. l (s i,j ,t i,j If )≠0, then the surface control vertex satisfies the adjustment condition; it should be noted that, due to the non-tensor product characteristics of the T-spline surface control mesh, the subscript numbers of the surface control vertices are all one-dimensional.

[0092] 3.4) Based on the local support of the surface blending function, add the surface guide points that satisfy the affected conditions from the set of surface guide points to the set of affected points, and then determine the affected region based on the control vertex boundary of the affected point set; the affected condition is: for surface guide points Q in the set of surface guide points... i,j If the set of control vertices of the surface to be adjusted is cp (k) There exists a certain control vertex V. l (k) Its mixing function is at the guide point Q on the surface. i,j The corresponding parameter position has a non-zero value, that is, B. l (s i,j ,t i,j If ) ≠ 0, then the guiding point Q of the surface i,j The affected conditions are met;

[0093] 3.5) Calculate the surface deviation vector based on the surface control vertices in the affected point set, calculate the adjustment vector of each surface control vertex in the adjustment area using the least squares asymptotic iterative approximation method, and then update the surface control vertices sequentially by superimposing the adjustment vectors, so as to finally realize the correction and update of each surface control vertex in the current surface sub-interval of the current surface region.

[0094]

[0095]

[0096] in, Let m represent the spatial coordinates of the l-th control vertex in the k-th and (k+1)-th iterations, and the adjustment vector in the k-th iteration, respectively. Let μ represent the asymptotic iterative approximation weight coefficients. s and m t Let represent the number of different parameters s and t in the set of guiding points on the surface, respectively. The surface guide point Q represents the surface guide point in the k-th iteration update. i,j The corresponding deviation vector, These are the control vertices of the surface. At the guide point Q on the curved surface i,j The product of the basis function values ​​in the periodic direction and the skin direction is the blending function B of the control vertex. l (si,j ,t i,j The surface control vertices are updated by adjusting the superposition of the vector and the current control vertex, thus obtaining the surface for this local fitting iteration.

[0097] 3.6) The surface control vertices in the modified and updated blade blade surface model are updated by interpolation. In specific implementation, the Nasri interpolation formula is used to transform the surface control vertices that meet the interpolation requirements, and then the blade blade surface model is updated.

[0098] 3.7) Repeat steps 3.1)-3.6) until the average fitting error of all surface sub-intervals in each surface region is less than the corresponding adaptive local fitting threshold or the number of iterations of each surface sub-interval reaches the maximum iteration value. Finally, the blade body shape generation process that meets the modeling accuracy requirements and key section interpolation is completed, and an overall smooth blade body surface model is obtained.

[0099] An example of this invention for modeling the curved surface of a certain type of blade Figure 6 As shown, this example first establishes an initial T-grid using the input profile described by periodic basis functions. Then, it achieves control mesh filling and subdivision using the proposed nearest-neighbor refinement criterion. Furthermore, by extracting the geometric features of the shape into discrete surface guide points, and combining this with a local fitting strategy, the surface is smoothed. Simultaneously, in each iterative adjustment, the surface is locally updated using the Nasri interpolation transformation formula. Ultimately, this approach simultaneously eliminates surface oscillation defects and performs key section profile interpolation. Figure 6 (a) shows the input key section profile and its control mesh distribution. Figure 6 (b) is the design shape guide curve established through geometric feature extraction. Figure 6 (c) represents the final smooth blade skin surface. Compared to the traditional NURBS surface, the number of control points for the generated T-spline surface is reduced from 1127 to 636, and the total global modeling error of the skinning process is only 0.873. Moreover, the generated surface is smooth and continuous overall. Therefore, it can be considered that this method can meet the requirements for high-precision T-spline surface modeling of blade height.

Claims

1. A method for shaping the leaf blade based on T-spline partial skinning, characterized in that, Includes the following steps: 1) Based on the input blade cross-sectional profiles, a topological T-network is constructed using a combination of T-spline local skinning and the nearest neighbor refinement criterion at the middle boundary. This yields the T-spline control mesh model of the blade surface and serves as the initial blade surface model. Specifically, 1) refers to: Based on the input blade section profiles, a topological T-network is constructed using T-spline local skinning to obtain the initial T-spline control mesh. Then, the initial T-spline control mesh is refined by inserting intermediate secants and refining the mesh using the nearest neighbor refinement criterion to obtain the T-spline control mesh model of the blade surface. The steps for inserting the intermediate section line between two adjacent blade section profiles and refining the mesh in the initial T-spline control mesh are as follows: S1: After interpolating the current two blade section profiles, obtain the midline between the current two blade section profiles. ; S2: Select the current middle intercept line Find the midpoint between the two nodes with the largest spacing along the cross-section direction of the current blade profile and these two nodes. The nearest point is denoted as the nearest control vertex. The blade section profile containing the nearest control vertex is denoted as the nearest neighbor profile. The other blade section profile is denoted as the opposite side profile. ; S3: First, adjust the side profile. Discretize and then use the nearest neighbor profile The same node vector interpolation reconstructs a dashed curve Next, take the dashed curve. Top and nearest control vertex Control vertices at positions corresponding to the same node value Then the dashed curve Control vertex on As the opposite side profile The new control vertex on the corresponding T-grid vertical edge , will control the vertex Insert into the opposite side profile On the corresponding T-mesh edge, then the nearest control vertex is selected. and opposite side profile Control vertex on The midpoint of the spatial coordinates is used as the current intermediate intercept. The coordinates of the control vertex at the node value corresponding to the vertical edge are used as the new control vertex of the surface control mesh, thereby realizing the control of this intermediate intercept line in the T mesh. The longitudinal edges of the grid corresponding to the cross-sectional profiles of the blades on both sides are refined and updated; S4: Repeat S2-S3 until the current intermediate cutoff line. If the number of control vertices is greater than the preset number, the resulting intermediate cutoff line will be... As the distribution of control vertices between the longitudinal edges of the current two blade section profiles in the initial T-spline control mesh, the longitudinal edges corresponding to the current two blade section profiles are updated to achieve the refinement of the control mesh; 2) After uniformly sampling and interpolating the profile of each blade section, multiple shape guide curves are obtained, and then the comprehensive curvature of all surface guide points on each shape guide curve is calculated; 3) Divide the surface region according to the current blade blade surface model to obtain multiple surface regions. Based on the comprehensive curvature of all surface guide points on multiple shape guide curves, calculate and determine whether each surface region meets the preset accuracy. If it does, the current blade blade surface model is used as the overall smooth blade blade surface model; otherwise, each surface region is continuously corrected and updated, and the control vertices in the surface model are locally interpolated and transformed until each surface region meets the preset accuracy, and finally the overall smooth blade blade surface model is obtained.

2. The method for leaf blade shaping based on T-spline partial skinning according to claim 1, characterized in that, In step S1, a four-point interpolation subdivision method is used to interpolate the current two blade section profiles. The interpolation formula is as follows: in, This indicates the interpolation point between the current two blade profiles. , This indicates the control vertices that have the same node values ​​in the current two blade profiles. These represent the distances to the interpolation points on the left and right sides, respectively. The two more distant control vertices, It is the distance to the interpolation point Two more distant control vertices The influence weighting coefficient.

3. The method for leaf blade shaping based on T-spline partial skinning according to claim 1, characterized in that, Specifically, 2) refers to: 2.1) Uniformly sample each blade section profile in the direction of parameter t at the first sampling frequency to obtain the sampling point set corresponding to each blade section profile; interpolate and fit the sampling point set of each blade section profile into multiple third-order B-spline curves in the direction of parameter s and use them as shape guidance curves. 2.2) Each shape guide curve is sampled and discretized at the second sampling frequency to obtain multiple sampling points on each shape guide curve. The sampling points whose distance from the blade section profile is less than the preset distance are offset so that the sampling points are positioned between different input profiles, thereby obtaining the set of curved surface guide points. 2.3) For the guide points of the surface with the same s-parameters, interpolate them into third-order B-spline curves in the t-direction using periodic boundary conditions to obtain the corresponding auxiliary curves; 2.4) Calculate the combined curvature of each surface guide point using the shape guide curve where the surface guide point is located and the corresponding auxiliary curve.

4. The method for shaping a leaf blade based on T-spline partial skinning according to claim 3, characterized in that, For the overall curvature of each of the surface guide points, calculate the curvature value of the shape guide curve in the s-direction at that surface guide point. The curvature value of the auxiliary curve in the t direction at the guide point of the surface. Calculate the curvature value in the s-direction. curvature value in the t direction and parameter The mean value is used as the composite curvature of the guiding point of the surface. .

5. The method for leaf blade shaping based on T-spline partial skinning according to claim 1, characterized in that, Specifically, 3) refers to: 3.1) Divide the surface region according to the current blade blade surface model. The longitudinal edge of the T-grid generated by the two blade cross section profiles is recorded as the boundary. The area between these two longitudinal edges is a surface sub-interval. The adaptive local fitting threshold of all surface sub-intervals in each surface region is calculated based on the average comprehensive curvature of each surface guide point in the surface sub-interval. 3.2) Calculate the deviation vector between each surface guide point in each surface sub-interval of each surface region and the corresponding spatial position point of the current blade surface model. The L2 norm of the deviation vector is recorded as the fitting error of each surface guide point. Then, calculate the average fitting error of the current surface sub-interval. When the average fitting error of each surface sub-interval is greater than or equal to the corresponding adaptive local fitting threshold, the preset accuracy is not met. The current surface sub-interval is recorded as the region to be fitted, and all surface guide points of the current surface sub-interval are added to the set of guide points to be approximated. 3.3) Select the control vertices of the surface in the current blade blade surface model that meet the adjustment conditions. Add to the set of adjusted vertices, and determine the adjustment region based on the surface control vertices in the set of adjusted vertices. The adjustment condition is: for the surface control vertices in the k-th iteration process... If there exists a surface guide point in the set of guide points to be approximated Its corresponding parameter value Located at the control vertex of the surface Within the local support range of the basis functions, the control vertex of the surface satisfies the adjustment conditions; 3.4) Based on the local support of the surface blending function, add the surface guide points in the set of surface guide points that satisfy the affected conditions to the set of affected points, and then determine the affected region based on the control vertex boundary of the affected point set; the affected condition is: for the surface guide points in the set of surface guide points... If a certain control vertex exists in the set of control vertices of the surface to be adjusted Its mixing function at the guide point of the surface If the value at the corresponding parameter location is non-zero, then the guide point of the surface... The affected conditions are met; 3.5) Calculate the surface deviation vector based on the surface control vertices in the affected point set, calculate the adjustment vector of each surface control vertex in the adjustment area using the least squares asymptotic iterative approximation method, and then update the surface control vertices sequentially by superimposing the adjustment vectors, so as to finally realize the correction and update of each surface control vertex in the current surface sub-interval of the current surface region. 3.6) Perform interpolation update transformation on the surface control vertices in the corrected and updated blade blade surface model to obtain the interpolated surface control vertices, and then update the blade blade surface model. 3.7) Repeat steps 3.1)-3.6) until the average fitting error of all surface sub-intervals in each surface region is less than the corresponding adaptive local fitting threshold or the number of iterations of each surface sub-interval reaches the maximum iteration value, then the overall smooth blade surface model is obtained.

6. The method for shaping a leaf blade based on T-spline partial skinning according to claim 5, characterized in that, In section 3.1), when the difference in average composite curvature between each surface sub-interval is of an order of magnitude greater than a preset difference, the average composite curvature of each surface sub-interval is smoothed to obtain the corresponding smoothed average curvature, and the average curvature of each surface guide point is updated. Then, the adaptive local fitting threshold of each surface sub-interval is calculated using the following formula based on the updated average curvature; otherwise, the adaptive local fitting threshold of each surface sub-interval is directly calculated using the following formula: in, This represents the adaptive local fitting threshold for each surface sub-interval. This represents the curvature correction factor for each surface sub-interval. Indicates the local fitting threshold of the interval. The maximum and minimum average curvature of the guiding points of the surface in each surface sub-interval. This is a coefficient used to balance the differences in average curvature across different intervals. This indicates taking the maximum value. It represents the average composite curvature of the guiding points of the surface within the sub-interval of the surface.

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