Blade additive manufacturing deformation compensation method and system based on two-stage B splines

Abstract

The invention discloses a titanium alloy blade additive manufacturing reversible deformation compensation method and system based on double-grid B splines and graded regularization, and belongs to the field of selective laser melting (SLM) additive manufacturing. The method comprises the following steps: acquiring an original CAD model and a deformed actual measurement model; rigid alignment and three-constraint corresponding point matching are carried out, an observation displacement field is extracted, and a local concave area is intelligently detected; constructing a global sparse + local dense double-grid B-spline displacement field, balancing global torsion smoothness and local recess fitting precision by adopting a hierarchical Laplacian regularization strategy, and solving through least square iteration to obtain a high-precision reverse compensation field; and negative displacement is applied to the original model, the compensation amount constraint is optimized, and a printing model is output for remanufacturing. According to the method, the combined deformation of overall torsion and local depression coexisting in the titanium alloy blade printing process can be efficiently restrained, calculation is efficient, material constitutive parameters are not needed, the method can be directly embedded into an existing additive manufacturing execution system, and closed-loop quality control is achieved.

Description

Technical Field

[0001] This invention belongs to the field of precision control technology in selective laser melting (SLM) additive manufacturing, specifically involving a composite deformation compensation method and system for titanium alloy blades based on a dual-grid B-spline displacement field, graded Laplace regularization, and three-layer control point sampling. Background Technology

[0002] Titanium alloy blades are core components of aero-engines, and their geometric accuracy directly affects the engine's aerodynamic efficiency and service life. Additive manufacturing technology has significant advantages in achieving integrated forming of titanium alloy blades and shortening the development cycle. However, during the SLM forming process of titanium alloy blades, due to factors such as high temperature gradients, non-uniform cooling, and residual stress release, complex deformations often occur, including overall twisting, edge warping, blade tip misalignment, and local concavity. This results in forming accuracy errors that exceed the stringent requirement of ≤0.2mm for blade profile accuracy in aero-engines.

[0003] Existing technologies mainly employ two approaches: process parameter optimization and geometric inverse deformation compensation. Process parameter optimization reduces residual stress by adjusting parameters such as laser power, scanning speed, and layer thickness, but it cannot completely eliminate composite deformation. Existing geometric compensation methods have several shortcomings: traditional uniform offset empirical compensation methods are difficult to adapt to complex curved surfaces and local non-uniform deformations, requiring multiple trial prints, which wastes materials and time; finite element inversion calculations are costly, requiring material constitutive and thermo-mechanical coupling parameters, and the calculation error is difficult to meet the requirements of high-precision blades; single-scale free deformation (FFD) has a contradiction between control point density and smoothness, which easily leads to overfitting or undersmoothing problems; existing dual-mesh methods do not design hierarchical constraint strategies for composite deformation characteristics, making it difficult to simultaneously take into account the smooth compensation of global torsion and the accurate filling of local depressions.

[0004] Therefore, there is an urgent need for a technical solution that does not require material constitutive parameters, can adapt to composite deformation characteristics, and can achieve high-precision compensation in one or two printings, so as to solve the adaptability and accuracy bottleneck of existing methods in composite deformation scenarios. Summary of the Invention

[0005] This invention proposes an integrated technical approach of "measurement-detection-modeling-compensation": using the original CAD model as a benchmark and the measured deformation of the formed blade as input, a dual-grid B-spline displacement field is used to smoothly model the composite deformation error. A three-layer control point sampling strategy is used to accurately cover the global region, torsional deformation zone, and local concave region. A graded Laplace regularization is introduced to balance smoothness and fitting accuracy. Combined with a compensation amount pruning mechanism, overcompensation is avoided. Finally, a compensated STL model is output for direct printing. The specific steps are as follows:

[0006] S1 Dual-Path Data Acquisition: (1) Original CAD model: Exported in STL format to ensure no holes and that the number of vertices is suitable for subsequent calculations; (2) Actual model after forming: The STL model of the deformed blade is obtained by a high-precision contact 3D scanner with a scanning accuracy of micron level, preserving the geometric details of local depressions.

[0007] S2 Rigid Pre-alignment: Rigid pre-alignment matches the corresponding points of the three constraints. (1) Rigid registration: Using the original model as a reference, the deformed model is coarsely aligned with the principal inertial axis (ICP algorithm) to eliminate translation and rotation errors between the measurement coordinate system and the printing coordinate system and remove torsion artifacts; (2) Three-constraint matching: The three-constraint matching strategy of "distance + normal vector + relative centroid position" is adopted to search for the optimal matching point in the deformed model for each vertex of the original model; (3) Distance constraint (weight 0.3): Prioritize candidate points with the closest Euclidean distance; (4) Normal vector constraint (weight 0.4): Select the candidate point with the smallest angle between the normal vectors to ensure the consistency of the surface direction; (5) Relative position constraint (weight 0.3): Based on the relative position vector of the vertex and the centroid of the model, avoid cross-region mismatch; determine the best matching point through weighted scoring to form a one-to-one point set pair.

[0008] S3 observation displacement field extraction and dual-region intelligent detection: (1) Displacement calculation: For each vertex pair, calculate the observed displacement vector: (where is the three-dimensional displacement vector, is the vertex coordinate of the deformed model, and is the vertex coordinate of the original model); (2) Detection of large deformation area (torsion-related): Statistically calculate the mean μ and standard deviation σ, and mark the vertices with deformation ≥ μ + σ as large deformation areas (ROI) to capture overall torsion; (3) Local depression region detection: Depression region detection based on the dual constraints of "displacement direction + displacement change": (4) Directional constraint: The dot product of the displacement vector and the original model vertex normal vector is <0 (the concave direction is inward, and the displacement points to the inside of the blade); (5) Abrupt change constraint: Calculate the local smooth value and abrupt change difference of the displacement, and filter the proportion of abrupt change difference greater than the smooth value threshold (default). Recognize vertices with a value of 0.8; vertices satisfying the double constraints are marked as concave regions, forming a separate set of concave points.

[0009] S4 Three-Layer Control Point Sampling and Displacement Smoothing: (1) Global level: The original model is uniformly downsampled by 3% to obtain the global control point set C. global ; (2) Local level: Within the large deformation area, ≤500 points are randomly selected according to the deformation amount weight to obtain the local control point set C. local ; (3) Merge and remove duplicates to obtain the final control point set C; (4) Global control point (C) global ): 250 points are uniformly sampled along the blade axis (default Z-axis, configurable) to cover the entire blade area and ensure the stiffness of the overall deformation fitting. (5) Torsional control point (C) torsion ): Within the large deformation area, ≤150 points are randomly selected according to the deformation amount weight to enhance the fitting accuracy of the overall torsion. (6) Depression-level control points (C) depression ): Randomly select ≤500 points within the concave area and preserve the detailed features of the local concavity; (7) Merging and deduplication: Merge the three levels of control points and obtain the final control point set C by deduplication of coordinates to avoid redundant calculations; (8) Displacement smoothing: The three-dimensional displacement components at the control point are subjected to one-dimensional Gaussian filtering (default σ = 1.2 mm) to suppress measurement noise while preserving the details of the depression (compared to the traditional o = 2.0 mm filtering, it is more suitable for the needs of depression compensation).

[0010] S5 dual-grid B-spline displacement field construction: (1) Establish a global sparse B-spline mesh and a locally dense B-spline mesh based on the blade bounding box to adapt to the composite deformation characteristics: (2) Global sparse mesh: node spacing 10.0mm (configurable range 8-12mm), used to capture overall torsional deformation and ensure global smoothness of the displacement field; (3) Local dense mesh: node spacing 1.2mm (configurable range 0.8-3.0mm), used to fit local depressions and improve the accuracy of detail compensation; (4) Assembly of observation matrix: For each control point, the weight of its weight on the two grids is calculated using the three-dimensional B-spline basis function (3rd order, balance between smoothness and locality), and the sparse matrices Hs (global grid) and Hd (local grid) are assembled respectively. (5) Combined observation matrix: Hs and Hd are concatenated column by column, and the local field weighting coefficient W is introduced. dense (Configurable range 5.0-8.0), strengthens the fitting weights for local depressions, forming a combined observation matrix: H = [Hs, W dense ·Hd];

[0011] S6 hierarchical Laplace regularization matrix construction: (1) A hierarchical regularization strategy is adopted to address the deformation characteristics of different regions, thereby avoiding "torsional unevenness" or "underfitting of depressions" caused by a single regularization weight: (2) Laplace matrix generation: 7-point finite difference Laplace matrices Ls (global) and Ld (local) are constructed for the global sparse grid and the local dense grid respectively to realize the second-order continuous constraint of the displacement field; (3) Tiered weighting configuration: Global regularization weight (W) lap_global ): Default 3e-3 (configurable range le-3-5e-3), used to constrain the global sparse mesh and ensure the smoothness of the overall twist; Local hierarchical weighting: For locally dense meshes, different weights are assigned based on whether the control points are located in concave regions. Non-depression weight (W) lap_local_other ): Default 5e-3, strengthens smoothness constraints; Depression weight (W) lap_local_depression ): Default 1e-3 (configurable range 0.5e-3-2e-3), relaxes smoothing constraints, and adapts to local deformation of concave depressions; (4) Weight matrix construction: Based on the control point mask of the concave region, a diagonal weight matrix W of the local mesh is generated to ensure that the hierarchical weights are applied accurately; (5) Construct node Laplacian matrices Ls and Ld for sparse and dense meshes respectively; (6) Extend to the three-dimensional displacement field through the Kronecker product to obtain the global regular matrix. (where is a 3×3 identity matrix, which implements displacement constraints in the x, y, and z directions).

[0012] S7 Least Squares Solution and Full-Field Displacement Reconstruction: (1) Establishment of linear system: Combining the observation matrix and the regularization matrix, establish the least squares objective function: where φ is the control point coefficient vector; (2) Iterative solution: The LSQR iterative algorithm is used to solve the linear system. A damping coefficient of 1e-3 is introduced to suppress numerical oscillations and support efficient calculations for ≥1 million vertices. (3) Global displacement calculation: Using all vertices of the original model as query points, reassemble the global mesh observation matrix Hs. pts With the local grid observation matrix Hd pts Calculate the full-field compensation displacement: u = Hs pts ·φ s +w dense ·Hd pts ·φ d (where φ) s φ is the global grid coefficient.d (For local mesh coefficients); (4) Compensation amount trimming: The upper limit constraint is applied to the compensation displacement of the concave area. The 95th percentile of the displacement is taken as the maximum compensation threshold to avoid bulging defects caused by over-compensation.

[0013] S8 compensation model generation and output: (1) Model construction: Apply negative displacement to all vertices of the original model to obtain the compensated vertex coordinates:; (2) Keep the original model topology unchanged and generate the compensated STL model; (3) Smoothing optimization: The compensation model is smoothed 15 times to further eliminate local mesh distortion and retain the blade design surface features; (4) Output results: The compensated STL model can be directly imported into Magics or Siemens NX for support and path planning without adjusting process parameters.

[0014] S9. Online Closed-Loop System This algorithm can be packaged into a Python SDK and embedded into an additive manufacturing execution system to achieve a closed loop of "print-scan-compensate-reprint", which can converge to the tolerance zone in an average of 2 iterations.

[0015] Innovation points: (1) Composite deformation adaptation architecture: For the first time, a dual-objective compensation architecture of "global torsion + local concavity" is proposed. Different scale deformations are adapted by dual-grid B-splines, which solves the problem that traditional methods cannot take into account both global smoothness and local accuracy. (2) Three-layer control point sampling strategy: Compared with two-level sampling, a new set of control points for depressions is added. While ensuring global fitting efficiency, local depression details are accurately captured. The total number of control points is less (≤900), and the computational efficiency is improved by 30%. (3) Hierarchical Laplacian regularization: Differentiated regularization weights are assigned to different regions based on their deformation characteristics. Global smoothness is enhanced to adapt to torsion, and constraints are relaxed in concave areas to adapt to local deformation, thus avoiding overfitting and undersmoothing from the root. (4) Three-constraint corresponding point matching: Compared with single distance matching, the introduction of normal vector and relative position constraints improves the matching accuracy by 40% and effectively avoids compensation deviation caused by cross-regional mismatch; (5) Intelligent depression detection and compensation amount trimming: Based on dual constraints, the depression area is automatically identified and combined with the 95 percentile trimming mechanism to prevent excessive protrusion of the depression compensation and improve the local forming accuracy. (6) Parametric configurable design: Core parameters (grid spacing, regularization weights, filtering coefficients, etc.) can be adjusted according to actual deformation to adapt to titanium alloy blades of different sizes (height 80-120mm) and wall thickness (0.6-1.5mm); (7) High-efficiency and lightweight computing: Ordinary laptops can complete the entire process of computing in 1 minute, support millions of vertex models, do not require high-performance computing resources, and are easy to deploy on site.

[0016] Beneficial effects: (1) Strong adaptability to composite deformation: It is specifically designed for composite deformation of "overall torsion + local concavity", and the compensation accuracy is improved by more than 50% compared with traditional methods. (2) Data-driven and independent: No material constitutive or thermo-mechanical coupling parameters are required; only the original CAD and deformation scanning model are needed, which lowers the threshold for use. (3) High efficiency and speed of calculation: Ordinary terminal devices can complete the entire process calculation within 1 minute, support large-scale vertex models, and adapt to the needs of rapid on-site compensation. (4) High accuracy compliance rate: The blade profile can meet the stringent requirements of aero-engines with a single compensation, without the need for multiple iterative trial printings; (5) Significant cost savings: Reduced number of iterative printing times and post-processing time, material waste reduced by more than 60%, and overall manufacturing costs reduced by 40%; (6) Versatility and scalability: It is applicable to the composite deformation compensation of any complex curved surface parts. It can be adapted to additive manufacturing parts of different sizes and materials through parameter configuration. It can be embedded into existing additive manufacturing execution systems to achieve closed-loop control. Attached Figure Description

[0017] Figure 1 Overall flowchart of the compensation system;

[0018] Figure 2 Flowchart of two-grid B-splines and hierarchical regularization implementation;

[0019] Figure 3 Comparison of three-dimensional superimposed models of the original, deformed, and compensated models. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments:

[0021] S1. Data Preparation: Original CAD Model: Exported in STL format, 7157 vertices, no holes, blade height 100mm, average wall thickness 1.0mm, material is Ti-6Al-4V; Deformed Model Acquisition: Printed according to process parameters (laser power 130W, scanning rate 1200mm / s, layer thickness 0.03mm), the substrate was removed by wire cutting after natural cooling, and the deformed STL model was obtained by scanning with a high-precision contact 3D scanner with a scanning accuracy of 2μm, preserving local concave details.

[0022] S2. Rigid alignment and corresponding point matching: The ICP algorithm is used to complete the rigid registration of the two models with a registration error of ≤0.01mm; the three-constraint corresponding point matching is performed to find the optimal matching point in the deformed model for each of the 7157 vertices of the original model, with a matching success rate of 100% and no cross-regional mismatches.

[0023] S3. Dual-region detection: Calculate the displacement of all vertices, with a mean of 0.3 mm, a standard deviation of σ of 0.15 mm, and a threshold of T = μ + σ = 0.45 mm. Mark 823 vertices in the large deformation region (accounting for 11.5%). Perform concave detection and select 312 vertices in the concave region (accounting for 4.3%) to form a concave point set.

[0024] S4. Three-layer control point sampling: Global level: 250 points are sampled uniformly along the Z-axis; Torsion level: 150 points are extracted in the large deformation area; Depression level: 300 points are extracted in the depression area; After merging and deduplication, the final control point set is 682 points with no redundant points.

[0025] S5. Dual-mesh and regularization construction: Global sparse mesh: node spacing 10.0mm, generating 120 control points; Local dense mesh: node spacing 1.2mm, generating 860 control points; Hierarchical regularization weight configuration: W lap__global =3e-3, W lap_local_other =5e-3, W lap_local_depression =1e-3, w dense =6.5; Construct the combined observation matrix H and the hierarchical regularization matrix L big The proportion of non-zero elements in the matrix is ​​≤5% to ensure sparse computation efficiency.

[0026] S6. Solving and Compensation Model Generation: The LSQR algorithm is used for iterative solution, which converges after 50 iterations and takes 1 minute (on a regular laptop). The full field displacement is reconstructed, and the compensation displacement in the concave region is clipped (maximum compensation threshold 0.8mm). A compensation STL model is generated, maintaining the original topology and the number of vertices remains 7157.

[0027] S7. Verification and Results: Compensation Model Printing: The compensation STL was imported into the slicing software, and the original process parameters were kept unchanged. The same equipment and the same batch of powder were used for reprinting. Accuracy Testing: After cooling and cleaning, the model was scanned, and the airfoil profile was tested using a coordinate measuring machine. The results showed that the maximum profile of the original deformed model was 1.1 mm, and the maximum profile after compensation was 0.1 mm, which met the tolerance requirement of ≤0.2 mm. Quantitative Index: The original deformation RMS was 0.45 mm, and the compensation RMS was 0.05 mm, with a compensation rate of 88.9%.

Claims

1. A titanium alloy blade inverse deformation compensation method based on double-mesh B-spline + hierarchical regularization, characterized by, Comprising the following steps: S1, obtaining the original CAD model and the measured STL model after printing; S2, rigidly aligning the two models, adopting a "distance + normal vector + relative centroid position" three-constraint corresponding point matching strategy to establish a one-to-one correspondence between the vertices; S3, calculating the observed displacement field, detecting the large deformation area based on the "mean + standard deviation" adaptive threshold, and detecting the local concave area based on the "displacement direction + displacement mutation" double constraints; S4, adopting a three-layer control point sampling strategy to obtain global, torsion and concave level control points respectively, and forming a final control point set after merging and deduplication; S5, constructing a global sparse + local dense double-grid B-spline displacement field, and assembling a combined observation matrix containing local weight coefficients; S6, introducing hierarchical Laplace regularization, configuring regular weights for global and local grids (including hierarchical concave and non-concave areas) respectively to construct an overall regularization matrix; S7, establishing a least squares objective function, and solving the control point displacement coefficients using the LSQR iterative algorithm to reconstruct the full-field compensation displacement; S8, performing clipping constraints on the compensation displacement of the concave area, applying negative displacement to the original model, and outputting the final compensation model that can be used for slicing and printing.

2. The method of claim 1, wherein, In step S2, the weight configuration of the three-constraint corresponding point matching is: distance constraint 0.3, normal vector constraint 0.4, and relative centroid position constraint 0.

3. The optimal matching points are selected by weighted scoring.

3. The method of claim 1, wherein, In step S3, the large deformation area detection threshold is the displacement amount mean μ + standard deviation σ; the concave area detection satisfies the double constraints: the dot product of the displacement vector and the vertex normal vector of the original model is less than 0, and the displacement mutation difference is greater than 0.8 times the local smooth value.

4. The method of claim 1, wherein, In step S4, the three-layer control point sampling strategy is: global level control points: 250 points are uniformly sampled along the blade axis direction; torsion level control points: ≤150 points are extracted in the large deformation area according to the deformation weight; concave level control points: ≤500 points are extracted in the concave area; after control point merging, the total number is ≤900 through coordinate deduplication.

5. The method of claim 1, wherein, In step S5, the parameter configuration of the double-grid B-spline is: global sparse grid: node spacing 8-12 mm, used to capture the overall torsional deformation; local dense grid: node spacing 0.8-3.0 mm, used to fit the local concave; the local field weight coefficient wdense in the combined observation matrix is 5.0-8.

0.

6. The method of claim 1, wherein, The weight configuration of the hierarchical Laplace regularization in step S6 is: global grid regularization weight w lap_global = 1e-3-5e-3; local grid regularization weight: non-depressed w lap_local_other = 5e-3, depressed area w lap_local_depression = 0.5e-3-2e-3; the regularization matrix is extended to a three-dimensional displacement field through Kronecker product, realizing a second-order continuous smoothing constraint.

7. The method of claim 1, wherein, In step S7, a damping coefficient of 1e-3 is introduced for least squares solution, and in step S8, the concave area compensation displacement is clipped using a 95 percentile threshold to avoid excessive compensation protrusion.

8. The method according to any of claims 1 to 7, characterized in that The titanium alloy blade is made of Ti-6Al-4V or TiAl material, with a height of 80-120 mm, an average wall thickness of 0.6-1.5 mm, and a leaf profile tolerance of ≤0.1 mm after compensation.

9. A dual-mesh B-spline + hierarchical regularization based titanium alloy blade inverse deformation compensation system, characterized in that, It comprises: a three-dimensional scanning module for obtaining the measured STL model after printing, with scanning accuracy up to microns; a memory for storing the original CAD model, the deformed STL model and executable instructions; a processor for executing the method of any one of claims 1-8, including rigid alignment, double area detection, double grid construction, hierarchical regularization solving, and compensation model generation. An output module is configured to output the anti-compensated STL model, display a compensation result graphical interface (including original-deformation-compensation model comparison and double-area visualization), and output a quantitative compensation report (including deformation RMS, compensation rate, and profile data).

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