Water turbine runner crack additive repair trajectory planning method based on regular trapezoidal grooves

Abstract

The invention provides a water turbine runner crack additive repair trajectory planning method based on a regular trapezoidal groove, and relates to the technical field of hydroelectric power generation equipment crack repair, and the method comprises the steps: obtaining a trapezoidal groove grid bottom tangent plane based on a region growth algorithm, and carrying out the layer-by-layer slicing of the trapezoidal groove through the tangent plane; obtaining a section contour of the trapezoidal groove, and segmenting the contour of the trapezoidal groove by using tangential features of contour points; extracting a boundary curve in the generatrix direction of the trapezoidal groove, and generating a continuous and smooth parameterized spline curve by using a spline curve interpolation method; equally-spaced track points between the two spline curves are obtained based on an isoparametric method, and the track points are connected to form an additive track in the trapezoidal groove. Geometric modeling, a parameterized spline curve theory and additive manufacturing are organically combined, and accurate trajectory planning under the special geometric structure of the trapezoidal groove is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of crack repair of hydroelectric power generation equipment, and particularly to a trajectory planning method for additive repair of cracks in a water turbine runner based on a regular trapezoidal groove. Background Art

[0002] As the core component of a hydroelectric power generation system, the water turbine runner is subjected to complex hydraulic loads, centrifugal forces generated by high-speed rotation, and corrosion and cavitation caused by fluid media for a long time, and is extremely prone to crack damage at key stress-bearing parts. If these cracks are not repaired in time, it will lead to a decrease in the operating efficiency of the runner, and even cause catastrophic accidents, resulting in huge economic losses and safety hazards. Traditional repair methods such as welding and machining have defects such as large heat-affected zones, deterioration of material properties, and low repair accuracy, and it is difficult to meet the high-precision and high-reliability operating requirements of water turbines.

[0003] In recent years, additive manufacturing technology has shown broad application prospects in the field of repair of large and complex components due to its advantages such as high material utilization rate, high machining accuracy, and large degree of freedom. However, before repairing the crack area of the water turbine runner, a regular trapezoidal groove structure is usually used for grooving, and this special geometric shape poses a severe challenge to additive repair. Current additive repair trajectory planning methods are mostly designed for simple planes or regular surfaces, and the research on trajectory planning for special geometric structures such as trapezoidal grooves is still insufficient. The existing methods mainly have the following problems: First, the trapezoidal groove is sensitive to the cutting plane, and it is necessary to ensure that the first-layer trajectory covers the bottom plane first; second, the filling strategy of traditional layer-by-layer slicing cannot meet the additive trajectory requirements of the trapezoidal groove, resulting in uneven material accumulation at the edge of the repair area; third, the existing trajectory generation algorithms are difficult to ensure the smooth transition of a whole continuous trajectory, and it is difficult to ensure the consistency of repair quality. Summary of the Invention

[0004] The purpose of the present invention is to provide a trajectory planning method for additive repair of cracks in a water turbine runner based on a regular trapezoidal groove. This method organically combines geometric modeling, parametric spline curve theory, and additive manufacturing, and realizes precise trajectory planning under the special geometric structure of the trapezoidal groove. This method can not only be used for high-quality repair of cracks in water turbine runners, but also has important significance for improving repair efficiency and extending the service life of equipment. At the same time, it provides a technical reference for the repair of similar structural damages of other large energy equipment, and has broad engineering application value and economic benefits.

[0005] In order to achieve the above technical features, the purpose of the present invention is realized as follows: A trajectory planning method for additive repair of cracks in a water turbine runner based on a regular trapezoidal groove includes the following steps: S1. Obtain the bottom cutting plane of the trapezoidal groove grid based on the region growing algorithm, and slice the trapezoidal groove layer by layer using the cutting plane; S2. Obtain the slice contour of the trapezoidal groove, and segment the trapezoidal groove contour by using the tangential features of the contour points. S3. Extract the boundary curve in the busbar direction of the trapezoidal groove, and generate a continuous and smooth parametric spline curve by using the spline curve interpolation method. S4. Based on the isoparametric method, obtain the equally spaced trajectory points between the two spline curves, and connect the trajectory points to form the additive manufacturing trajectory inside the trapezoidal groove.

[0006] Preferably, the specific steps in S1 are as follows: S11. Extract the bottom plane of the mesh model of the trapezoidal groove: Based on the plane region growing algorithm, start from the specified seed point, and gradually expand the region according to the preset conditions. The finally obtained region is the bottom mesh set of the trapezoidal groove. S12. After obtaining the bottom mesh set, construct an accurate tangent plane: By calculating the center point coordinates of all surface elements in the bottom mesh set, determine a reference point on the bottom plane , and through PCA analysis of the bottom mesh set, obtain the fitted normal vector N, which can be expressed as the point-normal form plane equation: ; where P represents any point on the plane, represents the center point coordinates, and N represents the plane normal vector; S13. Set the slicing parameters, including: slicing spacing d, total number of slicing layers n, bead width w, number of track lanes per layer and the slicing direction.

[0007] Preferably, for the plane region growing algorithm in S11, starting from the specified seed point, the specific steps of gradually expanding the region according to the preset conditions are as follows: Step 111: Select the seed triangular surface element located at the bottom of the trapezoidal groove, calculate the normal vector of this surface element, and take the normal vector and center of this surface element as the current plane parameters. Step 112: Then detect the adjacent surface elements. If the angle between the normal vector of the adjacent surface element and the current plane normal vector is less than the preset threshold, and the maximum distance between the adjacent surface element and the current plane is less than the given threshold, then include this adjacent surface element in the region. Step 113: Update the current plane parameters. By performing weighted averaging on the normal vectors of the current mesh surface elements, obtain the normal vector direction and plane equation of the plane. Step 114: Continuously iterate steps 112 - 113 until no new surface element that meets the conditions can be found. The finally obtained region is the bottom mesh set of the trapezoidal groove.

[0008] Preferably, in step 112, the preset threshold value ranges from 5° to 10°. The given threshold value ranges from 1 to 5 mm.

[0009] Preferably, the slice spacing d in S13 depends on the actual processing requirements; The total number of slice layers n is calculated by dividing the total height of the trapezoidal groove by the slice spacing; The number of track passes per layer is calculated based on the bead width and the width of the current layer; The slicing direction is along the positive or negative direction of the normal vector.

[0010] Preferably, S2 specifically includes the following steps: S21. Taking the bottom cutting plane and slicing parameters as a reference, and then implementing a layer-by-layer slicing algorithm. Each layer of cutting plane is expressed as: ; where i represents the i-th slice layer, i = 0, 1, 2,..., n - 1, and d represents the slice spacing; For each edge in the mesh model, determine whether the edge intersects with the current cutting plane. If it intersects, calculate the intersection point coordinates and store them. Using spatial partitioning technology, only perform intersection detection on the mesh regions that may intersect with the current cutting plane; within a cutting plane, all intersection points are connected according to certain rules to form the cross-sectional contour line of this layer. These contour lines are composed of multiple closed loops, representing the geometric characteristics of the trapezoidal groove at this height; S22. For the processed contour point sequence, calculate the tangential features at each point: For each point on the contour , calculate the tangent vector of this point through its adjacent points , and the calculation methods include: Based on forward difference: ; Based on central difference: ; Based on local polynomial fitting, first fit a section of the curve near the point with an n-order polynomial, and then calculate the derivative of the polynomial at this point as the tangent vector; in addition, the curvature also needs to be calculated, representing the degree of curvature of the curve at this point, obtained through the rate of change of the tangent vector; the tangential features of the point also include the continuity of the change of the tangent vector, quantified by calculating the angle between adjacent tangent vectors: ; where is the angle between adjacent tangent vectors, and are adjacent tangent vectors; S23. Use the calculated tangential features above to achieve automatic segmentation of the contour: The basic idea of segmentation is to identify the positions where significant changes in the tangential features occur on the contour, and these positions usually correspond to the feature turning points of the trapezoidal groove geometry.

[0011] Preferably, the segmentation method in S23 includes: a segmentation method based on a threshold, setting a curvature threshold or a threshold for the change in the angle of the tangent vector , when the included angle between the adjacent tangent vectors of a certain point satisfies the following conditions, mark this point as a segmentation point; ; or the included angle between adjacent tangent vectors: ; A segmentation method based on clustering, clustering the contour points according to the tangential features: the direction of the tangent vector and the curvature, and different clusters correspond to different segments; through these methods, the continuous contour curve is segmented into multiple discrete segments.

[0012] Preferably, S3 specifically includes the following steps: S31. Based on the obtained segmented slice contour of the trapezoidal groove, clarify the bus direction, that is, the main axis direction or the machining direction of the groove body. In each slice contour, identify the boundary segment parallel to the bus direction. The specific method is to analyze the direction characteristics of the slice contour point set, calculate the included angle between the line connecting adjacent points and the preset bus direction, and when the included angle is less than the threshold, determine that this segment is the boundary in the bus direction; for complex contours, use principal direction analysis to decompose the contour into different direction segments and select the boundary curve consistent with the bus direction; The processed boundary point set is interpolated through spline curve technology to generate a continuous and smooth mathematical expression.

[0013] Preferably, S32 specifically includes: First, perform parameterization processing, assign parameter values to each data point, and adopt a cubic B-spline curve model, and its mathematical expression is: ; where, is the k-th order B-spline basis function, is the control point, and u is the parameter; Considering the characteristics of the slice contour, arc length parameterization is usually more suitable, that is, the parameter interval is proportional to the arc length between adjacent points, and it can better maintain the curve shape characteristics.

[0014] Preferably, S4 specifically includes the following steps: S41. Based on the two smooth parameterized spline curves obtained in step three, construct a parameter domain mapping of the additive manufacturing trajectory of the trapezoidal groove. Let the two boundary spline curves be respectively and , where \(u\in[0,1]\) is the curve parameter. By establishing the parameter domain \([0,1]\times[0,1]\), a two-parameter mapping function \(S(u,v)\) is introduced, where \(u\) is along the direction of the spline curve and \(v\) represents the relative position between two curves; uniformly sample within this parameter domain to obtain a series of parameter points , where , and , \(m\) and \(n\) represent the number of sampling points in the \(u\) direction and the number of sampling points in the \(v\) direction respectively; S42. Map the sampling points in the parameter domain to the physical space, calculate the spatial coordinates of the corresponding trajectory points. For each parameter point , its corresponding spatial coordinates are obtained through the following mapping relationship: ; where and are isoparametric points on the boundary curve; Based on the calculated set of spatial coordinate points, connect the points row by row or column by column to form a continuous additive manufacturing trajectory path; S43. To ensure the smooth transition of the trajectory points between the boundary curves, resample the generated trajectory.

[0015] Preferably, the S43 specifically includes: aiming at the unique geometric features of the trapezoidal groove, adopting an adaptive parameter adjustment strategy to optimize the distribution of trajectory points in the high-curvature region to ensure the smooth transition of the filling trajectory; at the same time, by constructing a discrete geometric model of the trapezoidal groove, performing collision detection between the trajectory and the wall surface, and adjusting the inclination angle of the wall surface trajectory to ensure that all trajectory points are inside the trapezoidal groove and meet the safety distance constraint.

[0016] The present invention has the following beneficial effects: 1. To ensure the integrity of the bottom tangent plane of the trapezoidal groove and give priority to ensuring the effective coverage of the first-layer trajectory, this method uses a region-growing algorithm to extract the bottom reference tangent plane and perform precise layer slicing based on this plane. Through this strategy, it can ensure that the first-layer filling trajectory fully covers the bottom plane, improve the bonding quality between the repair layer and the base material, and avoid the problem of uneven deposition caused by reference deviation.

[0017] 2. Aiming at the problem that the traditional layer-slicing filling strategy is difficult to adapt to the geometric features of the trapezoidal groove, by extracting the slice contour and performing reasonable segmentation, the isoparametric method is used to calculate the filling trajectory points for the segmented boundary curves to ensure the uniform distribution of the trajectory points inside the trapezoidal groove and optimize the material deposition path.

[0018] 3. To improve the smoothness and continuity of the trajectory and prevent trajectory mutations from affecting the repair quality, this method uses spline curve interpolation to smoothly fit the boundary curve in the generatrix direction, ensuring that the trajectory maintains good continuity. In addition, during the trajectory generation process, a curvature constraint optimization method is adopted to adjust the distribution of trajectory points, ensuring smooth transitions between trajectories, improving the stability of the filling path, and ultimately enhancing the consistency and smoothness of the repair layer quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described below in conjunction with the drawings and embodiments.

[0020] Figure 1 It is a specific flowchart for the implementation of the present invention.

[0021] Figure 2 It is a trapezoidal groove workpiece designed by the present invention.

[0022] Figure 3 It is a workpiece and a trapezoidal groove grid model of the present invention.

[0023] Figure 4 It is the extraction result of the cutting plane grid of the present invention.

[0024] Figure 5 It is a diagram of the calculation result of the plane parameters of the present invention.

[0025] Figure 6 It is a visualization diagram of the cutting plane of the present invention.

[0026] Figure 7 It is a diagram of the parameter setting for layer-by-layer slicing of the present invention.

[0027] Figure 8 It is the sliced contour data of the present invention.

[0028] Figure 9 It is a single-layer sliced contour of the present invention.

[0029] Figure 10 It is the tangent vector of the contour points of the present invention.

[0030] Figure 11 It is the segmentation of the trapezoidal groove contour of the present invention.

[0031] Figure 12 It is the extracted boundary curve of the present invention.

[0032] Figure 13 It is the spline interpolation of the boundary curve of the present invention.

[0033] Figure 14 It is the resampling of the boundary curve of the present invention.

[0034] Figure 15 It is the filling trajectory points of the present invention.

[0035] Figure 16 Parametrize the trajectory of the present invention.

[0036] Figure 17 Adjust the attitude of the sidewall trajectory of the present invention. Detailed implementation manners

[0037] The following further describes the implementation manners of the present invention with reference to the accompanying drawings.

[0038] Embodiment 1: Refer to Figure 1 , a trajectory planning method for additive repair of cracks in a hydraulic turbine runner based on a regular trapezoidal groove, comprising the following steps: S1. Obtain the bottom cutting plane of the trapezoidal groove grid based on the region growing algorithm, and slice the trapezoidal groove layer by layer using the cutting plane; S11. First, it is necessary to extract the bottom plane of the grid model of the trapezoidal groove. This process is based on the plane region growing algorithm, starting from a specified seed point and gradually expanding the region according to preset conditions. The specific steps include: Step 111: Select the seed triangular element located at the bottom of the trapezoidal groove, calculate the normal vector of this element, and use the normal vector and the center of this element as the current plane parameters; Step 112: Then detect adjacent elements. If the angle between the normal vector of the adjacent element and the current plane normal vector is less than a preset threshold (usually 5° to 10°), and the maximum distance between the adjacent element and the current plane is less than a given threshold (usually set to 1 - 5 mm), then include this adjacent element in the region.

[0039] Step 113: Update the current plane parameters. By performing weighted averaging on the normal vectors of the current grid elements, the normal vector direction and the plane equation of the plane can be obtained.

[0040] Step 114: Keep iterating steps 2 - 3 until no new element that meets the conditions can be found. The finally obtained region is the bottom grid set of the trapezoidal groove.

[0041] S12. After obtaining the bottom grid set, construct an accurate cutting plane: By calculating the center point coordinates of all elements in the bottom grid set, determine a reference point on the bottom plane , through performing PCA analysis on the bottom grid set, obtain the fitted normal vector N, which can be expressed as the point - normal form plane equation: ; where P represents any point on the plane, represents the center point coordinates, and N represents the plane normal vector; S13. To perform layer-by-layer slicing, slicing parameters also need to be set, including: slicing spacing d (depending on actual processing requirements), total number of slicing layers n (which can be calculated by dividing the total height of the trapezoidal groove by the slicing spacing), bead width w, number of track paths per layer (calculated based on the bead width and the width of the current layer) and slicing direction (positive or negative direction along the normal vector).

[0042] S2. Obtain the slicing contour of the trapezoidal groove, and use the tangential features of the contour points to segment the trapezoidal groove contour; S21. Using the bottom cutting plane and slicing parameters as a reference, the layer-by-layer slicing algorithm can be implemented. Each cutting plane can be expressed as:

[0043] where i represents the i-th layer of slicing (i = 0, 1, 2,..., n - 1), and d represents the slicing spacing.

[0044] For each edge in the mesh model, determine whether the edge intersects the current cutting plane. If it intersects, calculate the intersection point coordinates and store them. To improve the calculation efficiency, spatial partitioning technology can be used to perform intersection detection only on the mesh regions that may intersect the current cutting plane. In a cutting plane, all intersection points are connected according to certain rules to form the cross-sectional contour line of this layer. These contour lines usually consist of multiple closed loops, representing the geometric features of the trapezoidal groove at this height.

[0045] S22. Calculating the tangential features at each point of the processed contour point sequence is the key step in segmentation. For each point on the contour, the tangent vector of this point can be calculated through its adjacent points . Common methods include: Based on forward difference: ; Based on central difference: ; Based on local polynomial fitting, first use an n-order polynomial to fit a section of the curve near the point , and then calculate the derivative of the polynomial at this point as the tangent vector. In addition, the curvature also needs to be calculated, which represents the degree of curvature of the curve at this point and is usually obtained through the rate of change of the tangent vector. The tangential features of the point also include the continuity of the change of the tangent vector, which can be quantified by calculating the angle between adjacent tangent vectors.

[0046] ; S23. Using the tangential features calculated above, automatic segmentation of the contour can be achieved. The basic idea of segmentation is to identify the positions where significant changes in the tangential features occur on the contour, and these positions usually correspond to the feature transition points of the trapezoidal groove geometry.

[0047] Common segmentation methods include: threshold-based segmentation methods, setting curvature thresholds or the threshold of the change in the angle of the tangent vector , when the included angle between adjacent tangent vectors at a certain point satisfies the following conditions, this point is marked as a segmentation point.

[0048] ; or the included angle between adjacent tangent vectors ; Clustering-based segmentation methods, clustering the contour points according to tangential features (such as tangent vector direction, curvature, etc.), and different clusters correspond to different segments; through these methods, the continuous contour curve can be segmented into multiple discrete segments.

[0049] S3. Extract the boundary curve in the direction of the trapezoidal groove busbar, and use the spline curve interpolation method to generate a continuous and smooth parametric spline curve; S31. Based on the obtained segmented slice contours of the trapezoidal groove, the busbar direction needs to be determined first, which usually refers to the main axis direction or the machining direction of the groove body. In each slice contour, the boundary segments parallel to the busbar direction need to be identified. The specific method is to analyze the direction characteristics of the slice contour point set, calculate the included angle between the line connecting adjacent points and the preset busbar direction, and when the included angle is less than the threshold, determine that this segment is the boundary in the busbar direction. For complex contours, principal direction analysis can be used to decompose the contour into different direction segments and screen out the boundary curves consistent with the busbar direction.

[0050] The processed boundary point set needs to be interpolated through spline curve technology to generate a continuous and smooth mathematical expression. First, perform parametric processing to assign parameter values to each data point. Use the cubic B-spline curve model, and its mathematical expression is: ; Among them, is the k-th order B-spline basis function, is the control point, and u is the parameter.

[0051] Considering the characteristics of the slice contour, arc length parameterization is usually more suitable, that is, the parameter interval is proportional to the arc length between adjacent points, which can better maintain the shape characteristics of the curve.

[0052] S4. Obtain the equally spaced trajectory points between two spline curves based on the isoparametric method, and connect the trajectory points to form the additive manufacturing trajectory inside the trapezoidal groove. It includes the following steps: S41. Based on the two smooth parametric spline curves obtained in Step 3, construct the parametric domain mapping of the trapezoidal groove additive manufacturing trajectory. Let the two boundary spline curves be and , where u ∈ [0, 1] is the curve parameter. By establishing the parametric domain [0, 1] × [0, 1], introduce the two-parameter mapping function S(u, v), where u is along the spline curve direction and v represents the relative position between the two curves. Uniformly sample within this parametric domain to obtain a series of parameter points , where , and , m and n represent the number of sampling points in the u direction and the number of sampling points in the v direction.

[0053] S42. Map the sampling points in the parametric domain to the physical space and calculate the spatial coordinates of the corresponding trajectory points. For each parameter point , its corresponding spatial coordinates are obtained through the following mapping relationship: ; where and are the isoparametric points on the boundary curves.

[0054] Based on the calculated set of spatial coordinate points, connect the points row by row or column by column to form a continuous additive manufacturing trajectory path.

[0055] S43. To ensure the smooth transition of the trajectory points between the boundary curves, resample the generated trajectory. For the unique geometric features of the trapezoidal groove, adopt an adaptive parameter adjustment strategy to optimize the distribution of the trajectory points in the high-curvature region to ensure the smooth transition of the filling trajectory. At the same time, by constructing a discrete geometric model of the trapezoidal groove, perform collision detection between the trajectory and the wall surface, and adjust the inclination angle of the wall surface trajectory to ensure that all trajectory points are inside the trapezoidal groove and meet the safety distance constraint.

[0056] Example 2: As Figure 1 shown, a method for planning the additive manufacturing repair trajectory of the crack of a hydraulic turbine runner based on a regular trapezoidal groove includes the following steps: Please refer to Figures 1 - 17 , the embodiments of the present invention provide a method for planning the additive manufacturing repair trajectory of the crack of a hydraulic turbine runner based on a regular trapezoidal groove, which is applied to the crack repair work of the hydraulic turbine runner and mainly includes the following steps: S1. Based on the region growing algorithm, obtain the bottom tangent plane of the trapezoidal groove grid and slice the trapezoidal groove layer by layer using the tangent plane. Specifically: S11. Take a Francis turbine runner of a certain hydropower station as the research object and design a trapezoidal groove test workpiece with the workpiece size of 510×550×100 mm. As Figure 2As shown, the designed workpiece contains three trapezoidal grooves. Take the No. 1 trapezoidal groove for testing. The dimensions of the No. 1 trapezoidal groove are as follows: the upper base length of the trapezoidal cross-section is 50 mm, the lower base length is 9 mm, and the depth is 50 mm; the trend of the trapezoidal groove is "S"-shaped, and the length is 510 mm.

[0057] Use a handheld laser scanner to scan the workpiece, and reconstruct the workpiece mesh model and the trapezoidal groove mesh model. The reconstructed model after scanning is as Figure 3 shown. In the figure, the green part is the workpiece mesh model, and the red part is the trapezoidal groove mesh model.

[0058] Extract the bottom plane of the trapezoidal groove mesh model through the plane region growing algorithm. Obtain the seed points through manual interaction. The selected coordinates are (1137.97, 94.0009, 808.488), and the triangular patch ID is 1011; set the angle threshold to 10 degrees, the distance threshold to 5 mm, and the minimum number of triangular patches in the region to 1. The extraction result of the cutting plane is as follows: As Figure 4 shown, the red part is the extracted mesh region.

[0059] S12. After obtaining the bottom grid set, an accurate cutting plane needs to be constructed. By calculating the average value of the center point coordinates of all the surface elements in the bottom grid set, a reference point on the bottom plane can be determined (1137.97, 94.0009, 808.488). Through PCA analysis of the bottom grid set, the fitted normal vector N (0.0197, 0.0013, -0.9998) is obtained. The equation of the cutting plane can be obtained as: 0.0197x + 0.0013y - 0.9998z + 785.7861 = 0; The calculation result of the cutting plane is as Figure 5 shown, giving a point on the plane and the normal vector of the plane.

[0060] The visualization of the cutting plane is as Figure 6 shown. In the figure, the blue arrow indicates the normal direction of the cutting plane, and this direction is consistent with the filling direction.

[0061] S13. In order to perform layer slicing, slicing parameters also need to be set. Set the slicing spacing d to 2 mm, the weld bead width to 8 mm, the initial trajectory point interval to 6 mm, and the slicing direction along the given plane normal direction.

[0062] S2. Obtain the slice contour of the trapezoidal groove, and segment the trapezoidal groove contour by using the tangential feature of the contour points. Specifically: S21. Taking the bottom cutting plane and the slicing parameters as the basis, the layer-by-layer slicing algorithm can be implemented. For each edge in the mesh model, it is necessary to determine whether it intersects with the current cutting plane. If an intersection occurs, the intersection point coordinates are calculated and stored. To improve the calculation efficiency, the spatial partitioning technique is used to limit the detection range and only process the mesh regions that may intersect with the current cutting plane. In the same cutting plane, all intersection points are connected in counterclockwise order to construct the cross-sectional contour curve of this layer. The contour curve of the trapezoidal groove consists of a closed polygon, which can be divided into 4 boundary curves according to the geometric characteristics of the trapezoidal groove. The calculation result of the slicing contour is as Figure 8 shown, where the white point set is the slicing contour of each layer, Figure 9 and

[0063]

[0063] is the set of contour points of a single layer. ; where i is the current point id.

[0064] Calculate the tangential feature of the current contour, take the tangential vectors of some points for output, and the result is as Figure 10 shown.

[0065] S23. Using the tangential features calculated above, the automatic segmentation of the contour can be realized. The basic idea of segmentation is to identify the positions where the tangential features on the contour change significantly, and these positions usually correspond to the feature turning points of the geometric shape of the trapezoidal groove. A threshold-based segmentation method is adopted, and the threshold of the tangential vector angle change degrees is set. When the included angle of the adjacent tangential vectors of a certain point satisfies the following conditions, this point is marked as a segmentation point.

[0066] ; Set the angle threshold to 45 degrees, and the contour of the trapezoidal groove can be divided into 4 boundary curves. The segmentation result is as Figure 11 shown, where the upper and lower two curves are the boundary curves in the busbar direction of the trapezoidal groove.

[0067] S3. Extract the boundary curves in the busbar direction of the trapezoidal groove, and use the spline curve interpolation method to generate a continuous and smooth parametric spline curve. Specifically: S31. Based on the obtained segmented slice contours of the trapezoidal groove, it is first necessary to clarify the busbar direction, which generally refers to the main axis direction or the machining direction of the groove. In each slice contour, the boundary segments parallel to the busbar direction need to be identified. The specific method is to first perform principal component analysis on the trapezoidal groove to determine the general trend of the trapezoidal groove, and then perform principal component analysis on each boundary curve. Compare the main direction of the boundary curve with the main direction of the trapezoidal groove, set the angle threshold to 45 degrees, and screen out the boundary curves that are consistent with the busbar direction.

[0068] Table 1 List of Principal Component Analysis

[0069] Calculate the main directions of the trapezoidal groove and the segmented boundary curves respectively, and calculate the angle between the main direction of the trapezoidal groove and the main direction of the segmented boundary. The obtained data are recorded in Table 1. It can be seen that the main directions of spline1 and spline2 meet the requirements of the angle threshold, and the extraction results are as Figure 12 shown.

[0070] S32. The processed boundary point set needs to be interpolated through spline curve technology to generate a continuous and smooth mathematical expression. First, perform parameterization to assign parameter values to each data point. Adopt the cubic B-spline curve model, and its mathematical expression is: ; where is the k-th order B-spline basis function, are the control points, and u is the parameter.

[0071] Considering the characteristics of the slice contour, adopt arc length parameterization, that is, the parameter interval is proportional to the arc length between adjacent points, which can better maintain the curve shape characteristics. The parameterization result of the boundary curve is as Figure 13 shown. After parameterization, the uniform consistency of the boundary curve sampling can be guaranteed.

[0072] S4. Based on the isoparametric method, obtain the equally spaced trajectory points between two spline curves, and connect the trajectory points to form the additive manufacturing trajectory inside the trapezoidal groove. Specifically: S41. Based on the two smooth parameterized spline curves obtained in step three, construct the parameter domain mapping of the trapezoidal groove additive manufacturing trajectory. Let the two boundary spline curves be and , where u ∈ [0, 1] is the curve parameter. By establishing the parameter domain [0, 1] × [0, 1], introduce the two-parameter mapping function S(u, v), where u is along the spline curve direction and v represents the relative position between the two curves. Uniformly sample in this parameter domain to obtain a series of parameter points , where , and , m and n represent the number of sampling points in the u direction and the number of sampling points in the v direction. The number of sampling points in the u direction is set to 100, and the result is as Figure 14 shown.

[0073] S42. Map the sampling points in the parameter domain to the physical space, and calculate the spatial coordinates of the corresponding trajectory points. For each parameter point , its corresponding spatial coordinates are obtained through the following mapping relationship: ; where and are the isoparametric points on the boundary curve.

[0074] Based on the calculated set of spatial coordinate points, connect the points row by row or column by column to form a continuous additive manufacturing trajectory path.

[0075] When the number of sampling points in the v direction is 3 (the number of weld beads is 3), the calculated trajectory points are as Figure 15 shown, where the red is the boundary curve and the blue is the internal filling trajectory points.

[0076] S43. To ensure the smooth transition of the trajectory points between the boundary curves, resample the generated trajectory. For the unique geometric features of the trapezoidal groove, adopt an adaptive parameter adjustment strategy to optimize the distribution of the trajectory points in the high-curvature region to ensure the smooth transition of the filling trajectory.

[0077] At the same time, by constructing a discrete geometric model of the trapezoidal groove, perform collision detection between the trajectory and the wall surface, and adjust the inclination angle of the wall surface trajectory to ensure that all trajectory points are inside the trapezoidal groove and meet the safety distance constraint.

[0078] The above are only the preferred embodiments of the present invention, and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A trajectory planning method for additive repair of cracks in a turbine runner based on regular trapezoidal grooves, characterized in that: The following steps are involved: S1. Obtain the bottom cutting plane of the trapezoidal groove grid based on the region growing algorithm, and use the cutting plane to slice the trapezoidal groove layer by layer; S2, obtaining the slice contour of the trapezoidal groove, and segmenting the trapezoidal groove contour using the tangential features of the contour points; S3, extracting the boundary curve in the direction of the trapezoidal groove busbar, and using the spline curve interpolation method to generate a continuous and smooth parameterized spline curve; S4. Based on the isoparametric method, equally spaced trajectory points between the two spline curves are obtained, and the trajectory points are connected to form an additive trajectory in the trapezoidal groove.

2. According to claim 1, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: The S1 specifically includes the following steps: S11, extracting the bottom plane of the trapezoidal groove mesh model: based on the plane region growing algorithm, starting from the specified seed point, gradually expanding the region according to the preset conditions, and the finally obtained region is the bottom mesh set of the trapezoidal groove; S12. After obtaining the bottom grid set, construct an accurate cutting plane: determine a reference point on the bottom plane by calculating the center point coordinates of all facets in the bottom grid set. , by performing PCA analysis on the bottom grid set, we can obtain the fitted normal vector N, which can be expressed as the point normal plane equation: ； Where P represents any point on the plane. represents the center point coordinates, and N represents the plane normal vector; S13, set the slice parameters, including: slice spacing d, total slice layer number n, weld width w, number of tracks per layer and the slice direction.

3. According to claim 2, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: The specific steps of the planar region growing algorithm in S11, starting from a specified seed point and gradually expanding the region according to preset conditions, are as follows: Step 111: Select a seed triangle face element located at the bottom of the trapezoidal groove, calculate the normal vector of the face element, and use the normal vector and center of the face element as current plane parameters; Step 112: Then detect the adjacent face element, if the angle between the normal vector of the adjacent face element and the normal vector of the current plane is less than a preset threshold, and the maximum distance between the adjacent face element and the current plane is less than a given threshold, then include the adjacent face element into the region; Step 113: Update the current plane parameters, and obtain the normal vector direction and plane equation of the plane by performing weighted averaging on the normal vectors of the current mesh face elements; Step 114: Steps 112-113 are iterated continuously until no new face element that meets the conditions can be found, and the finally obtained area is the bottom grid set of the trapezoidal groove.

4. According to claim 3, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: In step 112, the preset threshold value is 5° to 10°; The given threshold value is 1-5 mm.

5. According to claim 2, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: The slice spacing d in S13 depends on the actual processing requirements; The total number of slice layers n is calculated by dividing the total height of the trapezoidal groove by the slice spacing; The number of tracks per layer Calculated based on the weld width and the width of the current layer; The slicing direction is along the positive direction or the negative direction of the normal vector.

6. According to claim 2, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: The S2 specifically includes the following steps: S21, using the bottom cutting plane and slicing parameters as a reference, and then implementing a layer-by-layer slicing algorithm, each layer of the cutting plane is expressed as: ； Where i represents the i-th slice, i=0,1,2,...,n-1, and d represents the slice spacing; For each edge in the grid model, determine whether the edge intersects with the current cutting plane. If so, calculate and store the intersection coordinates. Use space partitioning technology to perform intersection detection only on the grid area that may intersect with the current cutting plane. In a cutting plane, all intersections are connected according to certain rules to form the cross-sectional contour lines of the layer. These contour lines are composed of multiple closed loops, which represent the geometric features of the trapezoidal groove at this height. S22. For the processed contour point sequence, calculate the tangential feature at each point: , calculate the tangent vector of the point through its adjacent points , the calculation methods include: Based on forward difference: ； Based on central difference: ； Based on local polynomial fitting, first use n-order polynomial fitting points A section of the curve near , and then calculate the derivative of the polynomial at this point as the tangent vector; in addition, the curvature needs to be calculated , which indicates the curvature of the curve at that point, obtained by the rate of change of the tangent vector; the tangent feature of the point also includes the continuity of the change of the tangent vector, which is quantified by calculating the angle between adjacent tangent vectors: ； in, is the angle between adjacent tangent vectors, and is the adjacent tangent vector; S23. Using the tangential features calculated above, automatic segmentation of the contour is achieved: the basic idea of ​​segmentation is to identify the locations where the tangential features on the contour change significantly, which usually correspond to the characteristic turning points of the trapezoidal groove geometry.

7. According to claim 6, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: The segmentation method in S23 includes: a segmentation method based on a threshold value, setting a curvature threshold value Or tangent vector angle change threshold , when the angle between the adjacent tangent vectors of a point satisfies the following conditions, the point is marked as a segmentation point; ； Or the angle between adjacent tangent vectors: ； The clustering-based segmentation method clusters the contour points according to the tangent features: tangent vector direction and curvature, and different clusters correspond to different segments; through these methods, the continuous contour curve is segmented into multiple discrete segments.

8. According to claim 1, a method for additive repair trajectory planning of a turbine runner crack based on a regular trapezoidal groove is characterized in that: S3 specifically includes the following steps: S31. Based on the obtained segmented slice contour of the trapezoidal groove, the generatrix direction, i.e., the main axis direction or the processing direction of the groove body, is clarified. In each slice contour, the boundary segment parallel to the generatrix direction is identified. The specific method is to analyze the directional characteristics of the slice contour point set, calculate the angle between the adjacent point connection line and the preset generatrix direction, and when the angle is less than a threshold, the segment is determined to be the generatrix direction boundary; for complex contours, the main direction analysis is used to decompose the contour into different direction segments, and the boundary curve consistent with the generatrix direction is screened out; S32. The processed boundary point set is interpolated by spline curve technology to generate a continuous and smooth mathematical expression.

9. The method for planning trajectory of crack additive repair of a turbine runner based on regular trapezoidal grooves according to claim 8, characterized in that: S32 specifically includes: First, parameterization is performed to assign parameter values ​​to each data point, and a cubic B-spline curve model is used, whose mathematical expression is: ； in, is the k-order B-spline basis function, is the control point, u is the parameter; Considering the characteristics of the slice contour, arc length parameterization is usually more suitable, that is, the parameter interval is proportional to the arc length between adjacent points, which can better maintain the curve shape characteristics.

10. The method for planning trajectory of crack additive repair of a turbine runner based on regular trapezoidal grooves according to claim 8, characterized in that: S4 specifically includes the following steps: S41. Based on the two smooth parameterized spline curves obtained in step 3, the parameter domain mapping of the trapezoidal groove additive trajectory is constructed. The two boundary spline curves are respectively and , where u∈[0,1] is the curve parameter. By establishing the parameter domain [0,1]×[0,1], a dual-parameter mapping function S(u,v) is introduced, where u is along the direction of the spline curve and v represents the relative position between the two curves. A series of parameter points are obtained by uniformly sampling in the parameter domain. ,in ,and , m and n represent the number of sampling points in the u direction and the number of sampling points in the v direction; S42, mapping the sampling points in the parameter domain to the physical space, calculating the spatial coordinates of the corresponding trajectory points, and for each parameter point , and its corresponding spatial coordinates are obtained through the following mapping relationship: ； in, and is an isoparametric point on the boundary curve; Based on the calculated spatial coordinate point set, the points are connected row by row or column by column to form a continuous additive trajectory path; S43: To ensure smooth transition of trajectory points between boundary curves, the generated trajectory is resampled.

11. According to claim 8, a method for planning trajectory of crack additive repair of a turbine runner based on regular trapezoidal grooves is characterized in that: The S43 specifically includes: targeting the unique geometric features of the trapezoidal groove, adopting an adaptive parameter adjustment strategy to optimize the distribution of trajectory points in the high curvature area to ensure a smooth transition of the filling trajectory; at the same time, by constructing a discrete geometric model of the trapezoidal groove, performing collision detection between the trajectory and the wall, adjusting the inclination angle of the wall trajectory, and ensuring that all trajectory points are located inside the trapezoidal groove and meet the safety spacing constraints.

Images