A method for milling and slotting cracks of runner blades of a hydraulic turbine based on three-dimensional measurement

Abstract

The application provides a water turbine runner blade crack milling and slotting method based on three-dimensional measurement, relates to the technical field of robot milling and slotting processing, and comprises the following steps: S1, a plurality of mark points are arranged near the crack, the coordinates of each mark point are scanned and extracted, and all the mark points are fitted to obtain a spline curve; S2, a water turbine blade surface model is established; S3, the water turbine blade surface model is cut to obtain a cutting region, a reference plane is constructed, each discrete point on the spline curve is projected onto the reference plane, the modeling section parameters of each discrete point at the projection point of the reference plane are determined, and a geometric body model expressing the crack is constructed; and S4, the water turbine blade surface model and the geometric body model are intersected to obtain a slotting region model, and a milling tool trajectory is calculated. The application has the beneficial effects that the depth and width of the slotting can be accurately controlled, the runner blade after the slotting is not affected, the repair quality of the runner blade can be improved, and the service life of the blade is prolonged.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot milling slot processing, and particularly relates to a milling slot method for cracks in runner blades of a hydraulic turbine based on three-dimensional measurement. BACKGROUND

[0002] The hydraulic turbine is an important hydroelectric power generation equipment, which converts water energy into electric energy. The runner blades of the hydraulic turbine are subjected to the impact of water flow, wear and corrosion during long-term operation, which may cause cracks and affect the normal operation of the hydraulic turbine. Therefore, regular maintenance and repair of the runner blades are key steps to ensure long-term stable operation of the hydraulic turbine.

[0003] A common repair method for the runner blades is to perform slotting on the crack area, then perform cladding filling, and finally perform polishing to restore the integrity and surface smoothness of the blades. Slotting is a key step in the repair process, which can help to clearly locate the cracks and provide a good basis for subsequent filling work. Accurate slotting is crucial for the repair of the runner blades. However, the current slotting method cannot accurately control the depth and width of the slotting, such as insufficient width and depth that cannot fully expose the cracks, and excessive width and depth that cause excessive damage to the blade structure. In addition, the current slotting method may also cause the surface of the slotted blade to be uneven and contain impurities, affecting the firm adhesion of the filling material and restoring the original strength and shape of the blade. SUMMARY

[0004] Therefore, in order to solve the problem that the crack area of the runner blade of the hydraulic turbine cannot be accurately slotted, the embodiments of the present application provide a milling slot method for cracks in runner blades of a hydraulic turbine based on three-dimensional measurement.

[0005] The embodiments of the present application provide a milling slot method for cracks in runner blades of a hydraulic turbine based on three-dimensional measurement, which comprises the following steps:

[0006] S1, a plurality of marker points are arranged along the crack direction near the surface crack of the runner blade, the depth of the crack area near each marker point is determined, the area around the crack on the surface of the runner blade is scanned and the coordinates of each marker point are extracted, all the marker points are fitted to obtain a spline curve describing the crack direction;

[0007] S2, the surface around the crack on the surface of the runner blade is scanned, and a surface model of the runner blade is established according to the scanning data;

[0008] S3. Obtain the cutting area by cutting the surface model of the turbine blade through the bounding box. Construct a reference plane in the cutting area according to the maximum crack depth. Project each discrete point on the spline curve onto the reference plane. Select the shaping section that can enclose the crack. Determine the shaping section parameters at the projection point of each discrete point on the reference plane. Construct a geometric model that expresses the crack based on all shaping section parameters.

[0009] S4. Find the intersection of the turbine blade surface model and the geometric model to obtain the slotted region model, and calculate the milling tool trajectory based on the slotted region model.

[0010] Furthermore, in step S3, the cutting area is obtained by using an OBB bounding box to cut the surface model of the turbine blade.

[0011] Furthermore, the method for constructing the reference plane in step S3 is as follows: establish an OBB bounding box coordinate system for the clipping region, take the centroid as the origin, and offset offset_h along the specified coordinate axis direction n to obtain a new centroid point. The reference plane can be determined based on the new centroid point and the specified direction n, where offset_h is the maximum crack depth.

[0012] Furthermore, the shape of the cross-section is quadrilateral.

[0013] Furthermore, the method for determining the shape section parameters at the projection point of each discrete point on the reference plane in step S3 is as follows:

[0014] Project all discrete points on the spline curve onto the reference plane, fit the projected points of all discrete points to obtain the projected spline curve, calculate the normal of the projected spline curve, obtain the tangent, principal normal and binormal, adjust the binormal to the normal vector of the reference plane, and recalculate the principal normal using the tangent and the adjusted binormal.

[0015] For a projection point P0 on the projected spline curve, find the corresponding discrete point on the original spline curve using the index. Calculate P0, Given the distance dis, determine the height h of the shape section as h = dis + Δh, where Δh is the redundant height, and set the width of the bottom edge of the shape section as L. bottom The angle between the base and the side is θ, and θ is less than 90°;

[0016] The cross-section of the shape is described by four vertices. The two vertices of the bottom edge of the cross-section are moved L from the projection point P0 along the positive and negative directions of its principal normal, respectively. bottom / 2 is obtained by moving the projection point P0 along its positive binormal direction by h to obtain point Ptop, and then moving Ptop along the positive and negative directions of the principal normal of P0 by L respectively. top / 2 to obtain the two vertices of the top bottom edge, and obtain the four vertex parameters of the shape section.

[0017] Further, in step S1, the marker point is a circular ring. The area around the crack on the surface of the turbine blade is scanned by a binocular structured light camera to obtain an RGB image and a depth image. The center of the marker point in the RGB image is extracted by an ellipse fitting algorithm to obtain the coordinates of the marker point.

[0018] Furthermore, the method for fitting all marker points to obtain spline curves describing crack orientation is as follows:

[0019] Based on the extracted marker coordinates, combined with the imaging principle, depth image and intrinsic parameter information of the binocular structured light camera, the three-dimensional coordinate information (X,Y,Z) corresponding to the marker coordinates (x,y) is solved.

[0020] Based on the obtained discrete marker point coordinate information, spline curves are used for fitting;

[0021] Adjust the direction of the binormal of the spline curve, and when fitting the spline curve to discrete points, calculate the tangent P at the discrete point p. t Principal normal P N and the secondary normal P b ;

[0022] The spline curve is offset along its principal normal direction by offset_w, which is determined by the crack width.

[0023] The discrete marker points on the spline curve are aligned along its principal normal P. N The new discrete points are obtained by offsetting the direction by offset_w, and then the spline curve is used again for fitting to describe the crack direction.

[0024] Furthermore, all the markers are located on the same side of the crack.

[0025] Furthermore, in step S2, when the crack length exceeds the range of a single scan, the curved surface around the crack on the turbine blade surface is scanned and measured multiple times. The surface data of the turbine blade is obtained by splicing the marker points to establish a curved surface model around the crack. The curved surface model around the crack is then stretched to construct a surface model of the turbine blade.

[0026] Furthermore, step S4 specifically includes:

[0027] The difference between the geometric model and the turbine blade surface model is calculated by performing a Boolean operation to obtain the grooved turbine blade surface model. The intersection of the grooved turbine blade surface model and the geometric model is then calculated to obtain the grooved region model. The grooved region model is then layered using a planar slicing algorithm, and the milling tool trajectory for each layer is calculated.

[0028] The beneficial effects of the technical solution provided by the embodiments of the present invention are as follows: The present invention provides a method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement. The method uses three-dimensional measurement to determine the grooving area based on crack information, thereby determining the milling tool trajectory. This method can accurately control the depth and width of the grooving, ensuring that the crack is fully exposed, while avoiding excessive damage to the blade structure and not affecting the runner blade after grooving. This can improve the repair quality of the runner blade and extend the service life of the blade. Attached Figure Description

[0029] Figure 1 This is a flowchart of a method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement according to the present invention;

[0030] Figure 2 This is a schematic diagram of a spline curve in the Flener coordinate system;

[0031] Figure 3 It is a schematic diagram of a spline curve describing the crack direction;

[0032] Figure 4 This is a schematic diagram of the curved surface model of the area surrounding the crack;

[0033] Figure 5 This is a schematic diagram of a water turbine blade surface model;

[0034] Figure 6 This is a schematic diagram of the reference plane;

[0035] Figure 7 This is a schematic diagram of the normal to the spline curve after projection;

[0036] Figure 8 This is a schematic diagram of the parameters of the cross-section of the shape;

[0037] Figure 9 This is a schematic diagram of the cross-section of the shape;

[0038] Figure 10 It is a schematic diagram of the geometric model;

[0039] Figure 11 This is a schematic diagram of the surface model of the turbine blade after slotting;

[0040] Figure 12 It is a toolpath diagram;

[0041] Figure 13 yes Figure 12 A partial detail of the tool path in the image. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings. The following description presents a preferred embodiment of the various possible embodiments of the present invention, intended to provide a basic understanding of the invention, but not intended to identify key or decisive elements of the invention or to limit the scope of protection sought.

[0043] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0044] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0045] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures. Also, it should be understood that, for ease of description, the dimensions of the various parts shown in the figures are not drawn to actual scale.

[0046] It should be noted that, unless otherwise explicitly specified and limited, the terms "installation" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0047] Please refer to Figures 1-13 The present invention provides a method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement. This method is applied to in-situ robotic milling for grooving cracks in turbine runner blades during crack repair. The method mainly includes the following steps:

[0048] S1. Multiple marker points are arranged near the crack on the turbine blade surface along the crack direction. The depth of the crack region near each marker point is determined. The area around the crack on the turbine blade surface is scanned, and the coordinates of each marker point are extracted. All marker points are fitted to obtain a spline curve describing the crack direction. Specifically:

[0049] S11. First, mark points are placed on the surface of the turbine blade along the crack direction. These mark points are generally circular. When placing the mark points, they should be as close to the crack as possible, and all mark points should be located on the same side of the crack. The number of mark points should not be too small, and they should reflect the crack trend characteristics as much as possible. Then, flaw detection is performed in the crack area near the mark points, and the depth of the crack area near the mark points is recorded.

[0050] S12. Install a 3D measurement head at the robot's end effector. A binocular structured light camera, such as a Nano camera, is typically chosen for this purpose. The binocular structured light camera scans the area surrounding the crack on the turbine blade surface to obtain RGB and depth images. Since the marker point is circular, its image is elliptical. To reduce the influence of the shooting angle on the identification of the circle's center, an ellipse fitting algorithm is used to extract the center of the marker point from the RGB image to obtain its coordinates.

[0051] S13. Fit the data to all marker points to obtain spline curves describing the crack orientation:

[0052] Based on the extracted marker coordinates, combined with the imaging principle, depth image and intrinsic parameter information of the binocular structured light camera, the three-dimensional coordinate information (X,Y,Z) corresponding to the marker coordinates (x,y) is solved.

[0053]

[0054] In the formula, the intrinsic parameter of the binocular structured light camera is: f x ,f y ,c x ,c y , where f x f represents the length of the focal length along the x-axis. y This represents the length of the focal length along the y-axis, (c x ,c y The pixel coordinates of the principal point are (x, y), the center coordinates of the marker point are (x, y), and its corresponding 3D coordinates are (X, Y, Z). D represents the pixel value at the (x, y) position in the depth map. In this embodiment, the binocular structured light camera uses millimeters for pixel values ​​and meters for Z coordinates; therefore, the value of D needs to be divided by 1000 to convert it to meters.

[0055] Based on the obtained discrete marker coordinate information, spline curves are used for fitting, that is, the three-dimensional coordinates of each marker point are used as discrete points to fit spline curves.

[0056] like Figure 2As shown, by adjusting the direction of the binormal of the spline curve, when fitting the spline curve to discrete points, the VTK interface is used to calculate the tangent, principal normal, and binormal of the discrete points. For example, the tangent P at discrete point p... t Principal normal P N and the secondary normal P b ;

[0057] The binormal line of the spline curve at point p is P b_L The direction is determined by discrete points on the curve and defined by the Fleischer coordinate system. The normal vector P of the turbine blade surface at point p is... n This can express the local characteristics of a turbine blade, with its direction defined by the global coordinate system. Since the reference coordinate systems of the two are different, the principal normals of discrete points on the curve are adjusted to ensure the offset curve accurately represents the crack. For point P, its tangent P... t The binormal remains unchanged, but is replaced by the surface normal vector at point P, i.e., P b =P n , by tangent P t and the secondary normal P b Recalculate the principal normal P using the outer product of vectors. N .

[0058] The fitted spline curve lies on the same side of the crack. To more accurately represent the crack, the spline curve can be offset along its principal normal direction. The offset of the spline curve along its principal normal direction is offset_w, which is determined by the crack width. The crack width can be determined by the distance between points on both sides of the crack. Half of the maximum width value width_max is taken as the offset, i.e., offset_w = width_max / 2.

[0059] like Figure 3 As shown, the discrete marker points on the spline curve are aligned along its principal normal P. N The new discrete points are obtained by offsetting the direction by offset_w, and then the spline curve is used again for fitting to describe the crack direction.

[0060] S2. Scan the curved surface surrounding the crack on the turbine blade surface and create a surface model of the turbine blade based on the scan data. Specifically:

[0061] like Figure 4 As shown, the three-dimensional point cloud data of the surface around the crack on the turbine blade is obtained by scanning and measuring the surface using the binocular structured light camera. The measured data is then modeled using reverse modeling software to obtain the surface model of the area around the crack.

[0062] like Figure 5As shown, the surface model is stretched to a thickness of h = 0.01m along the positive Z-axis. Each point in the surface model is offset by h along the stretching direction to obtain a new surface model. The stretched solid model is composed of two surfaces. Using point indices, the correspondence between the new surface and the original surface is established. The boundary information of the two surfaces is obtained, and based on their correspondence, the topological relationship of the boundaries is established. Finally, the two surface models are combined into a turbine blade surface model with thickness.

[0063] It should be noted that if the crack is long enough to exceed the single-scan range of the binocular structured light camera, multiple scans are required. When the crack length exceeds the single-scan range, the surface around the crack on the turbine blade is scanned and measured multiple times. Data on the turbine blade surface is obtained by stitching together marker points to establish a surface model around the crack. The surface model around the crack is then stretched to construct the turbine blade surface model.

[0064] S3. Obtain the cutting area by cutting the surface model of the turbine blade through a bounding box. Construct a reference plane in the cutting area according to the maximum crack depth. Project each discrete point on the spline curve onto the reference plane. Select a shape section that can enclose the crack. Determine the shape section parameters at the projection point of each discrete point on the reference plane. Construct a geometric model that expresses the crack based on all shape section parameters.

[0065] Milling grooving typically involves milling layer by layer, requiring a reference plane. To facilitate milling, the bottom surface of the geometric model should be parallel to the reference plane. This reference plane can be uniquely determined by the offset direction, offset_h, rotation angle around the X-axis, and rotation angle around the Y-axis, using a spline curve that describes the crack direction.

[0066] Specifically:

[0067] S31. Obtain the trimming region by cutting the turbine blade surface model using an OBB bounding box. That is, calculate the OBB bounding box of the turbine blade surface model, and use the bounding box to trim the turbine blade surface model to obtain a trimming region.

[0068] S32. Construct a reference plane: (e.g.) Figure 6 As shown, an OBB bounding box coordinate system (local coordinate system) is established for the clipping region. With the centroid as the origin, an offset of offset_h is made along the specified coordinate axis direction n to obtain a new centroid point. Based on the new centroid point and the specified direction n, a reference plane can be determined, where offset_h is the maximum crack depth, determined by comparing it with the crack depth near the marker point measured in step S1. The offset of the reference plane along direction n, the angles around the local coordinate system axes, and the angles of rotation are all custom parameters that can be adjusted.

[0069] S32. Determine the cross-sectional parameters at the projection points of each discrete point onto the reference plane. The cross-section is generally chosen from regular, easily describable geometric shapes, such as... Figure 8 As shown, the shape of the cross-section is a quadrilateral, and the cross-section parameters include the width of the bottom edge, the width of the top edge, the height of the quadrilateral, and the angles of the bottom edge and the side edge.

[0070] like Figure 7 As shown, all discrete points on the spline curve are projected onto the reference plane. The projected points of all discrete points are fitted to obtain the projected spline curve. The normal of the projected spline curve is calculated, and the tangent, principal normal and binormal are obtained. The binormal is adjusted to be the normal vector of the reference plane. The principal normal is recalculated using the tangent and the adjusted binormal.

[0071] For a projection point P0 on the projected spline curve, find the corresponding discrete point on the original spline curve using the index. Calculate P0, Given the distance dis, determine the height h of the shape section as h = dis + Δh, where Δh is the redundant height, and set the width of the bottom edge of the shape section as L. bottom The angle between the base and the side is θ, where θ is less than 90°; as described in this embodiment, the shape of the cross-section is an isosceles trapezoid, and the width of the base of the cross-section is...

[0072] like Figure 9 As shown, the cross-section of the shape is described by four vertices. The two vertices of the bottom edge of the cross-section are moved L from the projection point P0 along the positive and negative directions of its principal normal. bottom / 2 is obtained by moving the projection point P0 along its positive binormal direction by h to obtain point Ptop, and then moving Ptop along the positive and negative directions of the principal normal of P0 by L respectively. top / 2 to obtain the two vertices of the top bottom edge, obtain the four vertex parameters of the shape section, and store the four vertex parameters of the shape section.

[0073] This allows us to obtain the shape section parameters at the projection points of all discrete points on the reference plane, establish topological relationships based on the vertex data of the shape section, construct a triangular grid, and obtain a geometric model to represent the crack. Figure 10 The gray object is the geometric model.

[0074] S4. Find the intersection of the turbine blade surface model and the geometric model to obtain the slotted region model, and calculate the milling tool trajectory based on the slotted region model. Specifically:

[0075] S41, such as Figure 11As shown, the difference between the geometric model and the turbine blade surface model is calculated by performing a Boolean operation to obtain the grooved turbine blade surface model.

[0076] S42. Use the grooved turbine blade surface model and the geometric model to find the intersection and obtain the grooved region model.

[0077] S43. The slotted area model is layered using a planar slicing algorithm, such as... Figure 12 and 13 As shown, the slotted area is aligned to the local coordinate system, and a plane is cut along the coordinate axis Z. Given a certain z value, the boundary of the layer can be obtained. Then, the boundary is used to generate the milling tool path of the layer.

[0078] S44: Rotate the obtained path trajectory points to the global coordinate system to obtain the global toolpath.

[0079] In this document, the directional terms such as front, back, top, and bottom are defined based on the position of the components in the accompanying drawings and their relative positions to each other, solely for the purpose of clarity and convenience in expressing the technical solution. It should be understood that these are relative concepts and can vary depending on different methods of use and placement; the use of these directional terms should not limit the scope of protection claimed in this application.

[0080] Where there is no conflict, the embodiments and features described above can be combined with each other. The above descriptions are merely preferred embodiments of the present invention and are not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement, characterized in that, Includes the following steps: S1. Arrange multiple marker points along the crack direction near the crack on the surface of the turbine blade, determine the depth of the crack area near each marker point, scan the area around the crack on the surface of the turbine blade and extract the coordinates of each marker point, fit all marker points to obtain a spline curve describing the crack direction. S2. Scan the curved surface around the crack on the turbine blade surface and establish a turbine blade surface model based on the scanning data; S3. Obtain the cutting area by cutting the surface model of the turbine blade through the bounding box. Construct a reference plane in the cutting area according to the maximum crack depth. Project each discrete point on the spline curve onto the reference plane. Select the shaping section that can enclose the crack. Determine the shaping section parameters at the projection point of each discrete point on the reference plane. Construct a geometric model that expresses the crack based on all shaping section parameters. S4. Find the intersection of the turbine blade surface model and the geometric model to obtain the slotted region model, and calculate the milling tool trajectory based on the slotted region model.

2. The method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement as described in claim 1, characterized in that: In step S3, the cutting area is obtained by using an OBB bounding box to cut the surface model of the turbine blade.

3. The method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement as described in claim 2, characterized in that: The method for constructing the reference plane in step S3 is as follows: establish an OBB bounding box coordinate system for the clipping region, take the centroid as the origin, and offset offset_h along the specified coordinate axis direction n to obtain a new centroid point. The reference plane can be determined based on the new centroid point and the specified direction n, where offset_h is the maximum crack depth.

4. A method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement as described in claim 2 or 3, characterized in that: The shape of the cross-section of the design is quadrilateral.

5. The method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement as described in claim 4, characterized in that: The method for determining the shape section parameters at the projection point of each discrete point on the reference plane in step S3 is as follows: Project all discrete points on the spline curve onto the reference plane, fit the projected points of all discrete points to obtain the projected spline curve, calculate the normal of the projected spline curve, obtain the tangent, principal normal and binormal, adjust the binormal to the normal vector of the reference plane, and recalculate the principal normal using the tangent and the adjusted binormal. For a projection point P0 on the projected spline curve, find the corresponding discrete point on the original spline curve using the index. Calculate P0, The distance dis is used to determine the height of the shape section. , To account for redundant height, the width of the bottom edge of the aforementioned cross-section is set to [value missing]. The angle between the base and the side is θ, and θ is less than 90°; The cross-section of the shape is described by four vertices. The two vertices of the bottom edge of the cross-section are moved from the projection point P0 along the positive and negative directions of its principal normal, respectively. We obtain point Ptop by moving the projection point P0 along its positive binormal direction by h, and then moving Ptop along the positive and negative directions of the principal normal of P0 respectively. By obtaining the two vertices of the upper base, the four vertex parameters of the shaped cross section are obtained, where L top The width of the bottom edge of the cross-section of the shape.

6. The method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement as described in claim 1, characterized in that: In step S1, the marker point is a circular ring. The area around the crack on the surface of the turbine blade is scanned by a binocular structured light camera to obtain RGB and depth images. The center of the marker point in the RGB image is extracted by an ellipse fitting algorithm to obtain the coordinates of the marker point.

7. The method for milling and slotting cracks in turbine runner blades based on three-dimensional measurement as described in claim 6, characterized in that, The method for obtaining a spline curve describing the crack orientation by fitting all marker points is as follows: Based on the extracted marker coordinates, combined with the imaging principle, depth image and intrinsic parameter information of the binocular structured light camera, the three-dimensional coordinate information (X,Y,Z) corresponding to the marker coordinates (x,y) is solved. Based on the obtained discrete marker point coordinate information, spline curves are used for fitting; Adjust the direction of the binormal of the spline curve, and calculate the tangent at the discrete point p when fitting the spline curve to discrete points. Principal Normal and secondary normal ; The spline curve is offset along its principal normal direction by offset_w, which is determined by the crack width. The discrete marker points on the spline curve are aligned with its principal normal. The new discrete points are obtained by offsetting the direction by offset_w, and then the spline curve is used again for fitting to describe the crack direction.

8. The method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement as described in claim 1, characterized in that: All the markers are located on the same side of the crack.

9. The method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement as described in claim 1, characterized in that: In step S2, when the crack length exceeds the range of a single scan, the curved surface around the crack on the turbine blade surface is scanned and measured multiple times. The surface data of the turbine blade is obtained by splicing the marker points to establish a curved surface model around the crack. The curved surface model around the crack is then stretched to construct a surface model of the turbine blade.

10. The method for milling and grooving cracks in turbine runner blades based on three-dimensional measurement as described in claim 1, characterized in that, Step S4 specifically includes: The difference between the geometric model and the turbine blade surface model is calculated by performing a Boolean operation to obtain the grooved turbine blade surface model. The intersection of the grooved turbine blade surface model and the geometric model is then calculated to obtain the grooved region model. The grooved region model is then layered using a planar slicing algorithm, and the milling tool trajectory for each layer is calculated.

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