A high-quality polishing trajectory planning method for a robot for remanufacturing blades

Abstract

The application relates to the field of intelligent manufacturing, and discloses a high-quality grinding and polishing track planning method for a remanufactured blade robot, which comprises the following steps: determining a track plane for multi-layer grinding and polishing on a remanufactured blade grid surface; determining sequential intersection points between each layer of the track plane and triangular facets of the grid surface; fitting the sequential intersection points of each layer into a target curve path, and discretizing each target curve path according to an equal-arc-length interpolation method to obtain a tool contact point; determining a double-tool-axis vector of each tool contact point; generating a sampling point and determining a material removal function of the sampling point; combining the material removal function and a tool path according to a convolution operation, determining the residence time of each layer of tool contact points in a repair area through a truncated singular value decomposition method, and determining a robot grinding and polishing track according to the spatial coordinate information of a tool position point corresponding to the tool contact point, the double-tool-axis vector and the residence time. The method considers the influence of large deformation of a surface and uneven distribution of a repair area allowance on grinding and polishing effect, and realizes layered and point-by-point precision grinding and polishing processing of a remanufactured blade.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of intelligent manufacturing, in particular to a high-quality polishing trajectory planning method for a robot for remanufacturing a blade. BACKGROUND

[0002] Blade remanufacturing is an important link in the life cycle of an aero-engine, and the precise shaping and property control after additive repair directly affect the working performance and service life of the whole machine. Due to the problems of large deformation of the blade surface and uneven distribution of the machining allowance in the repair area, it is difficult to effectively ensure the surface quality of subsequent robot polishing processing. Robot trajectory planning is the key to ensuring the shape and property quality of the repair area. Most existing tool trajectories are planned based on the design of a parameterized curve surface according to the theoretical parameters of the blade, but there are still certain limitations when facing a remanufactured blade with a large surface deformation. Therefore, it is necessary to directly plan the trajectory based on the grid surface generated by the optical scanning system, and further optimize the calculation model of the machining pitch, tool step length and tool axis vector to avoid the over-polishing / under-polishing phenomenon caused by the parameterized curve surface. Most existing grid surface trajectory planning is used for numerical control milling or 3D printing, and after obtaining the intersection points of the trajectory plane and the grid edge, the tool contact points are directly output without further curve fitting and tool contact point discretization. In addition, the Preston material removal function used in the existing robot polishing trajectory is only used to compensate for the geometric dispersion error of the tool contact point, and is not used for real-time process parameter control processing in the uneven allowance distribution area. Therefore, it is necessary to propose a best polishing trajectory planning method for a remanufactured blade with a large surface deformation and uneven distribution of the machining allowance. SUMMARY

[0003] The purpose of the present application is to provide a high-quality polishing trajectory planning method for a robot for remanufacturing a blade, which fully considers the influence of large surface deformation and uneven distribution of the machining allowance in the repair area on the polishing effect, and realizes precise polishing processing of the remanufactured blade layer by layer and point by point.

[0004] To solve the above technical problems, the present application provides a high-quality polishing trajectory planning method for a robot for remanufacturing a blade, comprising:

[0005] determining a trajectory plane for multi-layer polishing on a grid surface of a remanufactured blade;

[0006] determining sequential intersection points between each layer of the trajectory plane and a triangular facet of the grid surface;

[0007] fitting the sequential intersection points corresponding to each layer of the trajectory plane into a target curve path, and discretizing each target curve path to obtain a tool contact point according to an equal arc length interpolation method;

[0008] determining a double tool axis vector for each tool contact point, the double tool axis vector comprising a main tool axis vector and a secondary tool axis vector;

[0009] increasing the number of trajectory planes and reducing the distance between tool contact points to generate dense sampling points;

[0010] determining a material removal function of the sampling points;

[0011] combining the material removal function with the tool path according to convolution operation, determining the dwell time of each layer tool contact point of the repair area by truncated singular value decomposition method, and realizing layered point-by-point control of precision machining;

[0012] determining the robot grinding and polishing trajectory of the remanufactured blade according to the spatial coordinate information of the tool position corresponding to the tool contact point, the double-tool-axis vector and the dwell time.

[0013] Optionally, determining the trajectory planes of multi-layer grinding and polishing on the grid surface of the remanufactured blade comprises:

[0014] taking the optical scanning grid surface model of the same-level adjacent or qualified remanufactured blade as the theoretical numerical model of the remanufactured blade;

[0015] specifying a plurality of feature points in the theoretical numerical model, and fitting a reference plane by using the feature points by least square method;

[0016] determining an initial trajectory plane by offsetting the reference plane by a safety distance;

[0017] determining a machining row distance by tool size, trajectory residual height or machining path number, and offsetting along the normal direction of the initial trajectory plane to obtain the remaining multi-layer trajectory planes.

[0018] Optionally, determining the material removal function of the sampling points comprises:

[0019] determining the directed distance between the sampling point and the grid surface of the blade blank along the rotation direction of the normal vector of the sampling point, taking the directed distance as the machining allowance of the sampling point, and determining the maximum machining allowance from the machining allowance;

[0020] determining the differential geometric information of the principal curvatures and their directions at the tool contact point, and determining the spatial pose relationship between the differential geometric information and the double-tool-axis vector according to Euler equation; the principal curvatures and their directions include the value and direction of the maximum principal curvature and the value and direction of the minimum principal curvature;

[0021] determining the contact pressure distribution model of the tool contact point along the principal curvature direction by Hertz contact theory; the parameters of the contact pressure distribution model include the relative elastic modulus of the remanufactured blade and the tool, the principal curvatures and their directions, and the geometric size of the contact profile;

[0022] Determine the grinding contact area according to the minor tool axis vector, and determine the material removal function of the tool contact point according to the contact pressure distribution model through the optimized Preston equation when the sampling point is located in the grinding contact area; wherein the coefficients are obtained by linear regression analysis method using orthogonal experimental results;

[0023] Determine the number of grinding layers according to the maximum machining allowance and the user-specified grinding depth, and determine the material removal function of each sampling point on each grinding layer through the material removal function of the tool contact point;

[0024] Rotate the material removal function of the sampling point to the local coordinate system in which the double-tool axis vector is located based on the spatial pose relationship.

[0025] Optionally, determine the double-tool axis vector of each tool contact point, which includes the major tool axis vector and the minor tool axis vector, including:

[0026] Search for the nearest grid vertex of the current tool contact point through the kd-tree data structure, determine the vertex unit normal vector using the area weight method, and use the vertex unit normal vector as the major tool axis vector of the current tool contact point;

[0027] Determine the 3rd NURBS curve tangent vector where the current tool contact point is located, project the 3rd NURBS curve tangent vector to the grid vertex tangent plane, and use the resulting unit vector as the minor tool axis vector of the current tool contact point.

[0028] Optionally, determining the sequential intersection points between each trajectory plane and the triangular facets of the grid surface includes:

[0029] Reconstruct the topological relationship of grid vertex-edge-triangle using the half-edge data structure, and determine the spatial intersection relationship and type between each trajectory plane and the triangular facets;

[0030] Determine the sequential intersection points between each trajectory plane and the triangular facets in turn according to the spatial intersection relationship and type through the region growing algorithm.

[0031] Optionally, the determination process of the spatial coordinate information of the tool position point includes:

[0032] Iteratively calculate the nearest grid vertex of the current tool contact point, determine the unit normal vector of the grid vertex by weighted average of the normal vectors of the triangular facets in the n-neighborhood of the grid vertex, and use it as the major tool axis vector of the current tool contact point;

[0033] Determine the spatial coordinate information of the tool position point corresponding to the current tool contact point by offsetting the difference between the tool radius length and the grinding depth in the direction of the major tool axis vector.

[0034] Optionally, determining the dwell time of each tool contact point of the repair area by the truncated singular value decomposition method comprises:

[0035] combining the material removal function with the tool path according to the convolution operation, and converting into a linear equation set for solving;

[0036] solving the non-homogeneous linear equation set of the large sparse matrix by the truncated singular value decomposition method to obtain the dwell time of each tool contact point, and using the overall offset method to ensure the non-negativity of the dwell time.

[0037] The method for planning a high-quality polishing trajectory of a robot for remanufacturing a blade comprises the following steps: determining a polishing trajectory plane for each layer on a grid surface of a remanufactured blade; determining sequential intersection points between each layer of the polishing trajectory plane and a triangular facet of the grid surface; fitting the sequential intersection points corresponding to each layer of the polishing trajectory plane into a target curve path, and discretizing each target curve path according to an equal-arc-length interpolation method to obtain a tool contact point; determining a double-tool-axis vector of each tool contact point, wherein the double-tool-axis vector comprises a main tool-axis vector and a secondary tool-axis vector; increasing the number of polishing trajectory planes and reducing the arc-length distance between tool contact points to generate dense sampling points; determining a material removal function of the sampling points; combining the material removal function with a tool path according to a convolution operation, and determining the dwell time of each tool contact point of a repair area by a truncated singular value decomposition method to realize layer-by-layer and point-by-point regulation and control of precision machining; and determining a robot polishing trajectory of the remanufactured blade according to the spatial coordinate information of a tool position point corresponding to the tool contact point, the double-tool-axis vector and the dwell time.

[0038] As can be seen, the method provided in the present application first determines a polishing trajectory plane for each layer on a grid surface of a remanufactured blade, and calculates sequential intersection points between the polishing trajectory plane and a triangular facet of the grid surface, then fits and discretizes the sequential intersection points to obtain a tool contact point, and determines a double-tool-axis vector of the tool contact point, generates sampling points, and then determines a material removal function of the sampling points, and then uses the material removal function to solve the dwell time of the tool contact point by a truncated singular value decomposition method to layer-by-layer and point-by-point regulate and control machining of a repair area with uneven residual distribution, and finally derives a robot polishing trajectory of the remanufactured blade according to the spatial coordinate information of a tool position point, the double-tool-axis vector and the dwell time. The present application fully considers the influence of large deformation of a surface and uneven distribution of residual of a repair area on polishing effect, and realizes layer-by-layer and point-by-point precision polishing machining of a remanufactured blade. BRIEF DESCRIPTION OF DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort.

[0040] Figure 1 A flowchart illustrating a high-quality grinding and polishing trajectory planning method for a remanufactured blade robot provided in this application embodiment;

[0041] Figure 2 This is a schematic diagram illustrating the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface calculated using the region growing algorithm in an embodiment of this application.

[0042] Figure 3 This is a schematic diagram illustrating the solution of the main tool axis vector at the tool contact point using the area weighting method in an embodiment of this application.

[0043] Figure 4 This is a schematic diagram illustrating the calculation of the double-tool axis vector at the tool contact point and the machining line spacing based on the projection of the cutting plane in this embodiment of the application.

[0044] Figure 5 This is a schematic diagram illustrating the solution of the material removal function at the sampling point using Hertzian contact theory and the optimized Preston equation in an embodiment of this application.

[0045] Figure 6 This is an overall flowchart of a high-quality grinding and polishing trajectory planning method for a remanufactured blade robot provided in an embodiment of this application. Detailed Implementation

[0046] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0047] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0048] This application provides a high-quality grinding and polishing trajectory planning method for remanufactured blade robots. Please refer to [reference needed]. Figure 1 and Figure 6 The method may include:

[0049] Step S101: Determine the trajectory plane of multi-layer grinding and polishing on the remanufactured blade mesh surface.

[0050] The number of trajectory plane layers is not limited in this embodiment and depends on the situation. The trajectory planes are parallel to each other.

[0051] It should be noted that this embodiment does not limit the method for determining the multi-layer trajectory plane, and can be set by the user.

[0052] As one possible implementation, determining the trajectory plane for multi-layer grinding and polishing on the remanufactured blade mesh surface includes:

[0053] Step S1011: Use the optical scanning mesh surface model of adjacent blades of the same level or blades that have been properly ground as the theoretical numerical model for remanufacturing blades.

[0054] Using the optical scanning mesh surface model of adjacent blades of the same level or blades that have been properly ground as the theoretical numerical model of remanufactured blades can avoid over-grinding / under-grinding caused by the deformation and failure of their parametric models.

[0055] Step S1012: Specify several feature points in the theoretical model, and use the feature points to fit the reference plane using the least squares method.

[0056] Feature points can be specified by the user through interactive selection in self-developed CAM software.

[0057] Step S1013: Determine the initial trajectory plane by offsetting the reference plane with a safe distance.

[0058] Step S1014: Determine the machining line spacing by tool size, trajectory residual height or number of machining paths, and offset along the normal of the initial trajectory plane according to the machining line spacing to obtain the remaining multi-layer trajectory plane.

[0059] It should be noted that when calculating machining line spacing, in addition to tool size, trajectory residual height or number of machining paths, other information can also be included in the calculation.

[0060] Step S102: Determine the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface in each layer.

[0061] In this embodiment, the method for determining the sequential intersection points is not limited and can be set arbitrarily. As one possible implementation, determining the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface in each layer includes:

[0062] Step S1021: Reconstruct the topological relationship of mesh vertices-edges-triangles using a half-side data structure, and determine the spatial intersection relationship and type between the trajectory plane and the triangle in each layer.

[0063] Step S1022: Based on the spatial intersection relationship and type, determine the sequential intersection points of the trajectory plane and the triangular facets in each layer using the region growth algorithm.

[0064] A schematic diagram illustrating the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface calculated using the region growing algorithm is shown below.Figure 2 As shown.

[0065] Based on the half-side data structure, establish the topological relationship between grid vertices, edges, and triangular faces. Determine the spatial intersection relationship and type between the trajectory plane and the triangular facets. Calculate the triangular facets that intersect with the trajectory plane using the region growing algorithm. Calculate the sequential intersection points sequentially using the line / face intersection principle.

[0066] The path curve is formed by fitting the sequential intersection points on each trajectory plane.

[0067] The toolpath is generated directly on the mesh surface by using the region growth algorithm and the equal arc length interpolation method, which fully considers the impact of blade curvature abrupt change and path calculation efficiency on the high-quality trajectory planning effect.

[0068] Step S103: Fit the sequential intersection points corresponding to each layer of the trajectory plane into a target curve path, and discretize each target curve path according to the equal arc length interpolation method to obtain the knife contact point.

[0069] The target curve path can be a 3rd order NURBS curve path or other spline curve paths; no specific limitation is made in this embodiment.

[0070] In one embodiment of this application, after obtaining the knife contacts, the process may further include storing each layer of knife contacts into a linked list data structure.

[0071] Similarly, sampling points are divided by increasing the number of path planes and reducing the arc distance between blade contacts.

[0072] Step S104: Determine the dual-axis vector for each of the tool contacts, wherein the dual-axis vector includes a primary tool axis vector and a secondary tool axis vector.

[0073] In one embodiment of this application, determining the dual-tool axis vector for each tool contact point, the dual-tool axis vector including a primary tool axis vector and a secondary tool axis vector includes:

[0074] The nearest grid vertex of the current tool contact point is searched using a kd-tree data structure. The vertex unit normal vector is determined using the area weight method, and the vertex unit normal vector is used as the main tool axis vector of the current tool contact point.

[0075] Determine the tangent vector of the 3rd order NURBS curve at the current tool contact point, project the tangent vector of the 3rd order NURBS curve onto the tangent plane of the grid vertex, and use the resulting unit vector as the secondary tool axis vector of the current tool contact point.

[0076] A schematic diagram of the tool contact point main tool axis vector solution based on the area weighting method is shown below. Figure 3 As shown; a schematic diagram of solving the double-blade axis vector of the tool contact point based on the projection of the tangent plane is shown below. Figure 4 As shown.

[0077] A local contact point coordinate system for the tool is established with the main tool axis vector as the z-axis, the secondary tool axis vector as the x-axis, and the cross product direction as the y-axis. The tool is then rotated by (α, β) angles along the y and z axes respectively to form a dual-vector control.

[0078] Step S105: Increase the number of trajectory planes and reduce the arc distance between tool contacts to generate dense sampling points.

[0079] Step S106: Determine the material removal function for the sampling point.

[0080] It should be noted that the material removal function for the sampling points is not limited in this embodiment and can be set by the user.

[0081] As one possible implementation method, the material removal function for determining the sampling points includes:

[0082] Step S1061: Determine the directed distance between the sampling point and the blade blank mesh surface along the rotation direction (α, β) of the normal vector of the sampling point, use the directed distance as the machining allowance of the sampling point, and determine the maximum machining allowance from the machining allowance.

[0083] It should be noted that the machining allowance is the directed distance from the sampling point along the main tool axis vector direction, that is, the rotation direction of its normal (α,β), to the remanufactured blade mesh model.

[0084] If the processing allowance of a sampling point is greater than zero, it can be stored in the corresponding array; if it is not greater than zero, it can be set to zero.

[0085] Step S1062: Determine the differential geometric information of the principal curvature and its direction at the tool contact point, and determine the spatial pose relationship between the differential geometric information and the dual tool axis vector according to the Euler equation; the principal curvature and its direction include the value and direction of the maximum principal curvature and the value and direction of the minimum principal curvature.

[0086] The material removal function of the sampling point is along the principal curvature direction. The directions of the principal tool axis vector and the secondary tool axis vector are not necessarily coincident with the principal curvature direction. Therefore, it is necessary to rotate the material removal function of the sampling point to the local coordinate system composed of the principal tool axis vector and the secondary tool axis vector.

[0087] Step S1063: Determine the contact pressure distribution model of the blade contact point along the principal curvature direction using Hertzian contact theory; the parameters of the contact pressure distribution model include the relative elastic modulus of the remanufactured blade and the cutting tool, the principal curvature and its direction, and the geometric dimensions of the contact profile.

[0088] It should be noted that, in addition to the relative elastic modulus of the remanufactured blade and the cutting tool, the principal curvature and its direction, and the geometric dimensions of the contact profile, the parameters of the contact pressure distribution model may also include other parameters.

[0089] Step S1064: Determine the grinding contact area based on the secondary tool axis vector, and when the sampling point is located in the grinding contact area, determine the material removal function of the tool contact point through the optimized Preston equation according to the contact pressure distribution model; wherein the coefficients involved are obtained by linear regression analysis using orthogonal experimental results.

[0090] It should be noted that when the sampling point is not located in the grinding contact area, the material removal function of the sampling point is set to zero.

[0091] Step S1065: Determine the number of grinding layers based on the maximum machining allowance and the grinding depth specified by the user, and determine the material removal function for each sampling point on each grinding layer through the material removal function of the tool contact point.

[0092] The number of grinding layers is obtained by dividing the maximum machining allowance by the grinding depth and rounding down. The material removal function is also the material removal depth per unit time.

[0093] A schematic diagram illustrating the solution of the material removal function at the sampling point using Hertzian contact theory and the optimized Preston equation is shown below. Figure 5 As shown.

[0094] Step S1066: Based on the spatial pose relationship, rotate the material removal function of the sampling point to the local coordinate system where the dual-blade axis vector is located.

[0095] Step S107: Based on the convolution operation, the material removal function is combined with the tool path, and the dwell time of each tool contact point in the repair area is determined by the truncated singular value decomposition method, so as to realize the precision machining of layer-by-layer point-by-point control.

[0096] It should be noted that the process for determining the dwell time is not limited in this embodiment and can be set by the user.

[0097] The residence time of each blade contact point in the repair area was determined using the truncated singular value decomposition method, including:

[0098] The material removal function is combined with the tool path based on the convolution operation and then converted into a system of linear equations for solution.

[0099] The non-homogeneous linear equations of a large sparse matrix are solved by truncated singular value decomposition to obtain the dwell time of each of the knife contact points, and the overall offset method is used to ensure the non-negativity of the dwell time.

[0100] By using the truncated singular value decomposition method and the material removal function to solve the dwell time of each blade contact, the repair area with uneven allowance distribution can be processed in layers and point by point to achieve high-quality grinding and polishing of remanufactured blades.

[0101] Step S108: Determine the robot polishing trajectory for the remanufactured blade based on the spatial coordinate information of the tool position corresponding to the tool contact point, the dual tool axis vector, and the dwell time.

[0102] The method in this embodiment first determines the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade, and calculates the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface. Then, it fits and discretizes the tool contact points, derives the double-tool axis vector of the tool contact points, generates sampling points, and determines the material removal function of the sampling points. Next, it uses the truncated singular value decomposition method to solve the dwell time of the tool contact points using the material removal function, so as to perform layered point-by-point controlled processing on the repair area with uneven material allowance distribution. Finally, it derives the robot grinding and polishing trajectory of the remanufactured blade based on the spatial coordinate information of the tool point, the double-tool axis vector, and the dwell time. This embodiment fully considers the influence of large surface deformation and uneven material allowance distribution in the repair area on the grinding and polishing effect, and realizes layered point-by-point precision grinding and polishing processing of the remanufactured blade.

[0103] Based on the above embodiments, in one embodiment of this application, the high-quality grinding and polishing trajectory planning method for remanufactured blade robots further includes a process for determining the spatial coordinate information of the tool position corresponding to the tool contact point, which includes:

[0104] Iteratively calculate the nearest mesh vertex of the current tool contact point, determine the unit normal vector of the mesh vertex by the weighted average of the normal vectors of the triangular facets in the n-neighborhood of the mesh vertex, and use it as the main tool axis vector of the current tool contact point;

[0105] The spatial coordinates of the tool position corresponding to the current tool contact point are determined by offsetting the tool radius length and the difference between the grinding depth and the main tool axis vector direction.

[0106] Spatial coordinate information includes coordinates along the x, y, and z axes.

[0107] Robotic belt grinding is a precision machining method characterized by flexible contact. The rubber contact wheel undergoes time-varying contact deformation due to normal grinding pressure, resulting in dynamic changes in the pressure distribution within the grinding contact area. Therefore, the material removal efficiency of each tool contact point dynamically varies with the pressure in the grinding contact area. Accurate material removal modeling of the tool contact points is crucial for achieving high-quality grinding of the repair area of ​​remanufactured blades. In this example, the flexible contact between the contact wheel and the curved workpiece satisfies Hertz's law. A pressure distribution model within the grinding contact area is constructed using Hertzian contact theory, and then the material removal function for each grinding tool contact point is derived based on the optimized Preston equation.

[0108] The pressure distribution within the grinding contact area of ​​each tool contact point is approximately elliptical. Let the tool feed rate direction be X. t Direction, the direction of the tool support axis is Z.t Establish the tool coordinate system with the direction of maximum principal curvature of the workpiece as X. cmax The direction of minimum principal curvature of the workpiece is Y. cmin The direction, the normal vector of the workpiece surface is Z. c Direction, establish a local coordinate system for workpiece contact. Then, in the contact profile of the current tool contact point, any sampling point (x... i ,y i The contact pressure p(x) i ,y i This can be represented as:

[0109] (1)

[0110] Among them, F n Let be the normal contact force between the tool and the workpiece, and let a and b be the major and minor semi-axes of the contact ellipse, satisfying the following relationship:

[0111] (2)

[0112] Where κ is the ratio of the major and minor semi-axis of the ellipse, ε(κ) is the elliptic integral of the second kind, E1* is the relative elastic modulus between the contact wheel and the workpiece, and A and B are the relative curvatures at the tool contact point, which can be calculated by the following formula:

[0113] (3)

[0114] Where E1 and E2 are the elastic moduli of the tool and the workpiece, respectively; v1 and v2 are the Poisson's ratios of the tool and the workpiece, respectively; R1 and Rʹ1 are the principal radii of curvature of the contact wheel at the tool contact point (the tool is cylindrical, 1 / R1 is the reciprocal of the tool radius, 1 / Rʹ1=0); R2 and Rʹ2 are the principal radii of curvature of the workpiece at the tool contact point; and γ is the angle between the tool and the workpiece in the principal curvature direction, which can be calculated using Euler's formula, i.e.:

[0115] (4)

[0116] Where Y t Z is the direction of the tool support axis. t X-direction of tool feed rate t The cross product direction.

[0117] The Preston equation is commonly used in the field of flexible grinding to predict material removal efficiency. It states that the material removal rate R(x,y) is proportional to the relative pressure and relative velocity between the tool and the workpiece, and can be expressed as:

[0118] (5)

[0119] Among them, V mThe relative velocity between the tool and the workpiece, in belt grinding, is due to the linear velocity v of the abrasive belt. s Much greater than the workpiece feed rate v w Therefore, it can be approximated as v s Coefficient k p These are constants related to factors such as the type of abrasive belt and the material of the workpiece, comprehensively reflecting the processing capabilities of the system platform.

[0120] Due to the abrupt curvature changes in the repair area and the uneven distribution of machining allowance at the tool contact point, this example introduces a power function to optimize the material removal rate function, thereby reflecting the coupling effect between various parameters in the grinding process and improving the prediction accuracy of the traditional Preston equation.

[0121] (6)

[0122] Where α and β are the coupling coefficients of feed rate and contact pressure, respectively. This is the optimized R(x,y). The coefficient k p α and β can be calibrated using linear regression analysis based on the results of orthogonal experiments on the grinding of curved sample bases.

[0123] In addition, the coordinates of the sampling point need to be transformed from the workpiece coordinate system to the tool contact point local coordinate system to determine whether the sampling point is within the tool contact point contact contour area. Specifically, the sampling point (SP) can be represented as:

[0124] (7)

[0125] in, These are the coordinates of the sampling point in the local coordinate system of the tool contact point. This refers to the spatial orientation of the workpiece coordinate system relative to the local coordinate system of the tool contact point. This represents the offset of the workpiece coordinate system from the origin of the local coordinate system at the tool contact point. and Combined, they form a homogeneous transformation matrix of the workpiece coordinate system relative to the local coordinate system of the tool contact point. The coordinates of the sampling point in the workpiece coordinate system.

[0126] In this example, the three-dimensional coordinates of the tool contact point and the dual-tool axis vectors are calculated, including:

[0127] The first trajectory plane is obtained by fitting the reference plane with the feature points selected by the user interaction and offsetting along the plane normal direction according to the safety distance. The first trajectory plane is determined as the initial trajectory plane.

[0128] The triangular facets that intersect with the mesh surface are calculated based on the region growth algorithm, and the spatial intersection type of the two is determined. The sequential intersection points are calculated sequentially using the line / face intersection principle.

[0129] The first machining path is obtained by fitting sequential intersection points using the 3rd NURBS curve fitting algorithm, and the tool contact points on the first machining path are discretized using the equal arc length interpolation method.

[0130] The processing row spacing is calculated based on the number of trajectories or the principle of equal residual height, and the subsequent trajectory plane is calculated by offsetting along the normal direction of the trajectory plane according to the row spacing;

[0131] The unit normal vector of the mesh vertex closest to the current tool contact point is regarded as the direction of the main tool axis, where the normal vector is calculated by the area-weighted average of the normal vectors of the triangular faces in the n-neighborhood of the mesh vertex.

[0132] Project the curve tangent vector of the current tool contact point onto the tangent plane of the nearest neighboring mesh vertex to obtain the direction of the secondary tool axis vector.

[0133] By optically scanning adjacent intact blades or blades that have already been properly ground, the theoretical model for the repaired blade is determined to be a triangular mesh surface model. This reduces deformation errors while avoiding over-grinding / under-grinding caused by parametric surface trajectory planning. Furthermore, generating the toolpath directly on the mesh surface avoids the time-consuming and complex reverse modeling process of converting the mesh surface to a parametric surface. In this example, the toolpath generation principle mainly involves calculating the sequential intersection points by intersecting a series of parallel sections with the triangular mesh surface. The reference plane is obtained by the user interactively selecting several feature points in the CAM software and fitting them using the least squares method. A safety distance S is offset along its normal direction. d The initial trajectory plane is determined by the machining line spacing L. L is mainly determined by the residual height, tool radius and surface curvature of the repair area, and is also affected by the height and width of the cladding layer.

[0134] Standard triangular mesh surfaces store vertex coordinates and unit normals of triangular faces in a disordered manner. Since subsequent work requires frequent and rapid determination of the intersection relationships and types between mesh edges and the trajectory plane, it is necessary to re-establish the geometric topological relationships of the mesh surface's vertices, edges, and triangular faces. In this example, a half-edge data structure is used to establish the above topological relationships, and a region growing algorithm is proposed to calculate the sequential intersection points between the mesh surface and the trajectory plane. The specific steps are as follows:

[0135] (1) Select a boundary edge (shared by only one triangular facet) as a seed edge and determine its intersection with the trajectory plane.

[0136] a) If there is no intersection, continue to search for its adjacent boundary edges to perform region growth, and repeat to (1).

[0137] b) If there are intersections, calculate the intersections and determine whether the intersections are vertices.

[0138] c) Search for its next edge to determine its intersection. If there is an intersection, calculate the intersection directly; otherwise, continue searching for its next edge and calculate the intersection.

[0139] (2) Region growth. Search for the opposite edge of the current intersecting edge (on the adjacent triangular facet), and then continue to (b). If the intersection is a vertex, discard it; otherwise, continue to (c).

[0140] (3) Repeat (2) until the boundary edge is encountered again, terminate the growth and calculate the last intersection point, and set the entry point and exit point based on the first and last intersection points.

[0141] (4) Repeat steps (1) to (3) until there are no more cut planes available for growth, and store the points of adjacent toolpaths in the order of Zig-Zag toolpaths.

[0142] Wherein, vertex A (x a , y a , z a ) and B(x b , y b , z b The sequential intersection points I of the grid edges formed by the trajectory plane. i (x) i , y i , z i ) can be represented as:

[0143] (8)

[0144] In the formula, (A, B, C, D) represent the coefficients of the plane equation.

[0145] In this example, sequential intersection points of each trajectory plane are fitted using a 3x3 NURBS curve to eliminate redundancy, self-intersections, and Z-shaped folds in the initial point cloud, resulting in a smooth and continuous toolpath. Traditional constant-chord height step-length methods discretize the toolpath based on curve curvature, generating sparse tool contacts in areas of low curvature and dense tool contacts in areas of high curvature. However, belt grinding involves surface contact, and the material removal profile of each tool contact contains several adjacent tool contacts. These material removal profiles are coupled, so excessively dense tool contacts can easily cause over-grinding, especially at extremely thin, abruptly curvature intake / exhaust edges. Therefore, this example proposes a constant-arc-length discretization method to discretize the toolpath, ensuring consistent curve arc lengths between adjacent tool contacts. This allows the tool contacts to be evenly distributed on the trajectory curve, and their density can be controlled by the number of tool contacts, reducing the possibility of over-grinding.

[0146] Discrete tool contacts may be located inside, on the edge, at the vertex of a triangular facet, or even off the mesh surface due to fitting errors. To improve the efficiency of trajectory calculation, this example treats the normal vector of the nearest mesh vertex to the current tool contact as the principal direction of the tool axis vector. Since the mesh surface only provides the normal vectors of the triangular facets and not the normal vectors of the mesh vertices, they can only be estimated using approximation methods. This example calculates the unit normal vector n by weighted averaging the normal vectors of the triangular facets in the neighborhood of the mesh vertex 1. i The weight is the area of ​​the triangle, that is:

[0147] (9)

[0148] Where m is the number of adjacent triangles of the i-th vertex, A i,j and n i,j Let A be the area and normal vector of the j-th neighboring triangle, respectively, and let A be the area and normal vector of the j-th neighboring triangle. i,j It is a function of its vertices (f(x)). i,j ,y i,j ,z i,j )).

[0149] The direction of the tool's secondary tool axis vector determines the contact posture between the tool and the workpiece, thus affecting the shape and area of ​​the material removal profile within the grinding contact area. In this example, the 3rd NURBS curve tangent vector Cʹ(u) at the current tool contact point is used. i Projecting the feed direction onto the tangent plane of the mesh vertices to obtain a smooth feed direction, such as... Figure 4 As shown, the direction of the secondary tool axis vector du can be expressed as:

[0150] (10)

[0151] A local coordinate system for the tool contact point is established with the main tool axis vector as the z-axis, the secondary tool axis vector as the x-axis, and the cross product direction as the y-axis. The system is then rotated by (α, β) angles along the y and z axes respectively to form a dual-vector control.

[0152] Calculate the tool position point and machining path line spacing, including:

[0153] Calculate the coordinates of the tool position point corresponding to the tool contact point by offsetting the distance between the tool radius length and the set grinding depth in the main tool axis vector direction;

[0154] The trajectory row spacing is calculated based on the number of paths or the equal residual height method for planar machining row spacing.

[0155] With the knife contact point P CC(i,j) Corresponding tool position P CL(i,j) This can be achieved by adjusting the tool's main axis vector direction n. i Upper offset tool radius R1 and grinding depth a p The difference in distance is expressed as:

[0156] (11)

[0157] The machining path spacing L is the distance between adjacent trajectory planes, which directly determines the residual material height (maximum thickness of the uncut volume) of the machined surface and affects the machining efficiency and surface quality of the remanufactured blade. The equal residual height trajectory method is often used for finishing path planning of complex curved surfaces, ensuring that the residual height between adjacent trajectories is equal. It is mainly related to the tool radius (R1), residual height (h), and radius of curvature of the tool contact point (R). Considering that the generatrix of the minimum principal curvature direction of a ruled surface blade is a straight line, the trajectory path spacing L can be calculated based on the plane machining path spacing of the equal residual height method. Specifically, L can be expressed as:

[0158] (12)

[0159] Based on the theory of convolution operations, the amount of material removed h(x) at each sampling point in the repair region is determined. k , y k , z k The dwell time t is a linear superposition of the material removed when the tool resides at each contact point. The dwell time t is calculated by solving a system of non-homogeneous linear equations for a large sparse matrix. Since the coefficient matrix R is a large sparse matrix, this equation is an ill-conditioned system without an exact solution. We previously proposed a singular value decomposition (SVD) method to solve this equation. The solution obtained by this method is related to the singular values ​​σ of the sparse matrix. i Inversely proportional, as the singular values ​​gradually decrease from large to small to zero, the dwell time value will fluctuate drastically with small changes in the singular values, thereby reducing the solution accuracy.

[0160] Therefore, in this example, the coefficient matrix R is reduced to a specified dimension R′ by utilizing the first k largest singular values ​​and their corresponding eigenvectors to avoid the impact of excessively small singular values ​​on computational accuracy. At this point, the dwell time t of the tool contact can be optimized to t′.

[0161] (13)

[0162] Where U and V are unitary matrices, and S is a diagonal matrix; σ i Let r be the diagonal element of S, and also the singular value of R; r is the rank of the coefficient matrix R, and h is the singular value of R. i Let u be the machining allowance value for the i-th sampling point. i v is the element in the i-th row of the diagonal in U. i Let i be the element of the i-th column on the diagonal of V.

[0163] The dimensionality reduction space k can be determined based on the distribution ratio of the singular values. When the distribution ratio η reaches a set value, the number of singular values ​​is taken as the value of k. In many cases, the reduction rate of singular values ​​is particularly fast, with the sum of the first 10% or even 1% of the singular values ​​accounting for more than 90% of the sum of all singular values. Therefore, this example defines a 90% distribution to truncate the singular values ​​in order to calculate the value of k. In this case, η can be expressed as:

[0164] (14)

[0165] Since the dwell time is non-negative, in order to improve the robustness of the above solution algorithm, this example performs an overall offset on the dwell time. That is, if the minimum value min(t) of the dwell time of the tool contact is negative, then the time value of each tool contact is reduced by its minimum value; if the dwell time of the tool contact is positive, then it remains unchanged.

[0166] (15)

[0167] Among them, t k For length of stay.

[0168] Furthermore, sudden changes in robot feed rate can easily cause severe vibrations during grinding, leading to over-grinding or even workpiece rejection. Therefore, the feed rate at each tool contact point needs to be constrained to [t]. l , t u To reduce vibration during grinding, i.e.:

[0169] (16)

[0170] Among them, t l For the minimum reference feed rate, t u t represents the maximum reference feed rate, h represents the machining allowance at the sampling point, and t represents the dwell time matrix.

[0171] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0172] The high-quality grinding and polishing trajectory planning method for remanufactured blade robots provided in this application has been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the solution and core ideas of this application. It should be noted that those skilled in the art can make several improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

Claims

1. A method for high-quality grinding and polishing trajectory planning for a remanufactured blade robot, characterized in that, include: Determine the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade; Determine the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface in each layer; The sequential intersection points corresponding to each layer of the trajectory plane are fitted into the target curve path, and the knife contact point is obtained by discretizing each target curve path according to the equal arc length interpolation method. Determine the dual-tool axis vector for each of the tool contacts, wherein the dual-tool axis vector includes a primary tool axis vector and a secondary tool axis vector; Increase the number of trajectory planes and reduce the arc distance between tool contacts to generate denser sampling points; Determine the material removal function for the sampling point; The material removal function is combined with the tool path based on the convolution operation, and the dwell time of each tool contact point in the repair area is determined by the truncated singular value decomposition method, so as to achieve layered point-by-point control of precision machining. The robot grinding and polishing trajectory for remanufacturing blades is determined based on the spatial coordinate information of the tool position corresponding to the tool contact point, the dual tool axis vector, and the dwell time. The trajectory plane for multi-layer grinding and polishing on the remanufactured blade mesh surface includes: The optical scanning mesh surface model of adjacent or properly ground blades of the same level is used as the theoretical numerical model for remanufactured blades. Several feature points are specified in the theoretical numerical model, and the reference plane is fitted using the least squares method with the feature points. The initial trajectory plane is determined by offsetting the reference plane by a safe distance. The machining line spacing is determined by the tool size, trajectory residual height, or number of machining paths, and the remaining multi-layer trajectory planes are obtained by offsetting along the normal of the initial trajectory plane according to the machining line spacing. Determining the dual-blade axis vector for each blade contact includes: The nearest grid vertex of the current tool contact point is searched using a kd-tree data structure. The vertex unit normal vector is determined using the area weight method, and the vertex unit normal vector is used as the main tool axis vector of the current tool contact point. Determine the tangent vector of the 3rd order NURBS curve at the current tool contact point, project the tangent vector of the 3rd order NURBS curve onto the tangent plane of the grid vertex, and use the resulting unit vector as the secondary tool axis vector of the current tool contact point.

2. The high-quality grinding and polishing trajectory planning method for remanufactured blade robots as described in claim 1, characterized in that, The material removal function for determining the sampling point includes: The directed distance between the sampling point and the blade blank mesh surface is determined along the rotation direction of the sampling point normal vector. The directed distance is used as the machining allowance of the sampling point, and the maximum machining allowance is determined from the machining allowance. Determine the differential geometric information of the principal curvature and its direction at the tool contact point, and determine the spatial pose relationship between the differential geometric information and the dual tool axis vector according to the Euler equation; the principal curvature and its direction include the value and direction of the maximum principal curvature and the value and direction of the minimum principal curvature; The contact pressure distribution model along the principal curvature direction of the blade contact point is determined by Hertzian contact theory; the parameters of the contact pressure distribution model include the relative elastic modulus of the remanufactured blade and the tool, the principal curvature and its direction, and the geometric dimensions of the contact profile. The grinding contact area is determined based on the secondary tool axis vector, and when the sampling point is located in the grinding contact area, the material removal function of the tool contact point is determined by the optimized Preston equation according to the contact pressure distribution model; the coefficients involved are obtained by linear regression analysis using orthogonal experimental results. The number of grinding layers is determined based on the maximum machining allowance and the grinding depth specified by the user, and the material removal function of each sampling point on each grinding layer is determined by the material removal function of the tool contact point. Based on the spatial pose relationship, the material removal function of the sampling point is rotated to the local coordinate system where the dual-blade axis vector is located.

3. The high-quality grinding and polishing trajectory planning method for remanufactured blade robots as described in claim 1, characterized in that, Determining the sequential intersection points between the trajectory plane and the triangular facets of the mesh surface in each layer includes: The topological relationship between mesh vertices, edges, and triangular faces is reconstructed using a half-side data structure, and the spatial intersection relationship and type between the trajectory plane and the triangular facet in each layer are determined. Based on the spatial intersection relationship and type, the sequential intersection points of the trajectory plane and the triangular facets in each layer are determined using a region growth algorithm.

4. The high-quality grinding and polishing trajectory planning method for remanufactured blade robots as described in claim 1, characterized in that, The process of determining the spatial coordinate information of the tool position point includes: Iteratively calculate the nearest mesh vertex of the current tool contact point, determine the unit normal vector of the mesh vertex by the weighted average of the normal vectors of the triangular facets in the n-neighborhood of the mesh vertex, and use it as the main tool axis vector of the current tool contact point; The spatial coordinates of the tool position corresponding to the current tool contact point are determined by offsetting the tool radius length and the difference between the grinding depth and the main tool axis vector direction.

5. The high-quality grinding and polishing trajectory planning method for remanufactured blade robots as described in any one of claims 1 to 4, characterized in that, The residence time of each blade contact point in the repair area was determined using the truncated singular value decomposition method, including: The material removal function is combined with the tool path based on the convolution operation and then converted into a system of linear equations for solution. The non-homogeneous linear equations of a large sparse matrix are solved by truncated singular value decomposition to obtain the dwell time of each of the knife contact points, and the overall offset method is used to ensure the non-negativity of the dwell time.

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