High-quality grinding and polishing trajectory planning method for blade remanufacturing robot

Abstract

The invention relates to the field of intelligent manufacturing, and discloses a high-quality grinding and polishing trajectory planning method for a blade remanufacturing robot, which comprises the following steps of: determining a multi-layer grinding and polishing trajectory plane on a grid curved surface of a remanufactured blade; determining a sequential intersection point between each layer of track plane and the grid curved surface triangular patch; fitting the sequential intersection points of each layer into target curve paths, and dispersing each target curve path according to an equal arc length interpolation method to obtain cutter contacts; determining a double-cutter-axis vector of each cutter contact; generating a sampling point and determining a material removal function of the sampling point; a material removal function is combined with a tool path according to convolution operation, and the residence time of each layer of tool contacts in the repair area is determined through a truncated singular value decomposition method; and the grinding and polishing track of the robot is determined according to the space coordinate information of the cutter location point corresponding to the cutter contact point, the double-cutter-axis vector and the residence time. The influence of large deformation of a molded surface and non-uniform allowance distribution of a repair area on the grinding and polishing effect is considered, and layered point-by-point precise grinding and polishing machining of the remanufactured blade is achieved.

Description

Technical Field

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

[0002] Blade remanufacturing is an important part of the life cycle of aircraft engines. The precise shaping and controllability of the blade after additive repair directly affect the working performance and service life of the whole machine. Due to the large deformation of the blade surface and the uneven distribution of machining allowance in the repair area, it is difficult to effectively ensure the surface quality of the subsequent robot grinding and polishing. Robot trajectory planning is the key to ensuring the quality of the repair area. Most of the existing tool trajectories are planned based on the blade theoretical parameter design surface, but they still have certain limitations when facing the remanufactured blades with large surface deformation. Therefore, it is necessary to consider the direct trajectory planning of the mesh surface generated by the optical scanning system, further optimize the calculation model of the machining line spacing, tool step length and tool axis vector, so as to avoid the over-grinding / under-grinding phenomenon caused by the parametric surface. The existing mesh surface trajectory planning is mostly used for CNC milling or 3D printing, and after obtaining the intersection of the trajectory plane and the mesh edge, it is directly used to output the tool contact point, without further curve fitting and tool contact discretization. In addition, the Preston material removal function used in the existing robot grinding and polishing trajectory is only used to compensate for the geometric discrete error of the tool contact point, and is not used for real-time control of process parameters at the uneven allowance distribution. Therefore, it is urgent to propose an optimal grinding and polishing trajectory planning method for remanufactured blades with large surface deformation and uneven allowance distribution. Summary of the invention

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

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

[0005] Determine the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade;

[0006] Determining sequential intersection points between the trajectory plane and the mesh surface triangular patches at each layer;

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

[0008] Determine a dual-tool axis vector for each tool contact point, wherein the dual-tool axis vector includes a primary tool axis vector and a secondary tool axis vector;

[0009] Increase the number of trajectory planes and reduce the arc length distance between knife contacts to generate dense sampling points;

[0010] determining a material removal function for the sampling point;

[0011] The material removal function is combined with the tool path according to the convolution operation, and the dwell time of each layer of the tool contact point in the repair area is determined by the truncated singular value decomposition method to achieve layered point-by-point precision machining;

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

[0013] Optionally, determining the trajectory plane of multi-layer polishing on the mesh surface of the remanufactured blade includes:

[0014] The optical scanning mesh surface model of the adjacent blade or the qualified blade that has been ground is used as the theoretical digital model of the remanufactured blade;

[0015] Specifying a number of characteristic points in the theoretical numerical model, and fitting a reference plane using the characteristic points by a least square method;

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

[0017] The machining line spacing is determined by the tool size, the residual height of the track or the number of machining paths, and the initial track plane is offset along the normal direction according to the machining line spacing to obtain the remaining multi-layer track planes.

[0018] Optionally, determining a material removal function for a sampling point comprises:

[0019] Determine the directed distance between the sampling point and the mesh surface of the blade blank along the rotation direction 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 allowances;

[0020] Determine the differential geometry information of the principal curvature and its direction at the knife contact point, and determine the spatial posture relationship between the differential geometry information and the dual knife axis vectors 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;

[0021] The contact pressure distribution model of the tool contact point along the main curvature direction is determined 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 main curvature and its direction, and the geometric dimensions of the contact profile;

[0022] The grinding contact area is determined according to 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 according to the contact pressure distribution model through the optimized Preston equation; the coefficients involved 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 grinding depth specified by the user, 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] Based on the spatial posture relationship, the material removal function of the sampling point is rotated to the local coordinate system where the dual-knife axis vector is located.

[0025] Optionally, determining a dual knife axis vector of each knife contact point, wherein the dual knife axis vector includes a primary knife axis vector and a secondary knife axis vector comprises:

[0026] Search the nearest mesh vertex of the current knife 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 main knife axis vector of the current knife contact point;

[0027] The tangent vector of the third-order NURBS curve where the current tool contact point is located is determined, and the tangent vector of the third-order NURBS curve is projected into the tangent plane of the mesh vertex, and the obtained unit vector is used as the secondary tool axis vector of the current tool contact point.

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

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

[0030] According to the spatial intersection relationship and type, the sequential intersection points of the trajectory plane and the triangular facets of each layer are determined in turn by a region growing algorithm.

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

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

[0033] The distance between the tool radius length and the grinding depth is offset in the main tool axis vector direction to determine the spatial coordinate information of the tool position point corresponding to the current tool contact point.

[0034] Optionally, determining the dwell time of each layer of the knife contact point in the repair area by truncated singular value decomposition method includes:

[0035] Combining the material removal function with the tool path according to a convolution operation and converting it into a linear equation system for solution;

[0036] The truncated singular value decomposition method is used to solve the non-homogeneous linear equations of the large sparse matrix to obtain the residence time of each knife contact point, and the overall offset method is used to ensure the non-negativity of the residence time.

[0037] The present application provides a high-quality grinding and polishing trajectory planning method for a remanufactured blade robot, comprising: determining a trajectory plane for multi-layer grinding and polishing on a mesh surface of a remanufactured blade; determining sequential intersection points between the trajectory plane of each layer and the triangular facets of the mesh surface; fitting the sequential intersection points corresponding to the trajectory plane of each layer 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; determining a dual tool axis vector for each tool contact point, the dual tool axis vector comprising a primary tool axis vector and a secondary tool axis vector; increasing the number of trajectory planes and reducing the arc length distance between tool contacts to generate dense sampling points; determining a material removal function for the sampling points; combining the material removal function with the tool path according to a convolution operation, determining the residence time of each layer of tool contacts in the repair area by a truncated singular value decomposition method, and realizing layered point-by-point precision machining; determining the robot grinding and polishing trajectory for the remanufactured blade according to the spatial coordinate information of the tool position point corresponding to the tool contact point, the dual tool axis vector and the residence time.

[0038] It can be seen that the method in the present application 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 fits and discretizes the tool contact point, and then determines the double tool axis vector of the tool contact point. After generating the sampling point, the material removal function of the sampling point is determined, and then the material removal function is used to solve the tool contact point residence time through the truncated singular value decomposition method, so as to perform layered point-by-point control processing on the repair area with uneven excess distribution, and finally derives the robot grinding and polishing trajectory of the remanufactured blade according to the spatial coordinate information of the tool position point, the double tool axis vector and the residence time. The present application fully considers the influence of large deformation of the surface and uneven distribution of the excess in the repair area on the grinding and polishing effect, and realizes layered point-by-point precision grinding and polishing of the remanufactured blade. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present application or the technical solutions of the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 A flow chart of a high-quality grinding and polishing trajectory planning method for a blade remanufacturing robot provided in an embodiment of the present application;

[0041] Figure 2 This is a schematic diagram of calculating the sequential intersection points between the trajectory plane and the mesh surface triangles by the region growing algorithm in the embodiment of the present application;

[0042] Figure 3 This is a schematic diagram of solving the main tool axis vector of the tool contact point according to the area weight method in the embodiment of the present application;

[0043] Figure 4 This is a schematic diagram of solving the double knife axis vector and machining line spacing of the knife contact point according to the projection of the cutting plane in the embodiment of the present application;

[0044] Figure 5 A schematic diagram of solving the material removal function of the sampling point by using the Hertz contact theory and the optimized Preston equation in the embodiment of the present application;

[0045] Figure 6 An overall flow chart of a high-quality grinding and polishing trajectory planning method for a remanufacturing blade robot provided in an embodiment of the present application. DETAILED DESCRIPTION

[0046] In order to enable those skilled in the art to better understand the present application, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work are within the scope of protection of the present application.

[0047] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and those skilled in the art may make similar generalizations without violating the connotation of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

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

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

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

[0051] It should be pointed out that the method for determining the multi-layer trajectory plane is not limited in this embodiment and can be set at will.

[0052] As an implementable method, determining the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade includes:

[0053] Step S1011: using the optical scanning mesh surface model of the adjacent blade of the same level or the qualified blade that has been repaired as a theoretical digital model of the remanufactured blade.

[0054] Using the optical scanning mesh surface model of the adjacent or qualified blades of the same level as the theoretical digital model of the remanufactured blade can avoid the over-grinding / under-grinding phenomenon caused by the deformation and failure of its parameter model.

[0055] Step S1012: specifying a number of feature points in the theoretical numerical model, and using the feature points to fit a reference plane using a least squares method.

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

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

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

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

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

[0061] In this embodiment, there is no limitation on the method for determining the sequential intersection points, which can be set at will. As an implementation method, determining the sequential intersection points between the trajectory plane and the mesh surface triangular facets of each layer includes:

[0062] Step S1021: reconstructing the topological relationship of mesh vertex-edge-triangle face using the half-edge data structure, and determining the spatial intersection relationship and type of the trajectory plane and triangular facets at each layer.

[0063] Step S1022: determining sequential intersection points of the trajectory plane and triangular facets in each layer in turn by using a region growing algorithm according to the spatial intersection relationship and type.

[0064] The schematic diagram of the sequential intersection points between the trajectory plane and the mesh surface triangles calculated by the region growing algorithm is as follows Figure 2 shown.

[0065] The topological relationship of mesh vertex-edge-triangle face is established according to the half-edge data structure, the spatial intersection relationship and type between the trajectory plane and the triangular face are determined, and the triangular face intersecting with the trajectory plane is calculated using the region growing algorithm. The sequential intersection points are calculated in turn through the line / surface intersection principle.

[0066] The sequential intersection points on each layer of the trajectory plane are fitted to form a path curve.

[0067] The tool path is generated directly on the mesh surface through the region growing algorithm and equal arc length interpolation method, which fully considers the influence of blade curvature mutation and path calculation efficiency on high-quality trajectory planning.

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

[0069] The target curve path may be a cubic NURBS curve path, or other spline curve paths, which is not specifically limited in this embodiment.

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

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

[0072] Step S104: determining a dual tool axis vector of each tool contact point, wherein the dual tool axis vector comprises a primary tool axis vector and a secondary tool axis vector.

[0073] In one embodiment of the present application, determining a dual knife axis vector of each knife contact point, wherein the dual knife axis vector includes a primary knife axis vector and a secondary knife axis vector includes:

[0074] Search the nearest mesh vertex of the current knife 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 main knife axis vector of the current knife contact point;

[0075] The tangent vector of the third-order NURBS curve where the current tool contact point is located is determined, and the tangent vector of the third-order NURBS curve is projected into the tangent plane of the mesh vertex, and the obtained unit vector is used as the secondary tool axis vector of the current tool contact point.

[0076] The schematic diagram of the main tool axis vector of the tool contact point is solved according to the area weight method. Figure 3 As shown; the schematic diagram of the double knife axis vector for solving the knife contact point according to the projection of the cutting plane is as follows Figure 4 shown.

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

[0078] Step S105: increasing the number of trajectory planes and reducing the arc length distance between knife contact points to generate dense sampling points.

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

[0080] It should be pointed out that in this embodiment, the material removal function of the sampling point is not limited and can be set at will.

[0081] As an implementation method, determining the material removal function of the sampling point includes:

[0082] Step S1061: determining 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, taking the directed distance as the machining allowance of the sampling point, and determining the maximum machining allowance from the machining allowances.

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

[0084] When the machining allowance of the 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 geometry information of the principal curvature and its direction at the tool contact point, and determine the spatial posture relationship between the differential geometry information and the dual tool axis vectors 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 main curvature direction. The directions of the main tool axis vector and the secondary tool axis vector do not necessarily coincide with the main curvature direction. Therefore, the material removal function of the sampling point needs to be rotated to the local coordinate system composed of the main tool axis vector and the secondary tool axis vector.

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

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

[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 based on the contact pressure distribution model through the optimized Preston equation; the coefficients involved are obtained through linear regression analysis method using orthogonal experimental results.

[0090] It should be pointed out 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: determining the number of grinding layers according to the maximum machining allowance and the grinding depth specified by the user, and determining the material removal function of each sampling point on each grinding layer through the material removal function of the tool contact point.

[0092] The maximum machining allowance is divided by the grinding depth and rounded to get the number of grinding layers. The material removal function is also the material removal depth per unit time.

[0093] The schematic diagram of the material removal function at the sampling point is solved by Hertz contact theory and the optimized Preston equation. Figure 5 shown.

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

[0095] Step S107: combining the material removal function with the tool path according to the convolution operation, determining the dwell time of each layer of tool contact points in the repair area by the truncated singular value decomposition method, and realizing layered point-by-point control and precision machining.

[0096] It should be noted that the process of determining the residence time is not limited in this embodiment and can be set at will.

[0097] The dwell time of each layer of knife contact in the repair area is determined by truncated singular value decomposition method, including:

[0098] Combining the material removal function with the tool path according to a convolution operation and converting it into a linear equation system for solution;

[0099] The truncated singular value decomposition method is used to solve the non-homogeneous linear equations of the large sparse matrix to obtain the residence time of each knife contact point, and the overall offset method is used to ensure the non-negativity of the residence time.

[0100] The material removal function is used according to the truncated singular value decomposition method to solve the residence time of each tool contact point, so as to carry out layered and point-by-point control processing on the repair area with uneven allowance distribution, so as to achieve high-quality grinding and polishing of the remanufactured blade.

[0101] Step S108: determining the robot grinding and polishing trajectory of the remanufactured blade according to the spatial coordinate information of the tool position point 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 fits and discretizes the tool contact point, and then derives the double tool axis vector of the tool contact point. After generating the sampling point, the material removal function of the sampling point is determined, and then the material removal function is used to solve the dwell time of the tool contact point by truncated singular value decomposition method, so as to perform layered point-by-point control processing on the repair area with uneven allowance distribution, and finally derives the robot grinding and polishing trajectory of the remanufactured blade according to the spatial coordinate information of the tool position point, the double tool axis vector and the dwell time. This embodiment fully considers the influence of large deformation of the surface and uneven distribution of machining allowance in the repair area on the grinding and polishing effect, and realizes layered point-by-point precision grinding and polishing of the remanufactured blade.

[0103] On the basis of the above embodiments, in one embodiment of the present application, the high-quality grinding and polishing trajectory planning method for remanufacturing blade robots also includes a process for determining the spatial coordinate information of the tool position point corresponding to the tool contact point, which process includes:

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

[0105] The distance between the tool radius length and the grinding depth is offset in the main tool axis vector direction to determine the spatial coordinate information of the tool position point corresponding to the current tool contact point.

[0106] The spatial coordinate information includes the coordinates of the three axes: x, y, and z.

[0107] Robotic belt grinding is a precision machining method with flexible contact characteristics, in which the rubber contact wheel undergoes time-varying contact deformation due to the normal grinding pressure, resulting in dynamic changes in the pressure distribution in the grinding contact area. Therefore, the material removal efficiency of each tool contact point changes dynamically with the pressure change in the grinding contact area. If high-quality grinding processing is to be achieved in the remanufacturing blade repair area, accurate material removal modeling of the tool contact point is the key. In this example, the flexible contact between the contact wheel and the curved workpiece satisfies Hertz's law. The Hertz contact theory is used to construct a pressure distribution model in the grinding contact area, and then the material removal function of each grinding tool contact point is derived based on the optimized Preston equation.

[0108] The pressure distribution in the grinding contact area of ​​each tool contact point is close to an ellipse. t Direction, the tool support axis direction is Zt The tool coordinate system is established by taking the direction of the maximum principal curvature of the workpiece as X. cmax Direction, the minimum principal curvature direction of the workpiece is Y cmin Direction, the workpiece surface normal vector is Z c direction, establish the workpiece contact local coordinate system. Then in the contact profile of the current tool contact point, any sampling point (x i ,y i ) of the contact pressure p(x i ,y i ) can be expressed as:

[0109] (1)

[0110] Among them, F n is the normal contact force between the tool and the workpiece, a and b are the major and minor axes of the contact ellipse, and satisfy the following relationship:

[0111] (2)

[0112] where κ is the ratio of the major and minor semi-axes of the ellipse, ε(κ) is the elliptic integral of the second kind, and E 1 * is the relative elastic modulus between the contact wheel and the workpiece, A and B are the relative curvatures at the knife contact point, which can be calculated by the following formula:

[0113] (3)

[0114] Where E 1 and E 2 are the elastic moduli of the tool and workpiece, respectively, v 1 and v 2 are the Poisson’s ratios of the tool and workpiece, R 1 and Rʹ 1 is the main curvature radius of the contact wheel at the tool contact point (the tool is cylindrical, 1 / R 1 is the inverse of the tool radius, 1 / Rʹ 1 =0), R 2 and Rʹ 2 is the principal curvature radius of the workpiece at the tool contact point, and γ is the angle between the tool and the workpiece in the direction of the principal curvature, which can be calculated using the Euler formula:

[0115] (4)

[0116] where Y t Z is the tool support axis direction t With tool feed speed direction X t The cross product direction of .

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

[0118] (5)

[0119] Among them, V m is the relative speed between the tool and the workpiece. During the belt grinding process, due to the belt linear speed v s Much larger than the workpiece feed speed v w , so it can be approximated as v s ; coefficient k p It is a constant related to the abrasive belt type and workpiece material, and comprehensively reflects the processing capability of the system platform.

[0120] Due to the sudden change of curvature in the repair area and the uneven distribution of machining allowance at the tool contact point, this example optimizes the above material removal rate function by introducing a power function to reflect the coupling process between the various parameters of the grinding process, thereby improving the prediction accuracy of the traditional Preston equation, that is:

[0121] (6)

[0122] Among them, α and β are the coupling coefficients of feed speed and contact pressure, respectively. is the optimized R(x,y). Coefficient k p , α, β can be calibrated according to the linear regression analysis method through the orthogonal experimental results of basic grinding of curved surface samples.

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

[0124] (7)

[0125] in, is the coordinate value of the sampling point in the local coordinate system of the knife contact point, is the spatial posture of the workpiece coordinate system relative to the local coordinate system of the tool contact point, is the offset of the coordinate origin of the workpiece coordinate system relative to the local coordinate system of the tool contact point, and Combined together, it is the homogeneous transformation matrix of the workpiece coordinate system relative to the local coordinate system of the tool contact point. is the coordinate value 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] Fitting a reference plane through feature points selected by user interaction, offsetting along the plane normal direction according to a safety distance to obtain a first trajectory plane, and determining the first trajectory plane as an initial trajectory plane;

[0128] The region growing algorithm is used to calculate the triangular facets that intersect with the mesh surface, and the type of spatial intersection between the two is determined. The sequential intersection points are calculated in sequence using the line / surface intersection principle.

[0129] The first machining path is obtained by fitting sequential intersection points according to a cubic NURBS curve fitting algorithm, and the tool contact points on the first machining path are obtained by discretization according to an equal arc length interpolation method;

[0130] Calculate the machining line spacing based on the number of trajectories or the principle of equal residual height, and calculate the subsequent trajectory plane according to the offset of the line spacing along the normal vector direction of the trajectory plane;

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

[0132] The curve tangent vector of the current tool contact point is projected 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 of the same level or blades that have been repaired and qualified, the theoretical model of the repaired blade is determined to be its triangular mesh surface model, which reduces the deformation error and avoids the over-grinding / under-grinding caused by parametric surface trajectory planning. In addition, directly generating the tool path on the mesh surface can avoid the time-consuming and complex reverse modeling process of converting the mesh surface into a parametric surface. In this example, the principle of tool path generation is mainly to calculate the sequential intersection points by intersecting a series of parallel sections with the triangular mesh surface. The reference plane is fitted by the least squares method by the user interactively selecting several feature points in the CAM software. By offsetting the safety distance S along its normal d To determine the initial trajectory plane, the other trajectory planes are calculated by the processing 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] The standard triangular mesh surface only stores the coordinate values ​​of the vertices and the unit normal vectors of the triangles in a disordered and unordered manner. Since the subsequent work needs to frequently and quickly determine the intersection relationship and type between the mesh edge and the trajectory plane, it is necessary to re-establish the geometric topological relationship of the vertex-edge-triangle of the mesh surface. In this example, the half-edge data structure is used to establish the above topological relationship, 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 triangle) as a seed edge and determine its intersection with the trajectory plane.

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

[0137] b) If there is an intersection, calculate the intersection and determine whether the intersection is a vertex.

[0138] c) Search for the next edge to determine its intersection. If there is one, calculate the intersection directly; if not, continue to search for the next edge and calculate the intersection.

[0139] (2) Region growth. Search for the reverse edge of the current intersection edge (on the adjacent triangle patch), and then continue to (b). If the intersection point is a vertex, discard it; if not, 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 section planes available for growth, and store the points of adjacent tool paths in the order of the Zig-Zag tool path.

[0142] Among them, vertex A (x a , y a , z a ) and B(x b , y b , z b ) and the sequential intersection points of the trajectory plane i (x i , y i , z i ) can be expressed as:

[0143] (8)

[0144] Where (A, B, C, D) represents the coefficients of the plane equation.

[0145] In this example, the sequential intersection points of each trajectory plane are fitted by a cubic NURBS curve, and the defects such as redundancy, self-intersection and Z-shaped folding in the initial point cloud are eliminated to form a smooth and continuous tool path. Considering that the traditional equal chord height step method can discretize the tool path according to the curve curvature, sparse tool contacts are generated in the area with small curvature, and dense tool contacts are generated in the area with large curvature. However, belt grinding belongs to surface contact. The material removal profile of the current tool contact contains several adjacent tool contacts, and the material removal profiles are coupled with each other. Therefore, too dense tool contacts can easily cause over-grinding, especially at the intake / exhaust edges with extremely thin size and sudden curvature changes. Therefore, this example proposes an equal arc length discretization method to discretize the tool path so that the arc length of the curve between adjacent tool contacts remains consistent. The tool contacts can be evenly distributed on the trajectory curve, and the density can be controlled by the number of tool contacts to reduce the possibility of over-grinding.

[0146] The discrete tool contact point may be located inside the triangle, at the edge, at the vertex, or even not on the mesh surface due to fitting errors. To improve the efficiency of the calculation trajectory, this example searches for the normal vector of the nearest mesh vertex of the current tool contact point as the main direction of the tool axis vector. Since the mesh surface only gives the normal vector of the triangle, but not the normal vector of the mesh vertex, it can only be estimated by an approximate method. This example calculates the unit normal vector n by the weighted average of the normal vectors of the mesh vertex 1-neighboring triangles. 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 are the area and normal vector of the jth neighborhood triangle, respectively, and A i,j is a function about 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, which in turn affects the shape and area of ​​the material removal profile in the grinding contact area. i ) is projected onto the tangent plane of the mesh vertex to obtain a smooth feed direction, such as Figure 4 As shown, the secondary tool axis vector direction du can be expressed as:

[0150] (10)

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

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

[0153] The distance between the tool radius length and the set grinding depth is offset in the main tool axis vector direction, and the tool position coordinates corresponding to the tool contact point are calculated;

[0154] Calculate the track stepover based on the number of paths or normal plane machining stepover with equal cusp height.

[0155] With knife contact P CC(i,j) The corresponding knife position P CL(i,j) By moving the tool axis vector n i Upper offset tool radius R 1 and grinding depth a p The difference distance is expressed as:

[0156] (11)

[0157] The machining line spacing L is the distance between adjacent trajectory planes, which directly determines the material residual height of the machined surface (the maximum thickness of the uncut volume) 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 surfaces. It can ensure that the residual height between adjacent trajectories is equal, which is mainly related to the tool radius (R 1 ), residual height (h), and tool contact point curvature radius (R). Considering that the minimum principal curvature generatrix of the ruled surface blade is a straight line, the track spacing L can be calculated based on the normal plane machining spacing of equal residual height. Specifically, L can be expressed as:

[0158] (12)

[0159] Based on the convolution operation theory, the material removal amount h(x k , y k , z k ) is the linear superposition of the material removal amount when the tool resides at each tool contact point. The residence time t is calculated by solving a non-homogeneous linear equation system of a large sparse matrix. Since the coefficient matrix R is a large sparse matrix, the equation is an ill-conditioned system without an exact solution. We previously proposed a singular value decomposition (SVD) method to solve the equation. The solution of this method is consistent with the singular value σ of the sparse matrix. i Inversely proportional to the value of the singular value, when the singular value gradually decreases from large to small to zero, the value of the residence time will fluctuate violently with the slight change of the singular value, thereby reducing the solution accuracy.

[0160] Therefore, in this example, the coefficient matrix R is reduced to the specified dimension R' by using the first k largest singular values ​​and their corresponding eigenvectors to avoid the influence of too small singular values ​​on the calculation accuracy. At this time, the dwell time t of the knife contact can be optimized to t'.

[0161] (13)

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

[0163] The dimension reduction space k can be determined according to the distribution ratio of the singular values. When the distribution ratio η reaches the set value, the number of singular values ​​is taken as the k value. In many cases, the singular values ​​are reduced very quickly, and the sum of the first 10% or even 1% of the singular values ​​accounts for more than 90% of the sum of all singular values. Therefore, this example defines a 90% distribution to perform singular value truncation to calculate the k value. At this time, 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 knife contact dwell time is a negative value, the time value of each knife contact is subtracted from its minimum value; if the dwell time of the knife contacts is a positive value, it remains unchanged.

[0166] (15)

[0167] Among them, t k For the dwell time.

[0168] In addition, the sudden change of the robot feed speed can easily cause severe grinding vibration, resulting in over-grinding or even grinding scrap of the workpiece. Therefore, the feed speed of each tool contact point needs to be constrained to [t l , t u ] to reduce grinding vibration, namely:

[0169] (16)

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

[0171] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0172] The above is a detailed introduction to the high-quality grinding and polishing trajectory planning method for the remanufacturing blade robot provided by the present application. This article uses specific examples to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the scheme of the present application and its core idea. It should be pointed out that for ordinary technicians in this technical field, without departing from the principles of the present application, several improvements and modifications can be made to the present application, and these improvements and modifications also fall within the scope of protection of the present application.

Claims

1. A high-quality grinding and polishing trajectory planning method for a blade remanufacturing robot, characterized in that: include: Determine the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade; Determining sequential intersection points between the trajectory plane and the mesh surface triangular patches at each layer; Fitting the sequential intersection points corresponding to the trajectory plane of each layer into a target curve path, and discretizing each target curve path according to the equal arc length interpolation method to obtain the knife contact point; Determine a dual-tool axis vector for each tool contact point, 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 length distance between knife contacts to generate dense sampling points; determining a material removal function for the sampling point; The material removal function is combined with the tool path according to the convolution operation, and the dwell time of each layer of the tool contact point in the repair area is determined by the truncated singular value decomposition method to achieve layered point-by-point precision machining; The robot grinding and polishing trajectory of the remanufactured blade is determined according to the spatial coordinate information of the tool position point corresponding to the tool contact point, the dual tool axis vector and the dwell time.

2. The high-quality grinding and polishing trajectory planning method for blade remanufacturing robot according to claim 1 is characterized in that: Determine the trajectory plane of multi-layer grinding and polishing on the mesh surface of the remanufactured blade including: The optical scanning mesh surface model of the adjacent blade or the qualified blade that has been ground is used as the theoretical digital model of the remanufactured blade; Specifying a number of characteristic points in the theoretical numerical model, and fitting a reference plane using the characteristic points by a least square method; Determine the initial trajectory plane by offsetting the reference plane by a safety distance; The machining line spacing is determined by the tool size, the residual height of the track or the number of machining paths, and the initial track plane is offset along the normal direction according to the machining line spacing to obtain the remaining multi-layer track planes.

3. The high-quality grinding and polishing trajectory planning method for blade remanufacturing robot according to claim 1 is characterized in that: The material removal function for determining the sampling points includes: Determine the directed distance between the sampling point and the mesh surface of the blade blank along the rotation direction 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 allowances; Determine the differential geometry information of the principal curvature and its direction at the knife contact point, and determine the spatial posture relationship between the differential geometry information and the dual knife axis vectors 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 of the tool contact point along the main curvature direction is determined 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 main curvature and its direction, and the geometric dimensions of the contact profile; Determine the grinding contact area according to 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 according to the contact pressure distribution model through the optimized Preston equation; the coefficients involved are obtained by linear regression analysis method using orthogonal experimental results; Determine the number of grinding layers according to the maximum machining allowance and the grinding depth specified by the user, and determine the material removal function of each sampling point on each grinding layer through the material removal function of the tool contact point; Based on the spatial posture relationship, the material removal function of the sampling point is rotated to the local coordinate system where the dual-knife axis vector is located.

4. The high-quality grinding and polishing trajectory planning method for blade remanufacturing robot according to claim 1 is characterized in that: Determine the dual knife axis vector of each knife contact point, wherein the dual knife axis vector includes a primary knife axis vector and a secondary knife axis vector. Search the nearest mesh vertex of the current knife 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 main knife axis vector of the current knife contact point; The tangent vector of the third-order NURBS curve where the current tool contact point is located is determined, and the tangent vector of the third-order NURBS curve is projected into the tangent plane of the mesh vertex, and the obtained unit vector is used as the secondary tool axis vector of the current tool contact point.

5. The high-quality grinding and polishing trajectory planning method for blade remanufacturing robot according to claim 1 is characterized in that: Determining the sequential intersection points between the trajectory plane and the mesh surface triangular patches at each layer includes: Reconstruct the topological relationship of mesh vertex-edge-triangle face using the half-edge data structure, and determine the spatial intersection relationship and type of the trajectory plane and triangular facets at each layer; According to the spatial intersection relationship and type, the sequential intersection points of the trajectory plane and the triangular facets of each layer are determined in turn by a region growing algorithm.

6. The high-quality grinding and polishing trajectory planning method for blade remanufacturing robot according to claim 1 is 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 knife contact point, determine the unit normal vector of the mesh vertex by weighted average of the normal vectors of the triangles in the n-neighborhood of the mesh vertex, and use it as the main knife axis vector of the current knife contact point; The distance between the tool radius length and the grinding depth is offset in the main tool axis vector direction to determine the spatial coordinate information of the tool position point corresponding to the current tool contact point.

7. The high-quality grinding and polishing trajectory planning method for a blade remanufacturing robot according to any one of claims 1 to 6, characterized in that: The dwell time of each layer of knife contact in the repair area is determined by truncated singular value decomposition method, including: Combining the material removal function with the tool path according to a convolution operation and converting it into a linear equation system for solution; The truncated singular value decomposition method is used to solve the non-homogeneous linear equations of the large sparse matrix to obtain the residence time of each knife contact point, and the overall offset method is used to ensure the non-negativity of the residence time.

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