A geodesic map-based complex curved surface turning machining path planning method

Abstract

The application discloses a complex curved surface turning machining path planning method based on geodesic map, and relates to the technical field of turning machining. The method comprises the following steps: discretely representing a curved surface by using a triangular mesh, and selecting a source point; determining an initial geodesic step and generating a plurality of first isoclines according to a residual height model based on the geometric parameters of the source point; generating a first intersection point corresponding to each first isocline to form a first circle of trajectory points; determining a geodesic step of a predecessor point and generating a second isocline by combining the geometric parameters of the predecessor point and the residual height model; generating a second intersection point through the second isocline, and a plurality of second intersection points form a next circle of trajectory points; until all circles of trajectory points are generated, connecting each circle of trajectory points in sequence to obtain a helix of a turning tool trajectory. The application can effectively reduce path redundancy and surface error by constructing a geodesic distance field and generating isoclines to plan a turning machining path of a complex curved surface, and has significant advantages in machining efficiency, trajectory rationality and surface consistency.

Description

Technical Field

[0001] This invention relates to a method for planning the machining path of complex curved surfaces based on survey maps, belonging to the field of turning technology. Background Technology

[0002] In the machining of complex curved surfaces, tool path planning plays a crucial role. A reasonable tool path can effectively improve machining efficiency, ensure machining accuracy, and reduce machining residual errors and surface roughness. Especially in slow tool servo turning technology, high-quality and high-efficiency machining of complex curved surfaces can be achieved through precise path planning.

[0003] Common toolpath planning methods include isoparametric methods, isoplanar methods, and isoresidual height methods. While isoparametric methods are computationally simple, they are poorly suited for surfaces with drastic curvature changes, easily leading to path overlap or excessive gaps. Isoplanar methods generate toolpaths through the intersection of parallel sections and the surface; while simple to implement, they struggle to ensure consistent residual heights in machining complex surfaces. Isoresidual height methods plan paths by controlling the residual heights between adjacent paths; this method improves surface quality but has high computational complexity, and current implementations are mostly based on Euclidean distances, failing to fully consider the geometric characteristics of the surface itself.

[0004] With the development of turning technology, the traditional Archimedes spiral projection method has become unacceptable for high-precision turning due to its inability to adaptively adjust the trajectory generation and surface geometry features, as well as its large fluctuations in residual height and inconsistent surface quality. Therefore, an efficient, accurate, and stable tool trajectory planning method is needed to support the high performance of slow-tool servo turning. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for planning the machining path of complex curved surfaces based on geodesic distance field. By constructing a geodesic distance field and generating contour lines, the machining path of complex curved surfaces can be planned, which can effectively reduce path redundancy and surface error, and has significant advantages in machining efficiency, trajectory rationality and surface consistency.

[0006] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0007] This invention provides a method for planning machining paths for complex curved surfaces based on survey maps, comprising:

[0008] S1. Obtain the surface to be processed and the surface processing quality parameters;

[0009] S2. Use triangular mesh to discretize the surface to be machined to obtain a triangular mesh of the surface, and select the turning rotation center of the surface as the source point;

[0010] S3. Calculate the geometric parameters of each vertex and the source point in the curved triangular mesh, as well as the geodesic distance from each vertex to the source point.

[0011] S4. Establish a three-dimensional local coordinate system at the source point;

[0012] S5. Construct a residual height model using surface machining quality parameters and a three-dimensional local coordinate system;

[0013] S6. Based on the geometric parameters of the source point, determine the geodesic step length according to the residual height model and generate multiple first contour lines. Generate the first intersection point through each first contour line to form the first circle of trajectory points.

[0014] S7. Select one of the trajectory points from the previous lap as the precursor point. Based on the geometric parameters of the precursor point, determine the geodesic step length of the precursor point according to the residual height model and generate the second contour line. Generate the second intersection point through the second contour line.

[0015] S8. Repeat S7~S8 until all the trajectory points of the previous cycle have been selected in sequence, and multiple second intersection points are obtained to form the trajectory points of the next cycle.

[0016] S9. Repeat S7~S9 until all loop trajectory points are generated. Connect each loop trajectory point in turn to obtain the turning tool trajectory spiral.

[0017] Furthermore, the surface machining quality parameters include residual height, tool radius, number of trajectory points, and rotation angle increment.

[0018] Furthermore, when selecting the turning center of the curved surface as the source point, if the source point is not a vertex of the curved surface triangular mesh, the curved surface triangular mesh is refined until the source point is located at a vertex of the curved surface triangular mesh.

[0019] Furthermore, the geometric parameters include the normal vector, normal curvature, and normal direction;

[0020] The normal vector is calculated by weighted averaging of the normal vectors of adjacent triangular mesh faces, and its expression is:

[0021] ;

[0022] ;

[0023] in, Indicates the first The normal vector of each vertex. Indicates the first The vertex corresponding to the first The area of ​​each adjacent triangular mesh face. Indicates the first The vertex corresponding to the first The normal vectors of adjacent triangular mesh faces. , , They represent the first The vertex corresponding to the first The vertex coordinates of adjacent triangular mesh faces. Indicates the first The set of adjacent triangular mesh faces of each vertex;

[0024] The normal curvature includes the maximum normal curvature and the minimum normal curvature, and the normal direction includes the direction of maximum normal curvature and the direction of minimum normal curvature. The methods for calculating the normal curvature and the normal direction include:

[0025] With the first Construct a two-dimensional local coordinate system with each vertex as the origin, and calculate the X-axis basis vector and Y-axis basis vector of the two-dimensional local coordinate system. The expressions are as follows:

[0026] ;

[0027] ;

[0028] in, For the first The X-axis basis vectors of a two-dimensional local coordinate system are constructed with vertices as the origin. For the first Construct the Y-axis basis vector of a two-dimensional local coordinate system with each vertex as the origin. For any one of the following: Non-collinear vectors;

[0029] Calculate the first in the two-dimensional local coordinate system. The curvature tensor of each vertex corresponding to the adjacent triangular mesh surface is expressed as follows:

[0030] ;

[0031] ;

[0032] in, Indicates the first The vertex corresponding to the first The curvature tensor of an adjacent triangular mesh surface, , , All are the first The vertex corresponding to the first The second type of basic quantity of adjacent triangular mesh faces;

[0033] According to the The curvature tensor of the triangular mesh surface containing each vertex is calculated from the curvature tensor of the adjacent surface triangular mesh surface. Its expression is as follows:

[0034] ;

[0035] in, Indicates the first The curvature tensor of the triangular mesh facet of the surface containing each vertex. , , All are the first The second type of fundamental quantity for the triangular mesh facet of the surface containing each vertex. Indicates the first The vertex corresponding to the first Voronoi area weights for adjacent triangular mesh faces;

[0036] The first Substituting the second type of fundamental quantities of the triangular mesh facets containing the vertices, we obtain the th... The expressions for the maximum normal curvature, minimum normal curvature, maximum normal curvature direction, and minimum normal curvature direction of each vertex are:

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] in, For maximum normal curvature, For minimum normal curvature, For the direction of maximum normal curvature, The direction of minimum normal curvature, Indicates intermediate parameters.

[0043] Furthermore, the three-dimensional local coordinate system uses the source point as the origin, the basis vectors in the tangent plane that are aligned with the X-axis or Y-axis of the global coordinate system as the X-axis basis vectors, the normal vector of the vertex where the source point is located as the Z-axis basis vectors, and the unit vectors of the cross product Z-axis and X-axis as the Y-axis basis vectors.

[0044] Furthermore, the expression for the residual height model is:

[0045] ;

[0046] in, represents a geodesic step length, represents a tool circular arc radius, represents a residual height, for a convex surface, for a concave surface, represents a maximum normal curvature, represents a minimum normal curvature, represents a tangent direction, represents a tangent direction between the maximum normal curvature direction and the tangent direction, represents a normal vector of the th vertex, represents a half-plane normal vector, represents an X-axis base vector of a three-dimensional local coordinate system, represents a Y-axis base vector of a three-dimensional local coordinate system, represents a rotation angle, represents a curvature radius of a triangular mesh surface, when the vertex is a source point, ; when the vertex is not a source point, ;

[0047] wherein the determination method of the convex surface and the concave surface is:

[0048] calculating a directional curvature, and an expression of the directional curvature is:

[0049] ;

[0050] wherein, represents a directional curvature, represents a tangent direction between the maximum normal curvature direction and the tangent direction, represents a maximum normal curvature, represents a minimum normal curvature.

[0051] when the directional curvature is greater than 0, the surface is a convex surface, and when the directional curvature is less than 0, the surface is a concave surface.

[0052] Further, the generation method of the first contour line comprises:

[0053] calculating a first circle track point number according to a rotation angle increment, and an expression of the first circle track point number is:

[0054] ;

[0055] wherein, represents a first circle track point number, represents a rotation angle increment;

[0056] The interval between adjacent contour lines is calculated according to the number of trajectory points in the first circle and the geodesic step length, and the expression is as follows:

[0057]

[0058] Wherein, represents the interval between adjacent contour lines, represents the geodesic step length;

[0059] A plurality of first contour lines are generated on the triangular mesh surface according to the interval between adjacent contour lines.

[0060] Further, one of the trajectory points in the previous circle is selected as a predecessor point, and the geodesic step length of the predecessor point is determined according to the residual height model based on the geometric parameters of the predecessor point, and a second contour line is generated, comprising:

[0061] One of the trajectory points in the previous circle is selected, if the trajectory point is on the vertex of the triangular mesh of the surface, the trajectory point is taken as the predecessor point, if the trajectory point is not on the vertex of the triangular mesh of the surface, the vertex of the triangular mesh of the surface closest to the trajectory point is taken as the predecessor point;

[0062] The geodesic step length of the predecessor point is calculated according to the geometric parameters of the predecessor point through the residual height model;

[0063] The geodesic distance of the second contour line is obtained by adding the geodesic step length of the predecessor point to the geodesic distance of the predecessor point;

[0064] The second contour line is generated on the triangular mesh of the surface according to the geodesic distance of the second contour line.

[0065] Further, before the second contour line is generated on the triangular mesh of the surface according to the geodesic distance of the second contour line, it further comprises: comparing the geodesic distance of the second contour line with the geodesic distance of the predecessor point, so that the geodesic distance of the second contour line satisfies the neighborhood constraint range, and the expression of the neighborhood constraint range is as follows:

[0066]

[0067] Wherein, represents the geodesic distance of the second contour line, represents the geodesic distance of the predecessor point, represents the interval between adjacent contour lines;

[0068] If the geodesic distance of the second contour line exceeds the neighborhood constraint range, the geodesic distance of the second contour line is changed to the endpoint value of the nearest neighborhood constraint range.

[0069] Further, the generation methods of the first intersection point and the second intersection point are the same, both comprising:

[0070] ​​According to the three-dimensional local coordinate system, the projection of each vertex on the corresponding contour surface about the half plane is calculated, and the expression is as follows:

[0071] ;

[0072] Wherein, The projection of the vertex about the half plane is represented, The vector from the source point to the vertex is represented, The half plane normal vector is represented;

[0073] The projection of each vertex about the half plane is traversed, if there is a vertex whose projection about the half plane is 0, the vertex is the first intersection point or the second intersection point, if there is no vertex whose projection about the half plane is 0, two adjacent vertices whose projections about the half plane are of opposite signs are found, and the first intersection point or the second intersection point is calculated by linear interpolation.

[0074] Compared with the prior art, the beneficial effects achieved by the present application are:

[0075] The complex curved surface turning machining path planning method based on the geodesic map provided by the present application constructs a geodesic map based on the geodesic distance on the curved surface, combines the effective radius of the tool and the residual height constraint, realizes accurate perception and adaptive control of the geometric features of the complex curved surface, and dynamically adjusts the trajectory step length; and directly arranges the tool path on the curved surface to generate a tool trajectory with consistent residual height distribution, so that the tool can maintain a constant material removal amount during the machining process, and the problems of overcutting or undercutting and projection distortion are avoided. BRIEF DESCRIPTION OF DRAWINGS

[0076] Figure 1 It is a flowchart of the complex curved surface turning machining path planning method based on the geodesic map in an embodiment of the present application;

[0077] Figure 2 It is a flowchart of generating the first circle of trajectory points in the complex curved surface turning machining path planning method based on the geodesic map in an embodiment of the present application;

[0078] Figure 3 It is a flowchart of generating the first circle of trajectory points in the complex curved surface turning machining path planning method based on the geodesic map in an embodiment of the present application;

[0079] Figure 4 It is a model diagram of discretely representing the measured curved surface by a triangular mesh in the complex curved surface turning machining path planning method based on the geodesic map in embodiment 2 of the present application;

[0080] Figure 5This is a schematic diagram of the geodesic map composed of the geodesic distances from each vertex to the source point in the complex surface turning machining path planning method based on the geodesic map in Embodiment 2 of the present invention;

[0081] Figure 6 This is a schematic diagram of the three-dimensional local coordinate system in the complex surface turning machining path planning method based on survey map in Embodiment 2 of the present invention;

[0082] Figure 7 This is a contour line diagram of the first trajectory points in the complex surface turning machining path planning method based on survey map in Embodiment 2 of the present invention;

[0083] Figure 8 This is a schematic diagram showing the distribution of the first trajectory points in the complex surface turning machining path planning method based on survey map in Embodiment 2 of the present invention;

[0084] Figure 9 This is a schematic diagram of the distribution of trajectory points in the complex surface turning machining path planning method based on survey map in Embodiment 2 of the present invention;

[0085] Figure 10 This is a schematic diagram of the machining path in the complex surface turning machining path planning method based on survey map in Embodiment 2 of the present invention. Detailed Implementation

[0086] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0087] Example 1:

[0088] like Figure 1 As shown, this embodiment of the invention provides a method for planning machining paths for complex curved surfaces based on survey maps, including the following steps:

[0089] S1. Obtain the surface to be machined and its machining quality parameters, including residual height, tool radius, number of trajectory points, and rotation angle increment.

[0090] S2. The surface to be processed is discretized using a triangular mesh to obtain a surface triangular mesh. The surface triangular mesh is composed of multiple triangular mesh patches, and the vertices of adjacent triangular mesh patches are shared.

[0091] When selecting the turning center of the curved surface as the source point, it should be noted that if the source point is not a vertex of the curved surface triangular mesh, the mesh needs to be refined. Refining the mesh means increasing the mesh density by adding new vertices to the existing edges or faces on the basis of the original triangular mesh (some triangular mesh patches can be subdivided). Therefore, in this embodiment, vertices are added at the turning center to refine the curved surface triangular mesh until the source point is on a vertex of the curved surface triangular mesh.

[0092] S3. Calculate the geodesic distance from each vertex to the source point and the geometric parameters of each vertex in the curved triangular mesh. The geodesic distance from each vertex to the source point forms a geodesic map set in the global coordinate system.

[0093] In this embodiment, the MMP method is used to calculate the geodesic distance. The MMP algorithm is a classic and stable precise path tracing algorithm. It completes path expansion and distance calculation by propagating a "window" containing geodesic information on an unfolded curved triangular mesh. The geodesic distance from the source point to any point in the window is calculated using its Euclidean distance.

[0094] In this embodiment, the geometric parameters include the normal vector, normal curvature, and normal direction, and their calculation methods are as follows:

[0095] The normal vector is calculated by weighted averaging of the normal vectors of adjacent triangular mesh faces, and its expression is:

[0096] ;

[0097] ;

[0098] in, Indicates the first The normal vector of each vertex. Indicates the first The vertex corresponding to the first The area of ​​each adjacent triangular mesh face. Indicates the first The vertex corresponding to the first The normal vectors of adjacent triangular mesh faces. , , They represent the first The vertex corresponding to the first The vertex coordinates of adjacent triangular mesh faces. Indicates the first A set of adjacent triangular mesh faces of each vertex.

[0099] Normal curvature includes maximum normal curvature and minimum normal curvature, and normal direction includes the direction of maximum normal curvature and the direction of minimum normal curvature. The methods for calculating normal curvature and normal direction include:

[0100] With the first Construct a two-dimensional local coordinate system with each vertex as the origin, and calculate the X-axis and Y-axis basis vectors of the two-dimensional local coordinate system. Their expressions are as follows:

[0101] ;

[0102] ;

[0103] in, For the first Construct the X-axis basis vectors of a two-dimensional local coordinate system with each vertex as the origin. For the first Construct the Y-axis basis vector of a two-dimensional local coordinate system with each vertex as the origin. For any one of the following: Non-collinear vectors.

[0104] In a two-dimensional local coordinate system, calculate the first... The curvature tensor of each vertex corresponding to the adjacent triangular mesh surface is expressed as follows:

[0105] ;

[0106] ;

[0107] in, Indicates the first The vertex corresponding to the first The curvature tensor of adjacent triangular mesh faces, , , All are the first The vertex corresponding to the first The second type of basic quantity of adjacent triangular mesh faces.

[0108] According to the The curvature tensor of the triangular mesh surface containing each vertex is calculated from the curvature tensor of the adjacent surface triangular mesh surface. Its expression is as follows:

[0109] ;

[0110] in, Indicates the first The curvature tensor of the triangular mesh facet of the surface containing each vertex. , , All are the first The second type of fundamental quantity for the triangular mesh facet of the surface containing each vertex. Indicates the first The vertex corresponding to the first Voronoi area weight of an adjacent triangle mesh patch.

[0111] Substitute the second type of basic quantity of the triangular mesh patch where the i-th vertex is located into the formula, and calculate the maximum normal curvature, minimum normal curvature, maximum normal curvature direction and minimum normal curvature direction of the i-th vertex, whose expressions are as follows:

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] wherein, is the maximum normal curvature, is the minimum normal curvature, is the maximum normal curvature direction, is the minimum normal curvature direction, represents an intermediate variable.

[0118] S4, establish a three-dimensional local coordinate system at the source point according to the geometric parameters of each vertex, and the construction method of the three-dimensional local coordinate system is to take the source point as the origin, take the basis vector aligned with the X axis or Y axis of the global coordinate system in the tangent plane as the X axis basis vector, take the normal vector of the vertex where the source point is located as the Z axis basis vector, and take the unit vector of the cross product of the Z axis and the X axis as the Y axis basis vector.

[0119] S5, construct a residual height model using the surface machining quality parameters and the three-dimensional local coordinate system, and the expression of the residual height model is as follows:

[0120] ;

[0121] wherein, represents the radius of curvature of the vertex, when the vertex is the source point, the curvature of the source point is the average curvature , and the calculation expression of the radius of curvature of the source point is as follows: ; when the vertex is not the source point, , represents the geodesic step length, represents the tool circular arc radius, represents the residual height, for convex surfaces, for concave surfaces, represents the maximum normal curvature,​​ Indicates the minimum normal curvature. Indicates the tangential direction. Indicates the tangential direction With the direction of maximum normal curvature The angle between them Indicates the first The normal vector of each vertex. Represents the normal vector of the half-plane. This represents the X-axis basis vector of the three-dimensional local coordinate system. This represents the Y-axis basis vector of the three-dimensional local coordinate system. This represents the rotation angle. When the vertex is the source point, the rotation angle is 0° or 360°. When the vertex is not the source point, the rotation angle is the increment of the rotation angle accumulated by the vertex index, that is, the vertex index multiplied by the rotation angle increment.

[0122] For use in residual height models Number or The number depends on whether the surface to be processed is a convex or concave surface. In this embodiment, the method for determining whether a surface is convex or concave is as follows:

[0123] The directional curvature is calculated using Euler's formula, and its expression is as follows:

[0124] ;

[0125] in, Indicates directional curvature. Indicates the tangential direction With the direction of maximum normal curvature The angle between them Indicates the maximum normal curvature. This represents the minimum normal curvature.

[0126] When the directional curvature is greater than 0, the surface is a convex surface; when the directional curvature is less than 0, the surface is a concave surface.

[0127] S6, Combination Figure 2 The geodesic step length can be calculated by substituting the known surface machining quality parameters and the geometric parameters of the source point into the residual height model.

[0128] The number of trajectory points in the first revolution is calculated based on the rotation angle increment (one of the known surface machining quality parameters), and its expression is:

[0129] ;

[0130] in, This indicates the number of points on the first lap of the trajectory. This indicates the increment of the rotation angle.

[0131] The interval between adjacent contour lines is calculated according to the number of trajectory points in the first circle and the initial geodesic step, and the expression is as follows:

[0132]

[0133] wherein, represents the interval between adjacent contour lines, represents the geodesic step.

[0134] The first contour line is generated on the triangular mesh surface according to the interval between adjacent contour lines.

[0135] The projection of each vertex on the first contour line on the half plane is calculated according to the three-dimensional local coordinate system, and the expression is as follows:

[0136]

[0137] wherein, represents the projection of the vertex on the half plane, represents the vector from the source point to the vertex, represents the normal vector of the half plane.

[0138] The projection of each vertex on the half plane is traversed, if there is a vertex whose projection on the half plane is 0, the vertex is the first intersection point or the second intersection point; if there is no vertex whose projection on the half plane is 0, two adjacent vertices whose projections on the half plane are of opposite signs are found, and the first intersection point is calculated by linear interpolation.

[0139] Therefore, the first contour line generates multiple lines at one time, each first contour line corresponds to generate a first intersection point, and all the first intersection points form the first circle of trajectory points.

[0140] S7, in combination Figure 3 , one trajectory point in the last circle of trajectory points is selected, if the trajectory point is at the vertex of the triangular mesh of the surface, the trajectory point is taken as the predecessor point, if the trajectory point is not at the vertex of the triangular mesh of the surface, the nearest vertex of the triangular mesh of the surface to the trajectory point is taken as the predecessor point.

[0141] The geodesic step of the predecessor point is calculated by the residual height model according to the geometric parameters of the predecessor point.

[0142] The geodesic distance of the second contour line is obtained by adding the geodesic step of the predecessor point to the geodesic distance of the predecessor point.

[0143] In the embodiment, the geodesic distance of the second contour line also needs to be compared with the geodesic distance of the predecessor point, so that the geodesic distance of the second contour line meets the neighborhood constraint range, and the expression of the neighborhood constraint range is as follows:

[0144] ​​​

[0145] wherein, represents the geodesic distance of the second contour line, represents the geodesic distance of the predecessor point, represents the distance between adjacent contour lines.

[0146] If the geodesic distance of the second contour line exceeds the neighborhood constraint range, the geodesic distance of the second contour line is changed to the end point value of the nearest neighborhood constraint range.

[0147] A second contour line is generated on the curved triangular mesh according to the geodesic distance of the second contour line. A second intersection point is generated by the second contour line, and the method is the same as that of the first intersection point, which will not be described here.

[0148] It should be noted that one second contour line is generated each time, and one second intersection point is generated for each second contour line.

[0149] S8, repeat S7-S8, sequentially select the next trajectory point in the previous circle of trajectory points, until all trajectory points in the previous circle of trajectory points are selected, to obtain a plurality of second intersection points, and all second intersection points form a next circle of trajectory points.

[0150] S9, repeat S7-S9 until all circle trajectory points are obtained, sequentially connect each circle of trajectory points to obtain a turning tool trajectory spiral line.

[0151] Example 2:

[0152] Based on example 1, this embodiment is for tool path planning of a star-shaped curved triangular mesh model as shown in Figure 4 The model has a total of 10734 vertices and 20482 triangular mesh patches.

[0153] It should be noted that all the following data units are in the International System of Units, and the length unit is mm and the angle unit is °.

[0154] The turning center of the curved surface is selected as the source point, as shown in Figure 4 The source point coordinates are (5.1160, 0.0046, 5.028), the geodesic distance of each vertex in the curved triangular mesh to the source point is calculated to generate a geodesic map, as shown in Figure 5 . Figure 5 The color from blue to red represents the gradual increase of the geodesic distance of each vertex on the curved surface to the source point.

[0155] The geometric parameters of all vertices in the curved triangular mesh are calculated, and in this embodiment, the values of the normal vector, principal curvature and corresponding principal direction of the source point are respectively: (0, -1, 0), = 0.1563, = 0.1563, (-0.9985, 0, -0.0543), (-0.0543, 0, 0.998).

[0156] Combining Figure 6 , a three-dimensional local coordinate system is constructed at the source point.

[0157] Combining the surface machining quality parameters and the three-dimensional local coordinate system, a residual height model is constructed. In this embodiment, the number of track points is 41, the curvature radius R of the source point is 6.3980, the residual height h is 0.01, and the tool circular arc radius r is 0.1. The geodesic step length d is obtained by substituting the residual height model, that is, d = 0.09.

[0158] In this embodiment, the rotation angle increment is 2°, and the number of first circle track points is calculated to be 180 including the source point.

[0159] The adjacent contour interval s = 0.0005 is calculated, and the contour generated with this interval is shown in FIG. 6. Figure 7

[0160] The projection of the points on the contour on the half plane is calculated , and the first circle driving point generated by using linear interpolation to accurately calculate the intersection position is shown in FIG. 7. Figure 8

[0161] According to the number of track points in the surface machining quality parameters, the track points in the first circle are sequentially used as driving points to recursively generate all circle track points, as shown in FIG. 8. Figure 9

[0162] Combining Figure 10 , all circle track points generated are sequentially connected to obtain a complete turning tool track spiral line, Figure 10 , and the red line in the figure is the machining path.

[0163] As can be seen from Figure 10 , at the junction of the concave and convex regions of the model, the track density shows obvious adaptive changes. In the concave surface region, the track spacing is appropriately increased to reduce the number of machining paths and improve efficiency; and after entering the convex surface region, the track density gradually increases to effectively ensure the machining quality and residual height control in the region with sharp curvature changes, fully embodying the response ability of the method to local geometric information. Moreover, the track transitions smoothly between different regions without obvious mutations or oscillation phenomena, indicating that the neighborhood constraint strategy plays a good role in suppressing track fluctuations, especially in regions with sharp curvature changes, the track still maintains high continuity and consistency, verifying that the method has strong robustness and stability when dealing with complex geometric features.

[0164] ​​​The above merely describes the preferred embodiments of the present application, and it should be pointed out that, for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present application, and these improvements and modifications should also be considered as the protection scope of the present application.

Claims

1. A geodesic map-based complex curved surface turning machining path planning method, characterized in that, The method comprises the following steps: S1, obtaining a to-be-processed curved surface and a curved surface machining quality parameter; S2, obtaining a curved surface triangular mesh by discretely representing the to-be-processed curved surface by using a triangular mesh, and selecting a curved surface turning center as a source point; S3, calculating geometric parameters of each vertex and the source point in the curved surface triangular mesh and geodesic distances from each vertex to the source point; S4, establishing a three-dimensional local coordinate system at the source point; S5, constructing a residual height model by using the curved surface machining quality parameter and the three-dimensional local coordinate system; S6, determining a geodesic step according to the residual height model and generating a plurality of first contour lines based on the geometric parameters of the source point, and generating a first circle of trajectory points by generating a first intersection point corresponding to each first contour line; S7, selecting one trajectory point in the last circle of trajectory points as a predecessor point, determining a geodesic step of the predecessor point according to the residual height model based on the geometric parameters of the predecessor point, and generating a second intersection point by generating a second contour line; S8, repeating S7-S8 until each trajectory point in the previous circle is sequentially selected, to obtain a next circle of trajectory points composed of a plurality of second intersection points; S9, repeating S7-S9 until all circles of trajectory points are generated, and sequentially connecting each circle of trajectory points to obtain a turning tool trajectory spiral line.

2. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, The curved surface machining quality parameter comprises a residual height, a tool circular arc radius, a number of trajectory point circles and a rotation angle increment.

3. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, In the step of selecting the curved surface turning center as the source point, if the source point is not a vertex of the curved surface triangular mesh, the curved surface triangular mesh is refined until the source point is located at a vertex of the curved surface triangular mesh.

4. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, The geometric parameters comprise a normal vector, a normal curvature and a normal direction; The normal vector is calculated by weighted average of normal vectors of adjacent triangular mesh facets, and an expression thereof is: ； ； wherein, denotes a normal vector of the th vertex, denotes an area of the th adjacent triangle mesh patch corresponding to the th vertex, denotes a normal vector of the th adjacent triangle mesh patch corresponding to the th vertex, , , denote vertex coordinates of the th adjacent triangle mesh patch corresponding to the th vertex, respectively, denotes a set of adjacent triangle mesh patches of the th vertex. The normal curvature comprises a maximum normal curvature and a minimum normal curvature, and the normal direction comprises a maximum normal curvature direction and a minimum normal curvature direction, and a calculation method of the normal curvature and the normal direction comprises: With the first Construct a two-dimensional local coordinate system with each vertex as the origin, and calculate the X-axis and Y-axis basis vectors of the two-dimensional local coordinate system. Their expressions are as follows: ； ； wherein, is the X-axis base vector of the two-dimensional local coordinate system with the is the Y-axis base vector of the two-dimensional local coordinate system with the is the X-axis base vector of the two-dimensional local coordinate system with the is the Y-axis base vector of the two-dimensional local coordinate system with the is any one vector not collinear with . Calculate the first in the two-dimensional local coordinate system. The curvature tensor of each vertex corresponding to the adjacent triangular mesh surface is expressed as follows: ； ； wherein, denotes the curvature tensor of the th adjacent triangle mesh patch corresponding to the th vertex, , , are the second type of fundamental quantities of the th adjacent triangle mesh patch corresponding to the th vertex. According to the first The curvature tensor of the triangular mesh surface where the vertex is located is calculated according to the curvature tensors of the adjacent triangular mesh surface patches corresponding to the vertex, and the expression is as follows: ； in, Indicates the first The curvature tensor of the triangular mesh facet of the surface containing each vertex. , , All are the first The second type of fundamental quantity for the triangular mesh facet of the surface containing each vertex. Indicates the first The vertex corresponding to the first Voronoi area weights for adjacent triangular mesh faces; The first Substituting the second type of fundamental quantities of the triangular mesh facets containing the vertices, we obtain the th... The expressions for the maximum normal curvature, minimum normal curvature, maximum normal curvature direction, and minimum normal curvature direction of each vertex are: ； ； ； ； ； wherein is the maximum principal curvature, is the minimum principal curvature, is the direction of the maximum principal curvature, is the direction of the minimum principal curvature, denotes an intermediate variable.

5. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, The three-dimensional local coordinate system takes the source point as an origin, takes a basis vector aligned with an X-axis or a Y-axis of a global coordinate system in a tangent plane as an X-axis basis vector, takes a normal vector of a vertex where the source point is located as a Z-axis basis vector, and takes a unit vector of a cross product of the Z-axis and the X-axis as a Y-axis basis vector.

6. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, An expression of the residual height model is: ； wherein, represents a geodesic step length, represents a tool circular arc radius, represents a residual height, for convex curved surface, for concave curved surface, represents a maximum normal curvature, represents a minimum normal curvature, represents a tangent direction, represents a tangent direction between the maximum normal curvature direction and the tangent direction, represents a normal vector of the th vertex, represents a half-plane normal vector, represents an X-axis base vector of a three-dimensional local coordinate system, represents a Y-axis base vector of a three-dimensional local coordinate system, represents a rotation angle, represents a curvature radius of a vertex, when the vertex is a source point, ; when the vertex is not a source point, ; A determination method of the convex curved surface and the concave curved surface comprises: calculating a directional curvature, and an expression thereof is: ； wherein, denotes the direction curvature, denotes the tangential direction between the maximum normal curvature direction denotes the maximum normal curvature, denotes the minimum normal curvature;​ When the directional curvature is greater than 0, the curved surface is a convex curved surface, and when the directional curvature is less than 0, the curved surface is a concave curved surface.

7. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, A generation method of the first contour line comprises: calculating a number of first circle trajectory points according to the rotation angle increment, and an expression thereof is: ； wherein, represents the first number of track points, represents the rotation angle increment; calculating a distance between adjacent contour lines according to the number of first circle trajectory points and the geodesic step, and an expression thereof is: ； wherein represents the distance between adjacent contour lines, represents the geodesic step; generating a plurality of first contour lines on the triangular mesh curved surface according to the distance between adjacent contour lines.

8. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, The step of selecting one trajectory point in the last circle of trajectory points as a predecessor point, determining a geodesic step of the predecessor point according to the residual height model based on the geometric parameters of the predecessor point, and generating a second intersection point by generating a second contour line comprises: Select one of the trajectory points in the last circle of trajectory points, if the trajectory point is on the vertex of the curved triangular mesh, the trajectory point is taken as the predecessor point, if the trajectory point is not on the vertex of the curved triangular mesh, the vertex of the curved triangular mesh closest to the trajectory point is taken as the predecessor point; According to the geometric parameters of the predecessor point, the geodesic step length of the predecessor point is calculated through the residual height model; The geodesic distance of the second contour is obtained by adding the geodesic step length of the predecessor point to the geodesic distance of the predecessor point; The second contour is generated on the curved triangular mesh according to the geodesic distance of the second contour.

9. The geodesic map-based complex curved surface turning machining path planning method according to claim 8, characterized in that, Before the second contour is generated on the curved triangular mesh according to the geodesic distance of the second contour, the method further comprises: comparing the geodesic distance of the second contour with the geodesic distance of the predecessor point, so that the geodesic distance of the second contour satisfies the neighborhood constraint range, and the expression of the neighborhood constraint range is: ； wherein, represents a geodesic distance of the second contour, represents a geodesic distance of the predecessor point, represents a distance between adjacent contours; If the geodesic distance of the second contour exceeds the neighborhood constraint range, the geodesic distance of the second contour is changed to the endpoint value of the nearest neighborhood constraint range.

10. The geodesic map-based complex curved surface turning machining path planning method according to claim 1, characterized in that, The generation methods of the first intersection point and the second intersection point are the same, and both comprise: According to the three-dimensional local coordinate system, the projection of each vertex on the corresponding contour on the half plane is calculated, and the expression is: ； wherein, denotes the projection of the vertex with respect to the half-plane, denotes the vector from the origin to the vertex, denotes the half-plane normal vector; If there is a vertex with a projection on the half plane of 0, the vertex is the first intersection point or the second intersection point; if there is no vertex with a projection on the half plane of 0, two adjacent vertices with different signs of the projection on the half plane are found, and the first intersection point or the second intersection point is calculated by linear interpolation.

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