A Path Planning Method for Non-Iso-Octave Developable Rotational Surfaces

Abstract

This invention provides a path planning method for non-equidistant developable surfaces of revolution. This method maps a three-dimensional surface to a two-dimensional plane, leveraging the advantages of planar path planning to solve key problems in the mapping process. This achieves efficient, accurate, and flexible path planning, and then remaps the planned path in the two-dimensional plane back onto the three-dimensional non-equidistant developable surface of revolution. This method provides strong technical support for the metal additive manufacturing of complex surfaces, especially for aerospace components such as thrusters and propellers, and has broad application prospects.

Description

Technical Field

[0001] This invention belongs to the field of electric arc additive manufacturing technology, and in particular, it is a path planning method for non-equidistant developable rotating surfaces. Background Technology

[0002] In the prior art, when printing components on regular rotating surfaces, a surface equidistant path planning algorithm based on voxelization and surface integration can be used to obtain equidistant contour offset paths and reciprocating straight line paths on layered surfaces.

[0003] However, existing technologies suffer from technical problems such as low computational efficiency and limited path types.

[0004] Specifically, existing technologies require voxelization of the sliced ​​surface, which involves a large number of discretization operations. This process is not only computationally intensive but also complex, resulting in low computational efficiency and extended overall process planning cycles, making it difficult to meet the demands of high-efficiency production. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention provides the following technical solutions.

[0006] A path planning method for non-equidistant developable surfaces of revolution includes: surface layering: by slicing the target surface and applying offset processing to the slice contours, the slice contours required for process planning are accurately obtained; parameter correspondence establishment: a one-to-one correspondence is established between the Z-axis coordinate value of each contour point in the slice contour and its corresponding radius of curvature R, providing basic parameter support for subsequent mapping calculations; surface-plane mapping implementation: relying on the geometric characteristics of the surface of revolution, the three-dimensional surface slice contours are mapped to a two-dimensional plane, reducing the complexity of path planning; segmented contour reorganization optimization: to address the problem of path discontinuity caused by the segmentation of the slice contours by the unfolded generatrix during the mapping process, an innovative "segmented contour point translation strategy" is proposed, which performs directional translation processing on the segmented contour point set to achieve efficient integration of the segmented contours; after the path planning in the two-dimensional plane is completed, the planned path is reverse-mapped to the original non-equidistant developable surface of revolution, finally completing the full-process path planning for this type of complex surface component.

[0007] Specifically, the present invention provides a path planning method for a non-equidistant developable surface of revolution, comprising the following steps: S1. Perform layer processing on the non-equidistant developable surface of revolution to obtain multi-layer slice contours. Offset each slice contour at an equal distance along the normal direction of each point on the surface to obtain the surface contour point set of each slice contour. S2. Establish the Z-axis coordinate value of each point in the current layer's surface contour point set. i Its corresponding radius of curvature R i The parameter correspondence between them; S3. Based on the parameter correspondence, the surface of the body of revolution is divided and unfolded with the generatrix of the non-equidistant expandable body of revolution as the reference. The circular contour of each layer of the surface is flattened into a straight line. The surface contour point set of each layer is mapped onto a two-dimensional plane to obtain the corresponding planar contour point set. S4. For the set of planar contour points, identify the dividing points on the plane, and perform directional translation processing on the divided point set to obtain the integrated planar contour point set; perform path planning within the integrated planar contour point set. S5. Map the path planning result directly back to the surface contour point set of each layer in step S1 to obtain the final surface path.

[0008] Specifically, step S1 involves: using the surface of revolution as the slicing reference plane, solving for the intersection lines between it and each triangular facet in the STL model, thereby generating the slicing profile and obtaining the point set of the surface of revolution profile; offsetting the surface of revolution at equal intervals along the normal direction at each point to obtain a new slicing profile, and performing slicing profile calculations sequentially to obtain the surface profile point set of all layers.

[0009] In step S1, the non-equidistant developable surface of revolution is in contrast to an equidistant developable surface of revolution. An equidistant developable surface of revolution is one whose surface unfolds without distortion. For an equidistant developable surface (also an equidistant developable solid of revolution), the distance between two distinct points on the surface and the unfolded plane remains unchanged after unfolding. For a non-equidistant developable surface (also a non-equidistant developable solid of revolution), the distance between two points changes due to distortion after unfolding.

[0010] In step S1, the slice outlines of each layer are offset at equal intervals along the normal direction of each point on the surface. This refers to the principle of unfolding the plane of the solid of revolution, which is the process of unfolding the slice outlines of each layer along the normal direction of each point on the surface of the solid of revolution.

[0011] Specifically, step S2 involves: for each layer of surface contour point set, traversing the point set to extract the maximum Z-axis. max Value point and minimum Z min The position index of the value point; for the interval [Z min Z max The arbitrary surface profile point set P in ] i (x i y i , z i The points of Z are established. i Its corresponding radius of curvature R i The correspondence is used to obtain the bus function. .

[0012] Step S3 includes busbar curve fitting and planar coordinate transformation. The busbar curve fitting is performed using a cubic B-spline curve to fit the Z-axis. i With R i The mapping relationship is obtained by fitting the corresponding relationship, and the fitting function formula is as follows: ; Among them, Z i It is the current height value, expressed via Z. i To find the current R i Value, N i,3 (Z i The basis functions of a cubic B-spline are: , .

[0013] The planar coordinate transformation adopts a combination of generatrix parameterization and rotation angle mapping. The specific steps are as follows: The arc length of the generatrix at any point As the vertical axis Y of the plane, the rotation angle θ is mapped to the horizontal axis X, R(Z) i Mapped to the Z-axis, the coordinate transformation relationship is as follows: .

[0014] The method for identifying contour segmentation points in step S4 is as follows: starting from the selected contour starting point, traverse all contour points and set a threshold. Calculate the difference in x-coordinates between two adjacent points. ,like If so, then the current point and its adjacent points are determined to be the dividing points.

[0015] In this invention, the directional translation process in step S4 is as follows: (1) Identification of contour segmentation points: Starting from the selected contour starting point, traverse all contour points and set a threshold. Based on geometric properties, it is easy to see that adjacent dividing points are symmetrical about the line X=0. Calculate the difference in x-coordinates between two adjacent points. , where x k Let x be the x-coordinate of the current point. k+1 This is the subsequent x-coordinate. If If so, then the current point and its adjacent points are determined to be the dividing points.

[0016] (2) Threshold Selection criteria: As can be seen from the above. The value of is related to the R value corresponding to the current coordinate point, and changes as the R value of the current coordinate point changes. Considering adjacent points in a conventional profile The value is extremely small; in practice, it can be selected as... This ensures the accuracy and robustness of segmentation point identification.

[0017] (3) Classification of contour points on the left and right sides: After identifying the contour segmentation points, based on the sequential arrangement characteristics of the path points, the two sets of continuous points between and outside the segmentation points can be directly defined as the two segments after contour segmentation. To clarify the left and right nature of the two sets of points respectively, the following judgment rule is formulated: Select any path point in the two sets of points and compare the coordinates. If the x-coordinates of all path points in one set of points are less than the x-coordinates of all path points in the other set of points, then the set of points with smaller x-coordinate values ​​is the left path point, and vice versa.

[0018] (4) Recombination of segmented contours: The left and right partitions of each segmented contour point have been classified. Based on this, the segmented contours can be reconstructed by unidirectional coordinate translation. For any contour point P on the left... i Translate it along the positive X-axis by a distance D i = 2πR i (For any point on the right contour, translate -D along the negative X-axis) i This allows for the recombination of the outlines (e.g.) Figure 3 (As shown).

[0019] In this invention, the specific steps for mapping step S5 back to the surface contour point set of each layer in step S1 are as follows: for any point coordinate P(x) on the plane p y p , z p The transformed surface contour coordinates P'(x,y,z) are: ; Where Z1 satisfies =0, .

[0020] Z1 is the current height value, which is an unknown parameter and is obtained through the definite integral mentioned above.

[0021] In this invention, the non-equidistant developable surface of revolution is an approximately developable surface. Based on steps S1-S3, a one-to-one mapping relationship is constructed between the surface contour point set and the planar contour point set. Furthermore, the path planning on the planar contour point set constructed based on step S4 can be mapped back to the surface contour point set using the method in step S5.

[0022] This invention simplifies path planning on non-equidistant developable surfaces of revolution (such as B-spline surfaces of revolution) by mapping the solid of revolution to a plane, and then mapping it back to the surface after planar path planning. It solves the technical problem of contour segmentation by the unfolded generatrix during the mapping process of non-equidistant developable surfaces of revolution, achieving effective integration of the segmented contours. It simplifies the process planning flow for multi-axis arc additive manufacturing of approximately developable surface components, improving process planning efficiency. Specifically, path planning on non-equidistant developable surfaces of revolution is specifically applied to its multi-axis arc additive manufacturing process planning, and is particularly suitable for the precise fabrication of core components in key industrial fields such as aerospace, shipbuilding, and energy equipment, such as the manufacturing scenarios of propellers and other components with stringent requirements for surface forming accuracy and manufacturing efficiency. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of a slice of the surface of a body of revolution in this invention; Figure 2 This is a schematic diagram of the approximate planar unfolding of the rotating body in this invention; Figure 3 This is a schematic diagram of the recombination of segmented contour point sets in this invention; Figure 4 This is a schematic diagram of the mapping of a planar path to a curved surface in this invention. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Figures 1 to 4 As shown, in a preferred embodiment, the present invention provides a path planning method for a non-equidistant developable surface of revolution, comprising the following steps: S1. Based on the contour solution model of sliced ​​components of a solid of revolution, see [link / reference] Figure 1 In the process planning, the surface of revolution is used as the slicing reference plane, such as... Figure 1 (b) Solve for the intersection lines between the surface of revolution and each triangular facet in the STL model to generate the slice profile. This intersection process can be equivalently viewed as an intersection operation between triangular facets. By offsetting the surface of revolution at equal intervals along the normal direction at each point, a new slice profile can be obtained. By performing slice profile calculations sequentially, the profile features of all layers can be obtained, such as... Figure 1 (c)

[0025] S2. Establish parameter correspondence: Construct a one-to-one correspondence between the Z-axis coordinate value of each contour point in the slice contour and its corresponding radius of curvature R. The specific operation is as follows: 1. For a slice contour, multiple coordinate points are closely arranged and connected end to end. Therefore, the maximum Z-axis of the surface contour is extracted by traversing the target point set. max Value point and minimum Z min Value point; 2. Establish the interval [Z] min Z max The relationship between Z and the radius of curvature R in the graph is derived from the generatrix function R. i =R(Z i For any point P in the interval, i (x i ,y i ,z i Z i The corresponding R i The value is: (1) S3. Surface-to-Plane Mapping Implementation: The definition of a surface of revolution is: a surface formed by rotating a generatrix around a given axis. Based on this geometric characteristic, surface-to-plane mapping can be implemented as follows: First, identify the generatrix corresponding to the solid of revolution, then unfold the surface of revolution using the generatrix as a reference—flattening the circular contour of each layer of the surface into an equivalent straight line, such as... Figure 2 (a) and (c) ultimately complete the mapping from the three-dimensional solid of revolution surface to the two-dimensional plane through the flattening of the generatrix (e.g., Figure 2 (b) The specific operation is as follows: (1) Curve fitting: The above S2 yields Z i The corresponding R i The corresponding values ​​are obtained by fitting a cubic B-spline curve, as shown in the following formula: (2) Among them, R(Z) i P represents the radius of curvature at the Z-axis coordinate of the contour point; i =(Z i R i ) represents the control vertex of the fit, N i,3 (Z i The basis functions of a cubic B-spline are: , (3) (2) Plane coordinate transformation: For non-equidistant developable solids of revolution (such as B-splines and parabolic solids of revolution), generatrix parameterization + rotation angle mapping is used: the arc length of the generatrix at any point is transformed. As the vertical axis Y of the plane, the rotation angle θ is mapped to the horizontal axis X, R(Z) i Mapped to the Z-axis, such as Figure 2 (b) The coordinate transformation relationship is: (4) S4. Segmented Contour Reassembly Optimization: Addressing the issue of path discontinuity caused by the segmentation of sliced ​​contours by the unfolded generatrix during mapping, an innovative "segmented contour point translation strategy" is proposed. This strategy performs directional translation on the segmented contour point set, achieving efficient integration of the segmented contours (e.g., ...). Figure 3 As shown in the image, the specific steps are as follows: 1. Through step S3 above, the planar mapping transformation of surface coordinates has been completed; 2. The key to identifying the path points on the left and right sides of the segmented contour is the acquisition of the segmentation points and the threshold. The value of .

[0026] (1) Identification of contour segmentation points: Starting from the selected contour starting point, traverse all contour points and set a threshold. Based on geometric properties, it is easy to see that adjacent dividing points are symmetrical about the line X=0. Calculate the difference in x-coordinates between two adjacent points. , where x k Let x be the x-coordinate of the current point. k+1 Let x be the x-coordinate of the subsequent point. If so, then the current point and its adjacent points are determined to be the dividing points.

[0027] (2). Threshold Selection criteria: As can be seen from the above. The value of is related to the R value corresponding to the current coordinate point, and changes as the R value of the current coordinate point changes. Considering adjacent points in a conventional profile The value is extremely small; in practice, it can be selected as... This ensures the accuracy and robustness of segmentation point identification.

[0028] (3) Classification of contour points on the left and right sides: After identifying the contour segmentation points, based on the sequential arrangement characteristics of the path points, the two sets of continuous points between and outside the segmentation points can be directly defined as the two segments after contour segmentation. To clarify the left and right nature of the two sets of points respectively, the following judgment rule is formulated: Select any path point in the two sets of points and compare the coordinates. If the x-coordinates of all path points in one set of points are less than the x-coordinates of all path points in the other set of points, then the set of points with smaller x-coordinate values ​​is the left path point, and vice versa.

[0029] (4) Recombination of Segmented Contours: Having completed the left and right partitioning and classification of each segmented contour point, the segmented contours can be reconstructed and joined together through unidirectional coordinate translation. For any contour point P on the left... i Translate it along the positive X-axis by a distance D i = 2πR i (For any point on the right contour, translate -D along the negative X-axis) iThis allows for the recombination of the outlines (e.g.) Figure 3 (As shown).

[0030] S5. After contour reconstruction and path planning are completed, no reverse translation operation is required. The planned path can be directly mapped back to the original surface, such as... Figure 4 The specific steps are as follows: After the planar path planning is completed, the planned path needs to be mapped back onto the curved surface. For any point coordinate P(x) on the plane... p ,y p ,z p Therefore, the transformed coordinates P'(x,y,z) are: (5) Where Z1 satisfies , .

[0031] It should be noted that if the planned outline is cut by a cylindrical generatrix, when mapping using the above method, part of the outline will be translated. After translation... However, since the translation amount is exactly an integer multiple of the circumference of the circle, there is no need to perform an additional reverse translation operation after path planning. The path can be accurately mapped back to the surface by directly substituting it into equation (5).

[0032] The above specific implementation method constructs a continuous correspondence of "ZR" by fitting cubic B-spline curves. Compared with the voxel-based discrete calculation of the prior art, it effectively reduces the parameter discretization error. At the same time, when mapping backward, it utilizes the characteristic that "the translation amount is equal to an integer multiple of the circumference" to avoid the contour offset caused by traditional rotation adjustment, ensuring that the final forming accuracy of the non-equidistant developable rotating surface meets the micron-level tolerance requirements of core components such as propellers and aerospace components.

[0033] The technical solution of this invention is applicable to metal printing equipment, such as robotic arms or CNC machine tools, welding torches, shielding gases, positioners, welding wires, etc. In implementation, it is particularly suitable for machine tools or other machining equipment that can establish corresponding coordinate systems for the robotic arm or CNC machine tool, such as tool coordinate systems or base coordinate systems. Specifically, model import, model slicing, path planning, etc., can be performed using appropriate process software.

[0034] The specific embodiments described in this invention are merely illustrative of the invention and are not intended to limit it. Those skilled in the art can make modifications to these embodiments without contributing any inventive step after reading this specification, but such modifications are protected by patent law as long as they fall within the scope of the claims of this invention.

Claims

1. A path planning method for a non-equidistant developable surface of revolution, characterized in that, Includes the following steps: S1. Perform layer processing on the non-equidistant developable surface of revolution to obtain multi-layer slice contours. Offset each slice contour at an equal distance along the normal direction of each point on the surface to obtain the surface contour point set of each slice contour. S2. Establish the Z-axis coordinate value of each point in the current layer's surface contour point set. i Its corresponding radius of curvature R i The parameter correspondence between them; S3. Based on the parameter correspondence, the surface of the solid of revolution is divided and unfolded with the generatrix of the solid of revolution as the reference. The circular contour of each layer of the surface is flattened into a straight line. The surface contour point set of each layer is mapped onto a two-dimensional plane to obtain the corresponding planar contour point set. S4. For the set of planar contour points, identify the dividing points on the plane, and perform directional translation processing on the divided point set to obtain the integrated planar contour point set; perform path planning within the integrated planar contour point set. S5. Map the path planning result directly back to the surface contour point set of each layer in step S1 to obtain the final surface path.

2. The method according to claim 1, characterized in that, Step S1 specifically involves: using the surface of revolution as the slicing reference plane, solving for the intersection lines between it and each triangular facet in the STL model, thereby generating the slicing profile and obtaining the point set of the surface of revolution profile; offsetting the surface of revolution at equal intervals along the normal direction at each point to obtain a new slicing profile, and performing slicing profile calculations sequentially to obtain the surface profile point set of all layers.

3. The method according to claim 1, characterized in that, Step S2 specifically involves: for each layer of surface contour point set, traversing the Z-axis coordinate values ​​of the point set and extracting the maximum Z-axis coordinate. max Value point and minimum Z min Value point; for the interval [Z] min Z max The arbitrary surface profile point set P in ] i (x i y i , z i The points of Z are established. i Its corresponding radius of curvature R i The correspondence is used to obtain the bus function. .

4. The method according to claim 3, characterized in that, Step S3 includes bus curve fitting and planar coordinate transformation.

5. The method according to claim 4, characterized in that, The busbar curve fitting is performed using a cubic B-spline curve to fit the Z... i With R i The mapping relationship is obtained by fitting the corresponding relationship, and the fitting function formula is as follows: ； Among them, R(Z) i P represents the radius of curvature at the Z-axis coordinate of the contour point; i =(Z i ,R i ) represents the control vertex of the fit, N i,3 (Z i ) is a cubic B-spline basis function, and N i,3 (Z i The cubic B-spline basis functions are: ， 。 6. The method according to claim 4, characterized in that, The planar coordinate transformation adopts a combination of generatrix parameterization and rotation angle mapping. The specific steps are as follows: The arc length of the generatrix at any point As the vertical axis Y of the plane, the rotation angle θ is mapped to the horizontal axis X, R(Z) i Mapped to the Z-axis, the coordinate transformation relationship is as follows: 。 7. The method according to claim 1, characterized in that, The method for identifying contour segmentation points in step S4 is as follows: starting from the selected contour starting point, traverse all contour points and set a threshold. Calculate the difference in x-coordinates between two adjacent points. ,like If x ∈ [a, b], then the current point and its adjacent points are determined as dividing points; where x ∈ [a, b]. k Let x be the x-coordinate of the current point. k+1 represents the x-coordinate of the subsequent adjacent points.

8. The method according to claim 7, characterized in that, The directional translation process in step S4 is as follows: In step S4, if If the current contour plane is mapped and then divided by the unfolded generatrix, then according to the Z described in step S2... i Value and radius of curvature R i Based on the parameter correspondence and combined with the principle of planar unfolding of the solid of revolution described in step S3, the contour point set on one side of the segmented contour is translated in the same direction; contour point P i Translation distance D i = 2πR i This allows for the recombination of the segmented contours.

9. The method according to claim 1, characterized in that, The specific steps for mapping step S5 back to the surface contour point set of each layer in step S1 are as follows: For any point coordinate P(x) on the plane... p y p , z p The transformed surface contour coordinates P'(x,y,z) are: ； Where Z1 satisfies , .

10. The method according to claim 1, characterized in that, The non-equidistant developable surface of revolution is an approximately developable surface.

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