A polishing path planning method for a complex curved surface

Abstract

The present application relates to a kind of complex surface grinding and polishing path planning method.Compared with the existing spiral trajectory planning method for complex hole surface, the method directly generates a non-bridging spiral trajectory to cover the entire three-dimensional hole surface, which avoids the problem of large amount of bridging between sub-regions caused by sub-region division, the generated spiral trajectory path is shorter, smoother, and the trajectory spacing is more consistent, and avoids the discontinuity and sharp turning of the trajectory, so that the motion path of the actuator is more smooth, the number of path discontinuities is also reduced, thereby avoiding the processing time and workpiece surface impact marks caused by tool lifting and actuator turning, therefore, the method generates trajectory for 3D surface grinding and polishing processing will improve 3D surface grinding and polishing processing efficiency and quality, reduce processing cost, improve tool and robot service life, with obvious economic significance.

Description

Technical Field

[0001] This invention relates to the field of polishing technology, specifically to a polishing path planning method for complex curved surfaces. Background Technology

[0002] Tool lifting and sharp turns in the polishing trajectory can cause stress fluctuations during processing, affecting the consistency of surface quality, which is particularly significant when polishing weakly rigid components. Using a helical trajectory for polishing large, complex 3D curved surfaces offers advantages such as fewer trajectory discontinuities and smoother turns. Generating shorter, smoother helical trajectories with fewer discontinuities is crucial for improving the polishing efficiency and surface quality consistency of large curved surfaces. However, for complex curved surfaces containing holes, traditional helical trajectory planning methods require adding extra boundaries to transform multi-connected regions into single-connected regions or divide them into several sub-regions. The trajectory must avoid these new extra boundaries, leading to problems such as inconsistent trajectory spacing, sharp trajectory turns, and numerous trajectory discontinuities requiring bridging. These issues result in large variations in material removal rate, longer processing paths, greater impact from actuator movement, and excessive tool lifting during the surface polishing process. This makes it difficult to optimize polishing parameters, increases polishing time, and reduces the consistency of polished surface quality, as well as the lifespan and accuracy of tools and robots.

[0003] Traditional methods for generating spiral trajectories mainly include methods based on medial axis trees, methods based on solving elliptic partial differential equations on disk-equivalent simply connected regions or toroidal-equivalent two connected regions, and methods based on conformal mapping of simply connected disks, squares, or two connected toroids. These methods either cannot be directly applied to complex porous surfaces, or when applied to complex porous surfaces, the generated paths are uneven, uneven, and discontinuous. Summary of the Invention

[0004] To address the problems of existing technologies, this invention provides a method for planning grinding and polishing paths for complex curved surfaces.

[0005] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: 1. A method for planning grinding and polishing paths for complex curved surfaces, the specific steps of which are as follows:

[0006] Step 1: Flatten the porous surface to be ground and polished onto a 2D plane using surface parametric methods.

[0007] Step 2: Determine whether there is a hole in the center of the region enclosed by the boundary line of the 2D parameter surface. If there is no hole, use disk slit mapping to map the 2D region containing the boundary onto the disk containing the slit using the conformal slit mapping method. If there is a hole, use annular slit mapping to map the 2D region containing the boundary onto the annular ring containing the slit using slit mapping.

[0008] Step 3: Generate a spiral trajectory with unequal spacing within the annular or circular domain of the slit mapping. The spiral trajectory is then mapped onto the 3D surface via the inverse mapping of the slit mapping to obtain the spiral machining trajectory of the 3D surface.

[0009] Step 4: Machining along the offset line of the curved surface to remove a small amount of machining residue.

[0010] Preferably, the surface parameterization method in step one is set to any one of the following: Boundary First Flattening (BFF) algorithm, Least square conformal maps (LSCM) algorithm, or discrete Ricci flow-based algorithm.

[0011] Preferably, the spiral trajectory in step three is formed by the offset of concentric circles with unequal radii. The offset speed of the spiral trajectory and the radius of the concentric circles are adjusted to avoid the generated unequal-spaced spiral lines intersecting with the slits in the image domain.

[0012] Preferably, in step three, it is necessary to check the overlapping and uncovered areas of the spiral processing trajectory. If there is too much overlap, the spacing between the concentric circles is increased and the path is regenerated. If there is an uncovered area, the spacing between the concentric circles is decreased and the path is regenerated. In this way, a spiral trajectory with appropriate spacing can be obtained for polishing 3D curved surfaces.

[0013] Preferably, in step four, when performing spiral trajectory grinding and polishing, there are a few unpolished areas near the boundary of the 3D curved surface. The area near the boundary is ground separately using a trajectory, or the path of grinding the boundary and the spiral path are integrated by using an X-shaped bridge or a Y-shaped bridge.

[0014] The beneficial effects of this invention are as follows:

[0015] 1. Compared to existing helical trajectory planning methods for complex perforated surfaces, this invention eliminates the need for additional boundary lines on the perforated surface and for dividing it into sub-regions for processing. Instead, it directly generates a non-bridging helical trajectory covering the entire 3D perforated surface, avoiding the problem of extensive bridging between sub-regions caused by sub-region division. Furthermore, since no additional boundaries are added, the trajectory does not need to avoid these boundaries through sharp turns or sacrificing spacing consistency. Therefore, the generated helical trajectory path is shorter, smoother, and has more consistent spacing. The non-bridging helical trajectory can be further bridged with the trajectory of the processing boundary to generate a fused trajectory. This fusion avoids trajectory discontinuities and sharp turns, resulting in a smoother actuator motion path and fewer path discontinuities. This avoids processing time consumption and impact marks on the workpiece surface caused by tool lifting and actuator turning. Therefore, the trajectory generated by this method for 3D surface grinding and polishing will improve the efficiency and quality of 3D surface grinding and polishing, reduce processing costs, and extend the service life of tools and robots, demonstrating significant economic benefits. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the process for generating 3D curved surface machining trajectory according to the present invention.

[0017] Figure 2 This is a schematic diagram of the central holeless 3D curved surface and the spiral polishing trajectory on the curved surface of the present invention.

[0018] Figure 3 This is a schematic diagram of the 3D curved surface with a central hole and the spiral polishing trajectory on the curved surface of the present invention.

[0019] Figure 4 This is a schematic diagram of the central hole-free planar aspect of the present invention.

[0020] Figure 5 This is a schematic diagram of the central hole of the present invention.

[0021] Figure 6 This is a schematic diagram of the central, holeless planar surface of the present invention mapped to the disk-shaped region via a slit mapping, and the concentric circles and spiral trajectories within the disk-shaped slit mapping domain.

[0022] Figure 7 This is a schematic diagram of the centrally perforated planar surface of the present invention, mapped to the annular region via a slit, and the concentric circles and spiral trajectories within the annular slit mapping domain.

[0023] Figure 8 This is a schematic diagram of the X-shaped bridging of the spiral trajectory and the boundary trajectory of the present invention.

[0024] Figure 9 This is a schematic diagram of the Y-shaped bridging of the spiral trajectory and the boundary trajectory of the present invention. Detailed Implementation

[0025] Example: Figures 1-9 The method for planning the polishing path of a complex curved surface is shown below, with the following specific steps:

[0026] Step 1: Flatten the porous surface to be ground and polished to 2D using surface parametric methods. According to... Figures 2 to 7 As shown in the content, a 3D surface has several holes. The goal is to flatten the 3D surface with holes into a 2D plane with holes through surface parameterization. There are various methods for surface parameterization, including Boundary First Flattening (BFF) algorithm, Least Square Conformal Maps (LSCM) algorithm, and algorithms based on discrete Ricci flow. Our algorithm does not limit the method used to flatten the surface to 2D; without loss of generality, we use the BFF algorithm for unfolding the 2D plane. Figure 4 , Figure 5 They are respectively Figure 2 Figure 3 The 2D plane is the result of flattening a 3D curved surface.

[0027] Step two: Determine if there is a hole at the center of the region enclosed by the 2D parametric surface boundary line. If there is no hole, use disk slit mapping to map the 2D region containing the boundary onto the disk containing the slit using a conformal slit mapping method. Figure 6 As can be seen from the content, the boundary of the region is mapped to the outer boundary of the disk and the inner arc-shaped slit. When there is an opening, annular slit mapping is used to map the region containing the boundary onto the annular ring containing the slit, according to... Figure 7 As can be seen from the content, the boundary of the region is mapped as the inner and outer boundaries of a circular ring and an inner arc-shaped slit;

[0028] Step 3: Generate a spiral trajectory with unequal spacing within the annular or circular domain of the slit mapping. The spiral trajectory is formed by offsetting concentric circles with different radii. Adjust the offset speed of the spiral trajectory and the radius of the concentric circles to avoid the generated unequal-spacing spiral line intersecting with the slit in the image domain. This trajectory is then mapped onto the 3D surface via inverse mapping of the slit mapping to obtain the spiral processing trajectory for the 3D surface. Check the overlapping and uncovered areas of this trajectory during polishing. If there is too much overlap, increase the spacing between the concentric circles and regenerate the path. If there are uncovered areas, decrease the spacing between the concentric circles and regenerate the path. This method yields a spiral trajectory with appropriate spacing for polishing 3D surfaces.

[0029] Step four: When using spiral trajectory grinding and polishing, there are a few unpolished areas near the boundary of the 3D curved surface. These areas can be ground separately using a trajectory, or a different approach can be used. Figure 8 and Figure 9The X-shaped or Y-shaped bridging method shown integrates the grinding boundary path and the spiral path into one.

Claims

1. A method for planning polishing paths on complex curved surfaces, characterized in that, The specific steps are as follows: Step 1: Flatten the porous surface to be ground and polished onto a 2D plane using surface parametric flattening. Step 2: Determine whether there is a hole in the center of the region enclosed by the boundary line of the 2D parameter surface. If there is no hole, use disk slit mapping to map the 2D region containing the boundary onto the disk containing the slit using the conformal slit mapping method. If there is a hole, use annular slit mapping to map the 2D region containing the boundary onto the annular ring containing the slit using slit mapping. Step 3: Generate a spiral trajectory with unequal spacing within the annular or circular domain of the slit mapping. The spiral trajectory is then mapped onto the 3D surface via the inverse mapping of the slit mapping to obtain the spiral machining trajectory of the 3D surface. Step 4: Machining along the offset line of the curved surface boundary to remove a small amount of machining residue; The spiral trajectory in step three is formed by the offset of concentric circles with different radii. The offset speed of the spiral trajectory and the radius of the concentric circles are adjusted to avoid the generated unequal-spaced spiral lines intersecting with the slits in the image domain. In step three, it is necessary to check the overlapping and uncovered areas of the spiral processing trajectory. If there is too much overlap, the concentric circle spacing should be increased and the path should be regenerated. If there is uncovered area, the concentric circle spacing should be decreased and the path should be regenerated. In this way, a spiral trajectory with appropriate spacing can be obtained for polishing 3D curved surfaces. When performing spiral trajectory grinding and polishing in step four, there are a few unpolished areas near the boundary of the 3D curved surface. The area near the boundary is ground separately by generating a trajectory, or the path of grinding the boundary and the spiral path are integrated by using X-shaped bridging or Y-shaped bridging.

2. The method for planning grinding and polishing paths for complex curved surfaces according to claim 1, characterized in that: The surface parameterization method in step one is set to any one of the following: Boundary First Flattening (BFF) algorithm, Least squareconformal maps (LSCM) algorithm, or discrete Ricci flow-based algorithm.

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