Grinding and polishing path planning method for complex curved surface

Abstract

The invention relates to a grinding and polishing path planning method for a complex curved surface. Compared with an existing spiral track planning method for a complex hole-containing curved surface, the method has the advantages that a non-bridging spiral track is directly generated to cover the whole three-dimensional hole-containing curved surface, so that the problem that a large number of bridging is needed for spiral tracks among sub-regions due to sub-region division is avoided; the generated spiral track path is shorter and smoother, track spacing is more consistent, track interruption and violent steering are avoided, the motion path of the actuator is smoother, the number of times of path interruption is reduced, machining time consumption caused by cutter lifting and actuator steering and impact traces on the surface of a workpiece are avoided, and therefore the machining efficiency is improved. When the track generated through the method is used for 3D curved surface grinding and polishing machining, the 3D curved surface grinding and polishing machining efficiency and quality can be improved, the machining cost is reduced, the service life of a tool and the service life of a robot are prolonged, and obvious economic significance is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of grinding and polishing, and particularly to a grinding and polishing path planning method for complex curved surfaces. Background Art

[0002] Lifting the tool and sharp turning in the grinding and polishing trajectory will cause force fluctuations during the machining process, affecting the consistency of the surface quality, which is particularly significant when grinding and polishing components with weak rigidity. Grinding and polishing large components with complex three-dimensional curved surfaces using a spiral trajectory has the advantages of fewer trajectory discontinuities and smoother turning. Generating shorter, smoother, and fewer-discontinuity spiral trajectories is crucial for improving the grinding and polishing efficiency and the consistency of surface quality of large curved surface construction. However, for complex curved surfaces with holes, traditional spiral trajectory planning methods need to convert multi-connected regions into single-connected regions or divide them into several sub-regions by adding additional boundaries, and the trajectory needs to avoid the newly added additional boundaries, which brings problems such as inconsistent trajectory spacing, sharp turning of the trajectory, and more trajectory discontinuities that need to be bridged. The above problems lead to large variations in the material removal rate during the curved surface grinding and polishing process, longer machining paths, larger actuator motion impacts, and excessive tool lifting times, which make it difficult to optimize the grinding and polishing parameters, increase the grinding and polishing duration, and also reduce the consistency of the grinding and polishing surface quality, the service life, and the accuracy of the tool and the robot.

[0003] Traditional spiral trajectory generation methods mainly include the method based on the medial axis tree, the method based on solving elliptic partial differential equations on a single-connected region equivalent to a disk or a two-connected region equivalent to an annulus, and the method based on conformal mapping of a single-connected disk, square, or two-connected annulus. The above methods either cannot be directly applied to complex porous curved surfaces, or the generated paths are uneven, not smooth, and have discontinuities when applied to complex porous curved surfaces. Summary of the Invention

[0004] In order to solve the problems of the prior art, the present invention provides a grinding and polishing path planning method for complex curved surfaces.

[0005] In order to solve the above technical problems, the present invention is realized through the following technical solutions: 1. A grinding and polishing path planning method for complex curved surfaces, and the specific steps are as follows:

[0006] Step 1, flatten the curved surface with holes to be ground and polished to 2D through surface parameterization;

[0007] Step 2: Determine whether there is a hole at the center of the area enclosed by the 2D parametric surface boundary line. When there is no hole, use the disk-shaped slit mapping to map the 2D area with boundaries to a disk with a slit through the conformal slit mapping method. When there is a hole, use the annular slit mapping to map the area with boundaries to an annulus with a slit through the slit mapping;

[0008] Step 3: Generate an unequally spaced spiral trajectory within the annular or circular domain of the slit mapping. This trajectory is mapped to the 3D surface through the inverse mapping of the slit mapping, and thus the spiral machining trajectory of the 3D surface can be obtained;

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

[0010] Preferably, the surface parameterization method in Step 1 is set to any one of the Boundary First Flattening (abbreviated as BFF) algorithm, the Least square conformal maps (abbreviated as LSCM) algorithm, and the algorithm based on discrete Ricci flow.

[0011] Preferably, the spiral trajectory in Step 2 is formed by offsetting concentric circles with different radii. Adjust the offset speed of the spiral trajectory and the radii of the concentric circles to avoid the intersection of the generated unequally spaced spiral line with the slit in the image domain.

[0012] Preferably, in Step 3, it is necessary to check the overlapping area and the uncovered area of the grinding and polishing of this machining trajectory. If the overlap is too much, increase the distance between the concentric circles and regenerate the path. If there is an uncovered area, decrease the distance between the concentric circles and regenerate the path. Through this method, a spiral trajectory with a moderate distance can be obtained for grinding and polishing the 3D surface.

[0013] Preferably, when performing spiral trajectory grinding and polishing machining in Step 4, there is a small amount of unpolished area in the area near the 3D surface boundary. A separate trajectory can be generated to polish the area near the boundary, or the path for polishing the boundary and the spiral path can be integrated into one by using the X-shaped bridging or Y-shaped bridging method.

[0014] The beneficial effects of the present invention are:

[0015] 1. Compared with the existing spiral trajectory planning methods for complex curved surfaces with holes, the proposed method does not require adding additional boundary lines to the curved surface with holes, nor dividing the curved surface with holes into several sub-regions for machining. Instead, it directly generates a non-bridged spiral trajectory that covers the entire three-dimensional curved surface with holes, avoiding the problem of a large number of bridges required for the spiral trajectories between sub-regions caused by sub-region division. At the same time, since no additional boundary is added, the trajectory does not need to avoid the additional boundary by sharp turning or sacrificing the consistency of the spacing. Therefore, the generated spiral trajectory has a shorter path, is smoother, and the trajectory spacing is more consistent. The non-bridged spiral trajectory can be further bridged with the trajectory of the machining boundary to generate a merged trajectory. This merging avoids the discontinuity and sharp turning of the trajectory, making the movement path of the actuator smoother and reducing the number of path discontinuities. Furthermore, it avoids the machining time consumption caused by tool lifting and actuator turning and the impact marks on the workpiece surface. Therefore, using 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 the processing cost, and extend the service life of the tool and the robot, which has obvious economic significance. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0017] Figure 2 is a schematic diagram of a 3D surface without a central hole and the spiral grinding and polishing trajectory on the surface according to the present invention.

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

[0019] Figure 4 is a schematic diagram of a flattened plane without a central hole according to the present invention.

[0020] Figure 5 is a schematic diagram of a flattened plane with a central hole according to the present invention.

[0021] Figure 6 is a schematic diagram of mapping the flattened plane without a central hole according to the present invention to a disk-shaped region through slit mapping and the concentric circles and spiral trajectories in the disk-shaped slit mapping domain.

[0022] Figure 7 is a schematic diagram of mapping the flattened plane with a central hole according to the present invention to an annular region through slit mapping and the concentric circles and spiral trajectories in the annular slit mapping domain.

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

[0024] Figure 9 is a schematic diagram of the Y-shaped bridging of the spiral trajectory and the boundary trajectory according to the present invention. Detailed implementation mode

[0025] Example: As Figures 1 to 9 shown in a polishing path planning method for complex curved surfaces, the specific steps are as follows:

[0026] Step 1, flatten the porous curved surface to be polished to 2D through surface parameterization. According to Figures 2 to 7 the content shown, there are several holes on a 3D curved surface. The 3D porous curved surface is flattened into a 2D porous plane through surface parameterization. There are various ways of surface parameterization, including the Boundary First Flattening (abbreviated as BFF) algorithm, the Least square conformal maps (abbreviated as LSCM) algorithm, the algorithm based on discrete Ricci flow, etc. Our algorithm does not limit the means of flattening the curved surface to 2D. Without loss of generality, we adopt the BFF algorithm for the unfolding of the 2D plane. Figure 4 、 Figure 5 are respectively Figure 2 Figure 3 the 2D planes after flattening the 3D curved surfaces shown;

[0027] Step 2, judge whether there is a hole at the center of the area surrounded by the boundary line of the 2D parameter surface. When there is no hole, use the disk-shaped slit mapping to map the 2D area with boundaries to a disk with a slit through the conformal slit mapping method. According to Figure 6 the content, the boundary of the area is mapped into the outer boundary of the disk and the inner circular arc slit. When there is a hole, use the annular slit mapping to map the area with boundaries to a ring with a slit through the slit mapping. According to Figure 7 the content, the boundary of the area is mapped into the inner and outer boundaries of the ring and the inner circular arc slit;

[0028] Step 3, generate an unequally spaced spiral trajectory in 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 radii of the concentric circles to avoid the generated unequally spaced spiral line intersecting with the slit in the image domain. This trajectory is mapped back to the 3D curved surface through the inverse mapping of the slit mapping, and the spiral machining trajectory of the 3D curved surface can be obtained. Check the overlapping area and uncovered area polished by this trajectory. If the overlap is too much, increase the distance between the concentric circles and regenerate the path. If there is an uncovered area, decrease the distance between the concentric circles and regenerate the path. Through this method, a spiral trajectory with appropriate spacing can be obtained for polishing the 3D curved surface;

[0029] Step 4, when using the spiral trajectory for polishing and machining, there are a small number of unpolished areas in the area near the boundary of the 3D curved surface. The area near the boundary can be polished by generating a separate trajectory, or Figure 8 and Figure 9The path of the polished boundary and the spiral path are integrated in the form of an X-shaped bridge or a Y-shaped bridge as shown.

Claims

1. A method for planning grinding and polishing paths of complex surfaces, characterized in that, the specific steps are as follows: Step 1, flatten the surface with holes to be ground and polished to 2D through surface parameterization; Step 2, determine whether there is a hole in the center of the area enclosed by the boundary line of the 2D parametric surface. When there is no hole, use the disk-shaped slit mapping to map the 2D area with boundaries to a disk with a slit through the conformal slit mapping method. When there is a hole, use the annular slit mapping to map the area with boundaries to an annulus with a slit through the slit mapping; Step 3, generate an unequally spaced spiral trajectory in the annular or circular domain of the slit mapping. This trajectory is mapped back to the 3D surface through the inverse mapping of the slit mapping, and the spiral machining trajectory of the 3D surface can be obtained; Step 4, machine along the offset line of the surface boundary to remove a small amount of machining residues.

2. The method for planning grinding and polishing paths of complex surfaces according to claim 1, characterized in that: the way of surface parameterization in Step 1 is set to any one of the Boundary First Flattening (abbreviated as BFF) algorithm, the Least square conformalmaps (abbreviated as LSCM) algorithm, and the algorithm based on discrete Ricci flow.

3. The method for planning grinding and polishing paths of complex surfaces according to claim 1, characterized in that: the spiral trajectory in Step 2 is formed by offsetting concentric circles with different radii, and the offset speed of the spiral trajectory and the radii of the concentric circles are adjusted to avoid the unequally spaced spiral line generated from intersecting with the slit in the image domain.

4. The method for planning grinding and polishing paths of complex surfaces according to claim 1, characterized in that: in Step 3, it is necessary to check the overlapping area and the uncovered area of the grinding and polishing of this machining trajectory. If the overlap is too much, the distance between the concentric circles is adjusted to be larger and the path is regenerated. If there is an uncovered area, the distance between the concentric circles is adjusted to be smaller and the path is regenerated. Through this method, a spiral trajectory with a moderate distance can be obtained for grinding the 3D surface.

5. The method for planning grinding and polishing paths of complex surfaces according to claim 1, characterized in that: when performing spiral trajectory grinding and polishing machining in Step 4, there is a small amount of unground area in the area close to the boundary of the 3D surface. A trajectory can be generated separately to grind the area close to the boundary or the path for grinding the boundary and the spiral path can be integrated into one by using the X-shaped bridging or Y-shaped bridging method.

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