Processing path planning method for complex curved surface

Abstract

The invention relates to a processing path planning method for a complex curved surface, and the method comprises the steps: projecting the complex curved surface to a disc-shaped regular region based on conformal mapping, planning a spiral track in the regular region, and carrying out the inverse mapping of the spiral track back to the complex curved surface, thereby obtaining a corresponding cutter contact. In order to solve the problem of non-uniform track spacing generated by isoparametric lines, the invention provides a method for optimizing track residual height uniformity in an original image direction corresponding to a mapped radius line cluster, so that the generated spiral track spacing is more uniform, the material removal rate fluctuation is smaller, and the processing residual height is more consistent. The generated spiral track has the advantages that the track covers a complex curved surface without interruption, steering is smooth, and a complex boundary is attached, the number of machining cutter lifting times, steering impact and the area of an area where the boundary cannot be machined are reduced, and therefore cutter lifting time is shortened, machining impact textures are weakened, the boundary machining quality is improved, and the machining efficiency is improved. And more efficient and high-quality machining of large complex weak-rigidity curved surface parts is facilitated.

Description

Technical Field

[0001] The invention relates to the technical field of complex curved surface processing, and in particular to a processing path planning method for a complex curved surface. Background Art

[0002] Discontinuities, sharp turns, and inconsistent track spacing in the machining trajectory will cause frequent tool lifts, large inertial impacts, and uneven material removal rates during machining. This will cause large fluctuations in machining force, resulting in obvious machining lines on the workpiece surface, increased impact wear on tools, machine tools, or robots, and other problems. To avoid excessive force fluctuations, the machining feed speed will also be limited, affecting machining efficiency. Inconsistent track spacing and incomplete coverage will cause inconsistent residual heights on the workpiece surface and the existence of unprocessed areas, seriously affecting the surface quality of the workpiece. These problems caused by discontinuities, sharp turns, uneven track spacing, and incomplete coverage in the machining trajectory are particularly obvious when machining large, complex, weakly rigid curved surface parts, and are in urgent need of optimization.

[0003] The use of spiral trajectories to process complex three-dimensional surfaces of large weakly rigid components has the advantages of less trajectory discontinuity, smooth turning, and the ability to fit complex boundaries for more complete coverage. Therefore, spiral trajectories are widely used in complex surface processing. However, the current method has poor spacing uniformity when generating spiral trajectories, which will cause inconsistent machining residual height and large fluctuations in material removal rate. Large fluctuations in material removal rate will in turn cause large fluctuations in machining force, resulting in obvious machining lines on the machined surface, limited machining feed, and increased tool and machine tool wear. Generating spiral trajectories with more uniform spacing is crucial to improving the machining efficiency of large curved surface components, surface quality consistency, and reducing tool and machine tool wear costs.

[0004] Traditional spiral trajectory generation methods mainly include methods based on medial axis tree and conformal mapping. The medial axis tree-based method gradually shifts the isoparametric trajectory toward the medial axis to obtain a spiral trajectory. The generated trajectory spacing has the best uniformity, but the trajectory generated by the medial axis tree method has slightly poor steering smoothness and needs to be further smoothed. In addition, this method can only generate trajectories in a 2D plane and cannot be applied to 3D surfaces. The spiral trajectory generation algorithm based on conformal mapping first maps the plane or surface to a simple area such as a disk, ring or rectangle, and then gradually shifts the concentric rings or rectangular isoparametric lines in the simple area to obtain a spiral trajectory. Since the conformal mapping isoparametric lines are infinitely differentiable, the generated spiral trajectory is relatively smooth, and this method ensures that the spiral trajectory can fit the complex boundary without interruption. However, since conformal mapping cannot guarantee uniform spacing of isoparametric lines, the spiral trajectory spacing generated by the algorithm based on conformal mapping is usually uneven.

[0005] In summary, it is necessary to propose a spiral trajectory planning algorithm suitable for complex surfaces, which can further optimize the trajectory spacing while ensuring that the spiral trajectory has few discontinuities, smooth turning, and trajectory fits the boundary. Summary of the invention

[0006] In order to solve the problems in the prior art, the present invention provides a method for planning a machining path for a complex curved surface.

[0007] In order to solve the above technical problems, the present invention is implemented by the following technical solutions: A method for planning a machining path for a complex surface, characterized in that it comprises the following steps:

[0008] Step 1: Select a point O on the surface S with only one boundary * , the surface S to be processed is mapped to the 2D disk area D through disk conformal mapping, point O * is mapped to the center O of area D;

[0009] Step 2: Select any radius in the disk mapping domain D The radius Preimage on the surface Parameterized representation, It is represented by the parameter t∈[0,1] as so It is also parameterized as And adjust the parameters to make the residual height of the subsequently generated spiral trajectory the most uniform;

[0010] Specifically, find a minimum evenly divisible positive integer greater than 2, so that when the radius is evenly divided into this number of parts, the machining residual height between any adjacent tool contact points is a fixed value and less than the maximum allowable residual height. Specifically, find a minimum evenly divisible positive integer n1 greater than 2, so that when t is evenly divided into n1+1 parts Any adjacent knife contact and The machining residual height between i=0,1,...n1-1 is a fixed value h1 and h1 is less than the maximum allowable residual height h max But when t is divided into n1 points There must be at least one pair of adjacent knife contacts and The machining residual height between j∈{0,1,...n1-2} is greater than the maximum allowable residual height h max . Let all the radii in the disk-shaped mapping domain be The corresponding minimum equally divided positive integer is {n1,n2,n3,...}, and the maximum value of the minimum equally divided positive integer set is the maximum value of the equally divided positive integer n max =max{n1,n2,n3,...}, It is an infinite set in the geometric sense, but it can still be expressed discretely as a finite set. For example, the surface boundary is divided equally by a larger number m according to the arc length, and the set of radii passing through each dividing point represents all radii in the disk mapping domain. Become a finite set In this way, we can get the corresponding finite set {n1,n2,...,n m} to find n max .like Figure 1 (a) m = 100, n max exist The value is 22. max Then again for all t∈[0,1],j=1,2,...,m perform parameter reordering so that when t is divided into n max +1 Any adjacent knife contact and i=0,1,…,n max -1 is a fixed value for the machining residual height and Less than the maximum allowable residual height h max .

[0011] Step 3: Re-parameterize all radii to ensure that when each radius is evenly divided into the corresponding minimum evenly divided positive integer parts, the machining residual height between any adjacent tool contact points is a fixed value and is less than the maximum allowable residual height; after the surface D is parameterized, the surface can be expressed by two parameters, one of which is t and the other is the radius angle θ;

[0012] Specifically, after parameter reorganization, the surface D can be expressed as D(t,θ) using two parameters (t,θ), where t∈[0,1] on D is given by and The parameters between them are transformed to obtain that θ∈[0,2π] is the circular angle on D. After D is parameterized by (t,θ), S is also parameterized by (t,θ) to S(t,θ) according to the mapping relationship. Towards adjacent isoparms The helix can be obtained by offsetting, where i = 0, 1, ..., n max -1,θ∈[0,2π].

[0013] Step 4: In the disk-shaped area, gradually shift the isoparametric line toward the adjacent isoparametric line to generate a spiral line as the processing path;

[0014] Step 5: According to the generated spiral knife contact L S Calculate the knife center motion trajectory L O and the knife axis vector The specific method is: offset each point on the spiral trajectory by a certain distance along the direction of its normal vector on the surface to obtain the corresponding tool center point, and at the same time calculate the tool axis normal vector corresponding to each tool contact point.

[0015] Specifically: Calculate the knife contact point L S The machining trajectory cannot be determined yet, and the tool center motion trajectory L is calculated based on the tool contact point. O and the knife axis vector There are many ways to do this. Without loss of generality, we can calculate the spiral trajectory L S Seeking the solution of Knife Heart L O and the knife axis vector L S (t) The normal vector of each point Pi along S at Pi Offset distance K c , we can get L O (t). The normal vector of the tool axis corresponding to the contact point Pi for:

[0016]

[0017] Where β is the inclination angle of the cutter shaft, usually 15 to 30°. The trajectory L O (t) Positive tangent direction.

[0018] In a specific implementation, the calculation method of the disk-shaped conformal mapping is not limited, and the calculation can be performed using Tutte's method or other equivalent methods.

[0019] In a specific implementation, in step 2, in order to discretely express the radius set corresponding to the surface boundary as a finite set, the surface boundary can be equally divided by a larger number according to the arc length, and the set of radii passing through each equally divided point is used to represent all radii in the disk mapping domain.

[0020] In a specific implementation, in step 5, the inclination angle of the cutter axis is usually selected to be between 15° and 30°, and the specific value can be adjusted according to processing requirements.

[0021] In a specific implementation, the machining path planning method is applicable to workpieces with complex curved surface structures, and can significantly improve machining efficiency and machining quality.

[0022] In a specific implementation, the method is suitable for processing large, complex, weakly rigid curved surface parts, which can significantly reduce processing costs and increase the service life of tools and robots.

[0023] The beneficial effects of the present invention are:

[0024] 1. The spiral trajectory generated by this method has the advantages of covering complex surfaces without interruption, smooth turning, and fitting complex boundaries. This is conducive to reducing the number of tool lifts, turning impact, and the area of ​​the boundary that cannot be processed, thereby reducing the time spent on tool lifts, weakening the processing impact texture, and improving the boundary processing quality, which is conducive to more efficient and high-quality processing of large, complex, weakly rigid surface parts.

[0025] 2. Compared with the method based only on conformal mapping, this paper proposes a spiral trajectory spacing optimization method with consistent residual height, which makes the processing material removal rate and residual height more consistent, reduces redundant processing, and shortens the trajectory, which further improves the surface quality and processing efficiency;

[0026] 3. This method generates trajectories for complex surface machining, which will improve the efficiency and quality of complex surface machining, reduce machining costs, and increase the service life of tools and robots, which has obvious economic significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a schematic diagram of the parameterization of the curved surface of the present invention being conformally mapped to a disk-shaped area and equal residual height in the radial direction.

[0028] Figure 2 It is a schematic diagram of generating a spiral by gradually shifting the isoparametric lines toward adjacent isoparametric lines of the present invention.

[0029] Figure 3 It is a schematic diagram of solving the tool center trajectory and the tool axis vector based on the spiral tool contact point of the present invention. DETAILED DESCRIPTION

[0030] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0031] Example: Figures 1 to 3 A complex surface machining path planning method is shown in Figure 1. Generating complex surface machining trajectory is divided into four steps:

[0032] The first step is to select a point O on the surface S with only one boundary. * , the surface to be processed is mapped to the 2D disk area D through disk conformal mapping, point O * is mapped to the center O of region D, such as Figure 1 As shown in (a) and (b), Figure 1 (a) The surface is conformally mapped to Figure 1(b) Disk-shaped region. Our algorithm does not restrict the calculation method of the disk-shaped conformal mapping. Without loss of generality, Tutte's method can be used to calculate the disk-shaped mapping of the surface S.

[0033] like Figure 1 As shown: the surface is conformally mapped to the disk region and parameterized with equal residual height in the radial direction. The disk in Figure (b) is obtained by conformally mapping the surface in Figure (a) through the disk. In Figure (b), the residual heights of adjacent knife contact points in the original image of Figure (a) are consistent for the same radius, and the number of knife contact points in the original image of Figure (a) is inconsistent for different radii. Figure (d) is the image of the re-parameterized surface. In Figure (d), the residual heights of adjacent knife contact points in the original image of Figure (c) are consistent for the same radius, and the number of knife contact points in the original image of Figure (c) is consistent for different radii.

[0034] The second step is to arbitrarily select a radius within the disk-shaped mapping domain D. The original image of the radius on the surface is remember It is represented by the parameter t∈[0,1] as so It is also parameterized as The parameter t can be adjusted as follows to make the residual height of the subsequent generated spiral trajectory the most uniform:

[0035] Find a minimum evenly divisible positive integer n1 greater than 2 such that when t is evenly divided into n1+1 parts Any adjacent knife contact and The machining residual height between i=0,1,...n1-1 is a fixed value h1 and h1 is less than the maximum allowable residual height h max But when t is divided into n1 points There must be at least one pair of adjacent knife contacts and The machining residual height between j∈{0,1,...n1-2} is greater than the maximum allowable residual height h max . Let all the radii in the disk-shaped mapping domain be The corresponding minimum equally divisible positive integer is {n1,n2,n3,...}, and the maximum value of the minimum equally divisible positive integer set is n max =max{n1,n2,n3,...}, It is an infinite set in the geometric sense, but it can still be expressed discretely as a finite set. For example, the surface boundary is divided equally by a larger number m according to the arc length, and the set of radii passing through each dividing point represents all radii in the disk mapping domain. Become a finite set In this way, we can get the corresponding finite set {n1,n2,...,n m} to find n max .

[0036] like Figure 1 As shown: In Figure (a), m = 100, n max exist The value obtained is 22.

[0037] Find n max Then again for all t∈[0,1],j=1,2,...,m perform parameter reordering so that when t is divided into n max +1 Any adjacent knife contact and i=0,1,…,n max -1 is a fixed value for the machining residual height and Less than the maximum allowable residual height h max .

[0038] like Figure 1 As shown in Figure (c), any After the upper t is divided into 22 parts, 22 tool contact points are generated. The machining residual height between adjacent tool contact points is consistent.

[0039] like Figure 2 As shown in the third step, after completing the parameter reorganization, the surface D can be expressed as D(t,θ) using the double parameter (t,θ), where t∈[0,1] on D is given by and The parameters between them are transformed, θ∈[0,2π] is the circular angle on D, and after D is parameterized by (t,θ), S is also parameterized by (t,θ) to S(t,θ) according to the mapping relationship. Towards adjacent isoparms The helix can be obtained by offsetting, where i = 0, 1, ..., n max -1,θ∈[0,2π].

[0040] like Figure 3 As shown: Step 4, only calculate the knife contact point L S The machining trajectory cannot be determined yet, and the tool center motion trajectory L needs to be calculated based on the tool contact point. O and the knife axis vector There are many ways to calculate this. Without loss of generality, we use the spiral trajectory L S Seeking the solution of Knife Heart L O and the knife axis vector L S (t) The normal vector of each point Pi along S at Pi Offset distance K c , we can get L O(t). The normal vector of the tool axis corresponding to the contact point Pi for:

[0041]

[0042] Where β is the inclination angle of the cutter shaft, usually 15 to 30°. The trajectory L O (t) Positive tangent direction.

[0043] In summary, a new spiral trajectory planning method for complex surface path planning is proposed. The innovation of this method is:

[0044] 1. Based on conformal mapping, the complex surface is projected onto a disk-shaped regular area, a spiral trajectory is planned within the disk-shaped regular area, and the spiral trajectory is inversely mapped back onto the complex surface to obtain the corresponding tool contact point.

[0045] 2. In order to solve the problem of uneven spacing of trajectories generated based on isoparametric lines of disk-shaped conformal mapping, a method is proposed to optimize the uniformity of trajectory residual height in the original image direction corresponding to the cluster of radial lines after mapping, so that the spacing of the generated spiral trajectories is more uniform, the material removal rate fluctuates less, and the processing residual height is more consistent.

[0046] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for planning a machining path for a complex surface, characterized in that: The following steps are involved: Step 1: Select a point on a surface with only one boundary, map the surface to be processed to a 2D disk-shaped area through disk-shaped conformal mapping, and the point is mapped to the center of the area; Step 2: randomly select a radius in the disk-shaped mapping domain, parametrically represent the original image of the radius on the surface, and adjust the original image parameters according to the following objectives so that the residual height of the subsequently generated spiral trajectory is the most uniform; specifically, find a minimum evenly divided positive integer greater than 2, evenly divide the parameters corresponding to the original image by this number, and use the original image parameter evenly divided point as the tool contact point. After adjusting the original image parameters, the machining residual heights between adjacent tool contact points are consistent and less than the maximum allowable residual height; Step 3: Re-parameterize all the original images corresponding to the radius, record the maximum value of the minimum average positive integer corresponding to all the original images of the radius on the circle as the average maximum value, divide the parameters corresponding to all the original images of the radius by this number, and take the average point of the original image parameters of the radius as the tool contact point. After adjusting all the original image parameters one by one, the machining residual height between adjacent tool contact points of the same original image is consistent and less than the maximum allowable residual height; after completing the parameter re-parameterization, the surface can be expressed by two parameters, one of which is obtained by re-parameterizing the corresponding parameters of all the original images of the radius, and the other parameter is the circumference angle corresponding to the radius; Step 4: In the disk-shaped area, gradually shift the isoparametric line toward the adjacent isoparametric line to generate a spiral line as the processing path; Step 5: Calculate the tool center motion trajectory and tool axis vector based on the generated spiral tool contact point. The specific method is: offset each point on the spiral trajectory by a certain distance along the direction of its normal vector on the surface to obtain the corresponding tool center point, and calculate the tool axis normal vector corresponding to each tool contact point.

2. The method for planning a machining path for a complex curved surface according to claim 1, characterized in that: The calculation method of the disk-shaped conformal mapping is not limited, and Tutte's method or other equivalent methods may be used for calculation.

3. The method for planning a machining path for a complex curved surface according to claim 1, characterized in that: In step 2, in order to discretely express the radius set corresponding to the surface boundary as a finite set, the surface boundary can be evenly divided by arc length using a larger number, and the set of radii passing through each evenly divided point can be used to represent all radii in the disk mapping domain.

4. The method for planning a machining path for a complex curved surface according to claim 1, characterized in that: In step five, the tool axis inclination angle is usually selected to be between 15° and 30°, and the specific value can be adjusted according to processing requirements.

5. The method for planning a machining path for a complex curved surface according to claim 1, characterized in that: This machining path planning method is suitable for workpieces with complex surface structures and can significantly improve machining efficiency and quality.

6. The method for planning a machining path for a complex curved surface according to claim 1, characterized in that: This method is suitable for the processing of large, complex, weakly rigid curved surface parts, and can significantly reduce processing costs and increase the service life of tools and robots.

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