A method for planning the machining path of complex surfaces

Abstract

This invention relates to a machining path planning method for complex curved surfaces. This method is based on conformal mapping, projecting the complex curved surface onto a disk-shaped regular region, planning a spiral trajectory within the regular region, and then inversely mapping it back onto the complex curved surface to obtain the corresponding tool contact point. Addressing the issue of uneven trajectory spacing generated by isoparametric lines, this invention proposes a method to optimize the uniformity of trajectory residual height along the preimage direction corresponding to the mapped radius line cluster. This results in more uniform spiral trajectory spacing, smaller fluctuations in material removal rate, and more consistent machining residual height. The spiral trajectory generated by this invention has the advantages of uninterrupted coverage of complex curved surfaces, smooth turning, and close fit to complex boundaries. This helps reduce the number of tool lifting operations, turning impacts, and the area of ​​unmachined boundary regions, thereby reducing tool lifting time, weakening machining impact textures, and improving boundary machining quality. This facilitates more efficient and high-quality machining of large, complex, weakly rigid curved surface parts.

Description

Technical Field

[0001] This invention relates to the field of complex surface machining technology, specifically a method for planning machining paths for complex surfaces. Background Technology

[0002] Discontinuities, sharp turns, and inconsistent trajectory spacing in the machining path can lead to frequent tool lifts, significant inertial impacts, and uneven material removal rates during machining. This results in large fluctuations in machining forces, causing noticeable machining marks on the workpiece surface and increased impact wear on tools, machine tools, or robots. To avoid exceeding the limits of force fluctuations, the machining feed rate will also be limited, affecting machining efficiency. Inconsistent trajectory spacing and incomplete coverage can cause inconsistent machining residual heights and unmachined areas on the workpiece surface, severely impacting workpiece surface quality. These problems caused by discontinuities, sharp turns, uneven trajectory spacing, and incomplete coverage in the machining path are particularly pronounced when machining large, complex, and weakly rigid curved surface parts, and urgently require optimization.

[0003] Helical trajectories are widely used in machining complex 3D curved surfaces of large, weakly rigid components due to their advantages such as fewer trajectory discontinuities, smoother turning, and ability to conform to complex boundaries for more complete coverage. However, current methods suffer from poor uniformity in the time interval of the generated helical trajectory, leading to inconsistent machining residual heights and large fluctuations in material removal rates. These fluctuations in material removal rates, in turn, cause large fluctuations in machining stress, resulting in noticeable machining textures, limited machining feed, and increased wear and tear on tools and machine tools. Generating helical trajectories with more uniform spacing is crucial for improving the machining efficiency, surface quality consistency, and reducing tool and machine tool wear costs for large curved components.

[0004] Traditional methods for generating spiral trajectories mainly include those based on medial axis trees and those based on conformal mapping. Medial axis tree-based methods progressively offset isoparametric trajectories towards the medial axis to obtain the spiral trajectory, resulting in the best uniformity of trajectory spacing. However, the smoothness of the turns generated by the medial axis tree method is slightly poor, requiring further smoothing of the turns. Furthermore, this method can only generate trajectories in a 2D plane and cannot be applied to 3D curved surfaces. Conformal mapping-based spiral trajectory generation algorithms first map the plane or curved surface to simple regions such as disks, rings, or rectangles, and then progressively offset the concentric rings or rectangular isoparametric lines within these simple regions to obtain the spiral trajectory. Since the isoparametric lines of conformal mapping are infinitely differentiable, the generated spiral trajectory is relatively smooth, and this method ensures that the spiral trajectory can fit complex boundaries without discontinuity. However, since conformal mapping cannot guarantee uniform spacing of the isoparametric lines, algorithms based on conformal mapping typically generate spiral trajectories with uneven spacing.

[0005] In summary, it is necessary to propose a spiral trajectory planning algorithm suitable for complex curved 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] To address the problems of existing technologies, this invention provides a method for planning the processing path of complex curved surfaces.

[0007] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution: a method for planning the processing path of complex curved surfaces, characterized by comprising the following steps:

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

[0009] Step 2: Arbitrarily select a radius within the disk-shaped mapping domain D. The radius The preimage on the curved surface Perform parameterized representation, and denote The parameter t∈[0,1] is represented as so It is also parameterized as And adjust the parameters to make the residual height of the subsequently generated spiral trajectory most uniform;

[0010] Specifically, we need to find a smallest positive integer greater than 2 such that when the radius is divided into that number of equal parts, the machining residual height between any two adjacent tool contacts is a fixed value and less than the maximum allowable residual height. Specifically, we need to find a smallest positive integer n1 greater than 2 such that when t is divided into n1+1 equal parts... Any adjacent tool contacts and The residual height between the machining operations is a fixed value h1, and h1 is less than the maximum allowable residual height h. max However, when t is divided into n1 points... There must be at least one pair of adjacent tool contacts. and The residual height between the machining operations is greater than the maximum allowable residual height h. max Let all radii within the disk-shaped mapping domain be... The corresponding smallest equally divided positive integers are {n1, n2, n3, ...}, and the maximum value of the set of smallest equally divided positive integers is denoted as the maximum value of the average division n. max =max{n1,n2,n3,...} Geometrically, it is an infinite set, but it can still be discretely expressed as a finite set. For example, the boundary of the surface can be divided equally by arc length using a large number m, and the set of radii passing through each dividing point can represent all radii within the disk-shaped mapping domain. Transform into a finite set This allows us to obtain the corresponding finite set {n1,n2,...,n} m n is obtained from} max .like Figure 1 In (a) m=100, n max exist The value at this point is 22. The value of n is then calculated. max Then again for all Perform parameter renormalization so that when t is equally divided into n max +1 serving Any adjacent tool contacts and The residual height between processing steps is a fixed value. and Less than the maximum allowable residual height h max .

[0011] Step 3: Perform parameter renormalization on all radii to ensure that when each radius is divided into the corresponding minimum positive integer parts, the machining residual height between any adjacent tool contact points is a fixed value and less than the maximum allowable residual height; After the surface D is parameter renormalized, the surface can be represented by two parameters, where one parameter is t and the other parameter is the radius circumferential angle θ;

[0012] Specifically: After parameter renormalization, the surface D can be represented by two parameters (t, θ) as D(t, θ), where t ∈ [0, 1] on D is determined by... and The parameter transformations between them yield θ∈[0,2π], which is the inscribed 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. The isoparametric lines on S are gradually transformed... To adjacent isoparametric lines The spiral can be obtained by offsetting, where i = 0, 1, ..., n max -1, θ∈[0,2π].

[0013] Step 4: Within the disk-shaped area, gradually shift the isoparametric lines to adjacent isoparametric lines to generate a spiral as the machining path;

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

[0015] Specifically: Calculate the knife contact point L S The machining trajectory cannot be determined yet; the tool center motion trajectory L is calculated based on the tool contact point. O and tool axis vector There are multiple methods for this calculation; without loss of generality, we use the spiral trajectory L... S Solve for the blade core L O and tool axis vector L S For each point Pi on (t), follow the normal vector of S at Pi. Offset distance K c L can be obtained O (t). Tool axis normal corresponding to contact point Pi for:

[0016]

[0017] Where β is the cutter axis tilt angle, typically chosen to be 15–30°. For trajectory L O (t) Positive tangent direction.

[0018] In one specific implementation, the method for calculating the disk conformal mapping is not limited; Tutte's method or other equivalent methods can be used.

[0019] In one specific implementation, in order to discretely represent the set of radii corresponding to the surface boundary as a finite set, the surface boundary is divided into 100 equal parts according to the arc length, and the set of radii passing through each equal division point represents all radii within the disk-shaped mapping domain.

[0020] In one specific implementation, in step five, the tool axis tilt angle is typically selected between 15° and 30°, and the specific value can be adjusted according to the processing requirements.

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

[0022] In one specific implementation, this method is applicable to the machining of large, complex, and weakly rigid curved surface parts, and can significantly reduce machining costs and extend the service life of tools and robots.

[0023] The beneficial effects of this invention are as follows:

[0024] 1. The spiral trajectory generated by this method has the advantages of uninterrupted coverage of complex curved surfaces, smooth turning, and close fit to complex boundaries. This helps to reduce the number of tool lifting operations, turning impact, and the area of ​​unprocessable boundary regions, thereby reducing tool lifting time, weakening machining impact texture, and improving boundary machining quality. This is conducive to more efficient and high-quality machining of large, complex, weakly rigid curved surface parts.

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

[0026] 3. The trajectory generated by this method for machining complex curved surfaces will improve the efficiency and quality of machining, reduce machining costs, and extend the service life of tools and robots, which has significant economic benefits. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the conformal mapping of the curved surface of the present invention onto the disk-shaped region and the equal residual height parameterization in the radial direction.

[0028] Figure 2 This is a schematic diagram of the spiral generated by the gradual shift of the isoparametric lines towards adjacent isoparametric lines according to the present invention.

[0029] Figure 3 This is a schematic diagram of the present invention for solving the tool center trajectory and tool axis vector based on the spiral tool contact point. Detailed Implementation

[0030] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0031] Example: Figures 1 to 3 This paper presents a method for planning the machining path of complex surfaces. Generating the machining trajectory of a complex surface involves four steps:

[0032] The first step is to select a point O on a surface S with only one boundary. * The surface to be processed is mapped to a 2D disk region D using disk conformal mapping, with point O... * Mapped to the center O of region D, such as Figure 1 As shown in (a)(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 disk-shaped conformal mapping. Without loss of generality, Tutte's method can be used to calculate the disk-shaped mapping of surface S.

[0033] like Figure 1 As shown: The surface is conformally mapped to the disk-shaped region and parameterized with equal residual height in the radial direction. In Figure (b), the disk shape is obtained from the surface in Figure (a) through the conformal mapping of the disk shape. In Figure (b), the residual height between adjacent tool contacts in the original image of Figure (a) is consistent for the same radius, while the number of tool contacts in the original image of Figure (a) is inconsistent for different radii. Figure (d) is the image of the surface after renormalization parameterization. In Figure (d), the residual height between adjacent tool contacts in the original image of Figure (c) is consistent for the same radius, while the number of tool contacts 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 preimage of the radius on the curved surface is remember The parameter t∈[0,1] is represented as so It is also parameterized as The parameter t can be adjusted in the following way to make the residual height of the subsequently generated spiral trajectory most uniform:

[0035] Find the smallest positive integer n1 greater than 2 such that when t is divided into n1+1 equal parts. Any adjacent tool contacts and The residual height between the machining operations is a fixed value h1, and h1 is less than the maximum allowable residual height h. max However, when t is divided into n1 points... There must be at least one pair of adjacent tool contacts. and The residual height between the machining operations is greater than the maximum allowable residual height h. max Let all radii within the disk-shaped mapping domain be... The corresponding smallest equally divisible positive integers are {n1, n2, n3, ...}, and the maximum value of the set of smallest equally divisible positive integers is denoted as n. max =max{n1,n2,n3,...} Geometrically, it is an infinite set, but it can still be discretely expressed as a finite set. For example, the boundary of the surface can be divided equally by arc length using a large number m, and the set of radii passing through each dividing point can represent all radii within the disk-shaped mapping domain. Transform into a finite set This allows us to obtain the corresponding finite set {n1,n2,...,n} m n is obtained from} 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 Perform parameter renormalization so that when t is equally divided into n max +1 serving Any adjacent tool contacts and The residual height between processing steps is a fixed value. and Less than the maximum allowable residual height h max .

[0038] like Figure 1 As shown: In Figure (c), any The upper part is divided into 22 equal parts, resulting in 22 tool contact points. The machining residual height between adjacent tool contact points is consistent.

[0039] like Figure 2 As shown: In the third step, after parameter renormalization, the surface D can be represented by two parameters (t,θ) as D(t,θ), where t∈[0,1] on D is determined by... and The parameter transformations between them yield θ∈[0,2π], which is the inscribed 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. The isoparametric lines on S are gradually transformed... To adjacent isoparametric lines The spiral 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 tool contact point L. S The machining trajectory cannot be determined yet; the tool center movement trajectory L still needs to be calculated based on the tool contact point. O and tool axis vector There are multiple methods for this calculation; without loss of generality, we use the spiral trajectory L... S Solve for the blade core L O and tool axis vector L S For each point Pi on (t), follow the normal vector of S at Pi. Offset distance K c L can be obtained O (t). Tool axis normal corresponding to contact point Pi for:

[0041]

[0042] Where β is the cutter axis tilt angle, typically chosen to be 15–30°. For trajectory L O (t) Positive tangent direction.

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

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

[0045] 2. To address the issue of uneven trajectory spacing generated by isoparametric lines based on disk conformal mapping, a method is proposed to optimize the uniformity of trajectory residual height along the original image direction corresponding to the mapped radius line cluster. This results in more uniform spacing of the generated spiral trajectories, smaller fluctuations in material removal rate, and more consistent processing residual height.

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

Claims

1. A method for planning the machining path of complex curved surfaces, characterized in that, Includes the following steps: Step 1: Select a point on a surface with only one boundary, and map the surface to be processed to a 2D disk region using disk conformal mapping. The point is mapped to the center of the region. Step 2: Select any radius within the disk-shaped mapping domain, parameterize the preimage of the radius on the curved surface, and adjust the preimage parameters according to the following objectives to make the residual height of the subsequently generated spiral trajectory most uniform: Specifically, find a minimum positive integer greater than 2, divide the parameters corresponding to the preimage by this number, and use the point where the preimage parameters are evenly divided as the tool contact point. After adjusting the preimage parameters, the machining residual height between adjacent tool contact points is consistent and less than the maximum allowable residual height. Step 3: Perform parameter reshaping on all preimages corresponding to radii. The maximum value of the smallest positive integer corresponding to all preimages of radii on the circle is recorded as the maximum value of the reshaping. Divide the parameters of all preimages of radii into this value, and use the point where the preimage parameters are evenly divided as the tool contact point. After adjusting all preimage parameters one by one, the machining residual height between adjacent tool contact points of the same preimage is consistent and less than the maximum allowable residual height. After parameter reshaping, the surface can be represented by two parameters, where one parameter is obtained by reshaping the parameters corresponding to all preimages of radii, and the other parameter is the circumferential angle corresponding to the radius. Step 4: Within the disk-shaped area, gradually shift the isoparametric lines to adjacent isoparametric lines to generate a spiral as the machining path; Step 5: Calculate the tool center motion trajectory and tool axis vector based on the generated spiral tool contact points. The specific method is: offset each point on the spiral trajectory by a certain distance along its normal vector direction on the curved 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.

2. The method for planning the machining path of a complex curved surface according to claim 1, characterized in that: In step two, in order to discretely express the set of radii corresponding to the surface boundary as a finite set, the surface boundary is divided into 100 equal parts according to the arc length, and the set of radii passing through each equal division point represents all radii in the disk-shaped mapping domain.

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

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