Five-axis machining residual tool path generation method based on anisotropic heat diffusion
By using a five-axis machining residual height tool path generation method based on anisotropic thermal diffusion, the problems of redundant paths and low efficiency in multi-axis machining of complex curved surfaces are solved, and high-quality and high-efficiency CNC milling is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
- Filing Date
- 2024-12-30
- Publication Date
- 2026-06-30
Smart Images
Figure CN122308268A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of CNC machining technology, and particularly relates to a method for generating equal residual tool paths in five-axis machining based on anisotropic thermal diffusion. Background Technology
[0002] Multi-axis machining of complex surfaces is a key technology in parts production because it offers additional flexibility and performance. This technology allows for continuous control of the tool's position and orientation, resulting in better control of the machining process. However, this performance advantage also brings greater technical challenges, especially in toolpath planning. Machining efficiency and machining quality are the two most important goals for improving the added performance of multi-axis machining. This mainly involves the lateral distance, feed direction, and smoothness of the toolpath covering the entire machined surface, as well as optimizing the degree of variation in the tool axis direction and its smoothness. These two aspects are interconnected and jointly affect machining efficiency and machining quality. Due to the importance of toolpaths, extensive research has been conducted on toolpath generation over the past few decades. Among these, projection-based and isoplanar-based methods are the most widely used in commercial computer-aided manufacturing systems due to their versatility and robustness. However, an inherent drawback of these methods is that redundant paths may be generated in regions where the normal or projection vectors of intersecting planes are approximately perpendicular to the normal direction of the surface, thereby reducing machining efficiency and damaging the machined surface. To address this issue, mapping-based methods have been developed, which involve flattening a triangular mesh to a planar region to facilitate toolpath generation, and then reversing the mapping to obtain the desired CC curve. However, due to the nonlinearity of the mapping, it is difficult to precisely control the lateral step distance. Curve offset-based methods are effective for controlling the lateral step distance of the toolpath and the residual height of the machined surface, but they require reliable and accurate self-intersection detection and removal, and are extremely time-consuming. Recently, a toolpath generation method based on geodesic distance fields has emerged, proposing a recursive generation process for toolpath contours based on geodesic distance fields. However, this method requires iterative toolpath generation for each toolpath, resulting in high time costs. Therefore, a Poisson equation for the optimal toolpath length is constructed, and the toolpath is calculated using the finite element method.
[0003] Therefore, proposing a method for generating equal residual tool paths in five-axis machining based on anisotropic thermal diffusion to solve the difficulties in the existing technology is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention
[0004] This invention proposes a method for generating equal residual height tool paths in five-axis machining based on anisotropic thermal diffusion. The method uses thermal diffusion to calculate equal residual height tool paths, thereby realizing the generation of equal residual height tool paths for multi-axis machining of complex curved surfaces, thus improving the quality and efficiency of CNC milling finishing products.
[0005] To achieve the above objectives, the present invention adopts the following technical solution:
[0006] A method for generating equal-residual-height toolpaths for five-axis machining based on anisotropic thermal diffusion includes the following specific steps:
[0007] S1: Perform triangular meshing on the input workpiece to be processed according to the preset size constraints;
[0008] S2: Determine the machining tool, preferred tool axis direction, and preferred feed direction based on the preset machining requirements;
[0009] S3: Determine the location of the heat source based on the surface characteristics of the workpiece to be processed and the preferred feed direction requirements;
[0010] S4: Determine the anisotropic thermal diffusivity coefficient constrained by the residual height based on the surface features of the workpiece, the tool features, and the tool axis direction. Use the thermal diffusivity method to generate the tool contact curve, and then obtain the tool path.
[0011] Optionally, in the above method, the mesh size in S1 meets the preset size constraint, and the workpiece to be processed after triangular meshing is further refined.
[0012] Optionally, in the above method, the machining tool in S2 is pre-selected according to the machining process requirements and accessibility of the workpiece to be machined, and the preferred tool axis direction and preferred feed direction are set and selected according to the specific process requirements.
[0013] The above method, optionally, includes the following specific content for S3:
[0014] When the workpiece to be processed has curved surface boundaries, and the curved surface is an open boundary curved surface, if the preferred feed direction is not specified to be parallel to a specific boundary, the heat source is set on all boundaries of the curved surface; otherwise, the partial boundary perpendicular to the preferred feed direction is selected as the heat source.
[0015] When the workpiece to be processed has a curved surface boundary, and the curved surface is a closed surface, if the preferred feed direction is not specified, the extreme point of the closed surface is selected as the heat source to generate the tool path; otherwise, the intersection of the plane perpendicular to the preferred feed direction and the current surface is selected as the heat source.
[0016] The above method, optionally, includes the following specific content in S4: Calculate the geodesic in the triangular surface using the thermal diffusion method; optimize the generation of the tool path curve based on the input surface features, tool, preferred tool axis direction, preferred feed direction, and define a thermal diffusion metric weight based on the residual height; thereby obtain a tool contact curve with equal residual height; and obtain the tool path by combining the tool axis direction and tool parameters.
[0017] Optionally, the workpiece to be processed can be a workpiece with a complex curved surface.
[0018] As can be seen from the above technical solution, compared with the prior art, the five-axis machining equal residual height toolpath generation method based on anisotropic thermal diffusion of the present invention has the following beneficial effects:
[0019] (1) This patent uses the thermal diffusion method to calculate the tool path with equal residual height. Compared with existing algorithms, this method can be applied to almost any type of geometric discretization, including regular meshes, polygonal meshes, and even unstructured point clouds. That is, this method can be well extended and has extremely high versatility.
[0020] (2) The equal residual height tool path generation method based on anisotropic thermal diffusion in this patent only involves sparse linear systems. It can be pre-decomposed once and quickly re-solved multiple times. This characteristic makes the thermal diffusion method particularly valuable for the parallel computation of path planning and greatly improves the computational efficiency.
[0021] (3) This patent generates tool paths with equal residual height by designing appropriate thermal diffusion measures. In addition, due to the inherent characteristics of the thermal diffusion method, the resulting tool path is naturally smooth, which is beneficial to improving the dynamic performance of the CNC machining system, thereby improving machining efficiency and machining quality. Attached Figure Description
[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.
[0023] Figure 1 This is a flowchart of the five-axis machining equal residual height tool path generation method based on anisotropic thermal diffusion disclosed in this invention;
[0024] Figure 2 This is a general geometric diagram for calculating the residual height of complex curved surfaces in multi-axis machining, as disclosed in this invention.
[0025] Figure 3 The tool path is obtained by the equal residual height tool path generation method disclosed in this invention;
[0026] Figure 4 The residual height is the result of the residual height calculation obtained by the equal residual height toolpath generation method disclosed in this invention, with the residual height constraint set to 0.001mm. Detailed Implementation
[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. 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 skilled in the art without creative effort are within the scope of protection of the present invention.
[0028] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
[0029] Reference Figure 1 As shown, the method for generating equal-residual-height toolpaths for five-axis machining based on anisotropic thermal diffusion includes the following specific steps:
[0030] S1: Perform triangular meshing on the input workpiece to be processed according to the preset size constraints;
[0031] S2: Determine the machining tool, preferred tool axis direction, and preferred feed direction based on the preset machining requirements;
[0032] S3: Determine the location of the heat source based on the surface characteristics of the workpiece to be processed and the preferred feed direction requirements;
[0033] S4: Determine the anisotropic thermal diffusivity coefficient constrained by the residual height based on the surface features of the workpiece, the tool features, and the tool axis direction. Use the thermal diffusivity method to generate the tool contact curve, and then obtain the tool path.
[0034] Furthermore, in S1, the original surface or model needs to be triangulated, and the size of the mesh must meet the constraints of the given dimensions to obtain accurate and stable calculation results. The workpiece to be processed after triangulation is then refined (a limit of a mesh sequence is defined, which is a mesh sequence that uses a certain subdivision rule (usually a weighted average) to insert new vertices into the given initial mesh, thereby continuously refining the mesh. The subdivision rule is repeatedly applied, and at the limit, the mesh converges to a smooth curve or surface) to meet the calculation accuracy requirements.
[0035] Furthermore, in S2, the machining tool is pre-selected based on the machining process requirements and accessibility of the workpiece to be machined, and the preferred tool axis direction and preferred feed direction are set and selected according to specific process requirements.
[0036] Specifically, the direction of the cutter axis needs to be set according to the specific process requirements. For example, for ball end mills, the angle between the cutter axis and the normal of the curved surface can be kept constant. For flat end mills, the forward tilt angle needs to be kept constant and greater than 0, while the side tilt angle needs to be kept constant and equal to 0. The preferred feed direction needs to be selected according to the processing requirements. For example, for blade processing, the feed direction is generally required to be parallel to its guideline to obtain better processing quality.
[0037] Furthermore, the specific content of S3 is as follows:
[0038] When the workpiece to be processed has curved surface boundaries, and the curved surface is an open boundary curved surface, if the preferred feed direction is not specified to be parallel to a specific boundary, the heat source is set on all boundaries of the curved surface; otherwise, the partial boundary perpendicular to the preferred feed direction is selected as the heat source.
[0039] When the workpiece to be processed has a curved surface boundary, and the curved surface is a closed surface, if the preferred feed direction is not specified, the extreme point of the closed surface is selected as the heat source to generate the tool path; otherwise, the intersection of the plane perpendicular to the preferred feed direction and the current surface is selected as the heat source.
[0040] Furthermore, the specific content in S4 is as follows: the geodesic in the triangular surface is calculated using the thermal diffusion method. Based on the input surface features, tool, preferred tool axis direction, preferred feed direction, and the defined thermal diffusion metric weight based on the residual height, the tool path curve is optimized for generation. Thus, a tool contact curve with equal residual height is obtained. The tool path is obtained by combining the tool axis direction and tool parameters.
[0041] Specifically, the thermal diffusion method calculates the evolution of heat distribution within a region at a given time t by initializing local heat sources on a surface. This method calculates geodesic distances by simulating the diffusion of heat in a non-homogeneous medium.
[0042]
[0043] Where α is the thermal diffusivity, Δ is the Laplace operator, the concentration of a substance can be expressed as u, and the more general form of the thermal equation can be defined as follows:
[0044]
[0045] in, For the gradient operator, k(x) is the reciprocal of the specific heat of the substance multiplied by the density of the substance at a given location; in an isotropic medium, D is in the form of a constant scalar multiplied by the identity matrix I. dIt has different eigenvalues in anisotropic media.
[0046] Furthermore, the workpiece to be processed is a workpiece with a complex curved surface, such as a triangular curved surface or a rhomboid curved surface.
[0047] In one specific embodiment, the workpiece to be processed is a triangular curved surface workpiece, then the standard discretization of the Laplace operator of vertex i is:
[0048]
[0049] Among them, A i It is one-third of the area of all triangles including vertex i, where j is all adjacent vertices of i, and α ij ,β ij It is the diagonal of the corresponding side. The heat flux gradient at the triangular face f can be calculated as:
[0050]
[0051] Among them, A f Let N be the area of the triangle, and N be its unit normal. i Let u be the i-th edge vector. i This is the value of the corresponding vertex.
[0052] The heat flux that diffuses anisotropically on the triangular surface can be calculated using the symmetric positive definite system in equation (2):
[0053]
[0054] Where, δ γ G is the Kronecker function over γ, D is a matrix containing the thermal diffusivity measure, and G is the Kronecker function over γ. i It is the gradient operator. Let b be a normalized vector field. The divergence vector can be used to calculate the final geodesic distance by solving a symmetric Poisson problem.
[0055]
[0056] Furthermore, a practical challenge in using the thermal diffusivity method to calculate geodesics in triangular surfaces is designing a suitable thermal diffusivity metric D to produce meaningful results.
[0057] First, calculate the geodesic distance function on the triangular surface S. The CC curve can then be defined as a set of values. Geometric properties such as the tangent direction and trajectory interval of the toolpath can be used to represent curved surfaces; This indicates that modifying the thermal diffusivity measure can change... This alters the shape of the toolpath. Therefore, the properties of the toolpath are affected by the thermal diffusivity D.
[0058] Due to the change in the tool axis direction during machining, for non-spherical end mills (flat-end mills, bullnose mills, etc.), the effective radii of curvature r1 and r2 of the generalized tool at the tool contact points p1 and p2 on adjacent toolpaths are usually different. Figure 2 As shown. Therefore, the relationship between the lateral step distance w and the residual height h during general milling can be expressed as:
[0059]
[0060] Where, k s Let p1 be the normal curvature perpendicular to the feed direction, p2 be the tool contact point on the adjacent toolpath corresponding to p1, and the lateral step w = ||p2-p1||.
[0061] Since the geodesic distances of the tool contact curves passing through p1 and p2 on adjacent toolpaths can be expressed as φ(p1) and φ(p2), the relationship between the lateral step w and the geodesic distance can be expressed as:
[0062]
[0063] in, Since it is a vector perpendicular to the tangent direction of the tool contact curve, it can be further expressed as... We can obtain:
[0064]
[0065] The thermal diffusivity metric D, based on the residual height, can represent the degree of difference between the curvature intensity of each triangle on the surface and a specified value. In this patent, this plane is selected as the reference for the thermal diffusivity metric; that is, when the curvature is 0 and the scallop height is h, the thermal diffusivity metric is set to 1, and the lateral step distance is set to... The value of the triangle As a baseline, rewritten as Then D can be defined as:
[0066]
[0067] It should be noted that substituting equation (10) into equation (5) and solving equation (6) yields the tool contact curve with equal residual height. Combining this with the tool axis direction and tool parameters, the tool path can be obtained. (See [reference]). Figure 3 and Figure 4 As shown, this is the tool path and its residual height calculation result obtained by the equal residual height tool path generation method provided in this embodiment of the invention. The residual height constraint is set to 0.001mm.
[0068] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to the method embodiments, the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.
[0069] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A method for generating a residual height tool path for five-axis machining based on anisotropic heat diffusion, characterized in that, The specific steps include the following: S1: Perform triangular meshing on the input workpiece to be processed according to the preset size constraints; S2: Determine the machining tool, preferred tool axis direction, and preferred feed direction based on the preset machining requirements; S3: Determine the location of the heat source based on the surface characteristics of the workpiece to be processed and the preferred feed direction requirements; S4: Determine the anisotropic thermal diffusivity coefficient constrained by the residual height based on the surface features of the workpiece, the tool features, and the tool axis direction. Use the thermal diffusivity method to generate the tool contact curve, and then obtain the tool path.
2. The method of claim 1, wherein the method is characterized by: The mesh size in S1 meets the preset size constraints, and the workpiece to be processed after triangular meshing is further refined.
3. The method of claim 1, wherein the method is characterized by: In S2, the machining tool is pre-selected based on the machining process requirements and accessibility of the workpiece. The preferred tool axis direction and preferred feed direction are set and selected according to the specific process requirements.
4. The method for generating equal-residual-height toolpaths for five-axis machining based on anisotropic thermal diffusion according to claim 1, characterized in that, The specific content of S3 is as follows: When the workpiece to be processed has curved surface boundaries, and the curved surface is an open boundary surface, if the preferred feed direction is not specified to be parallel to a specific boundary, the heat source is set on all boundaries of the curved surface; otherwise, the part of the boundary perpendicular to the preferred feed direction is selected as the heat source. When the workpiece to be processed has a curved surface boundary, and the curved surface is a closed surface, if the preferred feed direction is not specified, the extreme point of the closed surface is selected as the heat source to generate the tool path; otherwise, the intersection of the plane perpendicular to the preferred feed direction and the current surface is selected as the heat source.
5. The method for generating equal-residual-height toolpaths for five-axis machining based on anisotropic thermal diffusion according to claim 1, characterized in that, The specific content of S4 is as follows: The geodesic in the triangular surface is calculated using the thermal diffusion method. Based on the input surface features, tool, preferred tool axis direction, preferred feed direction, and the defined thermal diffusion metric weight based on the residual height, the tool path curve is optimized to generate. Thus, a tool contact curve with equal residual height is obtained. The tool path is obtained by combining the tool axis direction and tool parameters.
6. The method for generating equal-residual-height toolpaths for five-axis machining based on anisotropic thermal diffusion according to any one of claims 1-5, characterized in that, The workpiece to be processed is a workpiece with a complex curved surface.