WO2024050935A1 - Procédé de découpe de modèle tridimensionnel pour estampage et déchargement de haute qualité - Google Patents

Procédé de découpe de modèle tridimensionnel pour estampage et déchargement de haute qualité Download PDF

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Publication number
WO2024050935A1
WO2024050935A1 PCT/CN2022/127503 CN2022127503W WO2024050935A1 WO 2024050935 A1 WO2024050935 A1 WO 2024050935A1 CN 2022127503 W CN2022127503 W CN 2022127503W WO 2024050935 A1 WO2024050935 A1 WO 2024050935A1
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Prior art keywords
cutting
index
singular
triangle
singular points
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PCT/CN2022/127503
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English (en)
Chinese (zh)
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黄劲
鲍虎军
王诗怡
陈炯
高希峰
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浙江大学
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Publication of WO2024050935A1 publication Critical patent/WO2024050935A1/fr

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
    • G06T17/205—Re-meshing
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21D45/00—Ejecting or stripping-off devices arranged in machines or tools dealt with in this subclass
    • B21D45/02—Ejecting devices

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  • the invention belongs to the field of computer-aided design, and specifically relates to a three-dimensional model cutting method for high-quality stamping and discharging.
  • the existing technology usually breaks it down into a two-step solution: first, only considering the two indicators of cutting length (BL) and shape distortion (ED), the surface model parameters are into the plane area; then, the packing efficiency (PE) index is introduced in the plane area, and the plane packing efficiency (PE) is re-optimized while taking into account the cutting length (BL) and shape distortion (ED).
  • the texture atlas generated in the second step strongly depends on the parameterization in the first step.
  • the first step introduces a large number of redundant cuts or huge shape distortions, the final result will be The result falls into a local optimal solution, making it impossible to obtain high-quality stamping and discharge materials. Therefore, within the framework of two-step optimization, a parameterization technique that is conducive to plane texture re-optimization is crucial.
  • the purpose of this invention is to overcome the existing deficiencies and provide a three-dimensional model cutting method for high-quality stamping and discharging, thereby bridging the gap between the two-step optimization strategies in traditional cutting technology to meet the application requirements of high quality and high efficiency. . .
  • a three-dimensional model cutting method for high-quality stamping and layout including the following steps:
  • step S3 Connect the singular points simplified in step S1 to obtain a set of mutually perpendicular surface cutting edges;
  • step S1 includes:
  • ⁇ i and ⁇ j respectively represent the angle between any component of the four-symmetric direction field on triangle i and triangle j relative to the x-axis
  • ⁇ ij represents the angle difference between the x-axis parallel transmission of triangle i and triangle j
  • p ij represents Alignment jump between two triangle orientation fields
  • N( vi ) represents the set of triangles surrounding the vertex vi as the center
  • d( vi ) represents the angular deficit of the vertex vi
  • ⁇ b ( vi ) represents the integer basic index corresponding to the vertex vi .
  • the index ⁇ (vi ) corresponding to all vertices is formed into an index set I(vi ) , and the points corresponding to the non-zero elements in the set I(vi ) are extracted as singular points.
  • step S2 includes:
  • the index value corresponding to singular points, N represents the number of singular points of the four-symmetric direction field extracted in step S1;
  • ⁇ k represents the index vector of the k-th iteration
  • the initial value ⁇ 0 of the iteration is the ⁇ obtained in step S21
  • 0 represents the L0 norm
  • S k represents the simplified energy function value of the k-th iteration
  • E I ( ⁇ k ) represents the light of the four-symmetric direction field at the k-th iteration degree of compliance
  • w n is the weight value
  • ⁇ g is a vector composed of discrete Gaussian curvatures of all singular points, is the pseudo-inverse matrix of the Laplacian operator of the triangular mesh graph, and the superscript T represents the transpose.
  • step S3 includes:
  • the cutting lines intersect as perpendicularly as possible
  • the total length of the cutting line should be as short as possible.
  • step S31 is specifically:
  • p( ⁇ i , ⁇ j ) represents the shortest path along the grid line from point ⁇ i to point ⁇ j
  • d(.) represents the distance function
  • ⁇ k represents the k-th singular point
  • the calculation method of ( ⁇ i , ⁇ j )) is:
  • ⁇ m represents the m-th singular point
  • step S32 is specifically:
  • ⁇ k represents the k-th singular point
  • C t-1 represents the cutting edge set corresponding to the t-1th cutting
  • p( ⁇ k ,C t-1 ) represents the point ⁇ k to the cutting edge set C t- The shortest path along the grid lines of 1 ;
  • the shortest path p( ⁇ k ,C t-1 ) is merged into the cutting edge set to obtain the cutting edge set C t corresponding to the tth cut.
  • the present invention has the following beneficial effects:
  • the present invention provides a high-efficiency three-dimensional model cutting technical solution.
  • This technical solution can map the curved surface to a parameter domain shaped like a multi-connected square with low distortion, which is conducive to the subsequent optimization of plane packing efficiency, thereby achieving the purpose of high-quality and high-efficiency stamping and discharge.
  • the present invention found that the corner points of multi-connected squares have internal angles that are integer multiples of 90 degrees. When mapped to the cutting points of the curved surface, they correspond to angle deficits that are integer multiples of 90 degrees. Since the singular point of the four-symmetry direction field naturally satisfies this corner deficit property, this technical solution intends to draw on the technical ideas of the four-symmetry direction field and use it to design and guide the parameterization of high-quality and high-efficiency stamping and layout.
  • the present invention can efficiently and robustly obtain high-quality and high-efficiency stamping and discharging on several models, fully embodying the practical effect and value of the technology of the present invention. Compared with existing cutting technology, the present invention can obtain higher quality stamping and discharge materials, and improves the packaging efficiency (PE), cutting length (BL) and shape distortion (ED) indicators.
  • PE packaging efficiency
  • BL cutting length
  • ED shape distortion
  • Figure 1 is a flow chart of a three-dimensional model cutting method for high-quality stamping and discharging
  • Figure 2 is a schematic diagram of the three-dimensional model cutting method process using a specific input model as an example
  • Figure 3 is a statistical diagram of the relative improvement of PE, BL and ED indicators in the data set compared with the traditional method, where a-f is the comparative distribution diagram of the present invention and the VarCuts method, and g-l is the comparative distribution diagram of the present invention and the OptCuts method;
  • Figure 4 is a schematic diagram of the layout results of the three-dimensional model.
  • FIG. 1-2 it is a flow chart of a three-dimensional model cutting method for high-quality stamping and discharge provided in a preferred embodiment of the present invention.
  • the main steps include 4 steps, namely S1 ⁇ S4:
  • step S3 For the simplified singular points in step S2, optimize to obtain a set of mutually perpendicular surface cutting edges, and then cut the input model along the surface cutting edges into a model that is topologically homeomorphic to the disk;
  • the existing four-symmetry field generation technology often considers factors such as feature alignment and grid density. Such redundant constraints will not only lead to low solution speed, but also make the solution The device is stuck at the local optimal solution and cannot obtain the global optimal solution. Therefore, the goal of step S1 should be the optimization of the four-symmetry direction field under the intrinsic geometric characteristics of the model, that is, only considering the Gaussian curvature of the model without considering the alignment of the characteristic lines, etc. Other irrelevant factors.
  • the present invention introduces the evaluation energy of the smoothness of the four-symmetry direction field with respect to Gaussian curvature, thereby obtaining the four-symmetry direction field and singular points that meet the application goals.
  • the present invention adopts the form of piecewise constants, that is, on each patch of the triangular mesh, the direction field has a fixed direction. Since any two triangles in a triangular mesh in space are often non-coplanar, a local coordinate system needs to be introduced to consider the angle difference after parallel transmission of direction fields between different patches.
  • the smooth four-symmetry direction field is designed according to S11 to S15:
  • S11 Define a local coordinate system on each patch of the input model, where the x-axis is the unit vector on any side of the triangle, the y-axis is obtained by rotating the x-axis counterclockwise 90° in the triangle plane, and the z-axis is the x-axis Obtained by crossing the y-axis;
  • ⁇ i and ⁇ j respectively represent the angle between any component of the four-symmetric direction field on triangle i and triangle j relative to the x-axis
  • ⁇ ij represents the angle difference between the parallel transmission of the x-axis of triangle i and triangle j
  • the integer p ij represents the aligned jump between the two triangle orientation fields
  • the present invention provides an idea of merging and simplifying adjacent singular point pairs with indexes (-1, +1) under a topology that ensures the global four-symmetry direction field.
  • the method of simply merging the nearest (-1, +1) point pairs has two major disadvantages: on the one hand, it is difficult to determine a unified merging termination condition due to the geometric specificity of the model; on the other hand, it is difficult to determine only by the number of singular points. It is difficult to assess the degree of distortion after subsequent cuts. Therefore, the present invention provides a singular point simplification method that fully considers the inherent geometric shape of the model. Specifically, the singular point merging and simplification process in this embodiment is mainly implemented through step S2. The specific method is described in detail below:
  • the index value corresponding to singular points, N represents the number of singular points of the four-symmetric direction field extracted in step S1;
  • step S22 Enumerate all pairs of integer vectors ⁇ i and ⁇ j (i ⁇ j) to participate in the calculation of step S23, where the dimensions of ⁇ i and ⁇ j are the same as the dimensions of the index vector ⁇ , and ⁇ i has only the The i element is 1, the other elements are all 0, ⁇ j is similar, only the jth element is 1;
  • ⁇ k represents the index vector of the k-th iteration
  • the initial value ⁇ 0 of the iteration is the ⁇ obtained in step S21
  • 0 represents the L0 norm
  • S k represents the simplified energy function value of the k-th iteration
  • E I ( ⁇ k ) represents the four-symmetry direction field of the k-th iteration Smoothness
  • ⁇ g is a vector composed of discrete Gaussian curvatures of all singular points, is the pseudo-inverse matrix of the Laplacian operator of the triangular mesh graph, and the superscript T represents the transpose;
  • w n is the weight value
  • the calculation method is:
  • the simplified singular point set can finally be determined.
  • the present invention needs to connect the simplified singular points through cutting lines, thereby flattening the curved surface model to a planar area shaped like a multi-connected square with low distortion.
  • the following conditions need to be met in the process of connecting singular points: first, all singular points fall on the cutting line; second, the cutting lines should intersect as perpendicularly as possible; third, After the model is cut along the cutting line, it should be homeomorphic to the disc; fourth, the total length of the cutting line should be as short as possible.
  • the specific method of performing vertical cutting in step S3 is as follows:
  • step S31 Obtain the initial cut according to the topological characteristics of the input model: determine the genus of the input model. If the genus of the input model is greater than 0, execute step S311 and then proceed to step S32; otherwise, execute step S312 and then proceed to step S32;
  • each triangular grid is called cutting edges, and several cutting edges connected end to end are connected to form a cutting line.
  • p( ⁇ i , ⁇ j ) represents the shortest path along the grid line from point ⁇ i to point ⁇ j
  • d(.) represents the distance function
  • ⁇ k represents the k-th singular point
  • the calculation method of ( ⁇ i , ⁇ j )) is:
  • ⁇ m represents the m-th singular point
  • C t-1 represents the cutting edge set corresponding to the t-1th cut
  • p( ⁇ k ,C t-1 ) represents the shortest path along the grid line from point ⁇ k to the cutting edge set C t-1 ;
  • the vertical cutting of the complete three-dimensional model has been obtained, that is, the three-dimensional curved surface of any topological form can be cut along the cutting line into a surface that is homeomorphic to the disk.
  • step S4 The specific parameterization method of step S4 is briefly described below:
  • step S41 Cut the model along the cutting line obtained in step S3, and use the Tutte diagram embedding algorithm to deform the cut surface model into a flat space;
  • a i represents the area of the i-th triangle f i
  • J i represents the deformation Jacobian of the curved triangle under plane mapping
  • F-norm represents the square of the F-norm
  • the present invention has constructed a low-distortion mapping from a three-dimensional curved surface to a polygon-like shape, in order to achieve high-quality and high-efficiency stamping and discharging effects.
  • step S1 for each model in the effective data set, establish an optimization model based on the smooth energy mentioned above, and use the mixed integer optimization solver in the libigl code library to solve it to obtain the smooth four-symmetry direction field, and extract singular points according to the method mentioned above.
  • step S2 to iteratively simplify the singular points, and find the optimal (-1, +1) singular point pair for merging in each iteration. While reducing the number of singular points, the model after cutting is also considered. Degree of deformation.
  • the weight ratio between the shape distortion energy of the model and the number of singular points is 1:0.5, that is, ⁇ is set to 0.5. When the total optimization energy no longer decreases, the iteration stops.
  • step S3 Connect the simplified singular points according to the aforementioned step S3.
  • step S4 use the cutting line in step S3 to cut the model into a disc homeomorphic surface, and then perform low-distortion planar parametric mapping.
  • the cutting method of the present invention is named OrthoCuts. Compared with the original classic VarCuts method (Sharp N, Crane K. Variational surface cutting [J].
  • the present invention provides a discrete frequency distribution diagram of the relative improvement values (r PE , r BL , r ED ) of boxing efficiency, cutting length and shape distortion, as well as two relative improvement values Two-dimensional discrete distribution map under two combinations.
  • af is the comparison distribution diagram with VarCuts
  • gl is the comparison distribution diagram with OptCuts
  • a and g show the distribution of r PE
  • b and h show the distribution of r BL
  • c and i shows the distribution of r ED .
  • the present invention can achieve higher equipment performance at the same time. Box efficiency, shorter cutting length, and less distorted nesting effect.
  • the present invention also shows several sample results, as shown in Figure 4. It can be seen that the present invention can flatten the model with low distortion through mutually perpendicular cuts, such as The polysquare structure achieves high-efficiency and high-quality nesting results.

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Abstract

La présente invention se rapporte au domaine de la conception assistée par ordinateur. Est divulgué ici un procédé de découpe de modèle tridimensionnel pour un estampage et un déchargement de haute qualité. Le procédé comprend les étapes suivantes consistant à : 1) prendre en compte en totalité les informations géométriques d'une surface incurvée d'un modèle, générer un champ de direction à symétrie d'ordre quatre sur une surface incurvée d'entrée et extraire des points singuliers ; 2) réaliser une analyse de corrélation en utilisant le nombre de points singuliers et la longueur de lignes de découpe, et simplifier les points singuliers redondants ; 3) concevoir un ensemble de bords de découpe de surface incurvée perpendiculaires les uns aux autres, et découper la surface incurvée d'entrée en une structure homéomorphe à un disque circulaire tout en reliant les points singuliers ; 4) réaliser un paramétrage à faible distorsion sur la surface incurvée découpée et optimiser le résultat du paramétrage ; et 5) obtenir un estampage et un déchargement de haute qualité à l'aide d'un résultat d'optimisation de paramétrage plan. Le procédé présente les avantages suivants : l'efficacité élevée d'un polycarré est utilisée dans l'estampage et le déchargement, et les caractéristiques géométriques du polycarré sont prises en compte en totalité, de sorte à simplifier le fonctionnement, et à améliorer la robustesse ; de plus, la présente invention possède une valeur d'application pratique très importante pour l'estampage et le déchargement de haute qualité de tôles métalliques.
PCT/CN2022/127503 2022-09-05 2022-10-25 Procédé de découpe de modèle tridimensionnel pour estampage et déchargement de haute qualité WO2024050935A1 (fr)

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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109815527A (zh) * 2018-12-07 2019-05-28 上海赛科利汽车模具技术应用有限公司 一种热冲压模具的模面优化方法
CN110516388A (zh) * 2019-08-31 2019-11-29 大连理工大学 基于调和映射的曲面离散点云模型环切刀轨生成方法
US20200346420A1 (en) * 2017-10-27 2020-11-05 Technische Universität Berlin Auxetic Structure and a Method for Manufacturing an Auxetic Structure
CN113077553A (zh) * 2021-04-06 2021-07-06 华南理工大学 一种基于表面属性的三维模型分割方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20200346420A1 (en) * 2017-10-27 2020-11-05 Technische Universität Berlin Auxetic Structure and a Method for Manufacturing an Auxetic Structure
CN109815527A (zh) * 2018-12-07 2019-05-28 上海赛科利汽车模具技术应用有限公司 一种热冲压模具的模面优化方法
CN110516388A (zh) * 2019-08-31 2019-11-29 大连理工大学 基于调和映射的曲面离散点云模型环切刀轨生成方法
CN113077553A (zh) * 2021-04-06 2021-07-06 华南理工大学 一种基于表面属性的三维模型分割方法

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