• Title, Summary, Keyword: NURBS

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Integration of Geometrically Exact Shell Finite Element With Trimmed Surface Modeling base on the NURBS (기하학적으로 정확한 셀 유한요소와 NURBS기반의 Trimmed Surface 모델링과의 연동)

  • Choi Jin-Bork;Roh Hee-Yuel;Cho Maeng-Hyo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.794-801
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    • 2006
  • The linkage framework of geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating the given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES format file which is generated by the commercial CAD systems in the present study. Numerical examples shows the rate of displacement convergence according to the paramterization methods of the NURBS surface. NURBS can generate quadric surfaces in an exact manner. It is the one of the advantages of the NURBS. A trimmed NURBS surface that is often encountered in the modeling process of the CAD systems is also presented in the present study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS equation is compared to those of the previous reported FE shell elements in the selected benchmark problems.

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Implementation of NURBS interpolator (NURBS 보간의 적용)

  • 최인휴;양민양;이강주;김찬봉
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.51-54
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    • 2002
  • This paper deals with an implementation of NUBS interpolator and presents the process of its integration into PC-NC. For more accurate feed, NURBS algorithm is improved. Also, Evaluation of real time NURBS interpolator is provided to verify fred accuracy and geometrical accuracy of NURBS curve. NURBS machining of fee surface is simulated on the real time NC simulator so that machining time is compared to that of linear path machining.

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NURBS Post-processing of Linear Tool Path (미소직선 공구경로의 NURBS 변환)

  • Kim, Su-Jin;Choi, In-Hugh;Yang, Min-Yang
    • Proceedings of the KSME Conference
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    • pp.1111-1117
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    • 2003
  • NURBS (Non Uniform Rational B-Spline) is widely used in CAD system and NC data for high speed machining. Conventional CAM system changes NURBS surface to tessellated meshes or Z-map model, and produces linear tool path. The linear tool path is not good for precise machining and high speed machining. In this paper, an algorithm to change linear tool path to NURBS one was studied, and the machining result of NURBS tool path was compared with that of linear tool path. The N-post, post-processing and virtual machining software was developed. The N-Post post-processes linear tool path to NURBS tool path and quickly shades machined product on OpenGL view and compares a machined product with original CAD surface. A virtual machined model of original tool path and post-processed tool path was compared to original CAD model. The machining error of post-processed NURBS tool path was reduced to 43%. The original tool path and NURBS tool path was used to machine general model using same machine tool and machining condition. The machining time of post-processed NURBS tool path was reduced up to 38%.

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Automatic Mesh Generation on Poorly Parameterized NURBS Surfaces (불균일한 매개변수로 정의된 NURBS 곡면에서의 요소망 자동 생성)

  • 채수원;박정민
    • Journal of the Korean Society for Precision Engineering
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    • v.20 no.6
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    • pp.189-196
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    • 2003
  • The NURBS surfaces are widely employed for exchanging geometric models between different CAD/CAE systems. However if the input NURBS surfaces are poorly parameterized, most surface meshing algorithms may fail or the constructed meshes can be ill-conditioned. In this paper presents a new method is presented that can generate well conditioned meshes even on poorly parameterized NURBS surfaces by regenerating NURBS surfaces. To begin with, adequate points are sampled on original poorly parameterized surfaces and new surfaces are created by interpolating these points. And then, mesh generation is performed on new surfaces. With this method, models with poorly parameterized NURBS surfaces can be meshed successfully.

NURBS Surface Reconstruction from an Unstructured Point Cloud (비조직화된 점군으로부터 NURBS 곡면 모델의 생성)

  • Li, Ri-Xie;Kim, Seok-Il
    • Proceedings of the KSME Conference
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    • pp.1564-1569
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    • 2007
  • This study concerns an advanced NURBS surface reconstruction method, which is based on the NURBS surface model fitting to the unstructured point cloud measured from an arbitrary complex shape. The concept of generating a simple triangular mesh model was introduced to generate a quadrilateral mesh model well-representing the topological characteristics of point cloud. The NURBS surface reconstruction processes required the use of the various methodologies such as QEM algorithm, merging scheme of pair-wise triangular mesh, creation algorithm of $G^1$ continuous tensor product NURBS surface patch, and so on. The effectiveness and reliability of the proposed NURBS surface reconstruction method were validated through the simulation results for the geometrically and topologically complex shapes.

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The application of geometrically exact shell element to NURBS generated by NLib (기하학적으로 정확한 쉘 요소의 NLib에 의해 생성된 NURBS 곡면에의 적용)

  • Choi Jin-Bok;Oh Hee-Yuel;Cho Maeng-Hyo
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.301-308
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    • 2005
  • In this study, we implement a framework that directly links a general tensor-based shell finite element to NURBS geometric modeling. Generally, in CAD system the surfaces are represented by B-splines or non-uniform rational B-spline(NURBS) blending functions and control points. Here, NURBS blending functions are composed by two parameters defined in local region. A general tensor-based shell element also has a two-parameter representation in the surfaces, and all the computations of geometric quantities can be performed in local surface patch. Naturally, B-spline surface or NURBS function could be directly linked to the shell analysis routine. In our study, we use NLib(NURBS libraray) to generate NURBS for shell finite analysis. The NURBS can be easily generated by interpolating or approximating given set of data points through NLib.

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T-spline FEA for Trimmed NURBS Surface (트림 NURBS 곡면의 T-스플라인 유한요소해석)

  • Kim, Hyun-Jung;Seo, Yu-Deok;Youn, Sung-Kie
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.2
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    • pp.135-144
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    • 2009
  • In this present work, spline FEA for the trimmed NURBS surface of the 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional efforts for modeling of trimmed NURBS surfaces are needed and the information of the trimming curves and trimmed surfaces exported from the CAD system can be directly used for analysis. For this, trimmed elements are searched by using NURBS projection scheme. The integration of the trimmed elements is performed by using the NURBS-enhanced integration scheme. The formulation of constructing stiffness matrix of trimmed elements is presented. In this formulation, the information of the trimming curve is used for calculating the Jacobian as well as for obtaining integration points. The robustness and effectiveness of the proposed method are investigated through various numerical examples.

On Constructing NURBS Surface Model from Scattered and Unorganized 3-D Range Data (정렬되지 않은 3차원 거리 데이터로부터의 NURBS 곡면 모델 생성 기법)

  • Park, In-Kyu;Yun, Il-Dong;Lee, Sang-Uk
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.37 no.3
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    • pp.17-30
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    • 2000
  • In this paper, we propose an efficient algorithm to produce 3-D surface model from a set of range data, based on NURBS (Non-Uniform Rational B-Splines) surface fitting technique. It is assumed that the range data is initially unorganized and scattered 3-D points, while their connectivity is also unknown. The proposed algorithm consists of three steps: initial model approximation, hierarchical representation, and construction of the NURBS patch network. The mitral model is approximated by polyhedral and triangular model using K-means clustering technique Then, the initial model is represented by hierarchically decomposed tree structure. Based on this, $G^1$ continuous NURBS patch network is constructed efficiently. The computational complexity as well as the modeling error is much reduced by means of hierarchical decomposition and precise approximation of the NURBS control mesh Experimental results show that the initial model as well as the NURBS patch network are constructed automatically, while the modeling error is observed to be negligible.

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Simulation Study for the Application of NURBS Interpolator (CNC공작기계에 NURBS 보간 알고리즘 적용을 위한 시뮬레이션 분석)

  • 김태훈;고태조;김희술
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • pp.979-982
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    • 2001
  • In CNC machining, demands on precision machining of free formed surface model are increasing. Most of the CAD/CAM systems provide the NURBS(Non-Uniform Rational B-Spline) interpolator. NURBS is defined with NURBS parameter by control point, weight value and knot value. This paper shows the realtime NURBS interpolation algorithms and compared with each other. One is based on the equal length of curve segments rather than equal increment of the parameter Δu. The other is to limit the interpolation error to any desired level by adjusting the feedrate considering the curvature of the shape and sampling time.

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NURBS Interpolation Algorithm for CNC Machining with High Speed and High Precision (고속ㆍ고정도 CNC가공을 위한 NURBS 보간 알고리즘)

  • 김민중;송진일;권동수
    • Journal of the Korean Society for Precision Engineering
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    • v.17 no.1
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    • pp.192-197
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    • 2000
  • In CNC machining, a free curve is cut into small linear segments using the linear interpolation(G01) method. Therefore, the interpolation error along the curve is not constant due to the changing curvature. This paper presents a NURBS (Non-Uniform Rational B-Spline) interpolation algorithm for machining free curves with high precision and high speed. The proposed NURBS interpolation defines the tool path with NURBS parameters and limits the interpolation error to any desired level by adjusting the feed rate considering the curvature of the shape and sampling time. Both linear and NURBS interpolations are compared to show the validity of the proposed algorithm.

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