• Title, Summary, Keyword: NURBS

Search Result 261, Processing Time 0.05 seconds

NURBS Interpolation Strategies of Complex Surfaces in High Speed Machining

  • Ameddah, Hacene;Assas, Mekki
    • International Journal of CAD/CAM
    • /
    • v.11 no.1
    • /
    • pp.27-32
    • /
    • 2011
  • The increase in the productivity and the assurance of quality machining on the NC machines depends on, amongst other things, the perfection of the programming using adequate methods of interpolation. The programming language is until now based on the code ISO 6983 which defines the principles of the code G. This latter is not well adapted to the new strategies of machining imposed by the machining of complex surfaces and machining at high speed with the increasingly more severe requirements of precision. The CNC which adopt the interpolation of NURBS (Non Uniform Rational B-spline) are very rare (FANUC Siemens${\ldots}$). Based on the advantages of NURBS (continuity, flexibility, smoothing$.{\ldots}$), new formats G are currently developed but their use is still very limited. Our work consists on putting forward these new approaches of programming using the interpolation of NURBS. For this reason, a program capable to trace NURBS trajectories under Visual BASIC 6.0 was developed. This program was used thereafter in CAM software for the generation of NURBS formats like their new formats NC.

  • PDF

Spline FEM for Trimmed NURBS Surfaces (트림영역이 있는 NURBS 평면의 스플라인 유한요소해석)

  • Kim, Hyun-Jung;Seo, Yu-Deok;Youn, Sung-Kie
    • Proceedings of the Computational Structural Engineering Institute Conference
    • /
    • /
    • pp.63-66
    • /
    • 2009
  • 본 논문에서는 트림영역이 있는 NURBS 평면을 등기하 해석할 수 있는 방법을 제시한다. 기존 등기하 해석법으로 트림 NURBS 곡면을 해석하기 위해서는 해석 도메인이 여러 개의 사각형 패치로 분할되어있어야 한다. 그러나 본 연구에서 제안한 방법은 CAD에서 제공하는 트림곡선의 정보를 해석에 직접 사용할 수 있기 때문에 CAD 모델을 별도로 재구성해야하는 번거로움이 없다. NURBS 곡선 투영법을 이용하여 트림되는 요소를 찾고, 트림된 요소는 쿼드트리 분할법과 NEFEM에서 사용된 적분방법을 동시에 고려하면 어떤 경우의 트림 요소라도 적분이 가능하다. 다양한 수치 예제를 통하여 제안한 해석 방법을 검증하고, 기존의 등기하해석법으로 해석하기 어려운 다수의 트림영역이 존재하는 NURBS 평면을 해석하여 본 방법의 유용성을 검토한다.

  • PDF

A Study on the Acceleration and Deceleration Control of Free-Form Surfaces (자유곡면의 가감속 제어에 관한 연구)

  • Baek, Dae Kyun;Yang, Seung-Han
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.33 no.9
    • /
    • pp.745-751
    • /
    • 2016
  • This paper presents the acceleration and deceleration control of free-form surfaces. A rapid variation of acceleration (or Deceleration) drives the system into a machine shock, resulting in the inaccuracy of the path control of the NURBS curve. The pattern of acceleration control can be established using the curvature of the NURBS curve. The curvature can be easily calculated from the first and second derivative of the NURBS curve used in Taylor's expansion for NURBS interpolation. However, the derivatives are not used in the recursive method for NURBS interpolation. Hence, we attempted the difference-derivatives for calculating the NURBS curvature. Both, Taylor's expansion and the recursive method, are used jointly for controlling the acceleration in the same interpolation algorithm.

The NURBS Surface Deformation by Modified FEM for Virtual Design (가상 디자인을 위한 수정된 유한요소법을 이용한 NURBS 곡면 변형)

  • Kwon, Jung-Hoon;Chai, Young-Ho
    • 한국HCI학회:학술대회논문집
    • /
    • /
    • pp.480-485
    • /
    • 2006
  • 본 논문에서는 사용자가 NURBS 곡면을 다양한 형태로 변형을 손쉽게 할 수 있는 수정된 유한요소법을 이용한 곡면 변형의 방법을 제시한다. 수정된 유한요소법은 NURBS 기저함수를 전통적 유한요소법의 형상함수를 대신하여 유한요소해석을 한다. 모델링된 객체는 NURBS 곡면으로 이루어져 있고, 각각의 세그먼트별로 나누어진 기저함수와 제어점으로 구성되어있기 때문에 번거롭게 요소와 형상함수를 따로 구하지 않아도 되며, 자체 보간 방식이므로 기존의 유한요소법에 비해 적은 요소와 절점으로 곡면을 해석 할 수 있다. NURBS 곡면 변형은 각각의 제어점에 의해 구역이 나눠지고 각 구역은 변형될 지점과 가장 가까운 제어점으로 구성된 구역의 제어점들을 변형시킬 지점과 각 제어점의 거리 비례에 따라서 제어점 들의 속도가 지정되어 변형을 완성한다. 제시된 변형 방법은 다른 변형들과 같이 초기 입력에 의해 변형이 한 순간에 진행되는 것이 아니라 점진적 변형이 일어나며, NURBS 의 특징인 전체 제어점 변형으로 인해 의도하지 않은 변형이 일어나는 것을 변형 중간에 각각의 제어점의 속도를 제어함으로써 사용자의 의도한 변형으로 빠른 시간에 완성할 수 있게 된다.

  • PDF

Intelligent NURBS Surface Interpolation System with Embedded Online Tool-Path Planning (온라인 방식의 공구경로 계획을 내장한 지능형 NURBS 곡면 보간 시스템)

  • Koo, Tae-Hoon;Jee, Sung-Chul
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.23 no.9
    • /
    • pp.156-163
    • /
    • 2006
  • The purpose of this study is to improve the machining of free-formed NURBS surfaces using newly defined G-codes which can directly deal with shapes defined from CAD/CAM programs on a surface basis and specialize in rough and finish cut. To this purpose, a NURBS surface interpolation system is proposed in this paper. The proposed interpolation system includes online tool-path planning, real-time interpolation and feedrate regulation considering an effective machining method and minimum machining time all suitable for unit NURBS surface machining. The corresponding algorithms are simultaneously executed in an online manner. The proposed NURBS surface interpolation system is integrated and implemented with a PC-based 3-axis CNC milling system. A graphic user interface (GUI) and a 3D tool-path viewer which interprets the G-codes for NURBS surfaces and displays whole tool-paths are also developed and included in our real-time control system. The proposed system is evaluated through actual machining in terms of size of NC data, machining time, regulation of feedrate and cutting force focused on finish cut in comparison with the existing method.

Investigation on the Automatic Surface Generation for Extrusion Die of T-shaped Section using NURBS Surface and Area Mapping Method (NURBS 곡면과 면적 사상법을 이용한 T-형 압출 금형곡면의 자동생성에 관한 연구)

  • 임종훈;유동진
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.20 no.10
    • /
    • pp.208-217
    • /
    • 2003
  • In order to construct the extrusion die surface of T -shaped sections, an automatic surface construction method based on NURBS surface and area mapping method is proposed in the present work. In the present study, a center point for area mapping is determined by introducing the mapping concept based on constant area proportionality between original billet and final product. The characteristic points of inlet profile are determined using the traditional area mapping method and the root finding numerical method. The inlet and outlet profiles are precisely described with NURBS curves using the characteristic points of entry and exit sections. For the construction of NURBS surface, an interpolation method for the pre-determined two section curves has been developed to be used in the generation of interior control points and weights. To show the validity of the proposed method, automatic die surface generation is carried out for the T-shaped section and T-shaped section with rounded corners.

Investigation on the Description Method of Extrusion Die Surface using NURBS Surface and Area Mapping Method (NURBS 곡면과 면적사상법을 이용한 압출 금형 곡면의 표현방법에 관한 연구)

  • 유동진;권혁홍;임종훈
    • Transactions of Materials Processing
    • /
    • v.12 no.4
    • /
    • pp.348-357
    • /
    • 2003
  • In order to construct the extrusion die surface of arbitrarily shaped sections, an automatic surface construction method based on NURBS surface and area mapping method is proposed in the present work. A center point fur area mapping is determined by introducing the mapping concept based on constant area proportionality between original billet and final product. The characteristic points of inlet profile are determined using the traditional area mapping method and the root finding numerical method. The inlet and outlet profiles are precisely described with NURBS curves using the characteristic points of entry and exit sections. For the construction of NURBS surface, an interpolation method for the pre-determined two section curves has been developed to be used in the generation of interior control points and weights. To show the validity of the proposed method, automatic die surface generation is carried out for the several kinds of shaped sections.

A study on the real-time NURBS interpolation algorithm (실시간 NURBS 보간 알고리즘에 관한 연구)

  • 최인휴;양민양
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
    • /
    • /
    • pp.227-232
    • /
    • 2002
  • This paper presents an algorithm for general 2D and 3D NURBS interpolation and deals with command generation for 3 axes milling machining, including the feedrate control in order to meet two limitations, a geometrical accuracy and a dynamic restriction. Both of the maximum chordal error and the maximum acceleration specified by machine parameter lead to limit the allowable feedrate on the curvature of NURBS tool path. So, motion commands at every sampling time are continuously generated by those two limitations and programmed feedrate. Simulation results of interpolating several NURBS curves show that proposed NURBS algorithm is favorable in the machining free-form curve

  • PDF

Simultaneous 3D Machining with Real-Time NURBS Interpolation (실시간 NURBS 보간에 의한 동시 3차원 가공에 관한 연구)

  • Hong, Won-Pyo;Yang, Min-Yang;Lee, Eung-Ki
    • Journal of the Korean Society for Precision Engineering
    • /
    • v.19 no.5
    • /
    • pp.89-94
    • /
    • 2002
  • Increasing demands on precision machining using CNC machines have necessitated that the tool to move with a position error as small as possible in 3-dimensional (3D) space. This paper presents the simultaneous 3D machining with a retrofitted PC-NC milling machine. To achieve the simultaneous 3-axis motions, a new precision interpolation algorithm for 3D Non-Uniform Rational B-Spline(NURBS) curve is used. With this accurate and efficient algorithm for the generation of complex. 3D shapes, a real-time NURBS interpolator was developed using a PC and the simultaneous 3D machining is accomplished.

Automatic Generation System for Quadrilateral Meshes on NURBS Surfaces (NURBS 곡면에서 사각형 요소망의 자동생성 시스템)

  • Kim, Hyung-Il;Park, Jang-Won;Kwon, Ki-Youn;Cho, Yun-Won;Chae, Soo-Won
    • Proceedings of the KSME Conference
    • /
    • /
    • pp.894-899
    • /
    • 2000
  • An automatic mesh generation system with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed.. In this paper, NURBS surface geometries in the IGES format have been used to represent model shape. NURBS surface is represented as parametric surface. So each surface could be mapped to a 2D parametric plane through the parametric domain. And then meshes with quadrilateral elements are constructed in this plane. Finally, the constructed meshes are mapped back to the original 3D surface through the parametric domain. In this paper, projection plane, quasi-expanded plane and parametric Plane are used as 2D mesh generation plane. For mapping 3D surface to parametric domain, Newton-Rhapson Method is employed. For unstructured mesh generation with quadrilateral elements on 2D plane, a domain decomposition algorithm using loop operators has been employed. Sample meshes are represented to demonstrate the effectiveness of the proposed algorithm.

  • PDF