• International Journal of CAD/CAM
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• 제11권1호
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• pp.27-32
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• 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.

• 한국정밀공학회지
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• 제33권9호
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• pp.745-751
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• 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.

• 소성∙가공
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• 제12권2호
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• pp.151-160
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• 2003

In the present study, an advanced surface construction method based on NURBS surface scheme is proposed to construct the extrusion die surface. The inlet and outlet profiles we precisely described with NURBS curves using the cubic appropriate control points and weights. The interior control Points of surface are generated using the cubic interpolation of the weights at the inlet and outlet sections. In order to verify of the proposed method, automatic surface generation is carried out for the various types of extrusion die surface.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.151-165
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• 2002

An a1gorithmic approach to degree elevation of NURBS curves is presented. The new algorithms are based on the weighted blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (1) decompose the NURBS curve into piecewise rational Bezier curves, (b) elevate the degree of each rational Bezier piece, and (c) compose the piecewise rational Bezier curves into NURBS curve.

• 한국HCI학회:학술대회논문집
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• 한국HCI학회 2006년도 학술대회 1부
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• pp.480-485
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• 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.

• 한국정밀공학회지
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• 제23권9호
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• pp.156-163
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• 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.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2002년도 춘계학술대회 논문집
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• pp.227-232
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• 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

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 2003년도 춘계학술대회논문집
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• pp.343-346
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• 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. In the present study, a center point for area mapping is determined by introducing the marring concept based on constant area proportionality between original billet and final product. The characteristic points of inlet profile is 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.

• 한국정밀공학회지
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• 제19권5호
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• pp.89-94
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• 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.

• 대한조선학회논문집
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• 제32권3호
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• pp.29-36
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• 1995

본 연구는 선정된 기준선을 횡단면적 곡선(Sectional Area Curve:SAC)과 NURBS곡선을 사용하여 변환하는 기법을 내용으로 하고 있다. 즉, 선정된 기준선의 광역(global) 선형변환은 횡단면적 곡선의 기하학적 특성을 변형시켜 체계적으로 수행하고, 국소(local) 선형변환은 가중치의 증감과 조정점 이동 등을 통한 NURBS기법을 사용하였으며, 설계자는 이들 변환된 선형의 최종 횡단면적 곡선과 반폭도에서 기본적인 설계요구조건의 만족여부를 검토하게 된다.