• Journal of the Korean Society for Precision Engineering
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• v.23 no.9 s.186
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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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.471-474
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• 2004

In this paper, a NURBS surface interpolator is proposed which can deal with shapes defined from CAD/CAM programs on a surface basis and can improve contour accuracy. The proposed interpolator is based on newly defined G-codes and includes online tool-path planning suitable for NURBS surface machining. The real-time interpolation algorithm, considering an effective machining method for each machining process and minimum machining time, is executed in an online manner. The proposed interpolator is implemented on a PC-based 3-axis CNC milling system and evaluated through actual machining in terms of machining time and regulation of feedrate and cutting force in comparison with the existing method.

• 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.

• 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.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.10a
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• pp.784-787
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• 2002

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 sample 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.63-66
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• 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.

• Journal of the Korean Society for Precision Engineering
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• v.33 no.9
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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.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.8 s.197
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• pp.97-107
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• 2007

The present CNC machining system if without any CAM software has been limited to 2D or 2.5D plane cut using lines, arcs and curves. If the CNC is equipped with a surface interpolation module and a surface reorganizing module inside it, we can easily try 3D surface machining without aid of CAM software. The existing NURBS surface interpolator is simple and direct to use for a unit surface. However, it enables only machining of each reference surface individually even when machining a simple composite surface. In this paper, we propose a method which can unify and reorganize various reference surfaces with a newly defined NURBS surface cycle command: a multi-repetitive cycle command such as in a CNC turning center. We also introduce a reorganizing rule for reference surfaces using NURBS properties. The usefulness of the proposed method is verified through computer simulation.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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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.

• Transactions of Materials Processing
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• v.12 no.4
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• pp.348-357
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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. 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.