Papers by Keyword: Parametric Surface

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Authors: Yue Ping Chen, Xiao Dong Nie, Yan Hui Chen, Shi Dong Li
Abstract: Complex surfaces have been widely used in engineering. However, the current general-purpose CAD systems do not provide the modeling method of some kinds of complex surfaces such as parametric surfaces. In this paper, complex surfaces are generated by calculating the coordinates of the data points on the surfaces, creating the data files, importing the files into UG (Unigraphics), and then making use of the surface modeling functions of this software. Taking a bicubic B-spline surface for an example, the main steps of modeling of complex surfaces are presented and the modeling errors are analyzed in detail. A test is conducted to verify this approach.
Authors: Wei Min Yang
Abstract: In five-axis tool path planning, interference between the cutting tool and parametric surface is very critical. One way of doing interference detection is first to discretize the surface. In this article we develop a new approach to discretize parametric surface adaptively by applying curvature sphere. Layer by layer the original surface is discretized into triangle meshes bases on the polyline between the triangulated and un-triangulated areas of the surface. Triangles generated with our method are adaptive, which means the density of the triangles changes with the local curvature value of the surface. We also develop a method to deal with triangle meshes overlapping problem. So triangle meshes generated with our algorithm is without gaps or any overlapping problem. Finally a criterion is suggested when the generation should stop. The algorithm has been tested for some parametric surfaces and the result turns out to be satisfactory.
Authors: Zhi Qiang Zhang, Wen Jin Wang, Zhao Jian, Tai Yong Wang
Abstract: The part’s surface quality of NC machining is influenced by the chord error greatly. The confined chord error algorithm for machining complex parametric surface is proposed for controlling the chord error. The arc length error is utilized to control the chord error of the interpolated point indirectly. The arc length error of interpolated point is computed by trapezia expressions, the coordinate and the first order derivative of interpolated point is computed by the interpolation algorithm. The computed error of confined chord error algorithm is discussed and the simulation indicate that the destined precision of the chord error can be satisfied by this algorithm.
Authors: Ján Kráľ, Ján Kráľ
Abstract: Verification of programming of various control systems and production of mathematically defined shaped surfaces on 3D CNC milling machine is a challenging technological process. Appropriate design and optimization of tool path is essential for the production of high-quality surfaces with the required accuracy and roughness. This paper presents the design of shaped surfaces in various programming means in order to evaluate both the accuracy of the shape manufactured by the production machine and also by program created shapes for control systems of 3D milling machines. Based on the analysis of mathematically defined shaped surfaces to evaluate both accuracy of shape of 3D milling machine and also applied programs for the programming of the selected control system the shaped surface "Interface" was chosen. The advantage of mathematically described surface is a better way to evaluate the accuracy compare to surface modeled e.g. by Bezier ́s curves. Mathematically described surfaces enable us to optimize their shapes by available mathematical functions. Typical example the derivatives are, which make it possible to search extremes. Verification of the shaped surfaces accuracy according to created control programs was solved using the 3D Carl-Zeiss coordinate system and also HOLOS software. Verified programs for the NC machine programming were in CATIA V5, Pro/Engineer and EqCAM. The result is an optimally designed original EqCAM program for 3D CNC milling machine programming, which generates optimal NC codes and bypasses various built-in interpolations, and by precise control at every step it is possible to achieve maximum accuracy and quality of machined surface for each 3D CNC milling machine.
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