Zhou Lai-shui

Intelligent NURBS Interpolator Based on the Adaptive Feedrate Control

Abstract To satisfy the need for high-speed and high-accuracy machining of NURBS curve. Firstly the form of NURBS curve is analyzed and Talors expansion of the parameter u with respect to time t is used to obtain the algorithm of the first order approximation interpolation. Secondly, based on the algorithm of the controlled chord error interpolator, an intelligent interpolation algorithm of the adaptive feedrate control is proposed. According to the actual machining capacity of machine tools, this algorithm uses look-ahead method, which dispenses with the complicated computation of the end point estimation of NURBS curve, to analyze the curve segment required by the maximum deceleration distance. Thus, the feedrate could decrease in advance and vary with the curvature and the variation ratio of curvature, which makes machining motion quite smooth. Not only could high accuracy and fine surface quality be achieved during high-speed machining, but also the overload of cutter tools is avoided on corners. Finally, in order to facilitate the calculation of interpolation, the dynamic matrix representation and efficient algorithm of curvature computation of the NURBS curve are presented.

Uniform Coverage of Fibres over Open-contoured Freeform Structure Based on Arc-length Parameter

Abstract This article uses arc-length parameters for path planning to carry out robotic fibre placement (RFP) over open-contoured structures. This allows representing the initial path and offset points using an identical mathematical equation and computation by more simple arithmetic. With the help of classical differential geometry, the calculation of fiber-placing paths may be reduced to solution of initial-value problems of first-order ordinary differential equations in the parametric domain (parametrically defined mould surface) or in 3D space (an implicitly defined mould surface), thereby significantly improving on the existing methods. Compared with the conventional methods, the proposed method, besides its computational simplicity, has a better error control mechanism in computing the initial path and offset points. Numerical experiments are also carried out to demonstrate the feasibility of the new method in composite forming processes and also its potential application in computer numerical control (CNC) machining, surface trim, and other industrial practices.

Constructing G2 Continuous Curve on Freeform Surface with Normal Projection

Abstract This article presents a new method for G 2 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with prescribed tangent direction and curvature vector, respectively, at every point. First, a G 2 continuous curve is constructed in three-dimensional space. Then the curve is projected normally onto the given surface. The desired interpolation curve is just the projection curve, which can be obtained by numerically solving the initial- value problems for a system of first-order ordinary differential equations in the parametric domain for parametric case or in three-dimensional space for implicit case. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification so that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface. Numerical experiments demonstrate that it is effective and potentially useful in numerical control (NC) machining, path planning for robotic fibre placement, patterns design on surface and other industrial and research fields.

Shape Modification by Beam Model in FEM

Abstract Shape modification and deformation play an important role in the filed of geometry modeling, computer graphics, conceptual design and so on. A novel physically based shape modification approach is presented in this article, with beam model in finite element method (FEM). By means of interactively creating a beam with circle cross section based on pre-defined local coordinate system, the primitive geometry model is embedded in the beam globally or locally. After imposing external loads, such as concentrated force or couple, on selected nodes, their displacement can be computed. Moreover, deflection, axial deformation and twist angle of beam model can also be interpolated using shape function matrix. As a result, object is modified as a part of beam. The proposed approach is linear, simple and fast, by which stretch, bending, taping and twist deformation can be accomplished. Finally, some experimental results are given to demonstrate that the presented method is potentially useful in geometry modeling and shape design.

Erratum to “Uniform Coverage of Fibres over Open-contoured Free-form Structure Based on Arc-length Parameter” [Chinese Journal of Aeronautics 21(2008)571-577]

It is regretted that the author corrections requested at the proof stage were not made accurately. There are some incorrect typings in two equations which will lead to inaccurate results if readers perform calculations directly with