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Prediction of cutting forces in flank milling of parts with non-developable ruled surfaces

Chinese Journal of Aeronautics 2019年第7期32卷 1788-1796页

作者： Liping WANG Hao SI Liheng GU Department of Mechanical Engineering Tsinghua UniversityBeijing100084China Beijing Beiyi Machine Tool Co.Ltd. Beijing101300China

Predicting the cutting forces required for five-axis flank milling is a challenging task due to the difficulties involved in determining the Undeformed Chip Thickness(UCT) and CutterWorkpiece Engagement(CWE). To solve these problems, this paper presents a new mechanistic cutting force model based on the geometrical analysis of a flank milling process. In the model,the part feature and corresponding cutting location data are taken as input information. The UCT considering cutter runout is calculated according to the instantaneous feed rate of the element cutting edges. A solid-discrete-based method is used to precisely and efficiently identify the CWE between the end mill and the surface being machined. Then, after calibrating the specific force coef-ficients, the mechanistic milling force can be obtained. During the validation process, two practical operations, three-axis flank milling of a vertical surface and five-axis flank milling of a nondevelopable ruled surface, are conducted. Comparisons between predicted and measured cutting forces demonstrate the reliability of the proposed cutting force model.

关键词： Chip thickness Cutting force Five-axis flank milling Machining ruled surface

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Evolutions of the ruled Surfaces via the Evolution of Their Directrix Using Quasi Frame along a Space Curve

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Journal of Applied Mathematics and Physics 2018年第8期6卷 1748-1756页

作者： M. A. Soliman Nassar H. Abdel-All R. A. Hussien Taha Youssef Department of Mathematics Faculty of Science Assiut University Assiut Egypt

In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directr... 详细信息

关键词： ruled Surfaces Quasi Frame Frenet Frame Evolution of Space Curves

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A unified approach to kinematic synthesis of mechanism by adaptive curve fitting

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Science China(Technological Sciences) 2004年第1期47卷 85-96页

作者： WANG Delun WANG Shufen School of Mechanical Engineering Dalian University of Technology Dalian 116024 China School of Mechanical Engineering Dalian University of Technology Dalian 116024 China

A unified approach to kinematic synthesis of mechanism is presented in this paper. Firstly a new approach to adaptive curve fitting is presented, which leads the normal fitting error to be minimum for a series of given discrete points, including a plane curve fitting, a spherical curve fitting and a ruled surface fitting in terms of invariants of ruled surface. Approximate characteristic points and lines are defined, such as an approximate circle point, an approximate slide point, an approximate spherical cone point and an approximate constant axis with an approximate spherical image cone point and an approximate striction curve. Then,the ruled surface fitting will be converted into a space curve fitting and a spherical curve fitting by differential geometry. Based on these definitions and the adaptive curve fitting approaches, the unified mathematical model is set up for the kinematic synthesis of mechanism from planar, spherical to spatial motion. Finally, a planar mechanism or a spatial mechanism can be synthesized by means of searching for two approximate characteristic points, or a characteristic point and a characteristic line, even two characteristic lines. This puper lays a theoretic base for the existence of the best solution and the convergence of the optimum algorithm.

关键词： kinematics, mechanism synthesis, ruled surface, adaptive curve fitting.

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The Ricci Operator and Shape Operator of Real Hypersurfaces in a Non-Flat 2-Dimensional Complex Space Form

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Advances in Pure Mathematics 2013年第2期3卷 254-258页

作者： Dong Ho Lim Woon Ha Sohn Hyunjung Song Department of Mathematics Hankuk University of Foreign Studies Seoul Republic of Korea Department of Mathematics Yeungnam University Kyongbuk Republic of Korea

In this paper, we study a real hypersurface M in a non-at 2-dimensional complex space form M2(c) with η-parallel Ricci and shape operators. The characterizations of these real hypersurfaces are obtained.

关键词： Real Hypersurface η-Parallel Shape Operator η-Parallel Ricci Operator Hopf Hypersurface ruled Real Hypersurfaces

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