Slip-line modeling of machining with a rounded-edge tool—Part I: new model and theory

The effect of tool edge roundness attracts growing attention from the international machining research community due to ever accelerating applications of precision, super-precision, micro-, and nano-machining technologies in a wide variety of modern industries. A new slip-line model for machining with a rounded-edge tool and its associated hodograph are proposed in this paper. The model consists of 27 slip-line sub-regions, each sub-region having its own physical meaning. It is demonstrated that the model simultaneously takes into account nine effects, such as the shear-zone effect and the size effect, which commonly occur in machining. Eight groups of machining parameters, such as the ploughing (parasitic or non-cutting) force and the chip up-curl radius, can be simultaneously predicted from the model. Furthermore, the model incorporates eight slip-line models previously developed for machining during the last six decades as special cases. An additional special case that involves a parallel-sided shear zone can also be derived from the new model. A mathematical formulation of the model is established based on Dewhurst and Collins's (1973) matrix technique for numerically solving slip-line problems. A purely analytical equation is proposed to predict the thickness of the primary shear zone. This equation is also employed to predict the shear strain-rate in the primary shear zone.     

答YapH.P.和TeoS.K.问题

本文证得：如果Ｆ是Ｃｎ中的一条种路，则Ｇ中同时通过ｋ余弦ｅ１，ｅ２，．．．，ｅｋ而不通过Ｆ中的任一条边的圈最多只有一个且Ｇ中同时通过ｋ条弦ｅ１，ｅ２，．．．，ｅｋ的圈最多只有２个，进而由之给出了Ｍ（ｋ）的上界和ｍ（ｋ）的下界及ｍ（ｋ）＝（ｋ＋１）（ｋ＋２）／２成立的一个条件，否定地回答了ＹａｐＨ．Ｐ．和ＴｅｏＳ．Ｋ．１９８４年提出的一个问题。     

Hybrid Optical-Electronic Implementation of Morphological Edge Detection

ＨｙｂｒｉｄＯｐｔｉｃａｌ－ＥｌｅｃｔｒｏｎｉｃＩｍｐｌｅｍｅｎｔａｔｉｏｎｏｆＭｏｒｐｈｏｌｏｇｉｃａｌＥｄｇｅＤｅｔｅｃｔｉｏｎ￥ＹＵＡＮＳｈｉｆｕ；ＺＨＡＮＧＸｕｅｒｕ；ＺＨＡＯＳｈｉｊｉｅ；ＬＩＹａｎ；ＣＨＥＮＬｉｘｕｅ（Ｄｅｐａｒｔｍｅｎｔ...     

0－1多面体图连通度猜想的一个反例

本文给出０－１多面体图连通度猜想的一个反侧．由此说明０－１多面体图的连通度未必等于最小度．     

Forcing highly connected subgraphs

A theorem of Mader states that highly connected subgraphs can be forced in finite graphs by assuming a high minimum degree. We extend this result to infinite graphs. Here, it is necessary to require not only high degree for the vertices but also high vertex‐degree (or multiplicity) for the ends of the graph, that is, a large number of disjoint rays in each end. We give a lower bound on the degree of vertices and the vertex‐degree of the ends which is quadratic in k, the connectedness of the desired subgraph. In fact, this is not far from best possible: we exhibit a family of graphs with a degree of order 2^k at the vertices and a vertex‐degree of order k log k at the ends which have no k‐connected subgraphs. Furthermore, if in addition to the high degrees at the vertices, we only require high edge‐degree for the ends (which is defined as the maximum number of edge‐disjoint rays in an end), Mader's theorem does not extend to infinite graphs, not even to locally finite ones. We give a counterexample in this respect. But, assuming a lower bound of at least 2k for the edge‐degree at the ends and the degree at the vertices does suffice to ensure the existence (k + 1)‐edge‐connected subgraphs in arbitrary graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 331–349, 2007     

Analog vision chip for motion detection of an approaching object against a moving background based on the insect visual system

A network for motion detection of an approaching object without influence of the moving background was proposed based on the insect visual system. The two-dimensional array of the analog complementary metal oxide semiconductor (CMOS) circuits for extracting the edge signals of the approaching object without outputting those of the moving background was inserted at the first stage of the network. At the next stage, analog CMOS circuits for detection of approaching velocity and direction, which accept the extracted edge signals, were inserted based on the locust vision system. A chip of the proposed network was fabricated with the 1.2 mm CMOS process. It was clarified from the measured results and the simulation results with the simulation program with integrated circuit emphasis (SPICE) that the two-dimensional circuits of the first stage can only generate the signals of target edges. The measured results showed that the chip can detect the approaching velocity and direction of the target in the image which contains the moving background.     

Graphs G for which both G and G¯ are Contraction Critically k-Connected

 An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is called contraction critically k-connected. For k≥4, we prove that if both G and its complement Gˉ are contraction critically k-connected, then |V(G)|<k ^5/3+4k ^3/2. Received: October, 2001 Final version received: September 18, 2002 AMS Classification: 05C40     

具有缩影的图式流形的分类

在这篇文章中，通过使用扭转运算，我们获得了具有缩影的力图式流形的同胚分类。     

Anisotropic mesh adaptation for numerical solution of boundary value problems

We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004.     

Application of computer vision and laser interferometer to the inspection of line scale

In the paper machine vision, laser interferometer and coordinate measuring machine (CMM) are combined to develop a vision inspection system. The measurement capability of the developed system is investigated by measuring the distances between the lines on a standard line scale. The vision camera is used to replace the probe of the CMM to take the images of the interested lines on a line scale at two different positions. Meanwhile, the displacement of the CCD camera is measured using laser interferometer. Using subpixel edge localization and outlier-excluding least-squares regression, the distance between two interested lines is computed under an image plane coordinate system. By adding the displacement of the CCD camera measured using laser interferometer, the line space can be determined. Experiments have been performed repeatedly to measure the line space on the 1.00 and 300.0 mm line scales. Results indicate that the measured data only have a little fluctuation and are close to those obtained by the NML (National Measurement Laboratory, Taiwan).