Ordering Graphs with Cut Edges by Their Spectral Radii

Let gnk denote a set of graphs with n vertices and k cut edges. In this paper, we obtain an order of the first four graphs in gnk in terms of their spectral radii for 6 ≤ k ≤ n-2/3.

On Graphs with Cut Vertices and Cut Edges

Let G（n,k,t） be a set of graphs with n vertices,k cut edges and t cut vertices.In this paper,we classify these graphs in G（n,k,t） according to cut vertices,and characterize the extremal graphs with the largest spectral radius in G（n,k,t）.

The Existence of Even Regular Factors of Regular Graphs on the Number of Cut Edges

For any even integer k and any integer i, we prove that a （kr ＋i）-regular multigraph contains a k-factor if it contains no more than kr - 3k/2＋ i ＋ 2 cut edges, and this result is the best possible to guarantee the existence of k-factor in terms of the number of cut edges. We further give a characterization for k-factor free regular graphs.

Approach for Polishing Diamond Coated Complicated Cutting Tool: Abrasive Flow Machining(AFM)

Lower surface roughness and sharper cutting edge are beneficial for improving the machining quality of the cut?ting tool, while coatings often deteriorate them. Focusing on the diamond coated WC?Co milling cutter, the abrasive flow machining(AFM) is selected for reducing the surface roughness and sharpening the cutting edge. Comparative cutting tests are conducted on di erent types of coated cutters before and after AFM, as well as uncoated WC?Co one, demonstrating that the boron?doped microcrystalline and undoped fine?grained composite diamond coated cutter after the AFM(AFM?BDM?UFGCD) is a good choice for the finish milling of the 6063 Al alloy in the present case, because it shows favorable machining quality close to the uncoated one, but much prolonged tool lifetime. Besides, compared with the micro?sized diamond films, it is much more convenient and e cient to finish the BDM?UFGCD coated cutter covered by nano?sized diamond grains, and resharpen its cutting edge by the AFM, owing to the lower initial surface roughness and hardness. Moreover, the boron incorporation and micro?sized grains in the underly?ing layer can enhance the film?substrate adhesion, avoid the rapid film removal in the machining process, and thus maximize the tool life(1040 m, four times more than the uncoated one). In general, the AFM is firstly proposed and discussed for post?processing the diamond coated complicated cutting tools, which is proved to be feasible for improving the cutting performance

CUTTING-DIRECTION BURR FORMATION IN ORTHOGONAL PRECISION CUTTING

The cutting burr is one of the common phenomena occurring in metal cutting.In this paper,the forming processes,main effect factors and change law of the cutting direction burr in orthogonal cutting have been studied and related theories are analyzed based on the cutting experiments.The result shows that:(1)the forming processes of cutting direction burr consist of normal cutting,flexure deformation of end surface of workpiece,plastic effect,continuous cutting and shear break separating in orthogonal cutting;(2)a new phenomenon is found that cutting direction burr is formed with the shear break separation of the chip and workpiece machined surfaces;(3)the size of cutting direction burr varies with workpiece materials,cutting parameters and geometric parameters of the cutting tool.

Cutting edge curve models for equal pitch cutters and their applications

A mathematic model is established using infinitesimal geometry for the cutting edge design of special milling cutters which use equal lead helix as cutting edges; equations are given for front-end and proclitic surface of revolution of ball pillar milling cutters, ball taper milling cutters and angularly conical milling cutters; and corresponding models are established for the continuity cutting edge curves of milling cutters. Typical examples are given to illustrate the applications of mathematic models, which prove the correctness and applicability of these geometric models.

Cutting edge preparation of microdrills by shear thickening polishing for improved hole quality in electronic PCBs

Printed circuit boards(PCBs)are representative composite materials,and their high-quality drilling machining remains a persistent challenge in the industry.The finishing of the cutting edge of a microdrill is crucial to drill performance in machining fine-quality holes with a prolonged tool life.The miniature size involving submicron scale geometric dimensions,a complex flute shape,and low fracture toughness makes the cutting edge of microdrills susceptible to breakage and has been the primary limiting factor in edge preparation for microdrills.In this study,a newly developed cutting edge preparation method for microdrills was tested experimentally on electronic printed circuit boards.The proposed method,namely,shear thickening polishing,limited the cutting edge burrs and chipping on the cutting edge,and this in turn transformed the cutting edge’s radius from being sharp to smooth.Moreover,the edge–edge radius could be regulated by adjusting the processing time.PCB drilling experiments were conducted to investigate the influence of different cutting edge radii on wear,hole position accuracy,nail head value,and hole wall roughness.The proposed approach showed 20%enhancement in hole position accuracy,33%reduction in the nail head value,and 19%reduction in hole wall roughness compared with the original microdrill.However,a threshold is needed;without it,excessive shear thickening polishing will result in a blunt edge,which may accelerate the wear of the microdrill.Wear was identified as the primary factor that reduced hole quality.The study indicates that in printed circuit board machining,microdrills should effectively eliminate grinding defects and maintain the sharpness of the cutting edge as much as possible to obtain excellent drilling quality.Overall,shear thickening polishing is a promising method for cutting edge preparation of microdrills.Further research and optimization can lead to additional improvements in microdrill performance and contribute to the continued advancement of printed circuit board manufacturing.

Analysis of Machinable Structures and Their Wettability of Rotary Ultrasonic Texturing Method

Tailored surface textures at the micro- or nanoscale dimensions are widely used to get required functional performances. Rotary ultrasonic texturing （RUT） technique has been proved to be capable of fabricating periodic micro- and nanostructures. In the present study, diamond tools with geometrically defined cutting edges were designed for fabricating different types of tailored surface textures using the RUT method. Surface generation mechanisms and machinable structures of the RUT process are analyzed and simulated with a 3D-CAD program. Textured surfaces generated by using a triangular pyramid cutting tip are constructed. Different textural patterns from several micrometers to several tens of micrometers with few burrs were successfully fabricated, which proved that tools with a proper two-rake-face design are capable of removing cutting chips efficiently along a sinusoidal cutting locus in the RUT process. Technical applications of the textured surfaces are also discussed. Wetting properties of textured aluminum surfaces were evaluated by combining the test of surface roughness features. The results show that the real surface area of the textured aluminum surfaces almost doubled by comparing with that of a flat surface, and anisotropic wetting properties were obtained due to the obvious directional textural features.

An Indentation Method for Nanoprecision Measurement of Diamond Tool Edge Radius

In ductile mode cutting of brittle materials using di amond tools, such as ductile cutting of silicon and quartz for wafer fabrication , one of the key conditions for achieving ductile chip formation is to get the r ight ratio of tool cutting edge radius to the undeformed chip thickness. It has been shown that the undeformed chip thickness has to be in the order of nanomete rs and that the tool cutting edge radius has to be smaller than the undeformed c hip thickness. Therefore, nanoprecision measurement of diamond cutting tools has become a key issue for ductile mode cutting of brittle materials. In this paper , a non-destructive nanoprecision measurement method for diamond tool cutting e dge radius is presented. The basis of the method is that the exact profile of th e tool cutting edge can be perfectly copied by indenting the tool cutting edge o n the surface of a rigid-perfect plastic material, and that the copy of the pro file can be measured at nanoprecision level. Ideally, the first aspect of th e method is to make a perfect copy of the tool cutting edge profile by indentati on on the surface of a rigid-perfect plastic material which has no elastic spri ng back, so that a true copy of the tool cutting edge is maintained for subseque nt measurement. Since no rigid-perfect plastic material can be found in realit y, actual materials of rigid-elastic-plastic nature have to be used for the in dentation in the measurement method, and the material elastic error compensation coefficients have to be determined to cancel out the effect of elastic spring b ack. For the minimization of error compensation, criteria for the selection of t he optimal materials for the indentation measurement are found to be: 1) high ri gidity and high density, 2) large Young’s elastic modulus, and 3) low yield strength. One of such materials identified is copper. The second aspect of the method is to measure the radius of the indented profile on the surface of the ma terial. This can be achieved by using an atomic force microscope (AFM), and in t his paper the results for measurement of diamond tool edge radii of nanometer sc ales by indentation on a copper material are presented. The elastic error compen sation coefficient for the copper material is determined through the indentation of a tungsten carbide tool edge on the copper surface. By comparing the actual tool edge radius measured using SEM on the sectional view of the tungsten carbid e tool with the one measured from the copied profile of the tool edge on the cop per surface, the coefficient is obtained. Analysis is given for the accuracy of the proposed method, showing that as far as the elastic compensation coefficient is consistent with the material used for the indentation measurement, the only source of errors with the measurement will come from the device for measuring th e indented profile on the surface of the solid, in this case it will come from t he AFM which measures on the sub-nanometer scales.

Elastic-plastic finite element simulation for diamond turning process

Using general commercial software, a coupled thermo-mechanical plane strain larger deformation orthogonal cutting model is developed on the basis of updated Lagrangian formulation in this paper. The workpiece is oxygen free high conductivity copper (OFHC copper), its flow stress is considered as a function of strain, strain rate and temperature to reflect its realistic changes in physical properties. In order to take into account the cutting edge radius effects of the single crystal diamond tool, rezoning technology is introduced into this simulation model. Diamond turning process is simulated from the initial stage to the steady stage of chip formation, and the distribution of temperature, equivalent stress, residual stress, strain rate and shear angle are obtained. The simulated principal force is compared with published experiment data and they are found to be in good agreement with each other, but poor for thrust force due to no consideration of elastic recovery for machined surface in the elastic-plastic material model.

Pakistan-USA Student Dialogue： Using Videoconference for International Civic Engagement

The United States Department of State funded a project focused on civic engagement. The participants were students and faculty at five universities in Pakistan and in the USA. The author is a representative from one of the USA-based universities. In a fortnightly high-definition videoconference dialogue between students at University of Nebraska at Omaha and Quaid-i-Azam University in Islamabad, the goals of deepening understanding, challenging stereotypes and inspiring community change are being met. This paper will present the preliminary results of an ongoing assessment of how this project has resulted in meeting these goals and suggest what can be done in future projects that will better meet the goals. This will add to the emerging literature on civic engagement and conflict resolution by exploring use of cutting edge technology to build trust and understanding across the world＇s divide.

Edge preparation methods for cutting tools:a review

Edge preparation can remove cutting edge defects,such as burrs,chippings,and grinding marks,generated in the grinding process and improve the cutting performance and service life of tools.Various edge preparation methods have been proposed for different tool matrix materials,geometries,and application requirements.This study presents a scientific and systematic review of the development of tool edge preparation technology and provides ideas for its future development.First,typical edge characterization methods,which associate the microgeometric characteristics of the cutting edge with cutting performance,are briefly introduced.Then,edge preparation methods for cutting tools,in which materials at the cutting edge area are removed to decrease defects and obtain a suitable microgeometry of the cutting edge for machining,are discussed.New edge preparation methods are explored on the basis of existing processing technologies,and the principles,advantages,and limitations of these methods are systematically summarized and analyzed.Edge preparation methods are classified into two categories:mechanical processing methods and nontraditional processing methods.These methods are compared from the aspects of edge consistency,surface quality,efficiency,processing difficulty,machining cost,and general availability.In this manner,a more intuitive understanding of the characteristics can be gained.Finally,the future development direction of tool edge preparation technology is prospected.

Defining the effect of sweep tillage tool cutting edge geometry on tillage forces using 3D discrete element modelling

The energy required for tillage processes accounts for a significant proportion of total energy used in crop production.In many tillage processes decreasing the draft and upward vertical forces is often desired for reduced fuel use and improved penetration,respectively.Recent studies have proved that the discrete element modelling(DEM)can effectively be used to model the soil–tool interaction.In his study,Fielke(1994)[1]examined the effect of the various tool cutting edge geometries,namely;cutting edge height,length of underside rub,angle of underside clearance,on draft and vertical forces.In this paper the experimental parameters of Fielke(1994)[1]were simulated using 3D discrete element modelling techniques.In the simulations a hysteretic spring contact model integrated with a linear cohesion model that considers the plastic deformation behaviour of the soil hence provides better vertical force prediction was employed.DEM parameters were determined by comparing the experimental and simulation results of angle of repose and penetration tests.The results of the study showed that the simulation results of the soil-various tool cutting edge geometries agreed well with the experimental results of Fielke(1994)[1].The modelling was then used to simulate a further range of cutting edge geometries to better define the effect of sweep tool cutting edge geometry parameters on tillage forces.The extra simulations were able to show that by using a sharper cutting edge with zero vertical cutting edge height the draft and upward vertical force were further reduced indicating there is benefit from having a really sharp cutting edge.The extra simulations also confirmed that the interpolated trends for angle of underside clearance as suggested by Fielke(1994)[1]where correct with a linear reduction in draft and upward vertical force for angle of underside clearance between the ranges of-25 and-5°,and between-5 and 0°.The good correlations give confidence to recommend further investigation of the use of DEM to model the different types of tillage tools.

Forces in Hard Turning of 51CrV4 with Wiper Cutting Tool

For precision machining, the hard turning process is becoming an important alternative to some of the existing grinding processes. This paper presents an analytical model for predicting cutting forces in hard turning of 51CRV4 with hardness of 68 HRC. The cutting tool used is made from cubic boron nitride （CBN） with a wiper cutting edge. Formulas for differential chip loads are derived for three different situations, depending on the radial depth of cut. The cutting forces are determined by integrating the differential cutting forces over the tool-workpiece engagement domain. For validation, cutting forces predicted by the model were compared with experimental measurements, and most of the results agree quite well.

Development of a low-cost measurement system for cutting edge profile detection

The use of a compact disk （CD） pickup head as a displacement measurement system is described. The components contained in a pickup head are explained and how they are combined to obtain the functionality of a pickup head. The application of measuring a knife edge profile is introduced. The results reveal some insuffiencies with the current system. The cutting edge＇s radius of curvature can be estimated.

Cutting Edge科技最前沿

微软有句名言:微软唯一不变的就是变!科技也是这样,它已经渗入到我们生活中的方方面面,也在时时刻刻地改变着生活——剪刀可以"跑"到病人肚子里,"会找借口的盒子"能帮助你编织善意的谎言……

Regular Factor in Vertex Transitive Graphs

Let G be a fc-regular connected vertex transitive graph. If G is not maximal restricted edge connected, then G has a (k- 1)-factor with components isomorphic to the same vertex transitive graph of order between k and 2k-3. This observation strenghen to some extent the corresponding result obtained by Watkins, which said that fc-regular vertex transitive graph G has a factor with components isomorphic to a vertex transitive graphs if G is not k connected.

H-Eigenvalues of signless Laplacian tensor for an even uniform hypergraph

The signless Laplacian tensor and its H-eigenvalues for an even uniform hypergraph are introduced in this paper. Some fundamental properties of them for an even uniform hypergraph are obtained. In particular, the smallest and the largest H-eigenvalues of the signless Laplacian tensor for an even uniform hypergraph are discussed, and their relationships to hypergraph bipartition, minimum degree, and maximum degree are described. As an application, the bounds of the edge cut and the edge connectivity of the hypergraph involving the smallest and the largest H-eigenvalues are presented.