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Abstract The author presents a mathematical analysis of the geometry and mechanics of the metal-cutting process, covering two common types of geometry which occur in cutting. This analysis offers a key for the study of engineering problems in the field of metal cutting in terms of such fundamental quantities as strain, rate of shear, friction between chip and tool, shear strength of the metal, work done in shearing the metal and in overcoming friction, etc. The two cases covered are, in essence, that of a straight-edged cutting tool moving relative to the work-piece in a direction perpendicular to its cutting edge, termed “orthogonal cutting,” and that of a similar cutting tool so set that the cutting edge is oblique to the direction of relative motion of tool and work, termed “oblique cutting.” Equations are developed which permit the calculation of such quantities as those just enumerated from readily observable values. The theoretical findings are particularly applicable and significant in the case of present-day high-speed machining operations with sintered-carbide tools.

The mechanistic and unified mechanics of cutting approaches to the prediction of forces in milling operations are briefly described and compared. The mechanistic approach is shown to depend on milling force coefficients determined from milling tests for each cutter geometry. By contrast the unified mechanics of cutting approach relies on an experimentally determined orthogonal cutting data base (i.e., shear angle, friction coefficient and shear stress), incorporating the tool geometrical variables, and milling models based on a generic oblique cutting analysis. It is shown that the milling force coefficients for all force components and cutter geometrical designs can be predicted from an orthogonal cutting data base and the generic oblique cutting analysis for use in the predictive mechanistic milling models. This method eliminates the need for the experimental calibration of each milling cutter geometry for the mechanistic approach to force prediction and can be applied to more complex cutter designs. This method of milling force coefficient prediction has been experimentally verified when milling Ti6Al4V titanium alloy for a range of chatter, eccentricity and run-out free cutting conditions and cutter geometrical specifications.

In earlier papers [Opns. Res. 9, 849–859 (1961), and 11, 863–888 (1963)] the one-dimensional cutting stock problem was discussed as a linear programming problem. There it was shown how the difficulty of the enormous number of columns occurring in the linear programming formulation could be overcome by solving a knapsack problem at every pivot step. In this paper higher dimensional cutting stock problems are discussed as linear programming problems. The corresponding difficulty of the number of columns cannot in general be overcome for there is no efficient method for solving the generalized knapsack problem of the higher dimensional problem. However a wide class of cutting stock problems of industry have restrictions that permit their generalized knapsack problem to be efficiently solved. All of the cutting stock problems that yield to this treatment are ones in which the cutting is done in stages. In treating these practical cutting problems, one often encounters additional conditions that affect the solution. An example of this occurs in the cutting of corrugated boxes, which involves an auxiliary sequencing problem. This problem is discussed in some detail, and a solution described for the sequencing problem under given simplifying assumptions.

9R15. Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design. - Y Altintas (Manuf Autom Lab, Univ of British Columbia, Canada). Cambridge UP, Cambridge, UK. 2000. 286 pp. Softcover. ISBN 0-521-65973-6. $39.95.Reviewed by AA Ber (Dept of Mech Eng, Technion Israel Inst of Tech, Technion City, Haifa 32000, Israel).This reviewer wishes to congratulate the author for writing this book. This combination of the three subjects, Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design under one roof, is actually done for the first time. Furthermore, integration of these three subjects gives the readers, students (mostly graduates), design engineers, as well as practitioners, a better outlook on the subject dealt with in the book Manufacturing Automation. The book is well written, and the sequence of subjects is perfect. The author was aware that each of the major subjects can fill up a book by itself, and he mentioned it in the introduction. Inserting a Problem Section after each chapter, emphasizing the main points discussed in it, turns the work into a textbook. However, it can also serve as a reference book for engineers and practitioners. Chapter 1 is a general introduction to manufacturing and a short overview of what one will find in this book chapter by chapter. Chapter 2 presents the mechanics of cutting. It is introduced under the most classical approach and written in an orderly and systematic way, except for the section on Milling and Tool Breakage which introduces a refreshing modern approach. Most of the equations are brought in their final form, which is quite acceptable for graduate students, engineers, and practitioners. The nomenclature and symbols are sometimes confusing; the author mixes old American standards with the ISO standards and puts them together in the same equation. This reviewer suggests that in future editions only ISO standard 3002/I through IV be considered. In this chapter, this reviewer missed the roles of Surface Finish and Tolerances in the cutting operations. Tool life is defined geometrically and not in a modern way, namely “The tool terminates its life when it ceases to fulfill its function.” In other words, the tool life ends on reaching the geometrical life (as defined in the book), or when the Surface Finish exceeds the demand and or the part is out of the defined Tolerance. It is a pity that the author did not include a section dealing with tool materials in this chapter. The materials composing the tool play a major role in the mechanics of cutting. For example, the contact length between tool and chip is a function of the tool’s properties (primarily its thermal conductivity) and of other factors.In Chapter 3, the static and dynamic deformation in machining is treated in a very extensive and clear way that even this reviewer (whose field is not dynamics) could understand the factors and problems involved. The analysis presented emphasizes, by sample formulation, prediction of the magnitude and location of static deformation of bar turning and end milling. The section dealing with chatter is most impressively introduced. By introducing modal analysis techniques, the author shows how one can represent a complex machine tool structure using commonly used mathematical expressions and analyze the chatter as well as other sources of vibrations. In Chapter 4, the practical side of manufacturing is discussed. The author introduces the CNC technology and its principles of operation and leads the reader through NC programming of a part. The methodology of NC programming is well presented. All elements involved in CNC are discussed and theoretically supported. In the paragraph on Computer Assisted NC Part Programming, the author succeeded in showing in a compact and very clear form how complicated forms can be dealt with and successfully machined. The basics of Computer-Aided Manufacturing (CAM) is introduced. The author focuses on the teaching aspects of the subject. Chapter 5 contains conventional textbook material. The chapter is well written. The reader is led systematically through the various aspects of the CNC systems. A typical CNC machining center, including all necessary hardware, mechanical, electrical, and hydraulic and their combinations necessary to operate CNC systems, is well described. The various elements required, like machine tool drives, mechanical as well as electrical (and others), are described in detail and accompanied by the relevant formulation on which they are based upon. The mathematical modeling of drive systems is covered both in the time and frequency domain. The author directs some attention to the accuracy of the system. At the end of the chapter, the author presents an example of a design of an Electro-Hydraulic CNC Press Brake. The design contains the various elements of the system and may serve as a guide to the inexperienced reader (mostly students) while dealing with any CNC design. Chapter 6 is mostly an abstract of the author’s research works in the area of Sensor Related Machining. This chapter is based on material published by the author in various publications. The dominant direction is the one established by Prof Tlusty. It might have been more fruitful if the author had discussed other approaches as well. Basic principles and techniques appear in Chapters 7 and 8. Chapter 7 contains the Laplace and z Transforms and includes several examples. In Chapter 8, the author introduces Off-Line and On-Line Parameters Estimation with Least Squares. At the end of the book, one can find a very extensive bibliography covering all aspects of the subjects discussed in the book. This reviewer recommends Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design as a textbook for students, undergraduate as well as graduate. It can also serve as an excellent reference book for those engaged in manufacturing, ie, engineers, technicians, and other practitioners.

The three-dimensional (3D) theory of laser cutting is presented. The cutting efficiency determined by its ultimate parameters at different types of polarization is estimated. The physical reasons for limitations of ultimate cutting parameters at a plane P-polarized beam are displayed. In the case of cutting metals with a large ratio of sheet thickness to width of the cut, the laser cutting efficiency for a radially polarized beam is 1.5 - 2 times larger than for plane P-polarized and circularly polarized beams. The possibility of generating the radially polarized beam is discussed.

In this paper, the methods for stock cutting outlined in an earlier paper in this Journal [Opns Res 9, 849–859 (1961)] are extended and adapted to the specific full-scale paper trim problem. The paper describes a new and faster knapsack method, experiments, and formulation changes. The experiments include ones used to evaluate speed-up devices and to explore a connection with integer programming. Other experiments give waste as a function of stock length, examine the effect of multiple stock lengths on waste, and the effect of a cutting knife limitation. The formulation changes discussed are (i) limitation on the number of cutting knives available, (n) balancing of multiple machine usage when orders are being filled from more than one machine, and (m) introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts. The methods developed are also applicable to a variety of cutting problems outside of the paper industry.

A simple technique is described here that produces aligned arrays of carbon nanotubes. The alignment method is based on cutting thin slices (50 to 200 nanometers) of a nanotube-polymer composite. With this parallel and well-separated configuration of nanotubes it should be possible to measure individual tube properties and to demonstrate applications. The results demonstrate the nature of rheology, on nanometer scales, in composite media and flow-induced anisotropy produced by the cutting process. The fact that nanotubes do not break and are straightened after the cutting process also suggests that they have excellent mechanical properties.

Cutting of primers from reads is an important step of processing targeted amplicon-based next generation sequencing data. Existing tools are adapted for cutting of one or several primer/adapter sequences from reads and removing all of their occurrences. Also most of the existing tools use kmers and may cut only part of primers or primers with studied sequence of gene. Because of this, use of such programs leads to incorrect trimming, reduction of coverage, and increase in the number of false-positive and/or false-negative results. We have developed a new tool named cutPrimers for accurate cutting of any number of primers from reads. Using sequencing reads that were obtained during study of BRCA1/2 genes, we compared it with cutadapt, AlienTrimmer, and BBDuk. All of them trimmed reads in such a way that coverage of at least two amplicons decreased to unacceptable level (<30 reads) comparing with reads trimmed with cutPrimers. At the same time, Trimmomatic and AlienTrimmer cut all occurrences of primer sequences, so the length of the remaining reads was less than prospective.

Water-soluble graphene quantum dots (GQDs, ca. 10 nm in diameter) that exhibit bright blue photoluminescence (PL) are prepared by hydrothermal (chemical) cutting of oxidized graphene sheets (see figure). The mechanisms of the cutting and luminescence are discussed. This discovery of PL of GQDs may extend the range of application of graphene-based materials to optoelectronics and biological labeling.

We present a tree-search algorithm for two-dimensional cutting problems in which there is a constraint on the maximum number of each type of piece that is to be produced. The algorithm limits the size of the tree search by deriving and imposing necessary conditions for the cutting pattern to be optimal. A dynamic programming procedure for the solution of the unconstrained problem and a node evaluation method based on a transportation routine are used to produce upper bounds during the search. The computational performance of the algorithm is illustrated by tests performed on a large number of randomly generated problems with constraints of varying “tightness.” The results indicate that the algorithm is an effective procedure for solving cutting problems of medium size.

Reports the completion of four fundamental fluidic operations considered essential to build digital microfluidic circuits, which can be used for lab-on-a-chip or micro total analysis system (μTAS): 1) creating, 2) transporting, 3) cutting, and 4) merging liquid droplets, all by electrowetting, i.e., controlling the wetting property of the surface through electric potential. The surface used in this report is, more specifically, an electrode covered with dielectrics, hence, called electrowetting-on-dielectric (EWOD). All the fluidic movement is confined between two plates, which we call parallel-plate channel, rather than through closed channels or on open surfaces. While transporting and merging droplets are easily verified, we discover that there exists a design criterion for a given set of materials beyond which the droplet simply cannot be cut by EWOD mechanism. The condition for successful cutting is theoretically analyzed by examining the channel gap, the droplet size and the degree of contact angle change by electrowetting on dielectric (EWOD). A series of experiments is run and verifies the criterion.

An analysis of the chip geometry and the force system found in the case of orthogonal cutting accompanied by a type 2 chip has yielded a collection of useful equations which make possible the study of actual machining operations in terms of basic mechanical quantities. The shearing strain undergone by the metal during chip formation, and the velocities of shear and of chip flow are among the geometrical quantities which can be quantitatively determined. The force relationships permit calculation of such quantities as the various significant force components, stresses, the coefficient of friction between chip and cutting tool, and the work done in shearing the metal and in overcoming friction on the tool face. The experimental methods by which such analyses can be readily made are described. Observed and calculated values from typical tests are presented.

Cutting a cake, dividing up the property in an estate, determining the borders in an international dispute - such problems of fair division are ubiquitous. Fair Division treats all these problems and many more through a rigorous analysis of a variety of procedures for allocating goods (or 'bads' like chores), or deciding who wins on what issues, when there are disputes. Starting with an analysis of the well-known cake-cutting procedure, 'I cut, you choose', the authors show how it has been adapted in a number of fields and then analyze fair-division procedures applicable to situations in which there are more than two parties, or there is more than one good to be divided. In particular they focus on procedures which provide 'envy-free' allocations, in which everybody thinks he or she has received the largest portion and hence does not envy anybody else. They also discuss the fairness of different auction and election procedures.

The analysis of the mechanics of orthogonal cutting with a type 2 chip as presented in the first paper of this series can be extended by introducing those physical properties of the work material which control its plastic behavior. One evident plasticity condition is the equality of the shear stress on the plane of shear to the shear strength of the metal. If it is also assumed that the shear strength of the work material is a constant and is the only quantity controlling its plastic behavior, then a very simple additional plasticity condition is obtained by application of the principle of minimum energy. This condition is 2φ+τ−α=90°, where φ is the shear angle, τ the friction angle, and α the rake angle. This condition, however, is found by experiment to be a poor approximation in the case of polycrystalline metals. A very good approximation is obtained, though, if use is made of the fact that the shear strength of the polycrystalline metal is actually a function of the compressive stress on the shear plane. The resulting plasticity condition is cot (2φ+τ−α)=k, where k is the slope of the linear curve relating shear strength and compressive stress, and is thus a constant of the work material. Such a plasticity condition establishes a relationship between the force system and the geometry of chip formation, so that, if k and the shear strength be known for a given material, all forces involved in cutting it can be calculated with reasonably good accuracy directly from measurements of chip geometry only, without use of a tool dynamometer. This is of importance in the analysis of practical machining operations.

Political dialogue among citizens offers numerous potential contributions to American politics, but attainment of these benefits hinges largely on the extent to which conversations cross lines of political difference. In what contexts are cross-cutting interactions most likely to thrive? Using data from five surveys, we find consistent evidence that the workplace is the social context best positioned to facilitate cross-cutting political discourse. Political discussion in the workplace involves a large number of discussants, and it involves greater exposure to people of dissimilar perspectives than does discussion in contexts such as the family, the neighborhood, or the voluntary association. We next consider whether workplace-based interactions are capable of producing beneficial effects. Despite the notoriously weak nature of work-based social ties, we find evidence that workplace-based exposure to differing political views increases people’s knowledge of rationales for political perspectives other than their own and also fosters political tolerance.

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The cutting-stock problem is the problem of filling an order at minimum cost for specified numbers of lengths of material to be cut from given stock lengths of given cost. When expressed as an integer programming problem the large number of variables involved generally makes computation infeasible. This same difficulty persists when only an approximate solution is being sought by linear programming. In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the problem. The technique enables one to compute always with a matrix which has no more columns than it has rows.

In clinical practice, psychologists frequently participate in the making of vital decisions concerning the classification, treatment, prognosis, and disposition of individuals. In their attempts to increase the number of correct classifications and predictions, psychologists have developed and applied many psychometric devices, such as patterns of test responses as well as cutting scores for scales, indices, and sign lists. Since diagnostic and prognostic statements can often be made with a high degree of accuracy purely on the basis of actuarial or experience tables (referred to hereinafter as base rates), a psychometric device, to be efficient, must make possible a greater number of correct decisions than could be made in terms of the base rates alone. The efficiency of the great majority of psychometric devices reported in the clinical psychology literature is difficult or impossible to evaluate for the following reasons: a. Base rates are virtually never reported. It is, therefore, difficult to determine whether or not a given device results in a greater number of correct decisions than would be possible solely on the basis of the rates from previous experience. When, 1 From the Neuropsychiatric Service, VA Hospital, Minneapolis, Minnesota, and the Divisions of Psychiatry and Clinical Psychology of the University of Minnesota Medical School. The senior author carried on his part of this work in connection with his appointment to the Minnesota Center for the Philosophy of Science.

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