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2Chip formation fundamentals2.1 Historical introductionChapter 1 focused on the manufacturing organization and machine tools that surround the machining process. This chapter introduces the mechanical, thermal and tribological (fric- tion, lubrication and wear) analyses on which understanding the process is based.Over 100 years ago, Tresca (1878) published a visio-plasticity picture of a metal cutting process (Figure 2.1(a). He gave an opinion that for the construction of the best form of tools and for determining the most suitable depth of cut (we would now say undeformed chip thickness), the minute examination of the cuttings is of the greatest importance. He was aware that fine cuts caused more plastic deformation than heavier cuts and said this was a driving force for the development of more powerful, stiffer machine tools, able to make heavier cuts. At the same meeting, it was recorded that there now appeared to be a mechanical analysis that might soon be used like chemical analysis systematically to assess the quality of formed metals (in the context of machining, this was premature!).Three years later, Lord Rayleigh presented to the Royal Society of London a paper by Mallock (Mallock, 188182). It recorded the appearance of etched sections of ferrous and non-ferrous chips observed through a microscope at about five times magnification (FigureFig. 2.1 Early chip observations by (a) Tresca (1878) and (b) Mallock (188182)2.1(b). Mallock was clear that chip formation occurred by shearing the metal. He argued that friction between the chip and tool was of great importance in determining the defor- mation in the chip. He commented that lubricants acted by reducing the friction between the chip and the tool and wrote that the difficulty is to see how the lubricant gets there. He also wrote down equations for the amount of work done in internal shear and by friction between the chip and tool. Surprisingly, he seemed unaware of Trescas work on plasticity and thought that a metals shear resistance was directly proportional to the normal stress acting on the shear plane. As a result, his equations gave wrong answers. This led him to discount an idea of his that chips might form at a thickness that minimized the work of friction. With hindsight, he was very close to Merchants law of chip formation, which in fact had to wait another 60 years for its formulation (Section 2.2.4).Trescas and Mallocks papers introduce two of the main elements of metal cutting theory, namely plasticity and the importance of the friction interaction between chip and tool. Tresca was also very clear about the third element, the theory of plastic heating, but his interest in this respect was taken by reheating in hot forging, rather than by machining. In his 1878 paper, he describes tests that show up to 94% conversion of work to heat in a forging, and explicitly links his discussion to the work of Joule.In machining, the importance of heating for tool life was being tackled practically by metallurgists. A series of developments from the late 1860s to the early 1900s saw the introduction of new steel alloy tools, with improved high temperature hardness, that allowed higher and higher cutting speeds with correspondingly greater productivities. A classic paper (Taylor, 1907) describes the early work, from 1881 onwards, on productivity optimization through improved tool materials (high speed steels) and their best use.Thus, the foundations of machining theory and practice were laid between around 1870 and 1905. At this stage, with the minor exception of Mallocks work, the emphasis was on observing rather than predicting behaviour. This remained the case for the next 30 years, with huge collections of machinability (force and tool life) data (for example, Boston,1926; Herbert, 1928), and of course the introduction of even more heat resistant cemented carbide tools. By the late 1920s, there was so much data that the need for unifying theo- ries was beginning to be felt. Herbert quotes Boston (1926) as writing: If possible, a theory of metal cutting which underlies all types of cutting should be developed. . . . All this is a tremendous problem and should be undertaken in a big way.The first predictive stage of metal cutting studies started about the late 1930smid-1940s. The overriding needs of the Second World War may have influenced the timing, and probably the publication, of developments but also created opportunities by focusing the attention of able people onto practical metal plasticity issues. This first phase, up to around1960/65, was, in one sense, a backwards step. The complexity of even the most straight- forward chip formation for example the fact that most chips are curled (Figure 2.1) was ignored in an attempt to understand why chips take up their observed thicknesses. This is the key issue: once the chip flow is known, forces, stresses and temperatures may all be reasonably easily calculated. The most simple plastic flow leading to the formation of straight chips was assumed, namely shear on a flat shear plane (as described in more detail later in this chapter). The consequent predictions of chip thickness, the calculations of chip heating and contemporary developments in tribology relevant to understanding the chip/tool interaction are the main subjects of this chapter.This first stage was not successful in predicting chip thickness, only in describing its consequences. It became clear that the flow assumptions were too simple; so were thechip/tool friction law assumptions; and furthermore, that heating in metal cutting (and the high strain rates involved) caused in-process changes to a metals plastic shear resistance that could not be ignored. From the mid-1960s to around 1980 the main focus of mechan- ics research was exploring the possibilities and consequences of more realistic assump- tions. This second phase of predictive development is the subject of Chapter 6. By the1980s it was clear that numerical methods were needed to analyse chip formation properly. The development of finite element methods for metal cutting are the subject of Chapter 7 and detailed researches are introduced in Chapter 8.2.2 Chip formation mechanicsThe rest of this chapter is organized into three main sections: on the foundations of mechanics, heating and tribology relevant to metal machining. Appendices 1 to 3 contain more general background material in these areas, relevant to this and subsequent chapters. Anyone with previous knowledge may find it is not necessary to refer to these Appendies, at least as far as this chapter is concerned.The purpose of this section is to bring together observations on the form of chips and the forces and stresses needed to create them. The role of mechanics in this context is more to aid the description than to be predictive. First, Section 2.2.1 describes how chip formation in all machining processes (turning, milling, drilling and so on) can be described in a common way, so that subsequent sections may be understood to relate to any process. Section 2.2.2 then reports on the types of chips that have been observed with simple shapes of tools; and how the thicknesses of chips have been seen to vary with tool rake angle, the friction between the chip and the tool and with the work hardening behaviour of the machined material. Section 2.2.3 describes how the forces on a tool during cutting may be related to the observed chip shape, the friction between the chip and the tool and the plas- tic flow stress of the work material. It also introduces observations on the length of contact between a chip and tool and on chip radius of curvature; and discusses how contact length observations may be used to infer how the normal contact stresses between chip and tool vary over the contact area. Sections 2.2.2 and 2.2.3 only describe what has been observed about chip shapes. Section 2.2.4 introduces early attempts, associated with the names of Merchant (1945) and Lee and Shaffer (1951), to predict how thick a chip will be, while Section 2.2.5 brings together the earlier sections to summarize commonly observed values of chip characteristics such as the specific work of formation and contact stresses with tools. Most of the information in this section was available before 1970, even if its presen- tation has gained from nearly 30 years of reflection.2.2.1 The geometry and terminology of chip formationFigure 2.2 shows four examples of a chip being machined from the flat top surface of a parallel-sided metal plate (the work) by a cutting tool, to reduce the height of the plate. It has been imagined that the tool is stationary and the plate moves towards it, so that the cutting speed (which is the relative speed between the work and the tool) is described by Uwork. In each example, Uwork is the same but the tool is oriented differently relative to the plate, and a different geometrical aspect of chip formation is introduced. This figure illus- trates these aspects in the most simple way that can be imagined. Its relationship to theFig. 2.2 (a and b) Orthogonal, (c) non-orthogonal and (d) semi-orthogonal chip formation.turning milling and drilling processes is developed after first describing what those aspects are.Orthogonal and non-orthogonal chip formationIn Figure 2.2(a) the cutting edge AD of the plane tool rake face ABCD is perpendicular to the direction of Uwork. It is also perpendicular to the side face of the plate. As the tool andwork move past one another, a volume of rectangular section EFGH is removed from theplate. The chip that is formed flows with some velocity Uchip, which is perpendicular to the cutting edge. All relative motions are in the plane normal to the cutting edge. In this condition, cutting is said to be orthogonal. It is the most simple circumstance. Apart from at the side faces of the chip, where some bulging may occur, the process geometry is fully described by two-dimensional sections, as in Figure 2.1(b).It may be imagined that after reducing the height of the plate by the amount HG, the tool may be taken back to its starting position, may be fed downwards by an amount equal to HG, and the process may be repeated. For this reason the size of HG is called the feed, f, of the process. The dimension HE of the removed material is known as the depth of cut,d. Figure 2.2(a) also defines the tool rake angle a as the angle between the rake face and the normal to both the cutting edge and Uwork. (a is, by convention, positive as shown.)When, as in Figure 2.2(a), the cutting edge is perpendicular to the side of the plate, itslength of engagement with the plate is least. If it i