Introduction

Each science has its own history that marks the landmarks and milestones of its development. Knowing such a history, a specialist in the field should be able to determine the mainstream direction in its further development avoiding the known dead-ends. For example, the history of machine tools includes book on each particular machine (e.g., Woodbury R.S., History of the Milling Machine: A study in Technical Development, The Technology Press M.I.T., Gambradge, MA, 1960). Therefore, an objective and complete history of any science is of enormous significance and should be written by a group of specialists in the field to avoid the "personal" bias.

Unfortunately, this is not the case in metal cutting.

Old papers on metal cutting (when the content rather than the journal space was not of prime concern) took into considerations a number of known works. However, only works relevant (suitable, convenient by the authors' opinion) to the topic, are considered. New papers, due to the space limitation in journals, have no room to discuss the place of each particular paper in the development of metal cutting.

If one hopes to learn the history of metal cutting from the metal-cutting books published in last 20-30 years he/she will be rather disappointed. The following examples support my point:

• Zorev [1] presenting his vision of the metal cutting history, did not consider the Timme model, the Merchant force model, Lee and Shafer model, etc., i.e., models that did not "suite" his idea of metal cutting. However, Zorev pointed out that the known single-shear plane model was developed by Zvorykin in 1896 [2] and was justly criticized by Briks in the very same year [3]. Zorev also showed the place of his model in the context of the history of metal cutting.
• Boothroyd [4] started his version of metal cutting history describing achievements of R. Reynolds (1760) and J.Watt (1776), who had a little to do with the theory of metal cutting. Then the author points out that Timme (of unknown origin, probably from a terra incognita) and Tresca (a famous French scientist) were the first who tried to explain how chips are made. However, what they really did is not presented. The author states that in 1881 Mallock suggested correctly (in the author's opinion, a typical example of the "personal" bias) that the cutting process was basically one of shearing the work material to form the chip. Then Boothroyd pointed out that a step backwards (From which stage?) in the understanding (whose?) of the metal cutting process was taken in 1900 when Reuleaux suggested that a crack occurred ahead of the tool. Why this was a step backwards or by whom and how this was disproved are not indicated. A significant space in the history section dedicated to the achievements of Taylor who published one paper in 1907. Although this paper has enormous practical significance, it has little contribution to the metal cutting theory. Then, according to Boothroyd, metal cutting history had stalled until 1941 when Ernst and Merchant published their fundamental work. The end of the history is reached at this point.
• Shaw's book [5] contains as many as four rows in the history section referring readers to earlier books.
• Trent in his book [6] on metal cutting, section "Historical", presented a very brief history of manufacturing and did not touch the history of metal cutting at all.
• Oxley in his book [7], section "Historical" simply refers to Shaw [5] and Zorev [1].
• Boothroyd and Knight in their textbook "Fundamentals of Mechining and Machine Tool"[8] discussed the history of metal cutting only in the brief introduction to the chapter on mechanics of metal cutting and this discussion is actually a shortened version of that presented by Boothroyd earlier[4].
• Stephenson and Agapiou in their book on the theory and practice of metal cutting [9] spent a number of pages discussing historical development (Section 1.2). The authors discuss the history of manufacturing, machine tools, etc. paying a little attention to the history of metal cutting.

 

This short essay is to analyse the three missed chances in metal cutting history rather then present the complete historical picture. In each of these chances, the history of metal cutting could have advanced in different manner if specialists were more concerned about the achieved results.
 

Magic of the Single-Shear Plane Model

When one tries to learn the basics of the metal cutting theory, he/she takes a textbook on metal cutting (manufacturing, tool design, etc.) and then reads that the single-shear plane model of chip formation is at the very heart of this theory. Although a number of other models are known for specialists in the field, the single-shear plane model survived all of them and, moreover, is still the first choice for students textbooks (e.g. [10]). An explanation to this fact is that the model is easy to teach, to learn, and simple numerical examples to calculate cutting parameters can be worked out for student's assignments. Although it is usually mentioned that the model represents an idealized cutting process, no information about how far this idealization deviates from the practice is provided.

The single-shear plane model has been known since the last century and, therefore, cannot be referred to as the Merchant model. The model has been constructed using simple observations of metal cutting process [2]. To the best of the author's knowledge, Usachev [11] was probably the first who had studied the chip structure and introduced the shear and texture angles. The observations seem to have led to an idealized picture which is known as the model for orthogonal cutting (Fig. 1). The diagram, figure 1, shows a tool removing the stock of thickness t₁ by shearing it (as assumed) ahead of the tool in a zone which is rather thin compared to its length and thus it can be represented reasonably well by the shear plane AB. The position of the shear plane is customarily defined using the shear angle f, as shown in figure 1. After being sheared, the layer to be cut becomes the chip
 

which slides first along the tool rake face, following the rake's shape (a straight portion of the chip in figure 1), and then, beyond a certain point O on the tool face, curls away. It was further assumed in the model that the chip forms by the process of simple (pure) shearing.

Ernst and Merchant added a force system to the model [12]. As they assumed, this force system consists of a resultant force R_f on the tool face and the resultant force R _s on the shear plane. The most essential assumption for this model is that these forces are collinear; thus, in order to satisfy the requirement of static equilibrium, they must be equal in magnitude and opposite in direction as shown in figure 1. Using this force system and the principle of minimum energy, Merchant was able to derive equation for the shear angle.

The following are the drawbacks of the model:

• an infinitely great stress gradient must exists in the shear plane since the yield points of non-work-hardened and work-hardened machined material differ by a factor of 2-4
• a particle of material being machined in the shear plane must receive infinitely great accelerations since its velocity changes from the cutting speed to the chip velocity instantly
• the model does not account for a number of workpiece materials which cannot be deformed by shearing, as for example cast irons. When applied to the study of cutting process of ductile materials, the model cannot possibly explain chip formation as accomplished by simple shearing. The latter becomes obvious when a number of related manufacturing processes such as blanking, punching, etc. are considered, since these are also accomplished by simple shearing, however no chips are produced. Moreover, the indentation of a semi-infinite mass of a rigid, perfectly plastic material by a rigid straight-sided, acute-angled indenter or by a flat punch causes extensive shearing, however, the chip does not form even if an extremely high force is applied

When calculations based on the single shear model and the Merchant's force model concepts fail, imaginary high strain rates allegedly occurred in cutting were added with imaginary high temperatures in the deformation zone in orthogonal cutting were introduced just to save the concept. Sometimes this arsenal of material-behaviour-in-cutting inventions does yield satisfactory calculative results. But the calculative achievements last usually till a new experimental finding makes them inapplicable. Then new mathematical inventions are applied, instead of turning to look for the correct physical model.

The situation is similar to what it was for 1400 years, when the Ptolemaic model was reigning in science. The model was based on our very natural perception that all celestial bodies are rotating around us, as it is seen with our very eyes. This perception led to the natural concept that we on our Earth are the center of the universe. The concept of "us in the center of the world" corresponded to the philosophical, religious, and ideological believes of those times, so that the geocentric model got full official support.

To cope with this model, mathematical treatments were developed, in which planets had to rotate on hypocycles, the centers of which rotate on epicycles, the centers of which rotate on orbits around us. If the calculation results did not fit, one could always add as many rotary motions and cycles as needed for a fit.

The same tendency can be traced in metal cutting. When the principle of minimum energy, applied to the single-shear plane model, did not fit the experimental results, it was proclaimed (and published in ASME Journal of Engineering for Industry, Rubenstein, 1983 [13]) as "not applicable" in metal cutting. Hill [14] came even further drawing more general conclusion that "the comparative failure of the (Merchant) theory is almost certainly due to inadequacy of the minimum work hypothesis." In this statement, the principle, which is a physical law, became "a hypothesis" and since there is something wrong with the results in metal cutting, this "hypothesis" is generally wrong, And it seems that nobody wondered why one of the most fundamental principles of physics failed to work in metal cutting. When the direction of maximum deformation in metal cutting was found to be different than that of the shear plane, it was simply proclaimed [5] that in metal cutting the direction of maximum deformation may not coincide with the direction of maximum shear stress. Although it is at odds with the practice of material testing, nobody asked the simple question "why?" There are a number of other examples that make metal cutting a kind of "supernatural phenomenon".

What seems to be right is to understand the phenomena of metal cutting as an inherent part of engineering science. However, the author, after many years of Don Quixote'ing, came to the conclusion that the "why" scientist, devoted to explain the phenomena of his science, is the least successful, because the interest of people in understanding is very superficial. Real in-depth explanations of a natural phenomena, if any, are complicated and most often contradictory to our everyday machine-shop experience and existent concepts. They require time-consuming intellectual efforts from the readership (and particularly from the reviewers) or audience, and cannot be put in short exiting slogans, canons, rulings.

What people expect when they ask their why-question is not the deep explanation, but a quickly diagnosis, slogan, or formula. The natural desire to understand is usually satisfied by answers like "because of high temperatures, stain and strain rate occurred in cutting", "because of Oxley's model", "because of concentrated shear", "since it is proven by FEM", i.e simply just by naming a phenomenon (phenomena), a ruling, or an authority. Quite often, the desire is satisfied by a cited false, unrelated, or least related cause.

For example, it is widely recognized and sincerely believed in many metal cutting studies that seizure may reduce tool wear. In this connection, there is a lot of speculation about the "protective function of the built-up edge" even at the level of undergraduate text-books. A few explanations and supportive evidences have been provided. As such, the presence of the built-up edge on the rake face is considered as the most solid argument. Eventually, using a special quick-stop device, one may obtain the real shape and size of the built-up edge for given cutting conditions. Based on such post-process observations, it is commonly believed that the built-up edge somehow cuts the workpiece material serving in this sense as the cutting edge extension and, in doing so, protects the flank from wear (for example, page 62 in [15]).

However, the described idealistic picture does not hold when the tool life is considered. Difficulties arise when one seeks a correspondence between the maximum tool life and maximum seizure or, more precise, the stable built-up edge. Experimental evidence provided by many researches indisputably proves that the cutting speed (so the contact temperature at the tool/chip interface) corresponding to the maximum tool life is 2-5 times higher than the cutting speed corresponding to maximum seizure or the built-up edge. Moreover, no trace of seizure is observed under cutting conditions corresponding to the maximum tool life.

It is true that the built-up edge can be observed on the tool rake face in the region adjacent to the cutting edge and the mechanical properties of the built-up edge are high enough to protect this edge from wear. However, the logical question arises about existence of the built-up edge while cutting. The answer to this question is not straightforward. On one hand, the built-up edge is harder than the work material since it has been severely deformed. It is known that hardened steel can cut identical non-hardened steel. On the other hand, such cutting is not stable and the cutting regime used is much lower than that with the tool materials. Therefore, the likelihood that the built-up edge cuts the workpiece at the same regime as the tool material, is quite low.

The analysis of experimental data, micrographs of the built-up edge, studies of its structure, type of bonding, transmission electron microscope examinations enables us to suggest that the built-up edge is a post-cutting phenomenon. The deformation zone adjacent to the tool rake face is dynamic and ever-changing. The shape and location of this zone depend on the properties of the work and tool materials, chosen cutting regime, contact conditions at the chip/tool interface, and tool geometry. This zone is almost always 'coated' (from the chip side) by the material which would be the chip contact layer in its spreading over the tool/chip interface. Since the size of the deformation zone is continuously changing during the chip formation cycle, one may gain an incorrect impression about the dynamics of this zone by analysing its micrographs. From the micrographs, it appears that the material flows over the deformation zone considered as the built-up edge. However, a simple analysis of the stress distribution in this zone, slip line directions, and microhardness scanning analysis show that this is not the case although it is discussed in this manner since the last century. The system analysis shows that the deformation zone pushes the chip ahead which deforming in the direction of the maximum combined stress. If the cutting process is interrupted using a quick-stop device, part of the deformation zone adjacent to the rake face is observed but it does not serve as a proof that the built-up edge is a real phenomenon during metal cutting.

In this "built-up edge syndrome", which is quite common in metal cutting literature, the actual causes are replaced by irrelevant ones, just because they seem "better" for teaching and for presentations so that real physical explanations are not important.
 

Are There Physical Explanations At All?

In addition to cases where existing explanations are neglected, there are a number of phenomena in metal cutting for which we do not have physical explanations. The question then is, WHETHER these phenomena and events are explainable at all, i.e., if their explanations are possible, but not yet known, and will be found in the progress of science, OR that these phenomena are not explainable, and will never be, that is, their explanations do not exist, and never will.

During the history of metal cutting, more and more "unexplainable" phenomena have found scientific explanations. Therefore, it is our deep conviction and belief that eventually all the phenomena and events can obtain a full physical explanation, in logical wordy sentences, and not a quasi, by fitting mathematical formulas or calculations. It is expected that such an explanation will be based on explainable physical facts and laws, and not by naming an un axiomatic postulate, principles, or an authority (a "daddy", or "big brother") who said so.

On the other hand, the following may be the case. When a science is sufficiently developed to explain, but does not provide explanations, then the reason can be that the researchers did not search deeply for them, OR they are satisfied with a calculative or technological success, and accepted it as an explanation (the "built-up edge" syndrom), OR that they did not take into account all bodies, all factors, all interactions, participating in the event, i.e., that the physical model of the event (such as a model of chip formation) is either wrong or missing.

Theories, which are unable to provide physical explanations, quite often deny the existence of such explanations. It may be referred as the human "Malta Yok" syndrome. The saying is ascribed to a Turkish admiral, who was leading a fleet toward Malta, but failed to find the island. On return, he thus reported to the sultan that "Malta Yok", which means "There is no Malta".

One pictural example for this is the so-called the non-uniqueness of the machining process. Hill was probably the first specialist in the engineering plasticity who attempted to solve the metal cutting problem using the methods of engineering plasticity [16]. Analysing the Merchant solutions, he pointed out that it is incomplete, since the entire state of stress was not examined. Hill then proceeded to analyse this state of stress and using a new principle "on the limits set by plastic yielding to the intensity of singularities of stress" came to the conclusion that it may be fruitless to search for the unique solution in metal cutting. Dewhurst in his very convincing paper [17] provided further proofs to this point. Since both researchers used the engineering plasticity principles in their considerations, we may say that the non-uniqueness of the instant parameters of the metal cutting process is meant.

Subsequent researches argued for the uniqueness of the machined process. Instead of proving that Hill and Dewhurst solutions are wrong, they conducted experimental study using a wide range of machining parameters and concluded that the discussed non-uniqueness was not observed in their experimental results. They did not bother that, in their experiments [18] , the average (per cutting cycle) values of machining parameters have been measured while the instant values have been discussed by Hill and Dewhurst. Since the uniqueness was not found, it does not exist, i.e., the non-uniqueness "yok".

Some studies went even further arguing against the non-uniqueness of the machining process on the basis of results from their finite-element modelling (e.g. [19] ) which, being of steady-state nature since a stationary load was assumed, inherently cannot distinguish the instant values in the dynamic process. Once again, the non-uniqueness "yok".

Another example is about a crack occurred ahead of the tool. In 1900 Reuleaux suggested that such a crack forms ahead of the cutting edge. For many years this suggestion was considered as a step backwards in the understanding of metal cutting process [4]. The logic was very simple - since we could not find a crack, it does not exist, i.e, "yok". Even when Shaw published examples of such a crack[20], nobody seems to notices it. Nowadays, when SEM technic becomes available to study the metal cutting process, such crack was easily found [21]. An example of the discussed crack is shown in Fig. 2. Still, this finding did not produce any impression on the "specialist" in metal cutting - "yok" means "yok" and period.
 

One more example can be shown by consideration of the existent explanations for self-exited vibration (often referred to as chatter) in machining. These provide highly complicated but successful mathematical solutions to most practical problems of their dealing (trying to convince us that the machining system can be modelled as a linear system). Although the theories have very low prediction capability, the solutions seem fully satisfy the needs of those who provide the funding. Hence, there is no finding, no publications, not even considerations or discussion time (and, that more important, journals' space) for explanations. Because of the successes of mathematical solutions (the paper containing such solution have been recognized as the best publication), the physical ways of reasoning, proof, and explanations, are now almost completely extinguished in the analysis of machine tool vibrations. Mathematical approaches are considered omnipotent, to such an extent that a physical relation is not considered proven if the proof is not mathematical.

Mathematics as well as its most advanced numerical methods (like finite element modelling) are no more than a powerful tool that requires very skilful hands to handle. Unfortunately, despite the enormous effort and money that have been poured into creating analytical tools to add rigour and precision to the design of complex systems, a paradox remains. There has been a harrowing succession of flawed designs with fatal results - The Challenger, the Chernobyl, the Stark, the Aegis system in the Vincennes, Boeing 747 and 767 problems, and so on. Those failures exude a strong scent of experience or habits or both and reflect an apparent ignorance of, or disregard for, the limits of stress in materials and peoples under chaotic conditions. Successful design still requires expert tacit knowledge and intuitive "feel" based on experience; it requires engineers steeped in the understanding of existing engineering systems as well as in the new systems being designed.

With a computer model, however, analysis can be made quickly. The computer's apparent precision - six or more significant figures - can give engineers "an unwarranted confidence in the validity of the resulting numbers." However the question about who makes the computer model of the calculated matter is of more than passing interest. If the model is worked out on a commercially available analytical program, the researcher will have no easy way of discovering all the assumptions made by the programmer. Consequently, the researcher or designer must either accept of faith the program's results or check the results - experimentally, graphically, or numerically - in sufficient depth to be satisfied that the programmer did not make dangerous assumptions or omit critical factors and that the program reflects fully the subtleties of the designer's own unique problem.

To understand the hazards of using a program written by somebody else, one should realize the following facts. Because structural analysis and detailing programs are complex, the profession as a whole will use programs written by a few. These few will come from the ranks of structural 'analysis' and not from the structural 'designers.' Generally speaking, their manufacturing, design and experimental-site experience and background will tend to be limited. It is difficult to envision a mechanism for ensuring that the products of such a person will display experience and intuition of a competent researcher or designer. One needs to have courage and experience in order to be able to stand up to and reject or modify the results of a computer aided analysis and design.

The researchers and engineers who can "stand up to" a computer will be those who understand that software incorporate many assumptions that cannot be easily detected by its users but that affect the validity of the results. There are a thousand points of doubt in every complex computer program. Successful computer-aided modelling requires vigilance and the same visual knowledge and intuitive sense of fitness that successful researchers have always depended on when making critical conclusions.

If we are to avoid calamitous conclusions, it is necessary for researchers to understand that such errors are not errors of mathematics or calculation but errors of engineering judgment based on the lack of understanding the physical backgrounds.

Unfortunately, some researches do not seem to be aware of the simple fact that mathematics cannot create physics, physical bodies or phenomena, just as it cannot create biology, life, love, money, or the economy of a country, though it may be very helpful in all these endeavours. Mathematical models, including FEM models cannot output more physics than that was put into them. If a mathematical model or treatment is not based on the correct physical model of a physical event, then the theory is intrinsically unable to provide a physical explanation of the event.
 

Do We Really Need Physical Explanations and Understanding of Metal Cutting?

We perform all our bodily functions, from walking to thinking, without being able to fully explain or understand them. Most of our professional or leisure activities, like driving, using machinery, computers, TV and telephones, are performed without understanding the physical and other processes involved. Doctors may successfully cure their patients without real deep understanding of the illness and the effect of their treatment.

This list seems to be endless. And now, if we add to it the success of FEM modelling of the metal cutting process, the single-shear-plane model of chip formation, the famous Taylor equation, analyses of dynamic stability of the metal cutting process (etc., etc., etc.) that, considered together, is called the theory of metal cutting which proudly and consistently announces its inability to explain the basic phenomena, and indicates the non-existence of physical explanations, we should ask, why do we need explanations for, if life is so good without them.

The answer to this question is rather simple. As long as things proceed well, then we do not need to explain or to understand them. Moreover, explanations and quests for understanding would retard and disturb the well-going process (receiving funding, publishing award-winning papers, etc.). So it is with walking, and with any other industrial, scientific, or other activity.

However, if anything goes wrong with our walking, e.g., due to an illness or injury, then the understanding of the process involved is critical for the recovery. It is completely true when it is personal - here everyone insists on detailed explanations. In science and production it is not as sharp. Ideally, if anything goes wrong or breaks down in a production or research activity, or when a competing industrial or scientific group achieves better results, so that one is confronted with losing the market or the funding, then the understanding of the involved process becomes urgent. Although it should be the case, it is not always so in the real life.

For example, a recent CIRP working paper [22] states, "A recent survey by a leading tool manufacturer indicates that in the USA the correct cutting tool is selected less than 50% of the time, the tool is used at the rated cutting speed only 58% of the time, and only 38% of the tools are used up to their full tool-life capability. One of the reasons for this poor performance is the lack of the predictive models for machining." The same was found in an earlier survey of cutting regime selection on CNC machine tools in the American aircraft industry. If we recall that the United States now spends more than $115 billion annually to perform its metal removal tasks using conventional machining technology [23], the price of the lack of the predictive models for machining is evident.

The mentioned CIRP working paper [22] points out that numerous attempts to improve the theory proposed by Merchant failed to improve its predictive ability. Moreover, the original objectives of metal cutting research became somewhat obscure [24]. Instead of the original objective to establish a predictive theory, the center of gravity has been shifted to developing theories of descriptive nature which only explain post-process phenomena and thus have no prediction ability. As a result, no significant progress was made and, after many years of study, theory is still lagging behind practice. Shaw in his book ([5], p.200) which summarizes his lifetime of experience in the field, came to the discouraging conclusion that it is next to impossible to predict metal cutting performance.

From this one may conclude that a great need does exist for new ways, new developments and ideas in metal cutting studies. Unfortunately, this is not the case. University courses on metal cutting and, thus, the corresponding textbooks (e.g., [8, 10]) continue to teach Merchant's theory since it offers the simplest explanations for the metal cutting phenomena although no physical background is provided. Industry relies completely upon empirical data as presented by tool and machine tool manufacturers, as well as by professional engineering associations through handbooks and workshops. Since these recommendations do not originate from a common theory, they provide only a good "starting point" forcing users, at their own cost, to determine the optimal values of cutting parameters for separate applications. And, for an outside observer with an obscure knowledge of the field, it may appear that industry adapting well to this situation.
 

Chance Number One - Timme Model

To start, I would like to remind to my readers one known example from the History of Science. It deal with geo-centric (earth in the center) and helio-centric (sun in the center) model of our planetary system.

The first model was introduced by Aristotle and is based on the common observation that the celestial bodies rotate around us, and that we (particularly, the eye of the observer) constitute the center of the horizon, the center of the sphere of the sky, and thus the center of the world. The model enabled the needed calculations of the positions of planets. It corresponded to the stochastic doctrines of those times, and was accepted by all religions. Latter on, this model was "mathematically dressed" by Claudius Ptolemy (2^nd Century AD) and became know as Ptolemaic model which survived 1400 years.

Amazingly, the same observations of planet motions led Aristarchus of Samos (3^rd Century BC) to conclude that the Earth rotates round its axis and circles around the Sun. Thus, Aristarchus initiated the helio-centric model, with the Sun in the center of the Solar System. Though this is (as we know now) the physically right model, it contradicted the physically unsound Aristotle's model and thus was condemned, together with its creator.

As mentioned above, the single shear plane model was proposed in the 80-90th of the last century and was widely accepted. Tresca [25] and Timme [26] argued about the deformation mode in metal cutting. In 1880 Ivan Timme published his book on metal cutting [27] where he introduced his model shown in figure 3.
 

In his model, Timme considered the interaction of the model components, namely the cutting tool, the workpiece, and the chip. The cutting process was considered as cyclical and each cycle consists of two distinctive stages as shown in figure 3. At the first stage of a cycle, the cutting tool starts to advance into workpiece overcoming its resistance. As such, the resistance to the tool penetration grows proportionally to the compressed area of the workpiece material that results in an increase in the penetration force P. The first stage continues until the penetration force P becomes sufficiently large to break a small piece of workpiece material. Next, the second stage takes over. At this stage, the fragment moves along a particular sliding plane at angle Q₁. As such, the penetration force P gradually decreases that eventually ceases the sliding. Then the process repeats itself.

In the Timme model, it was recognized that:

• cutting process is cyclical
• relative motion of the model's components rather than steady-state mode represents chip formation

 

Chance Number Two - Merchant Solution

As stated above, Ernst and Merchant tried to analyze the single shear plane model quantitatively. Merchant [28], following the assumption made by earlier researchers that simple shearing is the prime deformation mode in metal cutting, added a force system to the model shown in figure1. In this figure, F_h and F_v are horizontal and vertical components of the external force per unit width which is applied to the tool. Their resultant is inclined, by hypothesis, at angle ½ p-g to the tool face, and hence at a downward angle l-g (g is the tool rake angle) to the horizontal as shown in figure 1. Thus
 

Let be the shear stress of workpiece material after the strain e. Considering the equilibrium of the chip, and resolving parallel to the line of shear, one finds

The external work done in removing unit volume of workpiece material is obtained from equation (2) as

To complete the analyses, one needs to relate f to l and g. Merchant assumed logically that these can be found using the principle of minimum energy (which must be applicable for any real physical system). In terms of metal cutting, Merchant [28] postulates that f is such that work done per unit volume is a minimum. The condition for this is

For simplicity, it is assumed that the state of friction over the area of contact between tool and chip can be adequately, though broadly, represented by a constant coefficient µ with a corresponding angle of friction l= tan^-1 µ.

Since seems to be a known function of f, calculable from the stress-strain curve in shear at the appropriate temperature and rate of strain, the solution of equation (5) can be obtained. If there were no work-hardening, the solution would be simply

From Merchant's measurements it appears that, within experimental error, f is in fact a function of a single variable ( l- g) but that this formula overestimates f by some 20 to 40 per sent in the range investigated. The discrepancy cannot be due to neglecting work-hardening because if this is included, the calculated value of f is still larger (except when l= 0, for which as follows from equation (6) f is always equal to 1/4p + ½ g). Merchant has attempted to improve the agreement by permitting the shear stress to vary with the normal pressure on the shear plane, but the required variation was found to be so great as to be physically out of the question, the pressure being only of the order of the yield stress.

It should be further noticed that if µ is regarded as constant along the tool, equation (5) implies that the cutting edge is a singularity for the state of stress in the chip. Thus, if the direction of the maximum shear stress at a point on the chip surface adjacent to the cutting edge were parallel to the shear line, equation (6) should take the following form
 

This means that the direction of the resultant stress acting on the tool face is a principal direction for the state of stress at the cutting edge and the other principal component of stress is zero. This formula, as found by Hill [14], overestimates , and correspondingly overestimates the resistance to machining. Moreover, it is certainly invalid for large negative rake angles since it is implies a negative f.

Using these considerations, Hill, instead of questioning the model, was of the opinion that the comparative failure of the theory is almost certainly due to the inadequacy of the minimum energy hypothesis.

It should be mentioned here that for many years multiple reasons were suggested to explain the discrepancy between the theoretical and experimental results. However, nobody points out that the greatest achievement of Merchant is that he proved that the known single shear plane model is not adequate.

Although a number of attempts have been made to suggest another model of chip formation e.g., [29-33], all of these still employ the essential features originally proposed by Merchant, namely

• the force resultants on the tool and on the shear plane are equal in magnitude and opposite in direction
• there is steady-state model of deformation in metal cutting
• the chip forms by the process of simple shear

A special note on the coefficient of friction in metal cutting

It is worthwhile to discuss here an issue that is often troublesome for many metal cutting researchers, namely, that the friction coefficient is not suitable for metal cutting studies.

As discussed, in the Merchant work [28], the friction coefficient µ is regarded as constant along the tool/chip interface. One should understand that, as a result, the distribution of the interface stresses is implicitly assumed to be uniform. It is true that , in general, the coefficient of friction for sliding surfaces remains constant within a wide range of relative velocity, apparent contact area, and normal load. In contrast, in metal cutting the coefficient of friction varies with respect to the normal load (the uncut chip thickness), the relative velocity, and the apparent contact area. The coefficient of friction in metal cutting was found to be so variable that Hahn [34] doubted whether this term served any useful purpose. Moreover, Kronenberg [35] suggested that it should be abolished altogether on the ground that it was positively harmful to keep it in circulation. Nevertheless, subsequent researchers paid a little attention to these warnings and, as a result, the same concept of the coefficient of friction is still in wide use in metal cutting publications.
 

Limiting value of the coefficient of friction

First of all, let us clarify the question about the possible values of the coefficient of friction. Sliding between two bodies under a normal load N is possible only by the application of a tangential force F. As such, the coefficient of friction µ at the interface is defined as

In plastic deformation processes one of the contact materials (the workpiece) deforms and in doing so slides against the harder surface (the tool). The frictional stress is generated, but there is a limit to the coefficient of friction. The interface shear stress cannot rise beyond a maximum given by the shear flow stress of the workpiece material, t_f ; at this point the workpiece refuses to slide on the tool; instead it deforms by shearing inside the body. Since according to the distortion-energy criterion the flow stress in shear t_f and the uniaxial yield stress s_y of the material are related as

It is instructive now to consider the values of the coefficient of friction obtained experimentally in metal cutting studies and those used in the modelling of metal cutting process.
 

The values reported in experimental studies

• Hill points out [14] that in the experiments of Merchant µ had values between about 0.5 and 1.0. Hill further points out that these high values are understandable since the chip surface, bearing on the tool, is freshly formed and should therefore be free from adsorbed films.
• Zorev [1] obtained experimentally and used in his calculations values of µ in a range of 0.6 - 1.8.
• Stephenson and Agapiou [9] discussed the results of friction coefficient measurements. Showing values of µ from a range of 0.6 -1.4, they, however, pointed out that values above 1.0 are not common.
• Kronenberg [37] reported a range of 0.77 -1.46.
• Armarego and Brown [38] reported a range of 0.8 - 2.0.
• Kato, Yamaguchi, and Yamada [39] reported a range of 0.41- 1.34 for light workpiece materials (aluminum, cupper, zinc).
• Finie and Shaw [40] reported a range of 0.88 - 1.85.

• Stenkowsky and Moon used µ = 0.2 in their FEM modelling [41].
• Komvopoulos and Erpenbeck used a range of 0.0 - 0.5 in their FEM modelling [42].
• Lin, Pan, and Lo used two values of the friction coefficient, namely, 0.074 and 0.073 in their FEM modelling [43].
• Lin and Lin used µ = 0.001 in their FEM modelling [44]. As might be expected, the calculated results are in good agreements with the results of their experiments.
• Stenkowsky and Carroll used µ = 0.3 in their FEM modelling [45].
• Zang and Bagchi [46] used the following values:

• Obikawa and Usui used µ = 0.6 in their computational machining of titanium alloy [47].
• Endres, DeVor, and Kappor used µ = 0.05, 0.10, 0.25, and 0.5 in their modelling of the cutting forces [48].
• Wu in his study [49] assumed the friction coefficient to be constant and equal to 0.3.

 
 

As seen, the values of the coefficient of friction used in the modelling of the cutting process are, in general, much lower than that obtained experimentally. One possible explanation for this fact is that the use of computer FEM programs automatically assumed validity of Eq. (11) and hence it is impossible to violate the relation between material characteristics. On the other hand, the experimental results, obtained using the single-shear plane model violate this relation. Therefore, there is only one conclusion - the single-shear plane model used in experimental studies and in FEM modelling is inadequate to describe the real cutting process.
 

Chance Number Three - Zorev's Book

It must be recognized that this work is the most extensive experimental work in the field. No one known study offers the results of so many scientifically conducted experiments performed using a number of different workpiece materials, tools, and cutting conditions. It is understood that it is next to impossible to accomplish all these by a single researcher. In reality, the book summarizes the results of many-year of experimental studies conducted by the leading in the former Soviet Union research institute which coordinated manufacturing activities in the USSR industry. Professor Zorev used to be a director of the institute and a chairman of its scientific committee where the main results presented in the book have been discussed in details. As a result, the book is a scholarly treatment of the Mechanics of Metal Cutting and represents a valuable source for researchers. The main points in the book have been presented clearly, argumentation is logical and well supported by multiple experimental results so that the book deserves to be considered as the Bible of Metal Cutting.

Unfortunately, that is not the case even though each serious study in the field sited it as a reference. It is also a pity that the translation and editing of the book are rather poor that make it very difficult to follow, particularly for a North-American reader who should spend a great deal of time to understand the meaning of 'plane chip formation', 'tangential stress', 'acute-angle cutting', 'angle of cut', 'shear rate vector', 'blue shortness', 'plastic shear force' etc. Page 55 reads as, "The resistance of the machined material to deformation in the plastic zone depends on the creep stress of the machined material..." May be it is so but a real cutting speed (something 1m/100years) should then be considered. Moreover, the designations of Russian workpiece and tool materials are used throughout the book without pointing out that practically all these materials have AISI analogs with which a North American reader is much more comfortable. Regardless of these shortcomings, the book is still a valuable source of information on metal cutting.

Unfortunately, the major finding made in the book have never been acknowledged by subsequent researchers. One reason for that, in our opinion, is that the book was much ahead of its time. If specialists were more patient and have gone through the text (which is difficult to follow due to translation), the history of metal cutting could have taken another direction. Hereafter I would like to discuss these "turning points":

• The book introduces the determination of the shape of the deformation zone using a slip-line approach. This consideration is in agreement with the theory of plasticity and offers the analytical determination of the initial and final boundary of the deformation zone. For the fist time (and for the last, unfortunately), the principal axes of deformation and true deformation of chip have been considered and the explanation is offered as being due to the fact that the orientation of the resultant chip texture does not coincide with the direction of plastic shear. Almost twenty years latter, Shaw [5] acknowledged the fact that the material flow in metal cutting will not occur at the maximum shear stress (p. 199), however no explanation to this extraordinary fact, which is at odds with common sense and material test practices has been provided. Other researches have not even mentioned this obvious fact.

• •It is proven in the book that the temperature at the tool/chip contact cannot be looked upon as a single universal factor which determines the influence of the cutting conditions on the chip formation process (even for a given rake angle and a given work material). The assumption that the thermal strain-hardening of steel as the temperature in the chip formation zone rises leads to a reduction of the deformation and the cutting ratio, has no basis and is not conformed by experiment. Later works (Oxley, Stephenson, etc.) did not comment on this experimental result while continuing their search for such a dependance.
• •It is demonstrated in many occasions by many carefully designed and conducted experiments that the deformation zone is "a living body" rather than having a defined shape which can be drawn as a chip formation model. There is no unique shear plane, the initial and final boundaries of this zone have ever-changing positions due to instability of the process of plastic deformation in the zone. This fact has never been acknowledged by subsequent researches who continue to represent a model of chip formation by a single picture, i.e., assuming the existence of its steady-state configuration.
• •A complex state of stress exist in the deformation zone. This stress is not steady-state and also non-uniform throughout this zone. As a result, the process of plastic deformation during chip formation is not a case of simple loading. Due to these phenomana, a precise solution of the chip formation problem cannot be obtained using the known methods of engineering plasticity. This conclusion is in good agreement with that of Hill. Nobody has commented on it since it does not suit the single-shear plane model.
• •The variation of the shear stress in the deformation zone can be accounted for by using a given complex state of stress in this zone. The resistance of workpiece material to deformation in the deformation zone is a function of this state. This conclusion is of enormous significance. The material aspect of metal cutting could advance much further if researchers looked for the complex state of stress in the deformation zone. Instead, simple shearing continues domunate the thinking process for the mechanism of plastic deformation in metal cutting and, therefore, nobody can explain why the chip forms in metal cutting and does not in indentation though simple shearing is considered to be the case in both.
• •Since two families of slip planes constitute the deformation zone, the process of pure shear is complicated by compressive strain. Although Oxley modeled the deformation zone by the same families of slip lines, he somehow missed this conclusion.
• •The maximum plastic deformation in the deformation zone takes place in the region adjacent to its final boundary. To admit this fact means to admit non-uniform state of stress and deformation in the deformation zone that are at odds with all the studies that followed. The book demonstrated that the influence of different cutting conditions on the chip formation process is interconnected and can be discussed in isolation only in the first approximation without making any general conclusions. The existing theoretical formulas for the chip formation process do not take into account the direct influence of the cutting speed, thus incorrectly reflecting the laws governing the chip formation at high cutting speeds. Most of these formulas are incorrect even at low cutting speed since they do not take into account the influence of the resistance of the workpiece material to plastic deformation.
• •The book offers a very good model for the mechanics of three-dimensional cutting process. Unfortunately very poor translation resulted in the use of the wrong terminology throughout the book and, as a result, this model is called in the book as the model for cutting at an acute(???) angle instead of a model for oblique or three-dimensional cutting. It is not a surprise that subsequent researches did not acknowledge the model.
• •The experimental part of the book includes the study of more than forty (!) workpiece materials carefully chosen to represent all groups of steels including plane low, medium, high carbon steels, low and high alloys, stainless steels and alloys. It is worthwhile to point here that for all the workpiece materials used in the study, their chemical composition, mechanical and physical properties have been actually measured and the results are presented in the book. Separate studies at low and the high cutting speed are presented. For the first time, the angle of action is considered as to be of prime importance. Unfortunately, this has been completely ignored by later studies.

For the first time, the nature of forces on the clearance face is considered and the influence of the machining conditions on these forces has been analyzed. The study reveals the significant influence of the properties of workpiece materials and process parameters on these forces. In light of these findings, the experimental measurements of the cutting forces and their dependance on the process parameters conducted later by other researches have not considered or even mentioned the discussed results. Up to date, the forces on the clearance face are not of interest for researchers in metal cutting though they claim they try to develop a predictive model for machining. When it comes to the analysis of the tool wear, it is recognized that the flank wear is of prime concern. As a result, all standards on the testing of tool life mainly consider this wear. I would like to mention here that the tool volumetric wear like any other wear is proportional to the energy passed over the wearing surface. It is only logical that one should recognize that flank forces play a significant role in metal cutting since all other tool-workpiece (chip) contact areas wear less than flanks (under commonly used cutting conditions) though the sliding speed is almost the same for all contact areas. Underestimations of the values and role of the flank forces is one of the barriers on the way to developing the real predictive model for machining.
 
 

References:
 

1.     Zorev, N. N., Metal Cutting Mechanics, Pergamon Press, Oxford, 1966.
2.     Zvorykin, K. A., On the force and energy necessary to separate the chip from the workpiece, (in Russian), St.Petersbourg, Vestnik Promyslennostie, 123, 1896.
3.    Bricks, A. A., Metal Cutting, (in Russian) St.Petersbourg, 1896.
4.    Boothroyd, G, Fundamentals of Metal Machining, Pitman Press, Bath (UK), 1965.
5.    Shaw, M. C., Metal Cutting Principles, Clarendon Press, Oxford, 1984.
6.    Trent, E. M., Metal Cutting Butterworth-Heinemann Ltd, Oxford, 1991.
7.    Oxley, P. L. B., Mechanics of Machining: An Analytical Approach to Assessing Machinability, John Wiley & Sons, New York, 1989.
8.    Boothroyd, G. and Knight, W. A., Fundamentals of Machining and Machine Tools, 2nd ed., M.Dekker, New York, 1989.
9.    Stephenson, D. A. and Agapionu, J. S., Metal Cutting Theory and Practice, Marcel Dekker, Inc., New York, 1997.
10.    DeGarmo, E. P., Black, J. T., and Kohser, R. A., Materials and Processes in Manufacturing, Prentice Hall, Upper Saddle River, NJ, 1997.
11.    Usachev, Ya. G., Phenomena Occurring During the Cutting of Metals, (in Russian), Izv. Petrogradskogo Politechnicheskogo Inst., XXIII, No.1, 1915, pp. 321-338.
12.    Ernst, H. and Merchant, M. E., Chip Formation, Friction, and High Quality Machined Surface, Surface Treatment of Metals, ASM, Cleveland, 1941, pp. 299-378.
13.    Rubenstein, S., a Note Concerning the Inadmissibility of Applying the Minimum Work Principle to Metal Cutting, ASME Journal of Engineering for Industry, vol. 105, 1983, pp. 294-296.
14.    Hill, R., The Mathematical Theory of Plasticity, Oxford University Press, London, 1950.
15.    Boyes, W. E., Dunlap, D. D., Hoffman, E. G., Jacobs, P., and Orady, E. A., Fundamentals of Tool Design, Third Edition, SME, 1991.
16.    Hill, R., the Mechanics of Machining: a New Approach, Journal of Mechanics and Physics of Solids, Vol. 3, 1954, pp. 47-53.
17.    Dewhurst, W., on the Non-uniqueness of the Machining Process, Proc. Roy. Soc. Lond., A, vol. 360, 1978, pp. 587-609.
18.    Stevenson, R.. and Stephenson, D. A., The Effect of Prior Cutting conditions on the Shear Mechanics of Orthogonal Cutting, ASME Journal of Engineering for Industry, vol. 120, 1998, pp.13-20.
19.    Madhavan, V. and Chandrasekar, S., Some Observations on the Uniqueness of Machining, in "Manufacturing Science and Engineering," Proceedings of 1997 ASME International Mechanical Engineering Congress and Exposition, November 16-21, 1997, Dallas, Texas, Vol. 6-2, 1997, pp.99-109.
20.    Sampath, W. S. and Shaw, M. S., Fracture on the shear plane in continuous cutting, in Proc. 11th NAMRI Conf, Dearborn, 281, 1983.
21.    Sidjanin, L. and Kovac, P., Fructure Mechanisms in Chip Formation Processes, Materails Science and Technology, Vol. 13, 1997, pp. 439-444.
22.    Jawahir, I.S. and van Luttervelt, C.A., Recent Developments in Chip Control Research and Applications, CIRP Annals, Vol. 42, 1983, pp. 659-693.
23.    Handbook of High-Speed Machining Technology, Ed.by R.I.King, Chapman and Hall, New York, 1985.
24.    Usui, E., Progress of "Predictive" Theories in Metal Cutting, JSME International Journal, Series III, vol. 31, 1988, No. 2, pp. 363-369.
25.    Tresca, H., Mémories Sur le Rabotage des Métaux. Bulletin de la Société D'encouragement Pour L'industrie Nationale, 1973, pp. 587-685.
26.    Timme, I, Mémories Sur le Rabotage des Métaux., St.Peterspurg, Russia, 1877.
27.    Timme, I. I., On the Resistance of Metal and Wood to Cutting, (in Russian), Dermacow Press House, St. Petersburg, 1880.
28.    Merchant, M.E., Mechanics of the metal cutting process, Journal of Applied Physics, vol. 16, 1945, pp. 267-275.
29.    Kececioglu, D., Shear-Zone Size, Compressive Stress, and Shear Strain in Metal-Cutting and Their Effects on Mean Shear-Flow Stress, ASME Journal of Engineering for Industry, February, vol. 81, 1960, pp. 79-86.
30.    Kobayashi, S. and Thomsen, E.G., Metal-Cutting Analysis-I: Re-Evaluation and New Method of Presentation of Theories, ASME Journal of Engineering for Industry, vol.83, 1962, pp. 63-70.
31.    Lee, E.H. and Shaffer, B.W., The Theory of Plasticity Applied to a Problem of Machining, ASME Journal of Applied Mechanics, Vol. 18, 1951, pp. 405-413.
32.    Loladze, T.N., Chip Formation in Metal Cutting, (in Russian), Moscow: Machgiz,1952.
33.    Ocusima, K. and Hitomi, K., An Analysis of the Mechanism of Orthogonal Cutting and Its Application to Discontinuous Chip Formation, ASME Journal of Engineering for Industry, vol.82, 1961, pp. 545-556.
34.    Hahn, R.S, Some Observations on Chip Curl in the Metal Cutting Process Under Orthogonal Cutting Conditions, ASME Journal of Engineering for Industry, Vol. 74, 1953, pp. 581-590.
35.    Finnie I. and Shaw M.C., The Friction Process in Metal Cutting. Trans. ASME, Journal of Engineering for Industry, 1956, Vol. 78, p.1649-1657.
36.    Kalpakjian, S., Manufacturing Processes for Engineering Materials, Third Ed., Addison-Wesley, Metro Park, California, 1997.
37.    Kronenberg, M., Machining Science and Application: Theory and Practice for Operation and Development of Machining Process, Pergamon Press, Oxford, 1966.
38.    Armarego, E.J.A. and Brown, R.H., The Machining of Metals, Prentice-Hall, Inc., Englewood Cliff, NJ, 1969.
39.    Kato, S., Yamaguchi, K., and Yamada, M., Stress Distribution at The Interface Between Tool and Chip in Machining, ASME, Journal of Engineering for Industry, vol. 93, 1972, pp. 683-689.
40.    Finnie, I. and Shaw, M.C., The Friction Process in Metal Cutting, ASME, Journal of Engineering for Industry, vol. 77, 1956, pp. 1649-1657.
41.    Strenkowski, J.S. and Moon, K-J., Finite Element Prediction of Chip Geometry and Tool/workpiece Temperatures Distributions in Orthogonal Metal Cutting, ASME Journal of Engineering for Industry, vol. 112, 1990, pp. 313-318.
42.    Komvopoulos, K. and Erpenbeck, S.A., Finite Element Modelling of Orthogonal Metal Cutting, ASME Journal of Engineering for Industry, vol.113, 1991, pp. 253 - 267.
43.    Lin, Z.C., Pan, W.C., and Lo, S.P., A Study of Orthogonal Cutting with Tool Flank Wera and Sticking Behaviour on the Chip-Tool Interface, Journal of Materail Processing Technology, vol. 52, 1995, pp.524-538.
44.    Lin, Z.C. and Lin, S.Y., A Coupled Finite Element Model of Thermo-elastic-plastic Large Deformation for Orthogonal Cutting, ASME Journal of Engineering for Industry, vol. 114, 1992, pp. 218 - 226.
45.    Strenkowski, J.S. and Carroll, J.T., A Finite Element Model of Orthogonal Metal Cutting, ASME Journal of Engineering for Industry, vol. 107, 1985, pp. 349 - 354.
46.    Zhang, B. and Bagchi, A. Finite Element Simulation and Comparison with Machining Experiment, ASME Journal of Engineering for Industry, vol. 116, 1994, pp. 289 - 297.
47.    Oikawa, T. and Usui, E., Computational Machining of Titanium Alloy - Finite elementa Modeling and a Few Results, ASME Journal of Engineering for Industry, vol. 118, 1996, pp. 208-215.
48.    Endres W.J., DeVor, R.E., and Kappor, S.G., A Dual-Mechanism Approach to the Prediction of Machining Forces, Part 2: Calibration and Validation, ASME Journal of Engineering for Industry, vol. 117, 1995, pp. 534-541.
49.    Wu, D.W., A New Approach of Funding the Transfer Function for Dynamic Cutting Processes, ASME Journal of Engineering for Industry, vol. 111, 1989, pp. 37-47.