Pattern of Change and Interrelation of Phenomena in the Process of Steel Cutting

A. N. Eremin

Purpose of the Investigation

The process of free and constrained cutting, from the physical point of view, is a complex process of deformation of the metal being transformed into chips. Despite the enormous number of experimental studies, which are of great practical significance, we still do not yet have a sufficiently clear idea of all the laws governing changes in the phenomena of the cutting process, of their interrelation, and of the causes of these changes. It is therefore understandable why, in the literature on cutting, there are still contradictory interpretations and assumptions on a number of questions concerning the process of chip formation.

It is enough to point to the existing contradictions in questions concerning the influence of cutting speed on the cutting force and on chip shrinkage. There are also opposing opinions about the dependence of chip shrinkage on the thickness of the cut. There is no unified conception of the process of formation and disappearance of the built-up edge on the cutter. The process of formation and change of irregularities on the machined surface is often explained incorrectly.

There are questions with which investigators have not dealt at all. For example, no one has investigated the regularities of change in the geometry (angle) of the built-up edge on the cutter or paid serious attention to the role of the geometry of the built-up edge in the cutting process. Likewise, no one has investigated the dependence between shrinkage and strengthening of the chip in the cutting of ferrous-carbon alloys, or compared this dependence with the analogous dependence in plastic compression of a specimen, etc.

From the examples cited it is evident how incomplete our knowledge still is on various questions of the cutting process, although in recent years certain advances have already been made in this direction [5].

The present work is an experimental-theoretical investigation of the phenomena of the process of free and constrained cutting of ferrous-carbon alloys. The work was carried out during the period 1937–1947.

The purpose of the investigation is to establish the regularities of change in the phenomena of the cutting process, their interrelation, and the causes of changes in the phenomena.

The geometry of the built-up edge on the cutter, the deformation and strengthening of the chip and of the compressed specimen, the forces and stresses in cutting and in plastic compression, and the finish of the machined surface were investigated. In addition, the cutting temperature on the faces of the cutter and in the chip, the properties of the deformed metal, friction on the faces of the cutter, and other phenomena of the cutting process were studied.

Conditions and Methodology of the Investigations

The entire experimental part of the investigations was carried out on the same specimens (blanks) made of carbon and chromium steels (Table 1).

Table 1

Characteristics of the steels tested

Designations: r -- rolled; n -- normalized; o -- annealed; $T'_{\text{init}}$ -- initial hardness by the Herbert pendulum (time in seconds); $T_0$ and $T'_0$ -- constants, conventional hardness (by time); $m$, $m'$ -- exponents.

The test cutters were made of high-speed steel (RF-1) and hard alloy (VK-8), of normal geometry (cutting angle $\delta = 35--105^\circ$; plan angles $\varphi = 0--90^\circ$ and $\varphi_1 = 0--10^\circ$; clearance angle $\alpha = 5--8^\circ$; nose radius $r = 0--6$ mm); cutters with a chamfer had a combined rake face (cutting angle $\delta_1 = 90^\circ$; chip-flow angle $\delta_2 \simeq 43^\circ$; chamfer width $k = a$ -- the chip thickness).

The cutting regime was varied within wide limits. The cutting speed $v$ was varied from 0.0007 to 640 m/min, the chip thickness $a$ from 0.01 to 1.0 mm, and the chip width $b$ from 0.1 to 3 mm. The temperature at the cutter ranged from 20 to 900°C.

Cutting was carried out on a lathe without lubrication or cooling, under conditions of absence of vibrations. The specimens were compressed on an Amsler press at a speed of 0.0008 m/min. The temperature was determined as follows: at the cutter, by a galvanometer, using the natural thermocouple method (cutter--work material); in the chip, approximately, by temper colors. In both cases preliminary calibration tests were performed. The hardness of the chips, of the cut surface, and of the compressed specimens (under the press) was measured with a Herbert pendulum (time in sec., 10 swings, with a ball $d = 1$ mm). Observation of built-up-edge formation on the cutter during cutting, and measurement of the angle and height of the built-up edge, were carried out by means of a special optical instrument designed by the author (Fig. 1). The cutting forces were measured with a three-component hydraulic tool holder. The magni-

The magnitude of the unevenness on the machined surface was determined by a profilograph operating by the method of intermittent probing [1]. Chip shrinkage was found either by weighing, or along the neutral line of the chips with the aid of a comparator. In all, about 5000 experiments were carried out. The material on cutting available in the literature was subjected to analysis.

Fig. 1

Results of the investigations

On the basis of theoretical analysis and experimental investigations, the author established that the principal cause of changes in all phenomena in the cutting process is the cutting temperature on the tool and in the chip.

The cutting temperature changes the conditions of friction on the faces of the tool, the initial properties of the metal being transformed into chip, and the actual geometry of the tool (through a change in the built-up-edge angle on the tool), as a result of which there occurs a change in the chip shrinkage $\zeta$, its hardness $T_c$, the force $P_z$ and cutting stress $\sigma_v$, a change in the cleanliness of the machined surface (due to unevenness), and other phenomena of the cutting process. It has also been established that the activity of the influence of various cutting factors ($v$, $a$, $b$, $\delta$, etc.) on changes in the phenomena of the cutting process depends only on the degree of their effect on the cutting temperature and on the volume of metal being deformed ahead of the tool.

The greater the cutting speed, the elements of the cut section, the cutting angle of the tool, and the initial hardness of the metal being machined, the higher the cutting temperature, and vice versa.

The general pattern of the laws governing change and the interrelation of phenomena in the cutting process under the influence of cutting temperature (for example, with an increase in cutting speed $v$) is presented in the diagram of Fig. 2. Here each curve has a typical character, identical for all metals investigated by the author (Table 1), and is confirmed by a large number of

experiments [2]. The latter are given in the present article only as separate examples to illustrate one or another proposition. In doing so, the examples have deliberately been taken from tests on different steels.

Fig. 2

It follows from Fig. 2 that, with an increase in the cutting temperature (with increasing \(v\), Figs. 2a and 3), the coefficient of external friction \(\mu\) on the front (and back) face of the cutter\(^1\) changes (Figs. 2b, 4) according to a curve having a maximum at the temperature on the cutter \(t^0_{tr} \simeq 600^\circ\text{C}\) [2]. A similar pattern of change in \(\mu\) was also observed by investigators in the friction of clean surfaces (iron–cast iron) [6] and in plastic compression [11] (Fig. 4a), and was also confirmed by extensive investigations of the cutting laboratory of TPI [3] (Fig. 5).

According to existing investigations by metallophysicists and metallographers, it is known that, under the influence of temperature, a characteristic phenomenon of blue brittleness arises in iron–carbon alloys. In this connection, the initial hardness \(T'_{iskh}\) (with respect to time) and other strength characteristics of the metal \((H_B, \sigma_s, \sigma_b)\) at first increase with increasing temperature (Figs. 2b, 6, 7), reaching a maximum at the temperature of blue brittleness (in cutting—in the chip) \(t^0_{sin}\), and then decrease. The plasticity characteristics of the metal (elongation \(\delta\%\) and reduction \(\psi\%\)) change in the opposite manner (Fig. 8).

Fig. 3

\(^1\) According to the well-known formula

\[ \mu=\frac{F}{N}, \]

where \(F\) is the force in the plane of the front (or back) face of the cutter,
\(N\) is the force normal to the same face of the cutter; these are obtained experimentally.

Fig. 4a

Fig. 5

Undoubtedly, for the same reasons and according to the same law, the initial characteristics of the steels being machined must change as the cutting temperature rises during the cutting process.

Fig. 6

In the cutting of iron–carbon alloys, as is known, the phenomenon of built-up edge formation on the cutter is observed (Fig. 9), distorting the actual geometry of the latter in the cutting process. Despite the fact that the na-

Fig. 7

the built-up edge has been studied for about 50 years; however, to this day there is no clear conception of the process of formation, change, and disappearance of the built-up edge on the cutter.

The author has established that the built-up edge is a part of the chip retained by friction (or by a land, on a cutter with a land) on the front face of the cutter.

Fig. 8

This confirms the supposition expressed by A. M. Rozenberg [12], and refutes the notions of the built-up edge as a stagnant zone of the deformed metal on the cutter (Usachev, Ernst, Kashirin, Rosenthein, and Ster—

Fig. 9

) or as an accumulation of the finest metal particles, scraped off by the cutting edge and pressed onto the front face of the latter (Taylor, Patkai, Krivoukhov, and others).

In reality, the built-up edge is formed from the chip as a result of simultaneous shear in it at the angle \(\delta_1\) and in a plane tangent to the cutting line (Fig. 10). The built-up edge is formed only at the moment when the chip is retained on the cutting edge by the contact surface under the influence of friction (or by the land).

With a change in cutting temperature (which affects friction and the properties of the metal being deformed (Fig. 2b, c)), the state, height \(h\), and angle \(\delta_1\) of the built-up edge on the cutter change (Fig. 2d). From an unstable (geometrically passive) state at room temperature \((t_1^\circ \approx 20^\circ\mathrm{C})\), the built-up edge gradually passes, with increasing temperature (and friction), into a more stable, active state. In this case the built-up edge is not located on the cutter continuously, in the form of a “stagnation zone.” On the contrary, it continuously appears and is torn away (sheared) from the cutter in the direction of chip motion under the influence of the force of metal deformation acting on the rear face of the built-up edge (Fig. 9). The flowing chip does not participate in tearing off the built-up edge, but contributes to removing it from the cutter. Removed built-up edges are visible on the contact surface of the chip in the form of serrations.

Fig. 10

The dependence of the built-up-edge angle \(\delta_1\) on the cutting temperature (Fig. 2d) is explained, apparently, by the fact that the temperature, by changing \(\mu\) and \(T'_{\mathrm{isk}}\) (Fig. 2b, c), changes the direction of the resultant force on the cutter \(R\) (Fig. 9), under the influence of which the shear angle in the chip \(\delta_1\) changes at the moment the built-up edge is formed. The height of the built-up edge \(h\) depends both on the angle \(\delta_1\) and on the volume of metal being deformed in front of the cutter. The greater the volume and the smaller the angle \(\delta_1\), the greater the height of the built-up edge, and conversely (Fig. 2d).

It has been proved theoretically and experimentally by the author (in experiments with cutters with a land) that, when cutting steel (Table 1), with an increase in temperature from \(20^\circ\mathrm{C}\) and above, the built-up edge on the cutter has its greatest height \(h_1^{\max}\) and the smallest angle \(\delta_1^{\min} = 42\text{–}45^\circ\) at the temperature \(t_1^\circ \approx 20^\circ\mathrm{C}\) (Figs. 2d, 11, 12).

With an increase in temperature, the built-up-edge angle increases to \(\delta_1^{\max} = \delta\), the cutting angle of the cutter, while its height falls to \(h^{\min} = 0\), at the critical temperature on the cutter \(t_3^\circ\) (Fig. 2d, dashed lines). At this moment the built-up edge on the cutter disappears and no longer appears, regardless of any further increase in temperature above \(t_3^\circ\).

The built-up edge disappears on the cutter not because it softens and is worn away by the chip (Rapatz, V. D. Kuznetsov, and others), but because at the temperature \(t_3^\circ\) shear in the chip (forming the front face of the built-up edge) occurs at the angle \(\delta_1 = \delta\), i.e., in the plane of the front face of the cutter. The magnitude of the cri-

critical temperature for the disappearance of the built-up edge on the cutter \(t^{\circ}_3\) is determined only by the cutting angle of the cutter \(\delta\). The smaller the angle, the smaller \(t^{\circ}_3\), and conversely (Fig. 13). For a cutter with cutting angle \(\delta \leq 45^\circ\), the critical temperature for the disappearance of the built-up edge is \(t^{\circ}_3 = t^{\circ}_1 \simeq 20^\circ\mathrm{C}\), since under these conditions the built-up-edge angle is also \(\delta_1^{\min'} \simeq 42^\circ\text{–}45^\circ\) (Figs. 12, 13). In all cases, an objective indication of the disappearance of the built-up edge on the cutter (at any value of \(t^{\circ}_3\)) is the moment when gloss appears on the contact surface of the chips.

Fig. 11

The regularity in the change of the geometry of the built-up edge on a cutter of normal form (without a chamfer) under the influence of the cutting temperature has a somewhat different character (Fig. 2г, solid lines). In this case, at a cutting temperature \(t^{\circ}_1 \simeq 20^\circ\mathrm{C}\), the built-up edge on the cutter is usually absent owing to weak friction on the rake face of the cutter (Fig. 2б), and therefore the built-up-edge angle \(\delta_1 = \delta_1^{\max} = \delta\) and \(h = 0\). The latter is clearly seen from Figs. 14 and 15, which show the dependence of the angle \(\delta_1\) and the height \(h\) of the built-up edge on the cutting speed and on the cutting angle of the cutter \(\delta\). The same is also observed in Fig. 16 when cutting with different chip thicknesses \(a\), and in Figs. 17, 17a when cutting steels of different initial hardness.

Fig. 12

With an increase in temperature (and friction) from \(20^\circ\mathrm{C}\) and higher, the activation of the built-up edge increases; its angle at first decreases to a certain value—

Fig. 13

Labels in the graph:

• Carbon steel
• \(a = 0.31\ \mathrm{mm}\)
• \(b = 1.5\ \mathrm{mm}\)
• \(\gamma = 90^\circ\)
• \(z = 0\)
• without cooling

Axis labels:

• Vertical axis: Angle \(\delta^\circ\)
• Horizontal axis: Divisions of the head dynamometer
• \(t^\circ C\)

Legend and annotations:

• \(x\): \(\delta = 92^\circ\)
• \(\circ\): \(\delta = 75^\circ\)
• \(\bullet\): \(\delta = 61^\circ\)
• \(\triangle\): \(\delta = 45^\circ\)
• steel 1045, \(H_B = 180\)
• \(\diamond\): \(\delta = 92^\circ\)
• \(\triangle\): \(\delta = 45^\circ\)
• \(H_B = 163\)
• \(\delta = 45^\circ\)
• \(\delta = 61^\circ\)
• \(\delta = 75^\circ\)
• \(\delta = 92^\circ\)

Fig. 14

Labels in the graph:

• Steel 5120
• \(\gamma = 90^\circ\)
• \(z = 0\ \mathrm{mm}\)
• Pobedit
• \(a = 0.31\ \mathrm{mm}\)
• \(b = 1.5\ \mathrm{mm}\)
• without cooling

Axis labels:

• Vertical axis: Angle \(\delta^\circ\)
• Horizontal axis: Speed \(V\), m/min

Annotations:

• \(\delta = 91^\circ\)
• \(\delta = 75^\circ\)
• \(\delta = 61^\circ\)
• \(\delta = 45^\circ\)
• \(C = \mathrm{const}\)

… angle $\delta_1^{\min}$ at temperature $t_2^\circ$¹, after which it begins to increase, again reaching the value $\delta_1^{\max}=\delta$ at the critical temperature for the disappearance of the built-up edge $t_3^\circ$.

Fig. 15

… of the built-up edge $t_3^\circ$. In connection with this, the height of the built-up edge changes according to a curve of the inverse order: at $t_1^\circ$ and $t_3^\circ$, $h=0$; at $t_2^\circ$, $h=h_2^{\max}<h_1^{\max}$.

Fig. 16

(Figs. 2g, 14, and 15). The angle of the built-up edge on the cutter, \(\delta_1\), determines the actual cutting angle in the cutting process.

The speed corresponding to the critical temperature at which the built-up edge on the cutter disappears, \(t^\circ_3\), is the critical cutting speed \(V_3\) (Fig. 2p). At all values \(V < V_3\) a built-up edge forms on the cutter; at \(V_3 > V_3\) the built-up edge is absent, and the actual cutting angle \(\delta_1 = \delta\), the angle of the cutter (Figs. 2g, 14, 16, 17).

The dependence of \(V_3\) on the cutting factors is determined by the equation

\[ V_3=\frac{C}{\delta a^x b^y}, \tag{1} \]

where \(C\) is a coefficient taking into account the initial properties of the material being machined and of the cutter, the condition of the cutter faces and edge, and the cutting conditions (with cooling, without cooling). \(x > y < 1\) are exponents of the influence of the thickness and width of the cut on the cutting speed.

Fig. 17. Chromium steels. Pobedit. \(\varphi = 90^\circ\); \(z = 0\) mm; \(a = 0.31\) mm; \(b = 1.45\text{–}1.6\) mm; without cooling. Cutting angle \(\delta^\circ\) versus speed \(V\), m/min. Curves labeled: stainless; 5140; 5120; \(\delta = 75^\circ\).

Fig. 17a. Carbon steels. Pobedit. \(\varphi = 90^\circ\); \(z = 0\) mm; \(a = 0.31\) mm; \(b = 1.45\text{–}1.8\) mm. Cutting angle \(\delta^\circ\) versus speed \(V\), m/min. Curves labeled: \(H_B = 260\); 1040; 1020; 1010; \(\delta = 75^\circ\).

Equation (1) has definite practical significance. For any specified cutting regime, by means of equation (1) it is possible to determine such a value of the speed \(v_3\) above which the built-up edge on the cutter will always be absent, which is very important for ensuring a high-quality finish of the machined surface.

If the cutting temperature changes the coefficient of friction on the cutter \(\mu\) and the actual cutting angle \(\delta_1\) (through the built-up edge), and also changes the initial properties of the deforming metal being converted into chip (\(T_{\text{init}}\), \(\sigma_v\), \(H_v\), etc.), then, undoubtedly, in connection with this, the degree of plastic deformation (shrinkage) of the chip must also change; and together with it the strengthening (hardness) of the chip, the cutting force, and the cutting stress must change as well.

The author has established that, as a result of the combined interaction of \(\mu\), \(T_{\text{init}}\), and \(\delta_1\) (Figs. 2b, c, d), with an increase in cutting temperature there occurs a change in the chip shrinkage \(\zeta\), its hardness \(T_k\) (strengthening), the cutting force \(P_z\), and the nominal stress \(\sigma_v\), according to the law of a typical curve (Fig. 2d) or one similar to it. When steels are cut (Table 1) with a normal cut—

with (without a chamfer) the typical curve has four phases of change in the temperature zones: \(t_1^\circ—t_2^\circ\); \(t_2^\circ—t_{tr}^\circ\); \(t_{tr}^\circ—t_{blue}^\circ\); \(t^\circ > t_{blue}^\circ\)¹).

In the first phase \((t_1^\circ—t_2^\circ)\) the typical curve (Fig. 2d) falls sharply owing to a decrease in the actual cutting angle \(\delta_1\) (Fig. 1g) and a reduction of the plastic properties of the metal under the influence of the blue-brittleness phenomenon.

In the second phase \((t_2^\circ—t_{tr}^\circ)\) the curve rises, reaching a second maximum at \(t_{tr}^\circ\), as a result of an increase in the angle \(\delta_1\) and in the coefficient of external friction on the cutter \(\mu\) (Figs. 2b, g).

In the third phase \((t_{tr}^\circ—t_{blue}^\circ)\) the curve again falls under the influence of the decrease in \(\mu\) and the increase in the hardness of the deformed metal (Fig. 2v), owing to the active manifestation of the blue-brittleness phenomenon.

In the fourth phase \((t^\circ > t_{blue}^\circ)\) the typical curve remains practically unchanged (slight slope), owing to the mutually opposite action of the coefficient of friction (decrease) and the increase in the plasticity of the deformed metal, converted into chips (Figs. 2b, v, 3–7).

If there were no influence of the built-up edge on the cutter, the typical curve would have the form of a continuously decreasing curve in the temperature zone \(t_1^\circ—t_{blue}^\circ\) (Fig. 2d, dashed line). It is precisely for this reason that the peak of the second maximum on the typical curve at \(t_{tr}^\circ\) is always located below the first maximum, at \(t_1^\circ \approx 20^\circ\mathrm{C}\).

As an example, experimental curves obtained by the author for steel 1035 (Table 1) are presented. Figure 18 shows the curve of change in chip shrinkage \(\zeta\) as a function of cutting speed \(v\), at different cutting angles of the cutter.

Fig. 18

A similar dependence for the cutting force \(P_z\) is shown in Fig. 19, and for the cutting stress \(\sigma_v\)—in Fig. 20. Curves obtained for other steels (Table 1) have an analogous character.

The sharp expression of the phases of the typical curve depends on the initial properties of the metal being machined (Table 1), the cutting angle, and the cutting temperature.

The interrelation between chip shrinkage and chip hardness (with respect to time) is evident, for example, from a comparison of Figs. 21 and 22 for steel 5120. The same is also observed for other steels (Table 1).

It has been established that the cutting speed in the cutting process of refractory metals (steel, Table 1) is only a temperature factor. Depending on the speed limits, i.e., the temperature zone, it is possible to obtain

¹) The temperature on the cutter \(t_1^\circ \approx 20^\circ\mathrm{C}\), \(t_2^\circ \approx 400^\circ\mathrm{C}\), \(t_{tr}^\circ \approx 580—600^\circ\mathrm{C}\), and \(t_{blue}\)—the temperature in the chip \(360—400^\circ\mathrm{C}\), depending on the initial hardness of the steel [2].

Fig. 19

Fig. 20

Fig. 21

any phase of variation of the typical curve (Fig. 2d). High-speed cutting is a special case of cutting at high temperatures, above \(t^{\circ}_{\mathrm{tr}}\) (Fig. 2).

No appreciable influence of cutting speed, as the speed of plastic deformation, has been found on the shrinkage and hardness (hardening) of the chip, on the cutting force and cutting stress, on the moment at which built-up edge disappears on the tool, or on other phenomena of the cutting process.

The variation of chip shrinkage and cutting force according to the law of the typical curve (Fig. 2d) makes it possible to reveal the causes of the existing contradictions in questions concerning the influence of cutting speed on cutting force, on chip shrinkage, and the influence on shrinkage of the thickness of the cut ([5; 7; 8; 9; 10] and many others).

Fig. 22

The observed, often contradictory, deviations in the experiments of many investigators for the dependence \(P_z=f(v)\) are explained exclusively by the difference in the limits of the temperature regime of cutting in which particular experiments were carried out. Depending on these limits, all existing experiments on cutting forces (for iron and steel) fit well into the corresponding phases of the typical curve (Fig. 23). The lines in Fig. 23 show the limits of the temperature regime of cutting in these investigations.

The thickness and width of the cut, like the cutting speed, influence the shrinkage and hardness of the chip and the cutting stress only as temperature factors. Depending on their combination, any zone of temperature variation may likewise be obtained and, consequently, any phase of variation of chip shrinkage, its hardness, and cutting stress according to the typical curve (Fig. 2d) [2]. Hence follows a particular law: for a given machined material and cutting angle of the tool, a cutting regime with constant temperature corresponds to an unchanged state of the machined metal \((\sigma_b,\ \sigma_s,\ H_B)\), a constant value of the coefficient of friction \(\mu\) on the faces of the tool, a constant effective cutting angle \(\delta_1\) (determined by the built-up-edge angle), constant shrinkage \(\zeta\) and hardness \(T_n\) of the chip, and constant cutting stress \(\sigma_y\).

Figure 24 shows a series of typical curves of chip shrinkage for steel 5120. Irrespective of the thickness of the cut and the cutting speed, each value of shrinkage \(\zeta=\mathrm{const}\) taken on the corresponding phases (branches) of the curves corresponds to a definite cutting temperature \(t^{\circ}=\mathrm{const}\), and conversely. Thus, for example, the line tangent to the tops of the “hump” (the second maximum)

of the curves in Fig. 24, corresponds to a constant critical temperature \(t^\circ_{mp}\) \((580—600^\circ C)\) and to a constant value of shrinkage \(\zeta \simeq 4\).

Fig. 23

Labels in the figure: force \(P_z\); typical cutting-force curve; temperature \(t\); \(t_2\), \(t_{mp}\), \(t_{\text{syn}}\); phases of the curve: 1, 2, 3, 4; investigators; limits of experiments.

Investigators listed in the figure: Nicolson; Chelyustkin; Taylor; Klopstock; Schlesinger; Isachev; Sellergen; Pattay; Kronenberg; Okoshi and Okoshi; Klopov; Lee and Schaeffer; Willix and Fife; D. Smith and Leigh; Stanton and Hyde; Boston and Krause; Wallace; Zorev; Kashiron; Besprozvannyi; Ernst; Albrecht; Eremin.

The existing opinion that, with an increase in the thickness of cut \(a\), the chip shrinkage \(\zeta\) decreases \([5]\), is a special case of cutting in the zone

Fig. 24

Labels in the figure: shrinkage \(\zeta\); cutting speed \(V\), m/min; steel 5120; \(\delta = 90^\circ\); \(t = 10\) mm; \(\varphi = 45^\circ\); \(\varphi_1 = 5^\circ\); \(\gamma = 0\); \(S = 0.44\) mm/rev, \(a = 0.31\) mm; \(0.22\), \(0.16\); \(0.11\), \(0.08\); \(0.055\), \(0.04\); \(a = 0.31\); \(a = 0.16\); \(a = 0.08\); \(a = 0.04\); gray; colors; gloss; “built-up edge.”

temperatures \(t^\circ_1 - t^\circ_2\), or \(t^\circ_{tr} - t^\circ_{sin}\) (Figs. 2d, 21, 24), i.e., a decrease in shrinkage in the first and third phases of the typical curve under the influence of temperature, but not of chip thickness.

The author has established that hardness \(T_h\) with respect to time (by the Herbert pendulum) is a sufficiently reliable characteristic of the hardening of the metal in the chip during cutting and in the specimen during plastic compression.

The hardening of the chip during cutting and of the specimen during compression depends on the degree of plastic deformation (shrinkage) and on the initial properties of the metal being deformed (Table 1). No noticeable influence of “rest” on the process of chip hardening was found, and no manifestation of “saturation” of chip hardening was observed, despite changes in cutting speed from 0.0007 to 640 m/min and chip shrinkage from \(\zeta = 1.3\) to \(\zeta = 10\).

Between hardness (with respect to time) and chip shrinkage during cutting of steels (Table 1) there is a definite dependence of the form

\[ T_h = T_0 \zeta^m, \tag{2} \]

while during plastic compression of specimens

\[ T_h = T'_0 \zeta^{m'}, \tag{3} \]

where \(T_0\) and \(T'_0\) are constants characterizing the initial properties of the metal being deformed, respectively during cutting \((T_{init})\) and during compression \((T'_{init})\). The constants \(T_0\) and \(T'_0\) are called the conditional hardness.

At the same degree of deformation (shrinkage) of the specimen and the chip, the hardness of the chip during cutting is always higher than that of the specimen during plastic compression, since \(T_0 > T'_0\). It may be assumed that this occurs as a result of the different flow conditions of the deformed metal in the one and the other process. The values of \(T_0\), \(T'_0\), and \(m\), \(m'\) are given in Table 1.

Between dependences (2) and (3) there exists the same analogy as in the regularities of the polytropes of stress \(\sigma\) under compression for a previously hardened (4) and an unhardened specimen (5) (Bolshanin M. A., Kuyin N. F., et al. [4]).

\[ \sigma = \sigma_0 \zeta^n \tag{4} \]

\[ \sigma = \sigma'_0 \zeta^{n'} \tag{5} \]

For example, Fig. 25 shows the dependence of chip hardness \(T\) on shrinkage \(\zeta\) for carbon steels 1010 and 1040 (Table 1). Despite a considerable change in cutting conditions, the arrangement of the points indicates that the hardness of the chip depends only on shrinkage, i.e., on the degree of hardening of the given metal. Similar dependences during plastic compression for the same steels are given in Fig. 26.

Fig. 25

Knowing the pattern of change and interrelation of the phenomena of the cutting process, it is not difficult to explain the pattern of change in the finish of the machined surface (Fig. 2e), since the latter is, in essence, the concluding phenomenon of the cutting process.

The principal characteristic of surface finish is the magnitude of the irregularities and roughnesses on the machined surface. In constrained cutting,

Fig. 2b

the magnitude of the irregularities \(H\) is composed of the height of the residual ridges \(H_{\mathrm{res}}\) and the height of the roughnesses on the cut surface \(H_{\mathrm{rough}}\).

\[ H = H_{\mathrm{res}} + H_{\mathrm{rough}} \tag{6} \]

In free cutting,

\[ H = H_{\mathrm{rough}} \]

\(H_{\mathrm{res}}\) is the geometric characteristic of surface finish. It depends on the profile of the cutter in plan \((r, \varphi, \varphi_1)\), the condition of the cutting edge, and the magnitude of the feed \(S\). \(H_{\mathrm{rough}}\) is not only a geometric but also a physical characteristic of the finish of the cut, since it depends on the temperature regime of cutting and the initial properties of the material being machined.

Like all phenomena of the cutting process (built-up edge, reduction and hardness of the chip, coefficient of friction on the cutter, etc.), surface finish changes under the influence of the cutting temperature (on the cutter and in the chip), which affects the magnitude of the roughnesses \(H_{\mathrm{rough}}\). The influence of temperature on the magnitude of \(H_{\mathrm{rough}}\) is exerted through changes in the friction on the rear face of the cutter (or of the built-up edge), the degree of plastic deformation (reduction) of the chip, the height of the built-up edge on the cutter, and shear displacements on the cut surface.

As a result of this, the pattern of change of the irregularities \(H\) with increasing cutting temperature is expressed by a curve (Fig. 2e) having a maximum at temperature \(t_2^\circ\), when the built-up edge on the cutter (of normal geometry, without a chamfer) reaches the height \(h_2^{\max}\) (Fig. 2g). To confirm this, Fig. 27 gives experimental curves of the change in the irregularities \(H\) as a function of cutting speed \(v\) (and consequently also of temperature, Figs. 2a, 3) and of the feed \(S\) for steels 1035 and 1040 (Table 1). The smaller \(S\), the lower \(H\), but the higher the \(v\) corresponding to the maximum of the curve. For all the steels investigated (Table 1), the curves have the same (typical) character, showing four phases of change in the irregularities \(H\) (Figs. 2e, 27) in definite temperature zones.

First phase (at \(t_1^\circ \simeq 20^\circ \mathrm{C}\)). The height of the irregularities \(H = \mathrm{const}\) and depends on the shear displacements (tears) on the cut surface, the magnitude of which is determined by the degree of deformation (reduction) of the chip.

Second phase \((t^\circ_1 - t^\circ_2)\). The height of the irregularities \(H\) increases to \(H_{2\max}\), as a result of an increase in the height of the built-up edge and in the coefficient of friction (Fig. 2g, b), and of a decrease in the tearing-off of the crests of the ridges \((l'_{\mathrm{res}})\) under the influence of a sharp decrease in chip shrinkage¹ (Fig. 2d).

Third phase \((t^\circ_2 - t^\circ_{\mathrm{mirr}}\), where the latter corresponds to the appearance of a mirror-like gloss on the cut surface). The height \(H\) decreases to \(H_{\mathrm{mirr}}\), at first sharply—under the influence of a decrease in the height of the built-up edge (Fig. 2g) and an increase in the tearing-off of the crests of the ridges with increasing chip shrinkage up to the temperature \(t^\circ_{\mathrm{res}}\) (Fig. 2d), then slowly—owing to a decrease in the coefficient of friction \(\mu\) (Fig. 2b) and a decrease in \(H_{\mathrm{rough}}\) on the cut surface.

Fig. 27

Fourth phase \((t^\circ > t^\circ_{\mathrm{mirr}})\). The cut surface has a mirror-like gloss. The roughness \(H_{\mathrm{rough}} = 0\). The height of the irregularities \(H = H_{\mathrm{mirr}} < H_{\mathrm{res}}\), as a result of the influence of the tearing-off of the crests of the ridges by the chip shrinkage \(\xi^{\min}_{\mathrm{sh}}\) (Fig. 2d). The larger the cutting angle of the tool \(\delta\), the greater the chip shrinkage \(\xi^{\min}_{\mathrm{sh}}\), the smaller \(H_{\mathrm{mirr}}\), and conversely. To obtain the highest surface finish, characterized by a mirror-like gloss and a height of irregularities \(H = H_{\mathrm{rough}} = 0\), it is not necessary to have a high cutting speed, a small feed, and a small depth of cut; it is important to have a cutting temperature \(t^\circ \geq t^\circ_{\mathrm{mirr}}\) and the tool angle in plan \(\mu_1 = 0^\circ\). From this point of view, it is advantageous to work with tools having negative rake angles and large feeds. From Fig. 28 it is clearly seen that the larger the feed value \(S\),

Fig. 28

the more rapidly the height of irregularities decreases to zero with increasing cutting speed. This also confirms that the chief factor governing surface finish is the cutting temperature.

the higher the cutting temperature, the lower the cutting speed corresponding to \(H_{\text{mic}}=0\), and conversely.

The proposition considered, which follows from the very essence of the phenomena of the cutting process, by no means rejects the practical use of high-speed cutting at temperatures \(t^\circ \ge t^\circ_{\text{zer}}\). In this case the cleanliness of the cut surface, although it in fact remains unchanged, since \(H_{\text{mic}}=0\), nevertheless the productivity of the cutting process increases in proportion to the increase in speed.

Conclusion

As a result of the investigation carried out on the cutting process of iron-carbon alloys, the following results have been obtained.

First, the regularity of change has been established for: the coefficient of external friction on the faces of the cutter \(\mu\), the geometry of the built-up edge on the cutter (the angle \(\delta_1\) and the height \(h\)), the chip shrinkage \(\zeta\) and its hardness \(T_h\), the force \(P_z\) and the cutting stress \(\sigma_z\), and the magnitude of irregularities on the machined surface \(H\).

Second, a single interrelation of the phenomena in the cutting process and the fundamental cause of their change—temperature—has been found.

All this makes it possible not only to explain the essence of the phenomena of the cutting process and to reveal the causes of the contradictions existing in the contemporary literature on cutting, but also to outline paths for further investigation of the cutting process.

References

1. Eremin A. N. Profilographing of Surfaces by the Method of Intermittent Sensing. Izvestiya TII, vol. 59, issue 1, 1939.

2. Eremin A. N. Deformation, Hardness, Force, and Surface Cleanliness in the Cutting Process. Izvestiya TPI, 1947.

3. Zimin Yu. P. Investigation of High-Speed Cutting of Steel. Izvestiya TPI, 1948.

4. Kuznetsov V. D. Physics of the Solid State. Vol. II, 1941.

5. Kuznetsov V. D. Physics of the Solid State. Vol. III, 1944.

6. Kunin N. F. Dependence of the Coefficient of External Friction of Split Iron on Cast Iron on Various Factors. ZhTF, vol. 3, 1933.

7. Krivoukhov V. A. Deformation of the Surface Layers of Metal in the Cutting Process. Mashgiz, 1945.

8. Kashirin A. I. Investigation of Vibrations in Metal Cutting. Publishing House of the Academy of Sciences of the USSR, 1944.

9. Kas'yan M. V. Cutting Speed at Optimal Chip Deformation. Izvestiya GIIM, book No. 14, 1941.

10. Klyushin M. I. and Fel'dshtein E. I. Influence of Speed on Cutting Forces at Positive and Negative Rake Angles of the Tool. Machine Tools and Instruments, No. 7–8, 1945.

11. Lashko N. F. et al. Plastic Deformation in Compression at High Temperatures. ZhTF, vol. 7, 182, 1937.

12. Rozenberg A. M. Experimental Investigation of the Process of Formation of Metal Chips. Izvestiya STI, vol. 51, issue 4, 1929.

1. An interesting phenomenon has been found: tearing-off of the crests of the ridges by the chip itself, owing to shrinkage of the latter across its width. The greater the longitudinal shrinkage of the chip, the greater its shrinkage across the width, the greater the tearing-off of the ridges, and conversely [2]. ↩↩