FACTORS INFLUENCING THE DEFORMATION PROCESS DURING CUTTING

A. M. ROZENBERG and K. A. NASSONOV

The cutting process is a process of plastic deformation of the layer of metal being removed. In order to remove a chip, a certain force must be applied to the cutting tool, called the cutting force.

Determining the magnitude of the cutting force is a necessary condition both in the calculation and design of metal-cutting machine tools and in determining the accuracy of machining parts.

For a known cross section of cut, the magnitude of the cutting force will depend on the physicomechanical characteristics of the metal being machined and on the degree of deformation of the layer being removed.

Consequently, a very important question in the theory of cutting is that of the factors influencing the degree of deformation of the chip at the moment of its formation. It should be noted that at present researchers have no common opinion on the question of the influence of various parameters of the cutting process on the degree of deformation of the chip, which qualitatively can be characterized by the magnitude of chip shrinkage.

In the technical literature one may encounter observations to the effect that, at a constant cutting angle, the magnitude of chip shrinkage is directly influenced by the physicomechanical characteristics of the metal being machined, the feed rate, the depth of cut, and other parameters.

Thus, for example, Prof. I. M. Besprozvannyi [1] notes that the magnitude of chip shrinkage depends directly on the plastic properties of the materials being machined. In the work of Prof. V. A. Krivoukhov and Candidate of Technical Sciences A. I. Nevzorov [2] there is the conclusion that “an increase in feed and depth of cut within the investigated range of their values leads to a decrease in longitudinal shrinkage \((\zeta)\); in this case the feed has a greater influence than the depth of cut.” Finally, in a textbook on metal cutting [3] there is an indication that “the angle \(\Theta\)\(^1\) also depends on the chip thickness, cutting speed, and physicomechanical properties of the metal being machined.”

One cannot but agree that the influence of all the factors listed above on chip shrinkage does take place; however, the physical interpretation of this influence, in our opinion, is often erroneous.

We believe that, for a given cutting angle, the magnitude of chip shrinkage (that is, the magnitude of deformation of the layer being cut) is completely and unambiguously determined by the value of the coefficient of friction between the chip and the front surface of the cutting tool. The influence of all other factors of the cutting process (speed, feed, depth, physicomechanical characteristics of the material being machined, cutting temperature) on shrinkage

\(^1\) \(\Theta\) is the angle determining the position of the plane of maximum tangential stresses and, consequently, the magnitude of chip shrinkage. In the present article, below, we shall denote this angle by \(\beta_1\).

the chip can manifest itself only through the corresponding change in the coefficient of friction.

But if, in the cutting process, at a given cutting angle there is a definite value of the coefficient of friction, then this value of the coefficient of friction corresponds to a quite definite value of chip compression, regardless of what values the other process parameters may have. Below we shall try to prove the point of view just stated.

In 1893 Prof. K. A. Zvorykin [4] analytically obtained an equation for the angle $\beta_1$,

\[ \beta_1 = 45^\circ - \frac{\delta}{2} - \left(\frac{\mu+\mu_1}{2}\right), \]

where: $\beta_1$ is the angle determining the position of the shear plane,
$\delta$ is the cutting angle,
$\mu$ and $\mu_1$ are the coefficients of external and internal friction.

Thus, already here there is an indication that the angle $\beta_1$ (and, consequently, the value of chip compression $\zeta$ determined by it) depends on the cutting angle and the coefficient of friction.

In the equation given by Prof. K. A. Zvorykin, neither the feed, the cutting speed, nor the physicomechanical characteristics of the metal, nor any other parameters of the cutting process have any independent influence on the angle $\beta_1$ (or on chip compression).

On the basis of experimental studies, in 1949 Prof. A. M. Rozenberg and Prof. A. N. Eremin [5] came to the conclusion that “with a change in temperature on the rake face, the coefficient of friction of the chip along the rake face and the geometry of the built-up edge change, which determines the direction of the resultant force on the rake face. The direction of the resultant force, in turn, determines the position of the plane of maximum shear stresses and the magnitude of compression.” That is, here too it is emphasized that the magnitude of compression depends only on the direction of the resultant force on the rake surface, which in turn is determined by the geometry of the tool (the rake angle) and the coefficient of friction. Other parameters of the cutting process can influence the magnitude of compression only insofar as they change the coefficient of friction of the chip along the rake surface.

This proposition is satisfactorily confirmed by the extensive experimental data of recent years obtained by various investigators.

Experimentally, the dependence $\zeta=f(\mu)$ for a constant rake angle $\gamma=+10^\circ$ was first obtained by N. N. Zorev [6]. Steels of various grades were machined. The graph presented by the author gave good coincidence of the experimental points for the most diverse steels on a single common curve. However, N. N. Zorev at the same time makes the reservation that, for different materials, owing to the difference in their mechanical properties, which determine the stress state of the plastic zone, the curves $\zeta=f(\mu)$ should not coincide. The author assumes that the good coincidence of the experimental points on one common curve $\zeta=f(\mu)$ is explained by the direct influence of cutting speed on the orientation of the principal axes of deformation in the plastic zone.

Such an assumption, in our opinion, is insufficiently convincing. Indeed, it is difficult to suppose that the combined influence of the mechanical properties of the material being machined and of cutting speed would in all cases lead to the coincidence of the experimental points on one common dependence. The existence of a single-valued relationship between chip compression and the coefficient of friction objectively indicates a definite role

coefficient of friction of the chip along the rake face in the process of chip formation. In this unambiguous relation \(\zeta=f(\mu)\), the various physico-mechanical characteristics of the metals being machined did not show their own independent influence on chip shrinkage.

Somewhat later, in 1952–1953, L. A. Khvorostukhin [7] established that the relation obtained by N. N. Zorev between the coefficient of friction and chip shrinkage is well confirmed when turning various grades of steel and for rake angles \(\gamma=+20^\circ;\ +10^\circ,\ 0^\circ,\ -10^\circ\) (Fig. 1).

Fig. 1.
Vertical axis: coefficient of friction \(\mu\). Horizontal axis: chip shrinkage \(\zeta\). Curves for \(\gamma=20^\circ\), \(\gamma=10^\circ\), \(\gamma=0^\circ\), \(\gamma=-10^\circ\). Legend: St. 10; 30KhGS; St. 4; 9KhS; ShKh-15; EYaT; 12KhN3; St. 30.

Table 1 gives the chemical composition of the steels subjected to machining. Some of their physico-mechanical characteristics are also indicated there.

Table 1

Here \(\sigma_0\) is the conventional yield point,
\(n\) is the exponent of the stress polytrope in compression,
\(H_B\) is Brinell hardness.

In this case, the experiments for each of the rake angles were carried out with different feeds, depths of cut, and at different cutting speeds.

However, all these factors, as well as the differences in the physico-mechanical characteristics of the steels being machined, did not reveal any independent influence in the dependence \(\xi=f(\mu)\). For each of the rake angles we observe a satisfactory coincidence of all experimental points on one common curve, and the relative positions of the experimental points on the graphs are not connected with any other parameters of the cutting process.

It is appropriate to note here that the dependence \(\xi=f(S)\), which Prof. V. A. Krivoukhov and Cand. Tech. Sci. A. I. Nevzorov [2] present in their work, was obtained by them in experiments conducted at a constant cutting speed. Under these conditions it is quite natural that, with an increase in chip thickness (feed), there was an increase in cutting temperature, accompanied by a decrease in the coefficient of friction of the chip on the rake face of the cutting tool, which also caused a decrease in the chip shrinkage with increasing feed. The latter is explained differently by the authors of the work. Their point of view will be clear from the following remark: “it is natural that at a high cutting speed, with a small chip thickness, the chip has time to heat up during deformation; with a greater chip thickness this may not occur. As a result, with an increase in feed \(S\), the chip shrinkage decreases.” Such an explanation, in our opinion, is unconvincing. First, if the chip thickness (feed) exerted a direct influence on the magnitude of chip shrinkage as a result of the different ability of chips of different thicknesses to be heated, then at a constant cutting temperature one would expect greater shrinkage for a thin chip. However, as experiments show [5, 8], chip shrinkage at a constant cutting temperature changes practically not at all with a change in feed. Moreover, in the same work under discussion the authors present a graph of the dependence \(\xi=f(V)\) at a constant feed \(S=0.15\ \text{mm/rev}\).

From this graph it is evident that, in the cutting-speed range \(50\text{—}600\ \text{m/min}\), chip shrinkage decreases noticeably with increasing cutting speed (and consequently with increasing cutting temperature). At the same time the chip is removed increasingly heated. If one were to adhere to the point of view of the authors of [2], then one should expect an increase in chip shrinkage, since at a constant chip thickness the more heated chip should deform more. In fact, however, this is not the case.

The unambiguous relation between the coefficient of friction and the degree of plastic deformation of the cut layer of metal, noted by N. N. Zorev and L. A. Khvorostukhin, occurs not only in the turning of steels. This is evidenced by the experiments of A. I. Promptov [9] on face milling of steels (Fig. 2).

It is obvious that if chip shrinkage increases with an increase in the coefficient of friction, then the relative shear \(\varepsilon\) will also increase. Figure 2 presents the graph \(\varepsilon=f(\mu)\). Plotted here are points obtained from experiments carried out on steels 10, 35, U10, 12KhN3A, and 40Kh with variation of the cutting parameters within the following limits: cutting speed \(V=56\text{—}450\ \text{m/min}\), feed per tooth \(S_z=0.027\text{—}0.21\ \text{mm/tooth}\), cutting depth \(t=1.5\text{—}8\ \text{mm}\), and principal cutting-edge angle \(\varphi=52\text{—}90^\circ\). From the graph given it is evident that the relative shear is satisfactorily determined by the coefficient of friction of the chip on the rake face when the cutting conditions are varied within fairly wide limits.

In Table 2 we present the results of experiments by Yu. A. Rosenberg [10] on the turning of gray cast iron.

Analysis of the table shows that, also in the turning of cast iron at a constant rake angle, the same qualitative relation is observed between the coefficient of friction and the degree of deformation, since with an increase in the friction angle \(\eta\) the angle \(\beta_1\)

decreases and, consequently, the chip shrinkage increases, since there is the following relationship between chip shrinkage and the angle \(\beta_1\):

\[ \zeta=\frac{\cos(\beta_1-\gamma)}{\sin\beta_1}. \]

Fig. 2

Table 2

To clarify the influence of the factors of the cutting process on chip deformation, the results of our experiments in turning EIIT steel and grade 40 steel in the cold and heated states are of definite interest. The heating of the workpieces being machined was carried out in a chamber-type electric furnace. The heating temperature \(T\) in the experiment was monitored with a special thermocouple. The cutting temperature \(t\) was measured by the natural-thermocouple method. Figs. 3, 4, and 5 show, respectively, the graphs

\[ t=f(T), \qquad \zeta_a=f(T) \quad \text{and} \quad \mu=f(T) \]

for six cutting speeds from 3 to 190 m/min.

From Fig. 3 it is seen that, with an increase in the preliminary heating temperature of the steel, the cutting temperature increases for all the cutting speeds investigated. It should be noted that for a cutting speed of 16 m/min, in the preheating-temperature range of \(250\text{--}350^\circ\mathrm{C}\), a considerable jump in cutting temperature is observed; and when turning at a speed of 33 m/min, a certain rise in cutting temperature is noticeable when the steel heating temperature is increased from 150 to \(270^\circ\mathrm{C}\). In carrying out the experiments, it could be found that when turning steel at a speed of 3 m/min, built-up edge occurred throughout the entire range of steel preheating temperatures up to \(600^\circ\mathrm{C}\). Only at \(T=700^\circ\mathrm{C}\) did the built-up edge

was not detected. During turning at a speed of 16 m/min, the disappearance of the built-up edge could be observed when the steel was heated to 300°C. If we turn to Fig. 6, where the dependences \(t = f(V)\) and \(\zeta = f(V)\), obtained in machining ÉYa1T steel in the cold state, are presented, it can be seen that the built-up edge occurred in the same range of cutting temperatures.

Consequently, the presence of a built-up edge was determined only by a certain temperature regime established on the front surface of the cutter, irrespective of the changes in the factors by which this regime was established. In turning cold steel, the cutting temperature changed as a result of changes in cutting speed; in the experiments with heated steel, it changed as a result of changes in the steel heating temperature at constant cutting speed. The zone of cutting temperatures at which a built-up edge occurs is bounded in Fig. 3 by a horizontal band.

Fig. 3

Analyzing the character of the change in chip shrinkage (Fig. 4) with increasing heating temperature of the stainless steel, it may be noted that chip shrinkage depends very strongly both on the degree of heating of the steel and on the cutting speed. The character of the curves \(\zeta = f(T)\) at \(V = 3\) m/min and \(V = 16\) m/min was determined by the presence of a built-up edge on the cutter. The moment of disappearance of the built-up edge was accompanied by an extremely sharp increase in chip shrinkage \((V = 16\) m/min) from \(\zeta_a = 2.2\) to \(\zeta_a = 5.8\). Such a sharp increase in chip shrinkage and, consequently, in the degree of plastic deformation, could not but be accompanied by intensive heat release, which apparently was reflected in the “jump” in cutting temperature noted above.

In addition, consideration of Fig. 4 shows that, for cutting speeds at which no built-up edge is present, chip shrinkage with increasing heating temperature changes along curves that have a maximum. Moreover, the maximum of the chip-shrinkage curve for lower cutting speeds is shifted into the region of lower steel heating temperatures and has a larger absolute value. Let us emphasize a certain feature of the cutting process that was revealed in machining heated ÉYa1T steel. This feature consists in the fact that a change in cutting temperature due to a change in the heating temperature of the steel exerted a different influ-

… influence on the nature of the change in chip shrinkage as compared with the influence that occurred when the cutting temperature changed owing to a change in cutting speed in turning steel in the cold state.

From Fig. 6 it is evident that, with an increase in cutting temperature above 600°C owing to an increase in cutting speed above 33 m/min (i.e., in the region where built-up edge is absent), a monotonic decrease in the magnitude of chip shrinkage is observed.

Fig. 4

Fig. 5

chip. In turning heated steel at a constant cutting speed (33, 65, 107, or 190 m/min, Fig. 4), however, when the cutting temperature, passing through the same values as in machining cold steel, was increased by increasing the heating temperature of the steel, one can observe a change in chip shrinkage along certain curves having a maximum. Consequently, the known proposition [8] that, in the cutting process (for the given specim…

of the material being machined and, at a constant rake angle, to a definite cutting temperature, irrespective of the method by which it is obtained, a constant chip shrinkage corresponds; this is valid only when machining low-alloy steels by cutting, both in the cold and in the heated state [11]. This rule does not apply to the cutting process of high-alloy steels (in particular, EYa1T steel) in the heated state.

Fig. 6

The presence of a built-up edge on the tool, its maximum development, and its disappearance are determined by the cutting temperature, irrespective of the method by which it is obtained. The validity of this proposition, as experiments show, extends to carbon steels [8, 11] and high-alloy steels (Figs. 3, 4, 6).

The curves of the change in chip shrinkage with heating of the steel can be explained if one also traces the nature of the change in the coefficient of friction between the chip and the rake face of the tool. Figure 5 presents the dependences \(\mu = f(T)\) for all the investigated cutting speeds. The values of the coefficient of friction for cutting speeds of 3 and 16 m/min were calculated by us only for those experiments in which no built-up edge was present. It is not difficult to note that the general character of the functional dependences \(\mu = f(T)\) is similar to that which we observed in analyzing the dependences \(\zeta_a = f(T)\). In all cases where, with a change in the heating temperature of the stainless steel, an increase in the coefficient of friction is observed, an increase in chip shrinkage could also be observed. A decrease in the coefficient of friction caused a corresponding decrease in shrinkage; the maximum of the coefficient of friction at a certain preheating temperature determines the maximum chip shrinkage at the same steel-heating temperature.

Thus, it may be stated that the character of the change in chip shrinkage at a constant cutting angle is determined by the corresponding change in the coefficient of friction between the chip and the rake face of the tool, as well as by the geometry of the built-up edge, if, in the cutting process, conditions are created for its formation. Since, within the scope of the present article, it is not possible to dwell on certain considerations concerning the causes of the observed character of the change in the dependences \(\mu = f(T)\), then...

Moreover, since this has no direct bearing on the question under discussion, we shall confine ourselves only to pointing out that in the process of machining heated EI1T steel by cutting, a certain feature was revealed, on which we have already briefly dwelt.

Figures 7, 8, and 9 present analogous dependences $\zeta_a=f(T)$, $\mu=f(T)$, and $t=f(T)$, obtained when turning heated EI1T steel at a constant cutting speed and with different feeds. Joint consideration—

Fig. 7

Fig. 8

—of these figures makes it possible to conclude that the feed affects the chip shrinkage and the coefficient of friction as does the temperature factor. This is evidenced by the circumstance that the maxima of the curves $\zeta_a=f(T)$ and $\mu=f(T)$ for different feeds occur at approximately the same cutting temperature, bounded in Fig. 9 by a horizontal band. The difference in the absolute values of the maxima of chip shrinkage and coefficients of friction for different feeds is explained by us by the different state of the metal being machined at the points of the maxima of the curves, owing to the different degree of its heating. It is quite natural that for differ—

different machined materials (or for different states of one and the same metal owing to different degrees of its heating), at a constant cutting temperature one should expect different values of the coefficient of friction and, consequently, of chip shrinkage.

Fig. 9

The fact that, with heating of EI1T steel, its physico-mechanical characteristics change is illustrated by Figs. 10, 11, and 12. Shown here are the dependences obtained by us of Brinell hardness on the heating temperature of the steel, and compression diagrams of EI1T steel specimens at temperatures of 20°C, 150°C, 300°C, 400°C, and 500°C. From these diagrams it is not difficult to obtain the values of the conventional yield point \((\sigma_0)\) and of the exponent of the stress polytrope \((n)\) in compression. These data are summarized in Table 3. The same table gives the values of the ultimate strength \((\sigma_v)\) at various heating temperatures of EI1T steel according to A. A. Shmykov [12].

Table 3

Analysis of Fig. 10 and Table 3 shows that, with an increase in the heating temperature of the steel, there is a monotonic decrease in all the listed physico-mechanical characteristics: \(H_B\), \(\sigma_v\), \(\sigma_0\), \(n\).

Consequently, with heating of EI1T steel its state changes, its physico-mechanical characteristics change, as a result of which we observed different values of the coefficient of friction at the maxima of the curves \(\mu = f(T)\), when the cutting temperature at different feeds had

approximately the same value (Figs. 8, 9). In addition, from a joint consideration of Figs. 4, 7, 10 and Table 3 it is evident that a monotonic change in the physico-mechanical characteristics of EIТ steel with heating does not entail a corresponding change in chip shrinkage. Consequently, it does not seem possible to put the change in chip shrinkage into direct dependence on the physico-mechanical properties of the metals being machined.

Fig. 10

Fig. 11

Fig. 12

We carried out investigations of the process of cutting heated stainless steel under sufficiently wide variations in cutting conditions. The cutting speed was varied within the range from 3 to 190 m/min, the feed from 0.23 to 0.6 mm/rev. Stainless steel heated from 20 to 700°C was subjected to turning, during which its physico-mechanical properties changed considerably. The tool was equipped with plates of hard alloys T15K6 and VK8.

Some of the experiments were carried out in turning cold and heated steel 40. In turning heated EIТ steel, certain features were revealed.

its machining by cutting in comparison with machining it in the cold state and with the cutting process for cold and heated carbon steels.

However, despite the considerable difference in cutting conditions, one can nevertheless see quite clearly the general interrelation of the phenomena of the cutting process.

In Fig. 13a, b, in the coordinates chip shrinkage \(\zeta_a\)—angle \(\omega\) and chip shrinkage \(\zeta_a\)—coefficient of friction \(\mu\), experimental points are plotted that were obtained in turning cold steel EYa1T and steel EYa1T heated to \(700^\circ\text{C}\) with a tool equipped

Fig. 13

with T15K6 and VK8 carbide, as well as experimental points obtained in turning cold and heated steel 40. All the experimental points, with a sufficient degree of accuracy, were arranged along a certain curve. The deviations of the experimental points from the curve in angle \(\omega\) do not exceed \(8\text{–}10^\circ\). At the same time, we note that the relative position of the experimental points on the graph is not associated with any particular cutting conditions. The angle \(\omega\) characterizes the direction of the resultant cutting force (Fig. 14).

Fig. 14

On the basis of Fig. 13a it may be concluded that there is a one-to-one relationship between the angle \(\omega\) and the chip shrinkage; consequently, the magnitude

the chip shrinkage at a constant tool rake angle is determined by the direction of the resultant cutting force.

However, the very direction of the resultant force depends on the coefficient of friction of the chip along the rake face. It is natural to expect that, if there is a relationship between the coefficient of friction and the direction of the resultant, on the one hand, and between the direction of the resultant and chip shrinkage, on the other, there must also be a single-valued relationship between the coefficient of friction and chip shrinkage. The character of the distribution of the experimental points in Fig. 13b convincingly confirms this proposition.

Thus, for a wide variation in cutting conditions for steels heated to different temperatures, the general interrelation of the phenomena in the cutting process, indicated by A. M. Rozenberg and A. N. Eremin, is preserved. The various machining conditions and cutting regimes did not show any independent influence in the dependence $\zeta_a = f(\mu)$.

In particular, the plasticity of the machined metal does not exert a direct influence on the magnitude of chip shrinkage. Thus it is quite indisputable that the plastic properties of EIIT steel and steel 40 changed with changes in their heating temperature. However, as is seen from Fig. 13, for the machined materials with different plastic properties as well, the single-valued relationship $\zeta = f(\mu)$ is preserved; the different plasticity did not show any independent influence in this dependence.

Summing up what has been said, it may be noted that a single-valued relationship between the coefficient of friction and the degree of plastic deformation of the cut layer, determined by chip shrinkage, is manifested under extremely broad cutting conditions. This relationship was obtained in turning and milling steels, in turning cast iron, in machining steels in the cold and heated state, for different geometries of the cutting tool, over a wide range of changes in cutting regimes (speed, feed, depth), i.e., the single-valued dependence of the degree of plastic deformation of the cut layer on the coefficient of friction is of a general character.

This circumstance objectively indicates that, for a given rake angle, the degree of plastic deformation of the cut layer of metal is ultimately determined only by the magnitude of the coefficient of friction of the chip along the rake face of the cutting tool.

The influence of cutting regimes and of the physico-mechanical properties of the machined materials on the degree of plastic deformation of the cut layer can manifest itself only through their corresponding influence on the change in the coefficient of friction of the chip along the rake face of the cutting tool. But if, in the cutting process at a given rake angle, a certain value of the coefficient of friction of the chip along the rake face of the cutting tool has been established, then this value of the coefficient of friction corresponds to a quite definite value of the degree of plastic deformation of the cut layer (or a definite value of chip shrinkage), regardless of what values the other parameters of the cutting process had at the same time.

REFERENCES

1. Besprozvannyi I. M.—Fundamentals of the Theory of Metal Cutting. Mashgiz, 1948.

2. Krivoukhov V. A., Nevzorov A. I.—The Process of Cutting Metals at High Speed. State Publishing House of the Defense Industry, Moscow, 1953.

3. Granovskii G. I., Grudov P. P., Krivoukhov V. A., Larin M. N., Malkin A. Ya.—Metal Cutting. State Scientific-Technical Publishing House of Machine-Building Literature, Moscow, 1954.

4. Zvorykin K. A.—The Work and Force Necessary for the Separation of Metallic Chips, 1893.

1. Rozenberg A. M., Eremin A. N.—On the theory of the process of cutting metals. Stanki i instrument, No. 10, 1949.

2. Zorev N. N.—Investigation of elements of the mechanics of the cutting process. Mashgiz, 1952.

3. Khvorostukhin L. A.—Calculation of forces in high-speed cutting on the basis of the physico-mechanical characteristics of metals. Dissertation, Tomsk, 1953.

4. Eremin A. N.—The physical essence of phenomena in cutting steels. Mashgiz, 1951.

5. Promtov A. I.—Dynamics of high-speed milling of steels with face mills. Dissertation, Tomsk, 1953.

6. Rozenberg Yu. A.—Investigation of the process of cutting gray cast iron. Dissertation, Tomsk, 1952.

7. Mostovoi V. M.—Investigation of the process of cutting steel with artificial preheating. Izvestiya TPI, vol. 75, 1954.

8. Shmykov A. A.—Handbook for the heat-treatment specialist. State Scientific and Technical Publishing House for Machine-Building Literature. Moscow, 1952.