STUDY OF FRICTION IN METAL CUTTING

A. M. ROSENBERG and A. N. EREMIN

In the process of metal cutting there is very considerable friction between the rake face of the tool and the chip sliding over it, as well as between the flank face and the machined surface. This friction occurs at high specific pressures on the rubbing surfaces, often measured in tens of kilograms per square millimeter. This friction is characterized by very high values of the coefficient of friction, which is explained by the relative cleanliness of the rubbing surfaces, free of oxides and adsorbed films. The cleanliness of the rubbing surfaces is the result of the fact that one of the rubbing surfaces, belonging to the chip or to the machined surface, has only just been formed in the cutting process; the other, belonging to the cutter, is continuously cleaned by the friction of the sliding chip or of the machined surface. Therefore the coefficients of friction in the cutting process often reach values \(\mu \ge 1\). At high cutting speeds, friction takes place under conditions of high temperatures, which may reach \(800\text{--}1000^\circ\). In the cutting process there are two sources of heat generation that heat the chip and the tool. One source is located in the zone of chip deformation (in the shear-plane zone), where heat is generated equivalent to the work expended on deforming the chip. The other source is located in the zone of friction of the chip along the rake face of the tool and in the zone of friction of the machined surface against the flank face of the tool. Here heat is generated equivalent to the work of friction. Experiment shows that the temperatures in the zone of friction of the chip against the tool at high cutting speeds considerably exceed the temperatures in the zone of chip deformation. Thus, here the source of heating of the tool is the friction process.

All that has been stated above should lead us to the conclusion that friction in the process of wear and blunting of the cutting tool plays the principal role, since tool wear is nothing other than the abrasion of its rake and flank faces, occurring with different intensity at different temperatures. Both the abrasion process itself, which is effected by friction, and the temperatures determining its intensity depend to a considerable degree on friction. Therefore, naturally, without studying the friction accompanying the cutting process, it does not appear possible to approach the construction of a theory of wear and life of the cutting tool. In addition, the study of friction in the cutting process is also of interest from the standpoint of revealing the laws that determine the course of chip deformation, since nothing other than the coefficient of friction determines the direction of the resultant force on the rake face of the tool, and this direction, in turn, should, according to the views expressed already by Zvorykin, determine the degree of chip deformation and the position of the deformation zone.

All these considerations prompted us to undertake work on the experimental study of friction in the process of metal cutting.

Method for Determining Friction Forces and Coefficients of Friction in Metal Cutting

The study of the friction forces and coefficients of friction that occur in the process of cutting metals can be carried out only by performing the cutting process in its normal form. It does not appear possible to conduct this study on some simplified process—for example, by making one body, replacing the chip, slide over another body replacing the rake face of the tool. This is impossible because friction in the cutting process takes place under specific conditions characterized by very high specific pressures, a wide range of speeds and temperatures, and a special state of the rubbing surfaces, one of which (belonging to the chip or to the machined surface) continuously slides over the other (belonging to the tool), carrying out the process of friction with ever new areas entering this process, areas that have only just arisen during the separation of the chip from the metal.

Direct measurement of the friction forces in the cutting process is likewise hardly possible. The friction force can be determined with sufficient accuracy by calculation, by measuring in the experiment, with the aid of special dynamometers, the forces acting on the tool.

If the cutting process is carried out with the simplest of tools—a cutter (which is what we adopted in our work)—then, in the process of free cutting, it is sufficient to measure two components of the cutting force, one of which is directed along the direction of the cutting speed \((P_1)\), and the other perpendicular to the machined surface \((P_2)\). In the process of non-free cutting, three components \((P_z, P_x, P_y)\) must be measured. When calculating friction forces and coefficients of friction, it must be taken into account that on every cutting tool, in the cutting process, two groups of forces arise: one of them is located on the rake face and is directly associated with the process of chip formation. The other is located on the flank face, does not take part in the process of chip formation, and is determined by the elastic-plastic contact of the machined surface and the flank face over a very narrow portion of the flank face directly adjacent to the cutting edge. In Fig. 1 the group of forces on the rake face of the cutter includes the forces \(N\)—normal to the rake face, \(F\)—the friction force of the chip on the cutter, and \(R\)—their resultant. The group of forces on the flank face is \(N_1\), \(F_1\), and \(R_1\). Their total resultant \(R_0\) is resolved, for the process of free cutting, into the components \(P_1\) and \(P_2\), which can be measured experimentally by a dynamometer, since their direction is always known. If \(P_1\) and \(P_2\) have been measured in the experiment, it is not difficult to determine \(R_0\), but in order to carry out the further separation of the forces it is first necessary to be able to divide them into the two indicated groups, so that, from the forces measured by the dynamometer, the forces applied to the flank face can be subtracted, since we are primarily interested in the forces acting on the rake face. To determine the forces on the flank face we used the method developed by Prof. Rosenberg, which had been verified in a number of works and was described in detail in the article “Determination of Forces on the Flank Face of a Tool.”

Fig. 1

Having determined the forces applied on the rake face, it is not difficult to calculate the magnitude of the friction force \(F\) and the coefficient of friction \(\mu\), where by the coefficient of friction we mean the ratio \(\dfrac{F}{N}\). The coefficient of friction between the chip and the rake face of the tool was determined by us in the following way:

\[ \mu=\frac{F}{N}=\operatorname{tg}(\omega+\gamma) \]

\[ \operatorname{tg}\omega=\frac{P_2'}{P_1'}, \]

where \(P_2'\) and \(P_1'\) are the forces measured by the dynamometer, after subtracting the forces applied on the flank face in the same directions \((P_2''\) and \(P_1'')\).

These expressions serve to determine the coefficient of friction for the case of free cutting, when two components \((P_1\) and \(P_2)\) are measured by the dynamometer and the resultant of all forces on the tool is directed in a plane perpendicular to the cutting edge.

In the case of constrained cutting, three components \((P_z, P_x, P_y)\) are measured by the dynamometer. In this case the coefficient of friction is calculated from the following relations:

\[ \mu=\operatorname{tg}(\omega+\gamma^1) \]

\[ \operatorname{tg}\gamma^1=\operatorname{tg}\gamma\cos\{\psi-(90^\circ-\varphi)\} \]

\[ \operatorname{tg}\psi=\frac{P_y'}{P_x'} \]

\[ \operatorname{tg}\omega=\frac{P_x'}{P_z'\cos\varphi}, \]

where \(P_z'\), \(P_x'\), \(P_y'\) are the forces measured by the dynamometer, after subtracting the forces on the flank faces.

Experiments show that, for sharp tools, the forces on the flank faces are extremely small; in calculating the coefficient of friction they can have a noticeable effect only for very thin chips, and at thicknesses greater than \(0.15\) mm they may be disregarded.

Conditions for carrying out the experiments

We studied the dependence of the friction forces and of the coefficient of friction on the following factors:

1) the metal being machined,
2) the thickness of the layer being cut,
3) the cutting speed,
4) the rake angle of the tool,
5) the cutting temperature,
6) lubrication,
7) the material of the cutting tool.

The metals machined were the following: steel, lead, aluminum, red copper. The choice of precisely these metals is explained by the following considerations.

All four of these metals have four different melting temperatures, from \(327^\circ\) for lead to \(1300\)—\(1400^\circ\) for steel. Therefore, on the metals we selected, the influence of the spee-

the growth of deformation on their mechanical characteristics, since it is known that this influence is the smaller, the higher the melting temperature of the metal. Further, these metals, while possessing sufficient plasticity, have different abilities to retain the work hardening obtained as a result of plastic deformation. In addition, the selected metals have different properties during cutting. Thus, steel and aluminum form a built-up edge on the cutter within a certain range of cutting temperatures, whereas copper and lead, at any cutting temperatures not lower than room temperature, are machined without formation of a built-up edge.

The cutting speeds in the experiments were taken in two orders of magnitude: very low, within the range from 0.0003 m/min to 0.76 m/min, and ordinary—from 5 to 500 m/min. The very low cutting speeds, which we shall call “micro-speeds,” were used by us for the following reasons.

When the cutting speed is varied within the ordinary range of speeds used in production, a change in cutting speed is necessarily and inevitably accompanied by a change in cutting temperature. Therefore, at ordinary cutting speeds it is not possible to isolate the influence of only the speed itself on the phenomenon being studied. If, however, cutting is carried out at “micro-speeds,” then the heat arising in the cutting process has time to spread into the volumes of metal surrounding the cutting zone, and it may practically be considered that, by varying the cutting speed up to 0.76 m/min, we carried out the cutting process at a constant temperature, and the influence of temperature change on the phenomenon being studied was thereby excluded. Likewise, a change in chip dimensions and in cutting angle at high cutting speeds is necessarily accompanied by a change in cutting temperature. At “micro-speeds” this is also excluded. In addition, experiments at micro-speeds were convenient because, when cutting steel and aluminum at these speeds, no built-up edge is formed, and the tool in the experiment has a geometry undistorted by built-up edge. Thus, the total extreme limits of variation of speeds in our experiments exceeded 1,000,000 times.

In studying the coefficient of friction, cutters made of high-speed steel and of the hard alloys T15K6 and VK8 were used, which made it possible to reveal the influence of the grade of cutting alloy on the coefficient of friction. The cutting forces in the micro-speed experiments were measured by means of a special elastic dynamometer designed and manufactured in the metal-cutting laboratory of TPI. In the high-speed experiments the forces were measured with a sensitive hydraulic dynamometer of the design of the TPI metal-cutting laboratory.

Results of Experiments on Steel

For the experiments, steel with \(H_b = 170\) and steel 20 were taken. The micro-speed experiments were carried out only on steel with \(H_b = 170\), by the method of free cutting. At micro-speeds, cutters made of high-speed steel with rake angles \(\gamma = 0^\circ, 8^\circ, 14^\circ, 20^\circ, 30^\circ\), and \(40^\circ\) were used. The micro-speed experiments were carried out by planing a strip of steel having a thickness \(b \simeq 3\) mm and a length of \(\sim 60\) mm. Before removal of each new chip, the cutter was carefully lapped on both faces so that there would be absolutely no defects on the cutting edge. The experiments were carried out both without lubrication and with lubrication by vegetable oil, machine oil, and a one-percent soap solution in water.

In Fig. 2 are presented experiments carried out without lubrication with a cutter having rake angle \(\gamma = 30^\circ\), at cutting speeds \(V = 0.0011\) m/min, 0.0048 m/min, 0.035 m/min, 0.098 m/min, 0.280 m/min, and 0.760 m/min. In the lower part of the graph there are two bundles of straight lines, of which the upper one represents-

...shows the dependence of the force \(P_1\) on the chip thickness \(a\); the lower one, the dependence of the force \(P_2\) on the chip thickness. In the upper part of the graph is presented the dependence of chip shrinkage on chip thickness and cutting speed. Chip thicknesses in the experiments were taken up to \(0.25\) mm, since at greater thicknesses barely noticeable cracks arise in the chip and the regularities in the variation of the cutting forces and chip shrinkage become distorted, for a continuous chip passes into a shear chip. Each point on the graph is the average result of 5–10 measurements.

In considering Fig. 1, we first of all note that for each cutting speed its own pair of straight lines was obtained. None of the straight lines for the forces \(P_1\) and \(P_2\) passes through the origin; rather, they cut off on the axis a certain segment, which represents the forces on the rear face. If this segment is subtracted from the forces measured by the dynamometer, the forces on the rake face will be obtained; these, owing to the arrangement of the experimental points on the straight lines, will be directly proportional to the thickness of the layer being cut. Thus it may be stated that, provided the cutting temperature is constant—and this condition is exactly satisfied when working at micro-speeds—the forces applied to the rake face of the tool are directly proportional to the chip thickness.

Fig. 2

Further, Fig. 1 shows that with an increase in cutting speed, under the condition of constant cutting temperature and when working without lubrication, the cutting forces increase. In these experiments the cutting speed was varied by a factor of 700; in doing so the force \(P_1\) increased by 33%, and the force \(P_2\) by 200% (for a certain average chip thickness). The reason for this increase will be explained later. The forces \(P_1\) and \(P_2\) are represented by exactly straight lines. This indicates that, at each cutting speed, the coefficient of friction \(\mu\) will be a constant value and will not depend on the chip thickness \(a\). The upper part of the graph shows that chip shrinkage, like the cutting forces, increases with increasing cutting speed. Beginning with a chip thickness of \(a = 0.1\) mm, chip shrinkage does not depend on the chip thickness; at smaller thicknesses, however, it decreases. This is explained by the fact that, with very thin chips, on the cutting edge of the tool, which has some—even if very slight—rounding, a very small built-up edge is formed during work without lubrication; nevertheless, it changes the geometry of the cutter and reduces chip shrinkage.

Exactly the same graphs were obtained by us when working without lubrication with rake angles of 20 and 40°. These experiments also showed the rectilinear arrangement of the cutting-force lines, the increase in cutting forces with increasing speed, and the independence of chip shrinkage \(\zeta\) from chip thickness.

From the results of all these numerous experiments, carried out with the utmost care, the values of the coefficients of friction were calculated. These values of the coefficients of friction for various rake angles are presented as functions of cutting speed in Fig. 3. The same figure also presents the chip shrinkage.

Fig. 3 shows that the coefficient of friction increases with increasing cutting speed. In exactly the same way, chip shrinkage also increases with increasing cutting speed, with the exception of the case with a rake angle of \(40^\circ\), where it does not depend on speed.

The reason for the increase in chip shrinkage is the increase in the coefficient of friction. This becomes clear if we recall the equation obtained by Zvorykin,

\[ \operatorname{tg}\beta_1 = 45^\circ + \frac{\gamma}{2} - \frac{\tau}{2} - \frac{\theta}{2}, \]

where \(\beta_1\) is the shear angle,
\(\gamma\) is the rake angle,
\(\tau = (\omega+\gamma)\) is the angle of friction of the chip on the cutter.

As a result of the increase in chip shrinkage with cutting speed, the cutting force also increases. Here a discrepancy is obtained for the rake angle \(40^\circ\), at which the shrinkage remains constant.

Fig. 3 also shows that, in cutting without lubrication, the values of the coefficients of friction are extremely high; moreover, the coefficient of friction increases with an increase in the rake angle of the cutter. High values of the coefficient

Fig. 3

of friction in cutting steels occur because here we are in fact dealing with dry friction.

It was necessary to determine what the principal causes are of the increase in the coefficient of friction and in cutting forces with increasing cutting speed. There could be two such causes: an increase in the rate of deformation with increasing cutting speed could cause an increase in the stresses in the metal being deformed, or a reduction in the contact time between the chip and the rake face of the cutter with increasing cutting speed could reduce the lubricating effect produced by particles of air and the vapors contained in it, which penetrate onto the friction surfaces of the chip and the cutter. The first cause,

generally speaking, was unlikely, since the influence of deformation rate on stresses in steel at room temperatures is small, in view of the high melting temperature of steel; the increases in cutting forces that we obtained, however, were quite significant.

We resolved this question by using lubrication during cutting. We tested various lubricants: vegetable oil, mineral oil, and a 1% solution of soap in water. The best results for resolving the question posed were obtained with lubrication by a soap solution; when it was used, the influence of speed on the cutting forces, the coefficient of friction, and the chip shrinkage completely disappeared.

Figure 4 gives the results of experiments carried out with a cutter having a rake angle \(\gamma = 30^\circ\). The same graphs were obtained for rake angles of 1.8, 20, and 40°. They all give the same thing as is shown in Fig. 4.

Fig. 4

Figure 4 shows that the cutting forces and chip shrinkage, when the cutting speed is varied (and hence also the deformation rate), by more than a factor of 800, do not change within any noticeable limits. The points of all the numerous experiments carried out at different speeds lay well on the same lines. The coefficient of friction here is likewise found to be independent of the cutting speed. Thus it may be considered proven that, in cutting steel, the cutting speed through the deformation rate does not affect the cutting forces, stresses, or coefficient of friction. From this it may be concluded that, in cutting without lubrication, the coefficient of friction increases with increasing cutting speed because of a reduction in the effect of air penetrating to the rubbing surfaces.

Figure 5 presents the change in the coefficient of friction and in shrinkage when the rake angle is varied with lubrication by a soap solution. Figure 5 shows first of all that, with the use of lubrication, the coefficient of friction decreases extremely strongly. Its magnitude is reduced by approximately \(2 \tfrac{1}{2}\)–3 times when lubrication is used. Figure 5, moreover, shows-

shows that the coefficient of friction increases with an increase in the rake angle, just as was observed in cutting without lubricant (Fig. 3). The reasons for the influence of the rake angle on the coefficient of friction were studied by us in another work (see A. M. Rozenberg and Yu. P. Zimin, “Certain Questions of Friction in Metal Cutting”). That work established that the coefficient of friction on the front face of the tool, under the condition of maintaining a constant temperature, depends on the specific pressure on the rubbing surfaces, increasing as the specific pressure decreases. With an increase in the rake angle, as the experiments showed, the specific pressure decreases. This is what leads to an increase in the coefficient of friction when the rake angle of the tool is increased.

Fig. 5

Experiments on cutting steel at medium cutting speeds

This series of experiments was carried out by the method of free cutting with high-speed-steel tools at cutting speeds from 1.5 to 70 m/min. The chip width in all these experiments was taken as 3 mm, and the depth of cut as 0.214 mm. The tools had rake angles of 0, 10, 20, and 30°. The purpose of the experiments was to determine the influence of cutting temperature on the coefficient of friction and on chip shrinkage when working with high-speed-steel tools having different rake angles. The cutting temperature in the experiments was measured by the natural thermocouple method. High-speed-steel tools were used in order to make it possible to compare the data obtained with the results of experiments conducted at microspeeds, which were likewise carried out with high-speed-steel tools. The coefficients of friction were calculated without taking into account the forces on the rear face of the tool, since, at the selected depth of cut, these forces were small in magnitude.

Figure 6 gives the results for the coefficients of friction obtained. Along the abscissa axis are plotted the readings of the galvanometer measuring the cutting temperature. Along the ordinate axis are plotted points corresponding to the coefficients of friction obtained in experiments at microspeeds of cutting for rake angles of 20° and 30°. Figure 6 shows that, at medium cutting speeds, we observe, just as at microspeeds, that the coefficient of friction is the higher, the larger the rake angle of the tool. With an increase in the cutting temperature, i.e., with an increase in the cutting speed, the coefficient of friction increases. In going from microspeeds to medium speeds, the coefficient of friction decreases somewhat. The reasons causing the increase in the coefficient of friction with an increase in cutting temperature have not yet been clarified. They are all the more difficult to clarify because, within the range of medium cutting speeds at which our experiments were conducted, on the tool

Fig. 6

the formation of a built-up edge takes place, which greatly distorts the geometry of the cutter. It should be noted that, in calculating the coefficient of friction, we considered the friction force to be located on the rake face of the cutter, which, generally speaking, is not entirely correct, since the chip slides along the rake face of the built-up edge. It does not seem possible, however, to assign the friction force to the rake face of the built-up edge, since the built-up edge is not a stable body with a precisely defined geometry. It disappears and reappears on the rake face of the cutter many times per second and, at different moments in time, has different dimensions or is entirely absent. Moreover, when a built-up edge is present, the chip experiences friction not only against the built-up edge, but also, behind the built-up edge, along the rake face of the cutter.

In Fig. 7, for various rake angles of the cutter, the dependences of chip shrinkage on cutting temperature are presented. Comparing these figures with Fig. 6, one can observe a coordinated change in chip shrinkage and the coefficients of friction, especially in the region of low cutting speeds during the transition from microspeeds, and also in the region of the highest speeds, where the built-up edge has already disappeared. Here, in parallel with an increase in the coefficient of friction, the chip shrinkage also increases. This provides good confirmation of Zvoreykin’s proposition that chip shrinkage is determined by the direction of the resultant force on the rake face of the cutter, which in turn depends on the coefficient of friction of the chip on the cutter.

Fig. 7

All the experiments in this series were carried out on the same steel with which the experiments at microspeeds had been conducted.

Experiments on Cutting Steel at High Cutting Speeds

This series of experiments was carried out in order to clarify the influence of a further increase in cutting temperature on the coefficient of friction. Here the influence of the grade of the cutting alloy on the coefficient of friction was also clarified. The experiments were carried out at cutting speeds from 20 to 450 m/min on steel 20, by the method of unfree cutting, at a cutting depth of 2 mm and a feed of 0.23 mm/rev. The experiments were conducted by the method of unfree cutting, since otherwise a very large amount of metal would have been required, which was not at our disposal. Cutting was performed with cutters fitted with carbide plates VK8 and T15K6. The rake angles of the cutters were taken as \(-10^\circ\), \(0^\circ\), \(+15^\circ\), \(+30^\circ\).

In Figs. 8, 9, 10, and 11 the results of experiments with T15K6 cutters are shown. Here the dependences of the cutting forces, chip shrinkage, and coefficient of friction on cutting speed are presented. In essence, these are dependences on cutting temperature. In these and subsequent graphs we plotted cutting speed on the abscissa axis, rather than galvanometer readings, since

the galvanometer readings obtained when working with different cutting alloys are not comparable with one another.

Figs. 8, 9, 10, 11 show that, with an increase in cutting speed (cutting temperature), all the quantities presented by us (cutting forces, coefficient of friction, chip shrinkage) initially increase, pass through a maximum, and then, with a further increase in cutting speed and

Fig. 8

temperature, decrease—at first rapidly, and then more and more slowly, tending toward a certain asymptote. Chip shrinkage and cutting forces at all cutting speeds have higher values for a larger cutting angle; the coefficient of friction, on the contrary, is higher for a larger

Fig. 9

rake angle, just as we observed down to the very lowest cutting speeds. The ranges of cutting speeds in which the coefficient of friction increases are characterized by an increase in chip shrinkage and cutting forces; conversely, where the coefficient of friction decreases, a simultaneous decrease in chip shrinkage and cutting forces is observed. The maximum values of the coefficient of friction, chip shrinkage, and cutting forces at the larger cutting angle correspond to lower speeds. Completely identical

the course of the curves of the coefficient of friction, chip shrinkage, and cutting force convincingly shows the interrelation among these quantities.

Fig. 10

Thus, the influence of the coefficient of friction on chip shrinkage and cutting forces is manifested here quite clearly.

Fig. 11

In Figs. 12, 13, 14, 15, 16, 17, 18 we present the results of tests with cutters fitted with VK8 inserts. From these graphs we can draw the same conclusions that we have just drawn from the tests with T15K6 cutters. Comparing the graphs constructed for cutters with VK8 inserts with the graphs for cutters with T15K6 inserts, one may state that all the characteristic points for cutters with VK8 inserts, at the same cutting angles, lie in the region of higher cutting speeds. The reason for this, in our opinion, is the higher thermal conductivity of the VK8 alloy. The VK8 alloy has a thermal conductivity of \(0.141\ \text{cal}/\text{cm}\cdot\text{sec}\cdot\text{deg}\), whereas the T15K6 alloy has a thermal conductivity of only \(0.065\ \text{cal}/\text{cm}\cdot\text{sec}\cdot\text{deg}\). Owing to this, at the same cutting speeds the temperature on the rake face of a cutter with VK8 alloy is lower than on the rake face of a cutter with T15K6 alloy, and that characteristic temperature at which the coefficient of friction, chip shrinkage, and cutting forces reach their greatest values will be attained, in work with VK8 alloy, at higher cutting speeds. We suppose that, for the same cutting angles, the temperatures at which...

Fig. 12

Graph labels:

• Force \(P\), kg
• Speed \(V\), m/min
• Steel 20
  VK8 tool
  \(\gamma=-10^\circ,\ \varphi=82^\circ\)
  \(S=0.23\ \text{mm/rev},\ t=2.05\ \text{mm}\)
• Non-free cutting
• Curves marked: \(P_z\), \(P_y\)

Fig. 13

Graph labels:

• Force \(P\), kg
• Speed \(V\), m/min
• Steel 20
  VK8 tool
  \(\gamma=0^\circ,\ \varphi=82^\circ;\ 90^\circ\)
  \(S=0.23\ \text{mm/rev},\ t=2.05\ \text{mm}\)
• Free cutting
• Non-free cutting
• Curves marked: \(P_z\), \(P_y\)

Fig. 14

Graph labels:

• Coefficient of friction \(\mu\)
• Speed \(V\), m/min
• Steel 20
  VK8 tool
  \(S=0.23\ \text{mm/rev},\ t=2.05\ \text{mm}\)
• Free cutting
• Non-free cutting
• Curves marked: \(\gamma=0^\circ,\ \varphi=82^\circ;\ 90^\circ\); \(\gamma=-10^\circ,\ \varphi=82^\circ\)

Fig. 15

Graph labels and annotations:

• Vertical axis: Chip compression, \(\xi\)
• Horizontal axis: Speed \(V\), m/min
• Steel 20
  Cutter VK8
  \(S = 0.23\) mm/rev, \(t = 2.05\) mm
• Non-free cutting
• Vibration
• \(\gamma = -10^\circ;\ \varphi = 82^\circ\)
• \(\gamma = 0^\circ;\ \varphi = 82 \div 90^\circ\)

Fig. 16

Graph labels and annotations:

• Vertical axis: Force \(P\), kg
• Horizontal axis: Speed \(V\), m/min
• Curves: \(P_z\), \(P_x\), \(P_y\)
• Steel 20
  Cutter VK8
  \(\gamma = 15^\circ,\ \varphi = 90^\circ\)
  \(S = 0.23\) mm/rev, \(t = 2.05\) mm
• Non-free cutting

Fig. 17

Graph labels and annotations:

• Vertical axis: Force \(P\), kg
• Horizontal axis: Speed \(V\), m/min
• Curves: \(P_z\), \(P_x\), \(P_y\)
• Steel 20
  Cutter VK8, \(\gamma = 29^\circ,\ \varphi = 90^\circ\)
  \(S = 0.23\) mm/rev, \(t = 2.05\) mm
• Non-free cutting

...the friction coefficient reaches its greatest value for the alloys VK8 and T15K6, the same despite the large difference in cutting speeds. We were unable to verify this assumption, since verification would have required calibrating natural thermocouples. For this it would have been necessary to have long rods of the hard alloys VK8 and T15K6, which we did not have at our disposal.

A comparison of the graphs constructed for the alloys VK8 and T15K6 also shows that the absolute values of the coefficients of friction for the alloy VK8 are higher than for the alloy T15K6. This comparison, of course, must be made only for identical cutting angles. The comparison also reveals that the chip shrinkages are higher for the alloy VK8. This circumstance additionally confirms the undoubted influence of the coefficient of friction on chip shrinkage. A comparison of the cutting forces shows that, in the region

Fig. 18

Graph labels: coefficient of friction $\mu$; shrinkage $\lambda$; speed $v$ m/min; $\gamma = 29^\circ$; $\gamma = 15^\circ$; steel 20; cutter VK8; $\varphi = 90^\circ$; $s = 0.23$ mm/rev; $t = 2.05$ mm; free cutting.

of high cutting speeds, on the descending branches of the curve, the cutting forces for the alloy VK8 are also substantially higher than for the alloy T15K6. The maximum values of the forces, however, will be higher, on the contrary, for the alloy T15K6, despite the lower values of chip shrinkage and of the coefficient of friction for this alloy. In our opinion, this is explained by the fact that these maximum values of the forces for the alloy T15K6 occur in the region of considerably lower cutting speeds than for the alloy VK8. At these lower cutting speeds the temperature on the chip shear plane, i.e., in the region of chip deformation, is lower because of the greater possibilities for heat removal. At lower temperatures the metal has higher strength properties, which is associated with higher values of the cutting forces.

These same graphs show that the magnitudes of the cutting forces depend on the material of the cutting tool, whereas it has always been assumed that the material of the cutting tool has no influence on the cutting forces. We see that the alloys VK8 and T15K6 give, at the same cutting speeds, different coefficients of friction, which in turn causes different chip shrinkage and cutting forces. A comparison of the graphs shows that when working with alloy VK8 in the region of high-speed cutting, the cutting forces prove to be noticeably higher than when working with alloy T15K6. The difference between the forces $P_x$ is especially large. It is possible that precisely because of this...

this it is observed that, when working with alloy VK8, more intensive wear of the tool along the rake face occurs than when working with alloy T15K6.

On the basis of the experiments described above, carried out over extremely broad limits of variation in cutting speed (from 0.001 to 450 m/min), it is possible to give a general schematic diagram of the change in the coefficient of friction, chip contraction, and cutting forces over the entire broad range of cutting speeds. This scheme is presented in Fig. 19. In the region of microspeeds, the coefficient of friction, chip contraction, and cutting forces increase with increasing cutting speed. Further, when the cutting speed passes beyond values of 1–2 m/min, together with a further increase in the coefficient of friction, the chip contraction and cutting forces begin to decrease, pass through a minimum, and then begin to increase again. This is connected with the appearance and development of a built-up edge on the tool, which reduces the cutting angle and therefore causes a decrease in chip contraction and cutting forces. With an increase in cutting speed, the rake angle on the built-up edge first increases, reaches a maximum, and then begins to decrease. This decrease in the rake angle on the built-up edge causes an increase in chip contraction and cutting forces. With a further increase in cutting speed, the built-up edge disappears, the cutting angle reaches its greatest value, and the chip contraction and cutting forces also approach their maximum values. They reach their greatest values at the moment when the coefficient of friction becomes greatest, and subsequently, as the coefficient of friction decreases, the cutting forces and chip contraction decrease with further increase in cutting speed.

Fig. 19

Experiments on Cutting Lead

Experiments with lead were carried out both at microscopic cutting speeds and at high speeds. At microspeeds the speeds varied from 0.001 m/min to 0.760 m/min. The rake angle varied from 10 to 60° (here we made use of part of the experiments of Prof. Rosenberg and Candidate of Technical Sciences Yu. P. Zimin in addition to those that were carried out by us).

In Fig. 20 are given the dependences of the cutting forces on chip thickness and cutting speed. As the graph shows, the cutting forces increase very strongly with increasing cutting speed. Noteworthy is the circumstance that, when cutting lead at microspeeds, the lines of cutting forces are not exactly straight, but somewhat curved. If the coefficients of friction are calculated from these experiments, we obtain the graph shown in Fig. 21. This graph shows that the coefficients of friction depend on the thickness of cut, decreasing as it increases. In Fig. 22 is presented the change in chip contraction. From comparison of the graphs it can be seen that, with an increase in the thickness of cut, the coefficient of friction decreases; this causes a decrease in chip contraction, which in turn decreases the specific work and gives a curved line of cutting force.

Text visible in the plot:

• Lead
• Cutter RF1
• $\gamma = 10^\circ$, $b = 8.1\ \mathrm{mm}$
• $v = 0.007\ \mathrm{mm/min}$
• $0.036$
• $0.098$
• $0.280$
• $0.700$
• Force $P$, kg
• Chip thickness $a$, mm
• Free cutting
• $V = 0.76$
• $V = 0.28$
• $V = 0.098$
• $V = 0.036$
• $V = 0.007$

Fig. 20

Text visible in the plot:

• Lead
• $\gamma = 10^\circ$
• Free cutting
• $v = 0.0075\ \mathrm{m/min}$
• $0.098$
• $V = 0.76\ \mathrm{m/min}$
• Chip thickness $a$, mm

Fig. 21

Text visible in the plot:

• Lead
• Cutter RF1
• $\gamma = 10^\circ$, $b = 8.1$
• Free cutting
• Shrinkage $\lambda$
• $V = 0.760$
• $V = 0.0075$
• $V = 0.0075\ \mathrm{m/min}$
• $0.036$
• $0.098$
• $0.280$
• $0.760$
• Chip thickness $a$, mm

Fig. 22

It should be noted that, at microspeeds, the effect of cutting speed on the coefficient of friction and on chip contraction proves to be opposite. Whereas the coefficient of friction decreases with increasing cutting speed, chip contraction increases. We are not yet able to explain this contradiction. The dependence of the coefficient of friction and chip contraction on cutting speed is shown in Fig. 23 for various rake angles. We see

Fig. 23

that the phenomenon indicated above is observed for a wide range of rake angles, from 10 to 60°.

Figure 24 shows the change in the coefficient of friction and chip contraction with variation of the rake angle. As the rake angle increases, the coefficient

Fig. 24

friction increases noticeably. This phenomenon was observed by us for all, without exception, of the metals that were used in our experiments. In calculating the coefficients of friction and the chip shrinkages for the construction of Fig. 24, we took the cut thickness as 0.4–0.5 mm.

When a lubricant is used, the cutting forces in cutting lead fall very sharply. Fig. 25 shows the cutting forces with kerosene lubrication. The graph shows that the influence of cutting speed when lubricant is used became less significant, but did not disappear altogether, as we had when cutting steel with lubrication. This is explained by the circumstance that lead is a very low-melting metal, and therefore it is very sensitive to the rate of deformation. When the cutting speed is increased, the rate of deformation increases, and the stresses that accompany plastic deformation increase. Therefore the cutting forces also increase with an increase in cutting speed.

Fig. 25

with cutting speed. Fig. 25 shows that the cutting forces when lubricant is used are expressed by straight lines; the chip shrinkage and the coefficient of friction do not depend on chip thickness.

Fig. 26 presents the influence of the rake angle on the coefficient of friction and chip shrinkage in cutting with lubrication. Here the coefficient of friction no longer depends on the rake angle, but increases with increasing cutting speed. Here we no longer observe the different influence of cutting speed on the coefficient of friction and chip shrinkage noted above. Both of these quantities increase with increasing cutting speed, and such a correspondence between their changes is quite logical.

Fig. 27 shows the change in the coefficient of friction and chip shrinkage in the region of medium cutting speeds, and Fig. 28 up to very high cutting speeds. These experiments were carried out by us by the method of free cutting. As we see, the coefficient of friction decreases continuously all the time with increasing cutting speed, remaining higher for a thinner chip. The chip shrinkage at a cutting speed of 3 m/min passes through a maximum value, and then continuously decreases, following the change in the coefficient of friction. The shrinkage also has a higher value for a thinner chip. Thus,

In the region of high cutting speeds, a logical correspondence is observed between the change in the coefficient of friction and the chip shrinkage.

Fig. 26

Labels in the figure:
Free cutting.
\(\mu\).
\(V = 0.106\ \text{m/min}\).
\(V = 0.0014\ \text{m/min}\).
Shrinkage \(\lambda\).
Angle \(\gamma^\circ\).
Legend: \(V = 0.0014\), \(0.0055\), \(0.036\), \(0.106\).
Lead; \(b = 8.2\ \text{mm}\).
Lubricant—kerosene.

In order to put forward assumptions about the causes of the change in the coefficients of friction and chip shrinkage in the region of high cutting speeds of cu-

Fig. 27

Labels in the figure:
\(\mu\).
Shrinkage \(\lambda\).
Speed \(V\ \text{m/min}\).
\(S = 0.13\ \text{mm/rev}\).
\(S = 0.25\).
Lead; \(\gamma = 10^\circ\); \(\varphi = 74^\circ\); \(t = 8\ \text{mm}\).
Non-free cutting.

... during our experiments the cutting temperature was measured by the natural-thermocouple method. Figs. 29 and 30 show the change in the coefficient of friction and in chip shrinkage at different cutting speeds as a function of the galvanometer readings. These graphs show that, at an unchanged cutting speed, and therefore also at a constant rate of deformation,

Fig. 28

the coefficient of friction and the chip shrinkage are the smaller, the higher the temperature on the front face of the cutter. Conversely, at constant temperature these two quantities increase with increasing cutting speed, i.e., the rate

Fig. 29

of deformation. Thus, it may be supposed that in all the graphs presented, two factors affect the coefficient of friction and chip shrinkage: temperature, with an increase in which they decrease, and the rate of deformation, with an increase in which they increase.

At microspeeds we observed that the cutting speed also affects the coefficient of friction; here the coefficient of friction decreased with an increase in cutting speed. It would be incorrect to suppose that this is the result of a rise in temperature, since at microspeeds the temperature may be regarded as constant. It is known that, in

Figure labels: \(V = 137\ \mathrm{m/min}\); \(V = 27.5\); \(V = 45\); \(V = 105\); \(V = 199\). Lead. Cutter RF1. \(\gamma = 10^\circ\), \(\varphi = 74^\circ\). \(t = 8\); \(S = 0.032\text{–}2.98\). Constrained cutting. Horizontal axis: galvanometer readings. Vertical axis: \(\xi\).

Fig. 30

dry friction the coefficient of friction exhibits a dependence on the specific pressure on the friction surfaces, decreasing as the specific pressure increases. The specific pressure between the chip and the front face of the cutter can be calculated if the area of contact between the chip and the front face of the cutter is measured. This area can be measured with sufficient accuracy from the trace left by the chip on the front face. A comparison of the coefficient of friction with the specific pressure is presented in Fig. 31. In this figure the values of the coefficients of friction are plotted for various microspeeds and various rake angles. Along the axis of abscissas are plotted

Figure labels: Vertical axis: coefficient of friction \(f\). Horizontal axis: normal stress \(\sigma_n\), \(\mathrm{kg/mm^2}\). Free cutting. Lead. \(b = 8.6\ \mathrm{mm}\). Legend: \(V = 0.014\ \mathrm{m/min}\); \(0.0055\); \(0.036\); \(0.106\).

Fig. 31

specific pressures between the chip and the front face of the cutter, in \(\mathrm{kg/mm^2}\), which in the figure are called normal stresses. Of course, one must bear in mind that only average values of the specific pressures are plotted here, obtained by dividing the normal force by the area of contact between the chip and the front face of the cutter. In reality, the specific pressure on the front face of the cutter is not constant over the entire area of friction. The graph shows that these average specific pressures vary, when the cutting conditions are changed, within extremely wide limits—from \(0.8\) to \(2.5\ \mathrm{kg/mm^2}\). All the experiments with a broad range of variation of rake angles and cutting speeds fit quite satisfactorily onto a single curve, showing that as the specific pressure increases the coefficient of friction decreases. Thus there is reason to suppose that the change in the coefficient of friction with changes in cutting speed and rake angle under conditions of cutting at microspeeds, when the cutting temperature remains constant, is the result of a change in the specific pressures on the friction surface between the chip and the cutter. From the same figure it can be seen that, for the same rake angles, higher specific pressures were obtained at higher cutting speeds. This is apparently explained by the fact that, when the cutting speed, i.e. the strain rate, is increased, the metal acquires higher strength properties and, when the chip contacts the front face of the cutter, can withstand higher compressive stresses.

Experiments on Cutting Aluminum

Experiments on cutting aluminum were carried out both at microspeeds and at high cutting speeds. At microspeeds the cutting speed varied from \(0.0048\ \mathrm{m/min}\) to \(0.960\ \mathrm{m/min}\).

Figure 32 presents the results of experiments without lubrication with a rake angle of \(30^\circ\). With a smaller rake angle, at microspeeds for aluminum

Fig. 32

Visible inscriptions in the figure:

• Aluminum (saw-cut)
• Cutter RF1
• \(\gamma = 30.5^\circ\)
• \(b = 4\ \mathrm{mm}\)
• \(V = 0.0075\ \mathrm{m/min}\)
• \(0.098\)
• \(0.280\)
• \(0.760\)
• \(P_1\)
• \(P_2\)
• Free cutting
• Force \(P\), kg
• Cut thickness, mm

it was not possible to work, since the chip came off very unevenly, breaking up into separate elements. Fig. 32 shows that the cutting forces vary in a perfectly straight-line manner with changes in the thickness of cut. With an increase in the cutting speed, the cutting forces increase sharply. Fig. 33 shows the shrinkage obtained in these experiments. Here it is seen that the thickness of cut does not noticeably affect the chip shrinkage, while

Fig. 33

with an increase in cutting speed the shrinkage increases noticeably. Judging from Fig. 32, the thickness of cut should not influence the coefficient of friction, since the forces \(P_1\) and \(P_2\) are arranged on the graph in a perfectly straight line.

Fig. 34 presents the change in cutting forces when cutting with lubrication. As a lubricant in cutting aluminum we used kerosene, which, as the experiments showed, completely eliminated the welding of the chip

Fig. 34

to the front face of the cutter, which in itself indicated a significant reduction in the coefficient of friction. From Fig. 34 it is seen that, when kerosene was used, the cutting forces decreased considerably; the influence of cutting speed also became less noticeable, but did not disappear entirely, as we had when using lubrication in the steel experiments. Fig. 35 presents—

...dependences of chip shrinkage and of the coefficient of friction on the chip thickness and on the speed when cutting with kerosene lubrication were obtained. The coefficient of friction when cutting with kerosene does not depend, to any noticeable degree, either on the chip thickness or on the cutting speed. Fig. 36 gives a comparison of the coefficients

Fig. 35

of friction and chip shrinkage when working without lubrication and with lubrication. When working without lubrication, with an increase in cutting speed both the coefficient of friction and the chip shrinkage increase. This in turn causes an increase in the cutting forces. When cutting with lubrication, the cutting speed has no effect on chip shrinkage and has an entirely insignif—

Fig. 36

—icant effect on the coefficient of friction. Hence it may be concluded that, when cutting aluminum with lubrication, the increase in cutting forces with increasing speed is the result of the influence of cutting speed, as the rate of deformation, on the strength properties of aluminum. This is quite probable, since aluminum is a comparatively low-melting metal.

Figure 37 shows the influence of the cutting angle on the coefficient of friction when cutting aluminum with kerosene lubrication at microspeeds. With an increase in the rake angle, the coefficient of friction increases considerably, i.e.

Fig. 37

here the same thing is observed as we had when cutting other metals.

Figures 38, 39, and 40 present the results of measuring the cutting forces when working at medium and high speeds. Here the experiments were carried out

Fig. 38

by the method of constrained cutting. The graphs show that, with increasing speed, the cutting forces first increase and then begin to decrease.

Figures 41 and 42 show the change in the coefficient of friction with a change in cutting speed. The coefficient of friction here changes similarly

in the way it changes when cutting steel, i.e., at first it increases, reaches its greatest value, and then first rapidly, and later slowly, decreases. But the maximum value of the coefficient of friction here is reached at lower cutting speeds than in the machining of steel. A larger rake angle here again corresponds to higher values of the coefficient of friction. The absolute values of the coefficients of friction are very

Fig. 39

high. As the graphs show, everywhere, with the exception of microspeeds, they are greater than unity.

In Fig. 43 the change in chip shrinkage with the change in cutting speed is presented. The chip shrinkage follows, in its change, the change in

Fig. 40

by a decrease in the coefficient of friction, but it should be noted that in the region of high cutting speeds, despite the fact that the coefficient of friction decreases only very slightly, remaining almost constant, the chip shrinkage continues to decrease rather rapidly with an increase in cutting speed.

Graph inscriptions: Cast aluminum. \(\gamma = 31^\circ\), \(\varphi = 75^\circ\), cutter RF1. Vertical axis: chip-shrinkage coefficient \(\xi\). Horizontal axis: speed \(V\), m/min. Curves: \(S = 0.2\) mm/rev; \(S = 0.4\); \(S = 0.8\).

Fig. 41

Thus, here the decrease in shrinkage cannot be explained solely by a decrease in the coefficient of friction. Apparently, the decrease in chip shrinkage here is also caused by an increase in the rate of deformation. With an increase in the rate of deformation the metal becomes less plastic,

Graph inscriptions: Free cutting. Cast aluminum. \(\gamma = 20^\circ\), \(\varphi = 90^\circ\), cutter RF1. Vertical axis: chip-shrinkage coefficient \(\xi\). Horizontal axis: speed \(V\), m/min. Curves: \(S = 0.2\) mm/rev; \(S = 0.4\).

Fig. 42

and therefore the shrinkage decreases. Confirmation of this, apparently, is also provided by the circumstance that the cutting forces in the region of high cutting speeds cease to decrease with an increase in cutting speed, despite the reduction in chip shrinkage. This is also a consequence of the influence of the increasing rate of deformation, since with an increase in the rate of deformation the strength properties of the metal increase.

In Fig. 44 the change in the coefficient of friction as a function of the cutting temperature, measured with a natural thermocouple, is shown. From this graph one gets the impression that the change in the coefficient of friction is governed by the temperature on the front face of the cutter, since the curves of the coefficient of friction, plotted for different cutting angles and feeds, are positioned in exactly the same way relative to the temperature axis.

Fig. 43

Graph labels: coefficient of friction \(\mu\); speed \(V\), m/min.
Material: aluminum (cast).
Feed: \(S = 0.2\), \(0.4\), \(0.8\) mm/rev.
Cutter: RФ1.
Angles indicated: \(\gamma = 20^\circ,\ \varphi = 79^\circ\); \(\gamma = 31^\circ,\ \varphi = 75^\circ\).

Fig. 44

Graph labels: coefficient of friction \(\mu\); galvanometer readings.
Material: aluminum (cast).
Feed: \(S = 0.2\), \(0.4\), \(0.8\) mm/rev.
Cutter: RФ1.
Inscription: unsteady cutting.
Angles indicated: \(\gamma = 20^\circ,\ \varphi = 79^\circ\); \(\gamma = 31^\circ,\ \varphi = 75^\circ\).

Cutting Experiments on Red Copper

Experiments on cutting red copper were of interest because this metal has a comparatively high melting temperature and, at the same time, does not produce a built-up edge on the cutter during cutting. Unfortunately, in our

we had at our disposal a very limited quantity of this metal, and for this reason we could not carry out all the experiments that would have been desirable. For the same reason we also could not check some of the experiments by repeating them. To this it must be added that the single red-copper blank that we had for the experiments had been cast by the plant with insufficient quality, as a result of which the casting proved porous. We made an attempt, using the resources of the laboratory, to remelt part of the blank; in doing so we obtained a dense casting, but one with a coarse-grained structure. All this greatly hindered our investigations and permits some of their results to be called into question.

Fig. 45

Text in the figure: red copper (cast); cutter RF1; \(\delta = 10^\circ\); \(b = 2.7\) mm; \(V = 0.0075\) m/min and \(0.760\) m/min; force \(P\), kg; thickness of cut \(a\), mm; free cutting; 1st chip; 2nd chip; \(P_1\); \(P_2\).

First of all we shall present the results of our experiments on the plant casting.

Figure 45 shows the results of measurements of cutting forces carried out at micro cutting speeds. Here, for each force, two curves are given: for the first chip and for the second. Before each first chip the cutter was sharpened; the second it removed without sharpening. The graph shows that the cutting forces for the second chip were obtained as considerably higher. The influence of cutting speed did not show itself here. Figure 46 gives the results of calculations of the coefficient of friction and measurements of chip shrinkage. The coefficient of friction and chip shrinkage, as well as the cutting forces, proved higher for the second chip, which is quite natural. The coefficient of friction depends neither on the cutting speed nor on the chip thickness. It is not clear why, at a constant coefficient of friction, the chip shrinkage falls as the thickness of cut increases (as a result of which the dependence of the cutting forces

on the chip thickness turned out not to be rectilinear, but curvilinear). It may be supposed that this was a result of the porosity of the metal.

Figs. 47 and 48 show the results of measuring cutting forces at medium and high cutting speeds for three different feeds. Here we

Fig. 46

observe a very considerable decrease in cutting forces with increasing cutting speed. Fig. 49 shows the change in the coefficient of friction, and Fig. 50 the chip shrinkage with the change in cutting speed. The coefficient of friction remains constant as the cutting speed changes, and its value coincides with the value obtained at microspeeds. The chip shrinkage decreases with increasing cutting speed, which in turn,

Fig. 47

![Figure 48]

Fig. 48

• Vertical axis: Force \(P\), kg
• Horizontal axis: Speed \(V\), m/min
• Curves: \(P_z\), \(P_x\), \(P_y\)
• Red copper (cast)
• Cutter RF1, \(\gamma = 10^\circ\), \(\varphi = 75^\circ\)
• \(S = 0.4\) mm/rev
• \(t = 3\) mm
• Free cutting

![Figure 49]

Fig. 49

• Vertical axis: Coefficient of friction \(\mu\)
• Horizontal axis: Speed \(V\), m/min
• Red copper (cast)
• Cutter RF1, \(\gamma = 10^\circ\), \(\varphi = 75^\circ\)
• \(t = 2.85\text{–}3\) mm

![Figure 50]

Fig. 50

• Vertical axis: Shrinkage \(a\)
• Horizontal axis: Speed \(V\), m/min
• Free cutting
• Red copper (cast)
• Cutter RF1, \(\gamma = 10^\circ\), \(\varphi = 75^\circ\)
• Legend:
• \( \times, \bullet \quad t = 3.0\) mm
• \( \circ \quad 2.85\) mm
• Curves:
• \(S = 0.07\) mm/rev
• \(S = 0.2\)
• \(S = 0.4\)

causes also a decrease in the cutting forces. Figs. 51, 52 show the change in the coefficient of friction and in chip shrinkage when the temperature on the front face of the cutter is changed. These graphs convince us that, at identical—

Fig. 51

Graph labels and inscriptions:

• \( \mu \)
• Red copper (cast)
• Cutter RF1, \(\gamma = 10^\circ,\ \varphi = 75^\circ\)
• \(\times\ S = 0.07\)
• \(\circ\ S = 0.2\)
• \(\bullet\ S = 0.4\)
• Free cutting
• Galvanometer readings

—temperatures, independently of the feed and cutting speed, the chip shrinkage proves to be the same, which convinces us of the influence of temperature, and not of the cutting speed, on chip shrinkage. This is quite probable,

Fig. 52

Graph labels and inscriptions:

• Shrinkage \(\lambda_a\)
• Galvanometer readings
• Red copper (cast)
• Cutter RF1
• \(\gamma = 10^\circ,\ \varphi = 75^\circ\)
• \(\times\ S = 0.07;\ t = 3\ \mathrm{mm}\)
• \(\bullet\ 0.40\quad 3.0\)
• \(\circ\ 0.20\quad 2.85\)
• Non-free cutting

since red copper has a high melting temperature and the influence of the rate of deformation on the properties of the metal should not be especially high for it—

especially significant. We observe that, as the cutting speed is increased, at a constant coefficient of friction the chip shrinkage decreases considerably; that is, here there is a discrepancy between the coefficient of friction and the chip shrinkage. Apparently, this discrepancy is explained by the fact that, as the cutting speed is increased, the tempera-

Fig. 53

ture rises, and this causes a change in the initial properties of the metal, which leads to a change in chip shrinkage.

Let us proceed to a description of the experiments on copper, which was obtained by us by remelting a factory billet. In Fig. 53 are presented the results of measuring the cutting forces for a feed of \(0.2\) mm/rev. As the graphs show, the cutting forces at first decrease rapidly and substantially, and then remain constant. Similar relationships were obtained by us at other feeds. Fig. 54 shows the influence of cutting temperature and feed on the coefficient of friction. The graph shows that, within a wide range of variation of temperature and feed, the coefficient of friction remains

Fig. 54

constant. Fig. 55 shows the dependence of chip shrinkage on temperature. In comparing all these figures with the corresponding ones for cast red copper, it can be seen that the dependences obtained are entirely analogous. The coefficient of friction has a higher value for the experiments of the second series. This is explained by the circumstance that in this series of experiments the cutter had a larger rake angle. Thus, for red copper as well, the same phenomenon is observed that we noted for other metals: the coefficient of friction increases with an increase in the rake angle of the cutter.

Fig. 55

Conclusions

We do not give a detailed analysis of the results we have obtained. This will be done by us in one of our subsequent works. We shall make only a brief conclusion.

1. For all the metals with which we conducted the investigation, the coefficient of friction in cutting increases with an increase in the rake angle of the cutter.

2. When cutting steel with a cutter of identical geometry, the coefficient of friction and the chip shrinkage change with a change in the cutting temperature; when the temperature is kept constant, however, they depend neither on the thickness of the cut nor on the rate of deformation.

3. When cutting steel, the material of the cutting tool has an influence on the coefficient of friction and on chip shrinkage.

4. When cutting steel under conditions of identical temperatures, the coefficient of friction and chip shrinkage, with constant cutter geometry, are constant, while the cutting forces on the rake face of the cutter are directly proportional to the thickness of the cut.

5. When cutting steel at microspeeds, with an increase in cutting speed the coefficient of friction and chip shrinkage increase if cutting takes place without lubrication. This is explained by the reduced penetration, onto the friction surfaces, of air particles that exert a lubricating effect.

6. When cutting lead, the coefficient of friction and chip shrinkage depend on the thickness of the cut, decreasing as it increases.

1. When cutting lead, the deformation rate affects the coefficient of friction and the chip shrinkage. As the deformation rate increases, the coefficient of friction and the chip shrinkage increase.

2. When cutting lead, as the cutting temperature increases, the coefficient of friction and the chip shrinkage decrease.

3. When cutting aluminum at microspeeds, the coefficient of friction and the chip shrinkage do not depend on the thickness of the cut. The forces on the front face of the cutter are then directly proportional to the thickness of the cut.

4. When cutting aluminum, as the deformation rate increases, the coefficient of friction increases only slightly.

5. When cutting aluminum, the cutting temperature affects both the coefficient of friction and the chip shrinkage.

6. When cutting red copper, the coefficient of friction depends neither on the deformation rate, nor on the thickness of the cut, nor on the cutting temperature.

7. When cutting copper, the chip shrinkage decreases with an increase in cutting temperature and does not depend on the thickness of the cut or on the deformation rate.

8. The use of lubricant in cutting very substantially reduces the coefficient of friction, the chip shrinkage, and the cutting forces.

9. The coefficient of friction in cutting can vary, depending on the cutting conditions and the type of metal being machined, over very wide ranges. Thus, in cutting without lubricant in our experiments, the coefficient of friction varied when cutting steel from 0.55 to 1.7; when cutting lead—from 0.42 to 0.85; when cutting aluminum—from 0.93 to 1.5; when cutting copper—from 0.6 to 0.7.