Justification of the Regularity of the Change in Surface Finish by the Phenomena of the Chip-Formation Process

A. N. Eremin
Candidate of Technical Sciences

An experimental study carried out by the author (1940) to determine the influence of cutting conditions on the surface quality in finish turning of steel 5120 without coolant gives a complete picture of the nature of the change in irregularities \(H\) as a function of \(v\) and \(S\), but it does not explain the essence of this phenomenon. To answer this question, it is necessary to turn directly to the process of chip formation, since all phenomena connected with this process are the principal sources of the causes that produce roughness on the machined surface.

According to the data of Wallichs and Frank, Schwerd, Dijdje, Ernst and Martellotti, Boston and Kraus, and other experimenters known in the Soviet literature on cutting, it has been established that the surface finish in machining ductile metals (steel) depends chiefly on the condition of the built-up edge on the cutter during chip removal.

Experiments show that, with the appearance of a built-up edge whose hardness is considerably higher than that of the material being machined (by 30–110% according to Gerber [1]), it is in fact not the cutter that cuts, but the built-up edge. Since the built-up edge usually has a blunted form, what actually takes place is not cutting, but tearing of the material; as a result, the machined surface becomes uneven and rough, with evident signs of destruction (deep grooves and scratches appear). The greater the size of the built-up edge, the stronger its destructive action on the surface. The form and dimensions of the built-up edge on the cutter depend, all other conditions being equal, on the cutting speed, the cutting angle, and the chip thickness, i.e., on the feed. It has been proved that a built-up edge does not form (with rare exceptions) when machining at high cutting speeds (70–150 m/min and higher) and when machining at very low speeds (1–3 m/min and lower). Built-up edge formation occurs only within a certain interval of speeds, the limits of which vary somewhat depending on the properties of the material being machined and the lubrication of the cutter. For illustration, Fig. 19^1) gives the dependence of the magnitude of the built-up edge on \(v\) and on the front angle of the cutter, according to the experiments of Wallichs and Frank, in machining steel without cooling. Examining microphotographs of various stages of built-up-edge formation according to the data of other investigators (Schwerd, Ernst and Martellotti, etc.), one can observe the same pattern of change of the built-up edge as in Fig. 19.

It is very important to note the circumstance that, in the general nature of the change of built-up edges under the influence of \(v\), the same law is observed as in the change of irregularities on the machined surface. In this it is not difficult—

^1) To avoid repetitions in the figures, the latter have a common serial numbering in all three articles by the author included in this collection.

one can be convinced of this if one compares the curves of variation of build-up (Fig. 19) with the curves of variation of irregularities (Fig. 13), according to the data of our experiments on steel 5120. In both cases the cutting speed has three zones of influence. The same can be seen from the experiments of Wallichs and Frank (Fig. 20) and Delpère, Fig. 21. The curves in Figs. 20 and 21 show the influence of \(v\) and \(S\) on the magnitude of surface irregularities, measured in the direction of feed

Fig. 19

of the cutter. Schims [7] obtained the same results in his experiments, machining materials of different hardness (Fig. 22).

The dimensions of the build-up also increase, and consequently the quality of the surface worsens, if the thickness of the removed chip is increased, i.e.

Fig. 20

if the amount of feed is increased (Schwerd, Ernst, Boston, Pryanichnikov, and others). This phenomenon is observed within the range of speeds conducive to the formation of build-up. Our observations of the character of the change in build-up on the cutter as a function of \(v\) and \(S\), when machining steel 5120, in general coincide with the data of other investigators. When \(S\) is varied over wide limits \((0.011 \div 0.76\ \text{mm/rev})\), the appearance of build-up on the cutter is not found at \(v \leq 2\ \text{m/min}\) and \(v > 150\ \text{m/min}\). For steel 5120, the greatest magnitude of build-up corresponds to \(v = 15—20\ \text{m/min}\) for all feed values \(S > 0.011\ \text{mm/rev}\). At \(S \leq 0.011\ \text{mm/rev}\), build-up on the cutter does not appear at all (Fig. 23).

Rozentein and Sterney [4], Rosenberg [3], and others, studying the chip-formation process, observed that, when machining at low cutting speeds, with an increase in chip thickness (and cutting angles) there is a tendency toward the formation, ahead of the cutter, of so-called leading

Fig. 21

cracks (Figs. 24–25). The magnitude of these cracks, as Fig. 25 shows, sometimes reaches enormous dimensions in comparison with the thickness of the removed

Fig. 22

Fig. 23

chips. The obvious character of chip separation, in the presence of leading cracks, inevitably leads to an increase in surface roughness, just as when built-up edges appear, but to a somewhat lesser degree (with an increase in the cutting angle, the tears increase).

Rappatz [5] believes that the main reason for the improvement in surface quality with increasing speed lies in the rise of the cutting temperature,

Fig. 24

as a result of the increase in the amount of heat released per unit time. To prove this, Rappatz carried out an experiment on machining a blank (Siemens-Martin steel, mild), preheated to 300—320°C.

Fig. 25

It turned out that the speed at which a smooth surface was first obtained decreased to 15 m/min, whereas when machining in the cold state this speed was equal to 40 m/min.

Rappatz is somewhat mistaken in putting forward the cutting temperature as the principal cause of the influence on surface quality. The cutting temperature, as a factor, does not participate directly in the formation of roughness, but

only promotes the formation or disappearance of built-up edges and advancing cracks with a change in cutting speed.

In machining tough metals, an increase in speed and feed (chip thickness) leads to significant changes in the chip shrinkage $\lambda$ (the ratio of the path traveled by the cutter to the length of the removed chip), the magnitude of which characterizes the degree of deformation of the metal transformed

Fig. 26

into a chip. The greater the chip shrinkage, the greater the deformation, and vice versa. In Fig. 26 a curve is given for the change in chip shrinkage as a function of $v$ when machining steel, according to the data of Leyenzetter, and in

Fig. 27

Fig. 27—according to the experiments of Klokov [2]. In both cases the curves show that, with an increase in $v$, chip shrinkage decreases significantly up to a certain limit, after which it remains constant.

Since, with an increase in \(v\), along with a decrease in chip shrinkage, there is an improvement in the smoothness of the machined surface, Leienzeter chose the shrinkage value \(\lambda\) for assessing the qualities of this surface.

The question arises whether the magnitude of chip shrinkage can serve to explain the causes of the formation and variation of irregularities on the machined surface as a function of \(v\) and \(S\).

Leienzeter’s index apparently justifies its purpose within those cutting-speed ranges in which, as \(v\) increases, both an improvement in surface smoothness and a decrease in shrinkage are observed (the 2nd and 3rd speed zones). This is indicated by the external similarity in the character of the shrinkage curves (Figs. 26, 27) to the curves of change in surface irregularities in the indicated zones of \(v\) in Figs. 13, 20, 21, and 22.

Fig. 28

Fig. 29

Passing into the region of low cutting speeds (1st zone, \(v \leq 10\text{—}15\ \text{m/min}\)), we see an entirely different picture in the relation between shrinkage and surface quality. As \(v\) decreases, chip shrinkage remains constant (Fig. 27), or may even increase, while the surface quality begins to improve again, which is clearly seen from the falling curves of the variation of irregularities \(H\) in Figs. 13, 20, 21. A contradiction results. Consequently, in the low-speed zone the magnitude of shrinkage cannot serve as a reflection (index) of the smoothness of the surface.

An even greater contradiction is revealed if we try to explain, by the magnitude of chip shrinkage, the cause of the change in surface quality with chip thickness (feed). Fig. 28 shows the curve of change in chip shrinkage as a function of its thickness in machining steel, from the experiments of Sokolov [6], and Fig. 29 in machining soft iron, according to Rosenberg’s investigations [3]. In both cases, as chip thickness increases, a decrease in its shrinkage is observed. At the same time, we know, from the experiments of Rosenhein and Sterney [4], Rosenberg, and others,

that, with an increase in chip thickness, the quality of the surface deteriorates as a result of the formation of leading cracks (at small \(v\)) and because of the growth of built-up edges within the limits of the 1st and 2nd zones of \(v\) (Fig. 13).

Consequently, as the chip becomes thicker its shrinkage decreases, while the cleanliness of the machined surface deteriorates (at the corresponding \(v\)); i.e., the result obtained is the complete opposite of what Leyenzetter proposed.

This shows that, by using the magnitude of chip shrinkage, it is impossible to give a complete explanation of the causes of changes in surface quality with \(v\) and \(S\), when the latter vary over wide limits.

Concluding here the analysis of the available experimental data on the process of chip formation, the following conclusions may be drawn:

1. The formation and character of the change in irregularities on the machined surface, as a function of cutting speed and feed, are explained mainly by the appearance of built-up edges on the tool and of leading cracks.

2. According to the phases of change in the built-up edge on the tool, the cutting speed has three zones of influence on surface cleanliness.

With an increase in \(v\) in the 1st zone, the built-up edge rapidly grows from 0 to a maximum, after which it begins to decrease to zero within the limits of the 2nd zone, and does not appear at all (or appears very rarely) in the interval of the 3rd zone of speeds.

1. An increase in chip thickness (feed) contributes to the growth of the built-up edge on the tool and to the formation of leading cracks. The former occurs within the limits of the \(v\) of the 1st and 2nd zones, the latter within the limits of the \(v\) of the 1st zone and below, i.e., in the region of speeds close to zero, where there is no action of the built-up edge at all.

2. The roughnesses arising on the surface under the influence of leading cracks and built-up edges on the tool characterize exclusively the cleanliness of the cut.

3. Depending on the degree of cleanliness of the cut, the theoretical height of the principal ridges of the profile, formed by the geometry of the tool in plan (Fig. 30), will increase or decrease when \(v\) and \(S\) change.^1

The conclusions presented make it possible, as a first approximation, to solve the problem posed at the beginning of the article—to explain the causes of the change in surface irregularities \(H\) as a function of \(v\) and \(S\) when machining steel 5120 (Figs. 13 and 16).

In Fig. 13 the upper point of inflection of each curve, determining the greatest height of irregularities \(H\), i.e., the worst surface quality at a given \(S=\mathrm{const}\), shows that when machining steel 5120, without the use of coolant, the greatest height of the built-up edge on the tool is obtained at \(v \simeq 15\ \mathrm{m/min}\). As was indicated above, the observations made of the appearance of the built-up edge on the tool fully confirm this fact. On surfaces machined at \(v = 15\ \mathrm{m/min}\), traces of destruction in the form of deep scratches and tears are always noticeable, especially at large values of \(S\). This is evidenced by the character and magnitude of the irregularities in the profilograms of Fig. 14.

The lowering of the maximum point of the curves \(S=\mathrm{const}\) (Fig. 13) with decreasing \(S\) depends on two causes:

1. On the reduction in the height of the principal ridges formed by the profile of the tool in plan (Fig. 30).

2. On the reduction of tears and roughnesses owing to the decrease in the magnitude of the built-up edge on the tool and of the leading cracks (at \(v = 15\ \mathrm{m/min}\) they are possible).

^1 The diagram in Fig. 30, constructed according to the formulas of S. D. Tyshina and V. K. Ilyin (Org-informatsiya, 1936, No. 11, p. 19), expresses the dependence of the theoretical height of the ridges of the surface profile on the geometry of the cutter in plan (\(R\), \(\varphi\), and \(\varphi_1\)) and on the feed \(S\).

From Fig. 13 it is evident that, as \(S\) decreases, there is also a gradual smoothing of the bend of the curves \(S=\mathrm{const}\), i.e., an erasure of the difference in the effect of cutting speed on the value of \(H\) in different zones of \(v\) (for example, at \(S=1\) and \(0.055\ \mathrm{mm/rev}\)).

On the \(H—S\) diagram (Fig. 16), this phenomenon is expressed by the position of the lines \(v=\mathrm{const}\), especially for \(v \geq 15\ \mathrm{m/min}\), directed toward the point \(O_2\) with coordinates: \(H_0=2.7\ \mu\); \(S_0=0.011\ \mathrm{mm/rev}\).

The point \(O_2\) shows that at \(S=0.011\ \mathrm{m/min}\) the cleanliness of the machined surface remains constant, independently of changes in \(v \geq 15\ \mathrm{m/min}\).

Obviously, by reducing the feed (chip thickness) to a very small value (in the present case to \(S=0.011\ \mathrm{mm/rev}\)), it is possible to reduce the built-up edge on the cutting tool to negligible dimensions and thereby bring to zero its harmful influence on surface quality even at \(v=15\ \mathrm{m/min}\). To verify this proposition, a series of experiments was carried out on machining surfaces with a feed \(S=0.011\ \mathrm{mm/rev}\) at \(v=5, 15, 60, 105\), and \(150\ \mathrm{m/min}\). The results of the experiments are given in Fig. 13 (lower line). From the arrangement of the points it is evident that, for all values of \(v\), the height of the irregularities is \(H \approx 3\mu\) (theoretically, according to Fig. 16, \(H=2.7\mu\)), and the curve \(S=0.011\ \mathrm{mm/rev}\) in this case represents a straight line without the characteristic bend at \(v=15\ \mathrm{m/min}\). This proves that at \(S=0.011\ \mathrm{mm/rev}\) there is in fact no harmful influence of the built-up edge, since its presence on the cutting tool was not detected at all by observations during the experiments. If it is assumed that, in the cutting process, a built-up edge nevertheless formed—as may be judged from the slightly matte gloss of the surface at \(v=15\ \mathrm{m/min}\)—then it (the built-up edge) was of such small dimensions that it did not exert any substantial influence on the magnitude of the surface roughness. The profilogram taken from the surface at \(v=15\ \mathrm{m/min}\) (Fig. 18) reveals no difference whatsoever in the micrometric profile as compared with other surfaces for \(v \leq 15\ \mathrm{m/min}\).

Fig. 30

Since the straight line \(S=0.011\ \mathrm{mm/rev}\) (Fig. 13) is at the same time also the line \(H=\mathrm{const}\approx 3\mu\), the feed \(S=0.011\ \mathrm{mm/rev}\) was therefore called the “critical feed,” and the value \(H\approx 3\mu\) (theoretical \(2.7\mu\)) the “critical cleanliness” of the surface. Both quantities determine the coordinates of the “critical point” \(O_2\) (Fig. 16), whose physical properties were discussed earlier.

To substantiate the law of the fall of the curves \(S=\mathrm{const}\) (Fig. 13) to the left and to the right of the inflection point, let us turn to the \(H—S\) diagram (Fig. 16). In considering the latter, the question arises why the lines \(v=\mathrm{const}\) have a variable angle of inclination to the \(S\) axis and are situated at different heights. For example, in the first zone of cutting speeds (\(v \leq 15\ \mathrm{m/min}\)), the line \(v=2\ \mathrm{m/min}\) lies lower and passes more steeply than the line \(v=15\ \mathrm{m/min}\). This may be explained by the fact that, when machining steel 5120 at a cutting speed of \(2\ \mathrm{m/min}\), built-up edges on the cutting tool are absen-

exist. The formation of irregularities with increasing \(S\) is affected only by the geometry of the cutter in plan and by the appearance of leading cracks, whose action is less harmful (at a cutting angle \(\delta = 70^\circ\)) for the surface than the action of built-up edges. With a decrease in feed (i.e., chip thickness), the influence of the leading cracks also decreases; therefore the line \(v=\mathrm{const}\) for \(2\ \text{m/min}\), when passing into the region of small \(S\), descends considerably below the line \(v=15\ \text{m/min}\).

With increasing speed, the harmful action of built-up edges begins to manifest itself, and the more strongly (in absolute value of \(H\)), the larger the selected value of feed. The latter is clearly noticeable from the sharp increase in the rise of the curves \(S=\mathrm{const}\) within the limits of the 1st zone of \(v\) in Fig. 13. If judged by the relative increase in irregularities, then the harmful action of built-up edges occurs more actively in the region of small \(S\) (Table 1).

Table 1

In accordance with this, the lines \(v=\mathrm{const}\) (in the logarithmic coordinates of Fig. 16) change their angle of inclination in the direction of decrease as \(v\) increases from 2 to \(15\ \text{m/min}\). (The rotation of the lines is relative to the point \(O_1\), located outside Fig. 16).

When passing into the 2nd and 3rd zones of cutting speeds (\(v>15\ \text{m/min}\)), the inclination of the lines \(v=\mathrm{const}\) continues to decrease, and their position, especially in the region of larger feeds, gradually lowers due to rotation relative to the point \(O_2\). At the same time, in Fig. 13 it can be seen that with an increase of \(v\) in the 2nd and 3rd zones, the position of the right-hand part of the curves \(S=\mathrm{const}\), from the point of inflection, becomes considerably lower than the left-hand part (1st zone), especially for large values of \(S\).

Can this phenomenon be explained only by a decrease in the harmful influence of built-up edges on the cutter in connection with increasing speed, or does some other factor of the chip-formation process begin to manifest its action here as well? To resolve this question, a comparison and analysis of the actual heights of irregularities \(H\) (Fig. 16) with the theoretical ones (Fig. 30) was carried out.

The result of the comparison is presented in Fig. 31.

The line of theoretical heights of the surface ridges passes more steeply toward the \(S\) axis and intersects a portion of the experimental straight lines \(v=\mathrm{const}\). This indicates a very interesting phenomenon. The greater \(v\) and \(S\), the lower the height of the actual irregularities in comparison with the theoretical ones, i.e., here there is, as it were, a cutting off of the ridges. For example, at \(S=1\ \text{mm/rev}\) and \(v=200\ \text{m/min}\), the height of the actual irregularities is 4.4 times smaller than the theoretical. At first glance this seems improbable and absurd. However, upon careful analysis of the chip-formation process, this phenomenon becomes quite explainable and real. As a first approximation one may suppose that the phenomenon of cutting off the irregularities occurs because of the transverse shrinkage of the chip and its work hardening. Under the influence of shrinkage, the chip becomes somewhat wider than the theoretical section, and since its hardness is always higher than the hardness of the material being machined—

(on 30–100% according to Herbert’s data), then during operation the chip, moving, begins to cut off, more precisely to shear off, the peaks of the irregularities left by the tool profile. To explain the process of cutting by the chip, the diagram in Fig. 32 shows the position of the tool in plan at the moment of operation, with the trace of the theoretical, i.e., undeformed chip section (shaded), and its actual section after shrinkage (indicated by the dotted line). From Fig. 32 it is seen that, during shrinkage, the deformed metal of the chip tends to move to the right, toward the side of least resistance, since to the left the widening of the chip is hindered by the as yet uncut metal of the workpiece.

Fig. 31

It is quite natural that, when expanding to the right, the chip cuts off the peaks of the irregularities, acting as a new cutting edge of the tool with a large rounding radius. This peculiar cutter-chip always travels somewhat ahead of the main cutter, owing to the advancing wave of plastic deformations.

The cutting property of the chip is obtained at the expense of so-called work hardening. According to Herbert, the hardness of the chip is the higher relative to the base material, the lower the initial hardness of the latter. Under the influence of work hardening from the preceding cut and the action of the advancing wave of plastic deformations (Fig. 33), the hardness of the irregularities is also somewhat higher than that of the base material; however, the hardness of the chip itself is so great that it permits these irregularities to be cut off completely.

Fig. 32

With an increase in cutting speed and feed, the cutting temperature also increases. The question arises why, nevertheless, the chip does not lose its hardness, and consequently its cutting property. Herbert established that, with increasing temperature, the machining hardness of the material (of the chip and of the workpiece) can vary within certain limits up to the time (Fig. 34) when it reaches a very high temperature causing already appreciable softening of the metal. Evidently, owing to this preser-

…of work hardening to considerable temperatures, and this can explain the preservation of the cutting property of the chip despite the increase in cutting speed and feed.

According to the available experimental data, it is known that the greater \(v\) and \(S\) (chip thickness), the smaller the shrinkage of the chip not only in the longitudinal direction (Figs. 26 and 27), but also in the transverse direction. Fig. 35 shows the dependence of the thickening of the chip (lower curve) and its widening (upper curve) on the magnitude of \(S\), according to Rosenberg’s experiments [10] with soft iron. From Fig. 35 it is evident that the widening of the chip increases together with an increase in feed, since the depth of cut (chip width) remains constant during the operation. Undoubtedly, the widening of the chip (at \(S=\mathrm{const}\)) will decrease as the speed increases.

If this is so, then why does the cutting off of irregularities nevertheless continue to increase with increasing \(v\), as Fig. 31 shows?

To explain this phenomenon it should be recalled that, with an increase in \(v\) in the 2nd and 3rd zones, the harmful influence of built-up edges on the cutter is reduced, as a result of which the finish improves (tears and scratches decrease), and consequently the overall height of the irregularities \(H\) on the machined surface also decreases. Thus, in the 2nd and 3rd speed zones, with an increase in \(v\), there occurs a decrease in irregularities simultaneously from two sides: from above—through the cutting off by the chip of the crests of the ridges (somewhat decreasing with increasing \(v\)) and from below—through a progressive decrease—

Fig. 33

(In the figure: “mild steel”; \(H_b=340\); “Zlatoust steel”; \(H_b=142\).)

Fig. 34

(Vertical axis: “Machined hole.” Horizontal axis: “Temperature,” °C.)

tion of depressions (tears and scratches) as the built-up edge on the tool disappears. This two-sided action also creates the phenomenon of an intensified reduction of the actual irregularities (even below the theoretical ones, Fig. 31) and explains the reason for the sharp decrease of the curves \(S=\mathrm{const}\) (Fig. 13) as \(v\) increases within the range from 15 to 150 m/min.

Conversely, with a decrease in \(v\) (2nd zone, Fig. 13), the cutting off of the ridges of the profile (from above) will undoubtedly increase, owing to the increase in chip shrinkage, but alongside this, under the influence of the growing built-up edges on the tool, additional tears and roughnesses (from below) also increase greatly, as a result of which the total height of irregularities \(H\) inevitably begins to increase, reaching a maximum at \(v \simeq 15\) m/min.

Fig. 35

Text and labels visible in the figure:
Vertical axis: “Shrinkage by thickness.”
Horizontal axis: “Chip thickness (feed), mm.”
Inset vertical axis: “Shrinkage by width.”
Inset horizontal axis: “Chip thickness.”
Annotation: “Soft iron. Cutting angle \(\delta = 65^\circ\). Chip width \(b = 5.3\) mm.”

How can it be shown why, with an increase of \(v>150\) m/min (Figs. 13 and 16), the magnitude of the irregularities \(H\), or, what is the same thing, the surface finish changes only slightly, and at \(v>200\) m/min remains almost unchanged for a given \(s=\mathrm{const}\) (Fig. 13)? This latter phenomenon may be explained on the basis of the following.

First, in machining steel 5120 (without coolant, at \(S \leqq 1\) mm/rev) at a cutting speed of 150 m/min and higher, stability in the cleanliness of the cut is achieved, since the harmful influence of built-up edge on the tool ceases; the appearance of such built-up edge was not observed even at large values of \(S\).

Second, at these cutting speeds stability is also achieved in chip shrinkage (for the given tool geometry), and consequently stability also in the cutting off of the peaks of the irregularities by the chip.

Both circumstances show that, with an increase of \(v>200\) m/min (at \(S=\mathrm{const}\)), there are no reasons for any further reduction of the irregularities on the machined surface, and therefore the quality of the latter must remain constant. This is confirmed by the horizontal direction of the lines \(S=\mathrm{const}\) (Fig. 13) in the region of \(v\) above 200 m/min.

Thus, the result of the analysis carried out shows that the law of variation of surface finish (irregularities \(H\)) as a function of changes in \(v\) and \(S\) fully corresponds to the laws of the chip-formation process. It could not be otherwise, since all phenomena connected with the chip-removal process (together with the tool geometry) are the principal causes of the appearance of irregularities on the machined surface.

Using this method of analysis, let us critically examine the results of the experiments of Wallichs and Frank on the finish machining of steel without cooling (Fig. 20). Here, first of all, attention is drawn to two maxima in the curves of irregularities (at \(S=\mathrm{const}\)). It may be assumed that, when the greatest irregularities are formed, with increasing \(v\), a similar fluctuation occurs in the dimensions of the built-up edge on the tool. If one compares the character of the cha-

changes in the roughnesses (Fig. 20) and build-up on the cutter (Fig. 19), also obtained in the experiments of Wallixa and Frank, then this assumption is justified. It should be pointed out that such a phenomenon, according to other investigations, has not been observed. For example, in our investigation with steel 5120, at the most diverse values of $v$, $S$, and $t$, the formation of two maxima in the roughness curves was not found (Fig. 13). Likewise, according to the experiments of Depiere (Fig. 21) and Schimtz (Fig. 22), who carried out tests with materials of different hardness, there is no sign of the appearance of two rises in the surface curves. Consequently, there are no grounds for assuming the existence of two maxima in the change of build-up either, as found in the data of Wallixa and Frank (Fig. 19). Analyzing our experiments on the study of the process of build-up formation (Fig. 23) and experiments carried out by other investigators, we likewise find no confirmation of the indicated phenomenon.

In addition, in the experiments of Wallixa and Frank (Fig. 20) there is a second, wholly unsubstantiated proposition. With an increase of $v$ from 30 m/min and higher, the roughnesses (measured in the feed direction) decrease the more rapidly, the greater $S$ is. It is unlikely that this circumstance corresponds to reality, since the height of the roughnesses should increase with an increase in $S$, under the influence of the tool geometry in plan. It is especially strange to see (Fig. 20) that the magnitude of the roughnesses at $S = 0.0425$ was greater than at $S = 0.67$ within the range of $v$ from 100 to 150 m/min. This phenomenon is confirmed neither by the results of our experiments (Figs. 12 and 16), nor by the experiments of Depiere (Fig. 21), and cannot be explained from the point of view of the phenomena of the chip-formation process if $\phi > 0^\circ$.

Conclusion

1. The investigation carried out shows that the regularity of the change in the cleanliness of the surface (roughnesses $H$) as a function of the change in $v$ and $S$ (Figs. 13 and 16) is fully explained by the phenomena of the chip-formation process.

2. The principal causes of the formation of roughness on the machined surface are build-up on the cutter and leading cracks, which, in turn, depend on $v$ and $S$ (chip thickness).

3. Roughnesses characterize only the cleanliness of the cut. The total height of the roughnesses on the surface, $H$, when measured in the feed direction, depends both on the cleanliness of the cut and on the height of the ridges formed by the profile of the cutter.

4. In the 1st zone, $v \le 15$ m/min, $H$ is affected by build-up on the cutter and leading cracks; in the 2nd and 3rd zones, $v = 15 \div 200$ m/min, by build-up (and deposits) on the cutter and the phenomenon of cutting by the chip, as a consequence of the transverse shrinkage of the latter.

5. With an increase of $v > 200$ m/min (at $S = \mathrm{const}$), the shrinkage of the chip and the cleanliness of the cut become stable; therefore there are no reasons for a further change in the roughnesses.

6. The cutting temperature (according to Rapatz) and the chip shrinkage (according to Lenzetter) are factors that do not give an exhaustive explanation of the regularity of the change of roughnesses on the surface when $v$ and $S$ are varied over wide limits.

7. The curves of surface cleanliness according to the experiments of Wallixa and Frank (Fig. 20) do not deserve confidence, since they cannot be analyzed from the standpoint of the phenomena of the chip-formation process.

8. The complete correspondence of the regularity of the change in surface cleanliness for steel 5120 (Figs. 13 and 16) with the phenomena of the chip-formation process ...

and once again confirms the reliability of the conclusions drawn from the experiments and provides a basis for the theoretical substantiation of the dependence \(H = f(v \text{ and } S)\).

1. The method of analysis presented makes it possible to carry out a theoretical verification of any experimental dependence of \(H\) as a function of any factor in the cutting process (tool geometry, coolant, quality of the material being machined, etc.), provided that chatter is absent.

LITERATURE

1. Herbert E.—Maschinenbau, 1937, p. 991; 1925, p. 72.
2. Klyushkin N. F.—Hard alloys and their application in metal cutting. Transactions of TsNIIMASH, 1938, p. 32.
3. Rosenberg A. M.—Experimental study of the process of formation of metal chips. Tomsk, 1929.
4. Rosengein V. and Stern A.—Proc. of the Inst. of Mech. Eng., London, 1925.
5. Rapatz F.—Abstract. Stahl und Eisen, 1920, p. 806.
6. Sokolov B. G.—On the form of roughing cutters. Proceedings of the former Don Polytechnic Institute. Vol. III, issue 1, 1914.
7. Glebov S. F.—Scientific foundations of the most advantageous cutting of metals. 1936.