Experimental Study of the Effect of Cutting Conditions on Surface Quality in Steel Machining

A. N. Eremin
Candidate of Technical Sciences

The dependence of the quality of the machined surface on the factors of the cutting conditions in finish turning is of substantial interest for modern production, since the absence of reliable experimental material on this question often places production in the face of considerable difficulties.

In recent years a large number of works on this question have been carried out both in the USSR and abroad, but all of them are characterized by extreme lack of system, often leading to completely incorrect and contradictory conclusions.

Taking into account the need of production to have the above-mentioned dependence, and bearing in mind the absence of the data necessary for establishing it, the author of the present work carried out experimental investigations in 1940 with the aim of:

1. Establishing the influence of cutting speed \(v\), feed \(S\), and depth of cut \(t\) on surface finish (characterized by the magnitude of the irregularities \(H\), in microns) in steel machining.

2. Giving a graphical and analytical expression of the dependence

\[ H_1 = f(v,\ S,\ t) \]

when the factors of the cutting conditions are varied over wide limits.

1. Relating and explaining the regularity of the change in surface quality by the phenomena of the chip-formation process. Owing to lack of space, the results of the investigation are presented here only for steel of one hardness.

Conditions and Methodology of the Investigation

The machining of surfaces was carried out on a lathe of the Izhevsk Plant (standard size \(175 \times 1000\), with individual drive), with fine regulation of the number of revolutions by means of an auxiliary rheostat. The object of the investigation consisted of specimens of chromium steel 5120 with the following characteristics: \(\sigma_B = 50.3\ \text{kg/mm}^2\); \(H_B = 137—144\); \(R_B = 77—78\); (elongation \(\delta_{10} = 27.5\%\), contraction, \(\psi = 70\%\)). The specimen dimensions were: length 200 mm, diameter 100—120 mm. The cutters (of size \(10 \times 10 \times 45\) mm) were made of high-speed steel with constant geometry: cutting angle \(\delta = 70^\circ\); angles in plan: \(\varphi = 45^\circ\) and \(\varphi_1 = 10^\circ\); clearance angle \(\alpha = 8^\circ\), radius \(r = 1.5\) mm. Grinding and sharpening of the cutters were performed on a grinding machine, followed by hand polishing of the cutting edge. For the experiment the cutters were fastened in a holder with the main cutting edge set horizontally at the height of the centers.

The components of the cutting conditions varied within the following limits:

The extreme values of \(v\) were limited by the kinematics of the machine tool and by the size of the diameter of the specimens. Under all conditions, machining of the surfaces was carried out without the use of cooling-lubricating fluids. All measures were taken to eliminate the harmful influence of chatter (vibrations) on the quality of the surface (size of the blank, rigid tool holder, elimination of play in the parts of the machine tool, etc.).

The irregularities \(H\) on the tested surfaces were measured in the direction

Fig. 1

of the feed motion, by the method of intermittent probing, on a profilograph designed by the author (Fig. 1). The instrument has the following data:

1. Measurement accuracy: 0.5 micron.
2. Magnification: vertically from 550:1 to 2000:1; horizontally from 12.5:1 to 100:1.
3. Recording of profilograms on film (automatically and manually).
4. Length of the section recorded—unlimited.

From each surface, 1–3 profilograms were taken in different sections. The test results showed that the length of the measured sections should be chosen depending on the feed, not exceeding 5–10 mm. In all, there were

More than 450 profilograms from 230 different surfaces machined with variable cutting conditions were studied.

From analysis of the profilograms it was possible to establish that, in almost every case, the surface profile contains random peaks and depressions which, rising above the general level of most irregularities, do not characterize the quality of the given surface by their magnitude. Figure 2 shows two profilograms obtained from different sections of one and the same machined surface. It is evident from Fig. 2 that, in magnitude, the upper profile differs from the lower one. However, if the two profiles are compared in terms of microstructure and the height of most irregularities, they differ little from one another, and therefore may be regarded as equivalent in quality.

Fig. 2

In order to exclude the influence of random peaks and roughnesses on the measurement results, the following method of processing profilograms was adopted.

The magnitude of the irregularities \(H\) (Fig. 2) was determined by the distance between the parallel lines \(ab\) and \(cd\), drawn tangentially to several crests (line \(ab\)) and depressions (line \(cd\)), with the calculation made so that the line cutting off crests and depressions (randomly rising above the level of the majority) would amount to no more than 2–3% of the profilogram length \(l\), taken as 100%. The values of \(H\) determined in this way are more comparable with one another and acceptable for characterizing the quality of surfaces.

Experimental results

Influence of depth of cut. Three series of experiments were carried out. The first—at a constant \(v = 61\ \text{m/min}\) and \(S = 0.22\ \text{mm/rev}\). For each value of \(t\), the length of the machined surface was \(l = 200\ \text{mm}\). The purpose of the experiments was to determine the simultaneous influence on surface finish of the depth of cut and tool dulling as a function of the length of pass.

Fig. 3

The result of measuring \(H\) over individual sections along the length of the specimen is shown in Fig. 3, from which it is evident that, when \(t\) changes by a factor of 7.5 (from 0.2 to 1.5 mm), the surface quality remains unchanged. The uniform scatter of the points within \(\pm 10\%\) relative to the averaged value

$H = 22.5$ m indicates that blunting of the cutter is also negligible. On this basis, in all subsequent investigations the length of the machined surfaces was taken as 20–30 mm.

The second series of experiments was carried out at $v = 15$ m/min with feeds $S = 0.055;\ 0.11;\ 0.22;\ 0.31$ mm/rev (Fig. 4). The purpose was to check how the effect of $t$ on the magnitude of $H$ changes as a function of $S$.

The third series—with constant $S = 0.22$ mm/rev and with $t$ varied in the interval from 0.13 to 2.9 mm—was carried out at three values $v = 36;\ 50$ and 95 m/min. Here it was intended to trace whether the effect of $t$ on $H$ changes with increasing $v$. The experimental results are shown in Fig. 5,

Fig. 4

Fig. 5

where, for comparison, measurements from the 1st series of experiments at $v = 61$ m/min are also plotted. The figures indicate the number of measurements.

From analysis of the diagrams (Figs. 3–5) it follows:

1. For given $S$ and $v$, and with all other conditions equal, the height $H$ does not depend on the change in $t$ within the limits from 0.1 to 3 mm. This is also proved by the profilograms presented in Fig. 6.

2. Irrespective of the depth of cut, the magnitude of the irregularities $H$ changes with changes in $S$ and $v$. In this case $H$ increases with increasing feed (Fig. 4) and decreases with an increase in speed from 15 m/min and above.

3. With increasing $v$, the degree of scatter of the points also decreases owing to the weakening of the harmful influence of tearing and roughnesses on the machined surface. The cleanness of the cut improves.

Effect of cutting speed and feed. Each series of experiments was carried out with one of the following values of $v = 2;\ 5;\ 8;\ 11;\ 15;\ 20;\ 33;\ (40),\ 60;\ 75;\ (80);\ 105;\ 150$ and 200 m/min,¹ but with different feeds $S = 0.055;\ 0.07;\ 0.11;\ 0.22;\ 0.31;\ 0.435;\ 0.51;\ 0.76$ and 1 mm/rev. Since the depth of cut

¹ The values of $v$ in parentheses refer to control experiments, the description of which is given below.

does not have a substantial effect on the surface quality, its magnitude was chosen arbitrarily: \(t = 0.4 \div 0.5\) and \(t = 1.0 \div 1.1\) mm.

The tools were used both sharp and somewhat dulled (having been in operation), taking into account that under production conditions either the one or the other may occur.

Fig. 6

Fig. 7

another. To obtain greater reliability in the conclusions, individual series of experiments were repeated 2–5 or more times. The test results are presented in the diagrams of Figs. 7–10. For comparison, in Fig. 10 at \(v = 15\) m/min

Fig. 8

the mean values of \(H\), taken from the experiments on depth of cut (Fig. 4), in which \(t\) varied from 0.13 to 2.2 mm, are plotted as bold (black) points. The number of measurements is indicated by numerals. The relative position of the indicated points among the others, marked in Fig. 10 under the correspond—

…of \(S\), once again proves that the height of the surface irregularities \(t\) does not depend on the depth of cut. From Figs. 7–10 it is evident that, despite the scatter of individual points, the general arrangement of the latter for all values of \(v\) has a rectilinear character with an inclination toward the \(S\)-axis. The straight lines \(v=\mathrm{const}\), drawn through the points, express the dependence of the averaged values of \(H\) on the magnitude of the feed.

Fig. 9

The direction and slope of the straight lines show that:

1. With an increase in \(S\) (at \(v=\mathrm{const}\)), the irregularities \(H\) increase continuously, i.e., the surface quality deteriorates, and conversely.

Fig. 10

1. With an increase in cutting speed, the degree of influence of \(S\) on the surface quality decreases, and the more so, the higher \(v\) is.

This is clearly noticeable also from the profilograms (Figs. 11, 12), given as an example for \(v = 60\) and \(150\) m/min.

Consequently, the straight lines \(v = \mathrm{const}\), representing the lines of simultaneous influence of \(v\) and \(S\) on the value \(H\), can be expressed by the equation:

\[ H = C S^x \tag{1} \]

Here: \(C\) is the coefficient corresponding to the given \(v = \mathrm{const}\)

\[ \text{at } S = 1 \ \text{mm/rev}; \quad C = H \text{ in microns.} \]

\(x\) is the exponent of the influence of \(S\). It depends on the value \(v = \mathrm{const}\).

Numerically, \(x = \tg \alpha\), where \(\alpha\) is the angle of inclination of the line \(v = \mathrm{const}\) to the \(S\)-axis (Figs. 7–10).

Fig. 11

Fig. 12

The values of \(C\) and \(x\) for all cutting speeds indicated in Figs. 7–10 are given in Table 1.

Table 1

A visual representation of the influence of \(v\) and \(S\) on the value \(H\) is given by the diagram \(H\)–\(v\) (Fig. 13). Here each curve \(S = \mathrm{const}\) is drawn through the points—

as averaged values of \(H\), taken along the lines \(v=\mathrm{const}\) from Figs. 7–10. As an example, points are plotted only for the upper curve \(S=1\ \mathrm{mm/rev}\).

From the character of the curves \(S=\mathrm{const}\), over the entire range \(v=2\div 200\ \mathrm{m/min}\), three sharply expressed regions (zones) of the influence of cutting speed are noteworthy. In the first zone, from 2 to \(15\ \mathrm{m/min}\), as \(v\) increases (with \(S=\mathrm{const}\)) there is a rapid growth of irregularities, reaching a maximum at \(v=15\ \mathrm{m/min}\). In the second zone, from 15 to 150–160 \(\mathrm{m/min}\), the opposite phenomenon is observed. The greater \(v\) is, the smaller the irregularities are, and the higher the surface quality. In this case, the improvement of the surface proceeds more intensively for larger values of \(S\) than for smaller ones, as is evident from the following example.

\[ S=0.055;\quad \text{at } v=15,\ H=10\ \mu;\quad \text{at } v=150,\ H=5\ \mu \]

\[ S=1.000;\quad \text{at } v=15,\ H=110\ \mu;\quad \text{at } v=150,\ H=20\ \mu. \]

In the first case (\(S=0.055\)) the irregularities \(H\) decreased by a factor of 2, and in the second by a factor of 5.5.

In the third zone, \(v=150\text{–}200\ \mathrm{m/min}\), at a constant feed value, the irregularities \(H\), and consequently the surface finish, remain almost constant.

Fig. 13

Fig. 14

This is seen from the arrangement of the curves \(S=\mathrm{const}\) in Fig. 13 and from the relative position of the points for \(v=150\) and \(200\ \mathrm{m/min}\) in Figs. 9 and 10. To illustrate the character of the change in irregularities as a function of cutting speeds in the different zones, Fig. 14 shows profilograms of surfaces machined at \(S=0.306\ \mathrm{mm/rev}\) with different \(v\). Upon transition into the region \(v>200\ \mathrm{m/min}\), the surface quality at \(S=\mathrm{const}\) remains unchanged regardless of any further increase in cutting speed (Fig. 13).

The general picture of the change in surface irregularities with \(v\) and \(S\), presented in the diagram of Fig. 13, is briefly explained by the following causes:¹ Within the limits of the 1st zone, \(v\le 15\ \mathrm{m/min}\), \(H\) is affected by built-up edges on the tool and by leading cracks.

In the 2nd and 3rd zones, \(v=15\text{–}200\ \mathrm{m/min}\), built-up edges and deposits on the tool, and the phenomenon of shearing off the peaks of the irregularities by the chip itself. The latter occurs—

¹ Discussed in more detail in the following paper of the present collection.

decreases as a result of the transverse shrinkage of the chip (chip widening) and its work hardening.

The constancy of the value of \(H\) (at \(S=\mathrm{const}\)) beyond \(v>200\ \mathrm{m/min}\) is explained by the stability of chip shrinkage and of the cleanliness of the cut.

The \(H\)—\(S\) diagrams (Figs. 7–10) and \(H\)—\(v\) diagrams (Fig. 13) make it possible to choose graphically the cutting conditions for any combination of \(v\) and \(S\) within the range \(v=2\text{–}200\ \mathrm{m/min}\) and \(S=0.05\text{–}1\ \mathrm{mm/rev}\) when machining steel 5120.

An analogous expression of the dependence

The selection of a cutting condition that ensures the required surface finish (by the value of \(H\)) can also be carried out analytically from equation (1), if in the latter the functional dependence of \(x\) and \(C\) on cutting speed is established.

Using the data of Table 1, in Fig. 15 a curve (broken line) is plotted expressing the dependence \(x=f(v)\) within the range of variation of \(v\) from 2 to \(200\ \mathrm{m/min}\). From the nature of the slope of the straight sections it is evident that, within the 1st zone, \(v<15\ \mathrm{m/min}\), the value of \(x\) decreases more rapidly than in the 2nd zone, \(v=15\text{–}150\ \mathrm{m/min}\), and very slightly in the interval of the 3rd zone, \(v>150\ \mathrm{m/min}\).

Fig. 15

Consequently, the higher \(v\), the smaller \(x\), and the smaller the degree of influence of \(S\) on the magnitude of the irregularities \(H\). This is fully consistent also with the indications of the curves \(S=\mathrm{const}\) in Fig. 13.

The equation of the straight sections of the curve \(x=f(v)\) (Fig. 15) in general form is:

\[ x=q-av \tag{2} \]

The values of \(a\) and \(b\) for all three sections are indicated in Fig. 15. Substituting the values of \(a\) and \(b\) into equation (2), we obtain:

for the 1st zone, \(v\le 15\ \mathrm{m/min}\),

\[ x_1=0.925-0.007v; \tag{3} \]

for the 2nd zone, \(v=15\text{–}150\ \mathrm{m/min}\),

\[ x_2=0.862-0.00278v; \tag{4} \]

for the 3rd zone, \(v>150\ \mathrm{m/min}\),

\[ x_3=0.535-0.0006v. \tag{5} \]

The equations of two adjacent zones give one and the same value of \(x\) when the boundary values \(v=15\) or \(150\) are substituted.

The values of the coefficient \(C = H\), for \(S = 1\) (equation 1), are given in Table 1 for the individual values of \(v\) according to Figs. 7—10. The continuous variation of \(C\) under the influence of \(v\) (within the range from 2 to 200 m/min) is expressed in Fig. 13 by the upper curve \(S = 1\) mm/rev. From the course of the curve it is seen that the dependence \(C\) has a different character in each speed zone. To simplify matters, the determination of \(C = f(v)\) was carried out in parts, within the interval of each zone, for

Fig. 16

which purpose a summary diagram \(H—S\) (Fig. 16), constructed from the data of Figs. 7—10, was used. For clarity, not all lines \(v = \mathrm{const}\) are plotted in Fig. 16.

Fig. 16 shows that the lines \(v = \mathrm{const}\) for the 1st zone, \(v < 15\) m/min, converge at one point \(O_1\) (outside the limits of Fig. 16) with coordinates: \(H_0 = 960\) and \(S_0 = 14\); conversely, all lines \(v = \mathrm{const}\) for the 2nd and 3rd zones, \(v = 15—200\) m/min, diverge from the common pole \(O_2\), with coordinates \(H_0 = 2.7\ \mu\); \(S_0 = 0.0011\) mm/rev. The presence of the poles \(O_1\) and \(O_2\) makes it possible to write, for the entire range of \(v\) from 2 to 200 m/min, a single equation of the form:

\[ H = H_0 \left( \frac{S}{S_0} \right)^x, \tag{6} \]

Here: \(H_0\) and \(S_0\) are the coordinates of the pole points \(O_1\) or \(O_2\); \(x = f(v)\) is the variable exponent of \(S\) in equation (1), determined for the corresponding zone of \(v\) by equations (3, 4 and 5). From comparison of equations (1) and (6) we find:

\[ C = H_0 S_0^{-x} \tag{7} \]

Substituting the values of \(H_0\), \(S_0\), and \(x\) corresponding to the specified zones of \(v\), we have:

\[ \text{1st zone } v \leq 15;\quad H = 960\,(0.0714\,S)^{0.925 - 0.007v} \tag{8} \]

\[ \text{2nd zone } v = 15—150;\quad H = 2.7\,(91\,S)^{0.862 - 0.00278v} \tag{9} \]

\[ \text{3rd zone } v > 150;\quad H = 2.7\,(91 \tag{10} \]

where \(H\) is in microns, \(S\) in mm/rev, \(v\) in m/min.

Expressing the dependence \(H=f(v,S)\), equations (8, 9, and 10) make it possible to determine analytically the values of the roughness \(H\) of the machined surface when \(S\) and \(v\) vary over wide limits: \(S \leqslant 1\) mm/rev, \(v=2\div 200\) m/min and higher.

Table 2 gives the results of calculating \(C\) and \(x\) from equations (7) and (3, 4, 5) for the values of \(v\) used in the experiments.

Table 2

The agreement of the values of \(C\) and \(x\) from Table 2 with the corresponding experimental data from Table 1 confirms the correctness of the equations that have been set up.

Since the graphical method for solving the dependence \(H=f(v,S)\) is considerably simpler and faster than the analytical one, from equations (8–10) one can construct a ray diagram \(H\)—\(S\), similar to Fig. 16, with lines \(v=\mathrm{const}\) plotted at any intervals within the ranges: \(v \leqslant 15\); 15–150; and 150–200 m/min and higher.

Law of scatter of the experimental data

The value \(H\), determined from the diagrams in Figs. 7–10 or from equations (8–10), is a certain averaged value of the height of the roughness of the machined surface. As is shown by the location of the experimental points relative to the straight lines \(v=\mathrm{const}\) in Figs. 7–10, the actual height \(H_1\) may be somewhat greater or less than the averaged \(H\) by an amount \(\Delta H\), where

\[ \Delta H=\pm\left(\frac{H_1}{H}-1\right) \]

in fractions of \(H\).

From analysis and comparison of the experimental data it has been established:

1. The value \(\Delta H\) varies within the limits from 0 to \(\pm 0.5\).
2. In the total set of experimental data, the values of \(\Delta H\) are distributed by sign (\(+\) or \(-\)) almost uniformly (\(+51.7\%\) and \(-48.3\%\) out of 100%).
3. No sharply expressed difference has been found in the influence of \(v\), \(S\), and \(t\) on the limits and the law of variation of \(\pm \Delta H\).

Consequently, it may be assumed that the scatter of the actual \(H_1\) was obtained chiefly through the influence of random causes: unavoidable errors in the tool geometry in plan \((r,\varphi_1)\) during sharpening and mounting in the tool post; fluctuations in the value of \(v\) in repeated experiments (Figs. 7–10); changes in the degree of sharpness of the cutting edges of the tools, etc.

The curve in Fig. 17 shows what number of measurements (experiments) \(N\), in % of the possible 100%, contains a given value of \(\pm\Delta H\), varying from 0 to \(\pm\Delta H_i\), where \(\Delta H_i\) is any value of \(\Delta H\) within the limits from 0 to \(\pm 0.5\).

For example: \(\pm\Delta H=0\) constitutes \(N=7.5\%\) out of 100%,

\[ \begin{array}{cccccc} & 0\div 0.05 & & & 31.5 & \\ & 0\div 0.1 & & & 56.0 & \end{array} \]

etc.

The inflection of the curve shows that all values \(\pm \Delta H = 0 \div 0.12\) constitute 65% of the cases out of 100% of possible measurements, while the values \(\pm \Delta H = 0.12 \div 0.5\) fall within 35%, i.e., make up the smaller share. On

Fig. 17

the basis of this it is possible to take, as a correction to the averaged height \(H\), the value \(\Delta H = \pm 0.12\).

Consequently, the most probable actual height of the irregularities is

\[ H_1 = (1 \pm 0.12)H \tag{11} \]

and equation (6) for the dependence \(H = f(v,S)\) assumes the final form:

\[ H_1 = (1 \pm 0.12)H_0\left(\frac{S}{S_0}\right)^x . \tag{12} \]

Control Experiments

The special feature of the diagram in Fig. 16 consists in the formation of a pole point \(O_2\) with coordinates: \(H_0 = 2.7\,\mu\) and \(S = 0.011\ \text{mm/rev}\). Being the geometric locus of the intersections of the straight lines \(v = \text{const}\), the point \(O_2\) has not only mathematical significance for substantiating dependence (6), but it also possesses a definite physical property, the essence of which is as follows.

When machining with feed \(S = 0.011\ \text{mm/rev}\), the magnitude of the irregularities \(H = 2.7\,\mu\) remains constant, regardless of the change in \(v\) within the range from 15 to 200 m/min and higher.

Because of this property, the point \(O_2\) may be called the “critical point,” and correspondingly \(S_0 = 0.011\ \text{mm/rev}\) the “critical feed,” and the height

of the roughnesses \(H_0 = 2.7\,\mu\)—the “critical roughness.” The formation of the “critical roughness” (and feed) is clearly seen from Fig. 13 in the smoothing of the bends of the curves \(S=\text{const}\) at \(v=15\ \text{m/min}\). The smaller \(S\) is, the smaller the bend of the curve, and consequently the smaller the effect of \(v\) on the height of the roughnesses \(H\). Obviously, by decreasing \(S\), one can select such a value of it that, for any value of \(v\), the surface finish (roughnesses \(H\)) will remain unchanged.

To check the coordinates of the “critical point” \(O_2\), a series of experiments was carried out—with constant \(S=0.011\ \text{mm/rev},^{1)}\) but with different \(v=5, 15, 60, 105, 150\ \text{m/min}\), at \(t=0.4\ \text{mm}\).

The results of the experiments are shown in Fig. 13 (lower line). The straight line drawn through the points corresponds to a constant roughness height \(H=3\,\mu\), which is greater than the theoretical value \((H_0=2.7\,\mu)\) by only \(0.3\,\mu\). Such agreement of the experimental data with the theoretical data is sufficient proof of the correctness of the assumption set forth above concerning the property of the “critical point” \(O_2\).

In addition, the experiments show that at \(S=0.011\ \text{mm/rev}\) the cutting speed \(v=15\ \text{m/min}\) does not have a harmful effect on the surface quality, and the roughness height \(H\approx 3\,\mu\) remains constant for \(v>15\ \text{m/min}\). This is evidenced not only by the position of the experimental points in Fig. 13, but also by the arrangement of the straight lines \(v=\text{const}\) (Fig. 16) for \(v\leq 15\ \text{m/min}\), as well as by the character of the profilograms in Fig. 18.

\(S=0.011\ \text{mm/rev}\), \(M=1000:1\)

\(v=5\ \text{m/min}\)

\(v=15\ \text{m/min}\)

\(v=60\ \text{m/min}\)

\(v=105\ \text{m/min}\)

\(v=150\ \text{m/min}\)

Fig. 18

On the basis of the evidence presented, it follows:

1. Independently of changes in \(v\) from 2 to 200 m/min and higher, the “critical height” of the roughnesses \(H_0=2.7\,\mu\) at \(S_0=0.011\ \text{mm/rev}\) is a constant quantity and corresponds to the highest quality of surface finish attainable in machining steel 5120 in the absence of lubrication, cooling, and vibration.

2. In the general case, the coordinates of the “critical point” \(O_2\) must depend on:

a) the physical properties of the material being machined,
b) the cutting angle and the degree of sharpness of the cutter blade,
c) the working conditions (with or without coolant).

1. The “critical height” of the roughnesses \(H_0=2.7\,\mu\) does not depend on the geometry of the cutter in plan \((r,\ \varphi,\ \varphi_1)\) when \(r\geq 0.1\ \text{mm}\), since at \(S_0=0.011\ \text{mm/rev}\) and \(r\geq 0.1\ \text{mm}\) the length of the arc of contact of the cutter tip with the machined surface is practically equal to the chord, and the rounded cutter works similarly to a cutter with a broad blade at \(\varphi_1=0^\circ\).

2. With a decrease in \(S<S_0\), the magnitude of the roughnesses \(H\) remains unchanged and equal to \(H_0\).

For the purpose of an additional check of the coordinates \((H_0\) and \(S_0)\) of the “critical point” \(O_2\) and of equation (6), two series of experiments were carried out at \(v=40\) and \(80\ \text{m/min}\) with different \(S\).

The results of the experiment are presented in Fig. 16, where the positions of the corresponding lines \(v=\text{const}\) (40 and 80 m/min) had been determined in advance analytically from equation (6).

\(^{1)}\) For this purpose, a special set of gears was installed in the lathe gearbox.

The location of the experimental points (Fig. 14) relative to the theoretical straight lines \(v=\mathrm{const}\) in both cases proves the practical suitability of the constructed relation (6) and confirms the invariance of the coordinates of the “critical point” \(O_2\): \(H_0=2.7\ \mu\); \(S_0=0.011\ \mathrm{mm/rev}\).

Conclusion

1. A wide range of variation of the components of the cutting conditions \((S=0.01—1.0\ \mathrm{mm/rev},\ t=0.1—3\ \mathrm{mm},\ v=2—200\ \mathrm{m/min})\) made it possible to cover in the investigation both the region of fine (diamond) turning and the region of rough finishing of steel 5120.

2. It has been established and confirmed that, when machining rigid (stable) workpieces in the absence of chatter, variation of the depth of cut from \(0.1\) to \(3\ \mathrm{mm}\) does not have a noticeable effect on surface finish.

3. For a given tool geometry, the cutting speed and feed actively affect the magnitude of the irregularities \(H\). Changing \(S\) from \(0.011\) to \(1\ \mathrm{mm/min}\) and \(v\) from \(2\) to \(200\ \mathrm{m/min}\) causes the value of \(H\) to fluctuate from \(3\) to \(120\) microns, i.e., by a factor of 40.

4. With an increase of \(S>0.011\ \mathrm{mm/rev}\), the magnitude of the irregularities \(H\) increases, and the faster in relative terms, the smaller \(v\) is.

5. At \(S<0.011\ \mathrm{mm/rev}\), regardless of the magnitude and the tool geometry in plan (for \(r\ge 0.1\ \mathrm{mm}\)), the magnitude of the irregularities \(H\cong 3\ \mu\) remains constant and corresponds to the highest quality of surface finish attainable in turning steel 5120 without coolant.

6. According to the nature of its influence on the magnitude \(H\), the range \(v=2—200\ \mathrm{m/min}\) is divided into 3 zones: \(v\le 15\); \(v=15—150\), and \(v=150—200\ \mathrm{m/min}\).

7. For all values \(S>0.01\ \mathrm{mm/rev}\), the greatest magnitude of irregularities \(H\) (the poorest surface quality) is obtained at \(v=15\ \mathrm{m/min}\)¹; the smallest is obtained at \(v=150—200\ \mathrm{m/min}\). In the region of small feeds the latter is also attainable when working with \(v<2\ \mathrm{m/min}\).

8. With an increase of \(v>200\ \mathrm{m/min}\), the value \(H\) remains constant (at \(S=\mathrm{const}\)).

9. The selection of a rational cutting condition for finish turning of steel 5120 may be carried out either analytically, by equation (6), or graphically, from the diagrams in Figs. 13 and 16.

10. The most probable height of the irregularities that may occur under a given cutting condition is determined by equation (12).

11. In order to increase productivity while leaving the surface quality unchanged (in terms of the value \(H\)), one should work (within \(v=2—200\ \mathrm{m/min}\)) with the larger \(S\), the correspondingly higher the chosen \(v\).

12. When passing into the region \(v>200\ \mathrm{m/min}\) (at \(H=\mathrm{const}\)), a further increase in productivity proceeds only at the expense of \(v\).

¹ More precisely—the smaller \(S\) is, the somewhat greater \(v\) is, and vice versa.

Noted Misprints