ON BUILT-UP EDGE FORMATION ON A CUTTING TOOL WITH A SHORTENED RAKE FACE

M. F. Poletika

(Presented by Prof. Dr. A. M. Rozenberg)

Cutting tools with a shortened rake face, or, what is the same thing, tools with a chamfer on the rake face, are used quite widely in industrial practice, since they exhibit higher durability than ordinary tools. At the same time, an artificial change in the length of the rake face is a very valuable method for investigating contact phenomena on the rake face, a method that has been used by many researchers [1, 2, 3].

A study of the process of cutting steel with chamfered tools, carried out in the cutting laboratory of the TPI by the author [4, 5, 6] and, independently of him, by M. I. Klushin in the city of Gorky [7, 8], showed that, with a small rake angle on the chamfer ($-10^\circ \div +20^\circ$), operation of a chamfered tool is necessarily accompanied by the formation of a built-up edge, which does not disappear either at microspeeds (less than $0.1 \div 0.5$ m/min) or at cutting speeds of 300–400 m/min. As is known, under such conditions a built-up edge is never observed on an ordinary tool. The constant presence of a built-up edge changes the usual character of the dependence of the cutting force and shrinkage on cutting speed. Instead of the typical hump-shaped curves, here we observe a monotonic, smooth decrease in chip shrinkage and in all components of the cutting force with increasing speed.

The stability of the built-up edge on a tool with a shortened rake face is explained by the fact that the presence of the chamfer makes such a tool similar to a punch, while the cutting process at microspeed resembles the process of a punch penetrating into metal. The stagnant zone that necessarily arises in front of the punch, with continuous motion of the tool, turns into a built-up edge; moreover, the configuration and conditions of existence of the built-up edge in this case no longer depend on friction on the chamfer on which it rests. As our investigations, performed by microscopic and metallographic methods, as well as Klushin’s investigations (cinematographic method), show, such features of the built-up edge on a chamfered tool are preserved even at high cutting speeds, hundreds of times exceeding the punch penetration speeds customary for mechanical tests.

Below we shall dwell on certain features of the process of built-up edge formation on a chamfered tool and on the influence of cutting factors on this process.

Mechanism of Built-Up Edge Formation and Its Configuration

Observations of the process of built-up edge formation on a tool with a shortened rake face during cutting at very low speeds [4, 6] showed that the built-up edge on a chamfered tool is formed from the stagnation zone immediately as the tool penetrates the metal, but it has no clear outlines. As the tool advances further, the built-up edge either breaks down, or shifts as a whole and leaves with the chip, but it is immediately replaced by a new built-up edge, etc. One phase of this continuous process can be seen in Fig. 1, which is a photograph of the side of the cutting zone, taken through a microscope during free planing of steel 20. The photograph records precisely the moment when the contours of the built-up edge have appeared and it, without having separated from the chip, has already begun to shift together with it along the chamfer.

Fig. 1.

The most correct way to represent the process of continuous formation and detachment of a built-up edge on a chamfered tool at microspeeds is as follows. The stagnation zone, arising under the pressure of the tool on the material being machined, subsequently moves together with the tool. The front edge of this zone is the front of a wave of very deep plastic deformation propagating ahead of the tool, in which compression predominates. Built-up edges are formed from the material of the stagnation zone with a certain periodicity; as a result, its volume changes continuously, increasing before separation of the built-up edge and decreasing after its separation.

As the cutting speed increases, the frequency of appearance and detachment of the built-up edge increases, but the nature of its destruction changes somewhat. Only the tip of the built-up edge is destroyed and carried away with the chip, while its base remains stable for a certain period of time. With a further increase in cutting speed, and at comparatively small absolute values of it (on the order of several meters per minute when cutting mild steel with a tool whose chamfer rake angle is \(0^\circ\)), the built-up edge becomes so stabilized that its detachments, which may involve both the tip of the built-up edge and the entire built-up edge, occur only rarely and are apparently caused by random factors.

Figure 2 presents a microphotograph of the cutting zone for the case of turning medium-hardness steel with a chamfered tool at a cutting speed of \(40\ \text{m/min}\). It is evident from it that the built-up edge is clearly separated from the undeformed material of the workpiece. The boundary between the built-up edge and the chip, on the contrary, is not clear along its entire length. In the regions adjoining the tip of the built-up edge, the strongly deformed layers of the built-up edge smoothly pass into the textured contact zone of the chip. Discontinuities are not noticeable here. A continuous process of plastic flow takes place.

The microphotograph shown illustrates a case of “free” chip flow, when the built-up edge completely covers the chamfer surface but does not extend onto the rake face beyond the chamfer. Under these conditions the tool contacts only the built-up edge, and the latter is as if a continuation of the tool body. Moving ahead of the tool, the built-up edge separates

the chip and deforms it through its entire thickness, that is, it exerts the same action as an ordinary tool. At the same time, however, the blunt tip of the built-up edge causes deep local deformation of the underlying layers. Ahead of the built-up edge there moves a zone that is small in volume but strongly textured. The material of this zone is partly spent on replenishing the tip of the built-up edge, and partly passes into the contact layer of the chip. The continuous growth of the tip of the built-up edge is compensated by the tearing away of its portions adjoining the chip and the machined surface, and also by the continuous squeezing-out of material from beneath the base of the built-up edge, which

Fig. 2.

leads to the appearance of a secondary chip resembling a burr. In addition, sometimes the built-up edge in its middle part extends onto the rake face beyond the chamfer, forming peculiar tongues that are periodically removed by the chip.

Thus, despite the relatively high stability of the built-up edge on a tool with a chamfer, here too it continuously changes its configuration; consequently, the experimentally obtained values of the chip-flow angle, its shrinkage, and other cutting parameters correspond to certain averaged dimensions and to the shape of the built-up edge. However, the fluctuations in the shape and dimensions of the built-up edge under the given cutting conditions on a tool with a chamfer are considerably smaller than on an ordinary tool.

Since the built-up edge is replenished with material only through the growth of its tip, while losing it to a considerable extent through the secondary chip and the “tongues” formed from the layers adjoining the chamfer surface, a slow displacement of layers takes place inside the built-up edge in the direction from the tip toward the base. As they move, the layers undergo additional deformation, which is clearly visible in Fig. 2: in passing from the tip to the base of the built-up edge the texture becomes increasingly dense. The degree of deformation of the contact layers of the built-up edge on the chamfer, judging from the texture, is extremely high. Our measurement of microhardness in the cutting zone (6) showed that under these conditions, with

of the initial microhardness of the steel (p. 30), \(H_{\text{p}} = 126\); the average microhardness of the chip is 268, the average hardness of the built-up edge is 357, and the hardness of the contact layer of the built-up edge reaches 500, i.e., it exceeds the average hardness of the built-up edge by 1.4 times and the hardness of the chip by almost two times. This indicates an extremely high strengthening of the contact layers of the built-up edge and, consequently, confirms the assumption of a high degree of their deformation.

Chip flow angle and chip shrinkage

When cutting with a conventional tool, the chip slides along the rake face of the tool; in the presence of a built-up edge, it first comes into contact with the built-up edge, after which it continues its motion along the rake face. A different picture is observed on a tool with a shortened rake face. On this tool the chip does not touch the rake face beyond the chamfer, if one does not count the edges of their intersection, where contact does occur. When a built-up edge is present on such a tool, the chip comes into contact only with it, and the direction of its flow (in the principal cutting plane) is determined by the geometry of the built-up edge. We have, so to speak, a natural (free) chip flow. During the cutting process the chip flow angle oscillates continuously within certain limits, but its average value for the given cutting conditions remains quite definite.

Fig. 3.

The chip flow angle (Fig. 3) is a function of the cutting speed, decreasing slightly as the latter increases. It is influenced much more strongly by the ratio between the width of the tool chamfer and the uncut chip thickness. With an increase in the ratio \(a/f\), where \(a\) is the uncut chip thickness and \(f\) is the chamfer width, the chip flow angle increases—at first rapidly, and then somewhat more slowly—as illustrated by Fig. 4, which shows the results of measurements of the chip flow angle when machining mild steel.

The degree of chip deformation, despite the blunt apex of the built-up edge, is very small. The shrinkage here is much less than when cutting with a conventional tool. At the same time, as the cutting speed increases, as can be seen in Fig. 5, chip shrinkage decreases smoothly, but so slightly that it may practically be considered constant.

Of greatest interest is the circumstance that the chip shrinkage proves to be the same for all three steels investigated, with a hardness range of \(H_B = 114 \div 240\), although the flow angle when machining the hardest steel is \(10^\circ\) smaller than for the mild steel. Particularly convincing in this respect is the graph of chip shrinkage versus the parameter \(a/f\) (Fig. 6), on which, in addition to our data, the results of M. I. Klushin’s experiments on steel 08 and on copper M2 are also plotted. In interpreting the results of Klushin’s experiments, the difference in chip widening was taken into account, since Klushin carried out the experiments under free cutting conditions, whereas we did so under non-

free. The degree of chip deformation when cutting with a chamfered tool proves to be the same even for metals so different in their mechanical properties as hard steel and copper. Meanwhile, when cutting the same metals with a conventional tool, the chip contraction is not the same and differs very substantially. Thus, according to the data of A. N. Eremin [9] and N. N. Zorev [1], at a rake angle of the tool \(\gamma = 20^\circ\) and at a high cutting speed corresponding to the sloping portion of the typical hump-shaped curve of chip contraction versus cutting speed,

Fig. 4.

Fig. 5.

when the contraction is approximately constant, it is equal to 1.95 for medium-hard steel (steel 40), 2.8 for mild steel (steel 20), and 4.5 for copper.

Thus, if the direction of chip flow is prescribed forcibly (a “normal” tool), the magnitude of chip contraction in a strong

degree depends on the material being machined. If, however, free chip flow is ensured (a tool with a shortened rake face), then the chip compression is constant for all materials being machined. It may be assumed that on a tool with a land the built-up edge always assumes such a configuration as corresponds to the minimum possible, under the given conditions, degree of deformation of the metal in the chip. Consequently, the minimum chip compression is the same for all metals and is determined only by the geometrical factor: the ratio of the thickness of the cut to the width of the tool land.

Fig. 6.

Cutting force on a tool with a land

The displacement of the built-up edge relative to the material being machined gives rise to resistance. The specific forces arising in this case are distributed along the contour of the blunt apex of the built-up edge and over the contact surface between the built-up edge and the chip approximately as shown in Fig. 7.

Part of these forces in the region of the apex of the built-up edge is mutually balanced; the remaining, predominant part is balanced by the forces \(P_z\) and \(P_x\) on the tool land. The cutting force is measured with a dynamometer, which, obviously, will record the resultant forces on the land. It does not appear possible here to determine the forces acting in the cutting zone.

Fig. 8 gives the results of measuring the components of the cutting force \(P_x\), \(P_y\), and \(P_z\) as functions of the thickness of the cut at a constant land width for the case of machining mild steel. In considering this graph, two facts attract attention: the comparatively large values of the force \(P_x\) and the unusual law of variation of this force. At first it increases, and with further growth of the thickness of the cut it begins to decrease smoothly. Both of these circumstances are explained by the peculiar role of the forces acting on the built-up edge from the side of the cutting surface—the forces “on the rear face of the built-up edge.”

On an ordinary tool, the forces on the rear face are small, and at the very large values of the chip-flow angle that we observe on a tool with a land, the force \(P_x\) on a normal tool is very small, or even negative. On a tool with a land this force is always positive and reaches rather high values, since the forces “on the rear face of the built-up edge” are very large.

Klyushin has examined in detail the process of transition from splitting to cutting. The moment of transition from splitting to cutting, as Klyushin correctly notes, must be characterized by the propagation of shear deformation through the entire thickness of the layer being removed. Continuing this reasoning further, we shall have to conclude that approximately this same moment corresponds to the appearance of a lateral force, i.e., the force \(P_x\). In the process of splitting the deformation is symmetrical

Fig. 7.

Fig. 8.

and this force is absent. As the transition to cutting proceeds further (for which it is necessary to reduce the ratio \(a/f\)), the force \(P_x\) will increase, as we see in Fig. 7. And only at small values of the thickness of cut, when the built-up edge decreases and the cutting conditions approach nor-

small, the force \(P_x\) begins to decrease with decreasing chip thickness, as it should.

The descending segment of the curve of the dependence of the force \(P_x\) on the ratio \(a/f\) is close to a straight line. Extending it to its intersection with the horizontal axis, we find the value of the ratio \(a/f\) corresponding to the transition from cutting to splitting. For steel 20 this value is approximately equal to 4; for ShKh15 steel it is half as large.

The cutting-force measurement data make it possible to calculate the normal and tangential specific forces on the contact surface of the built-up edge with the chamfer. As follows from Table 1, calculated for the case of operation of a tool with a chamfer width \(f = 0.6\) mm and a rake angle on the chamfer \(\gamma_\phi = 0^\circ\), the normal pressures on the chamfer are extremely high and increase continuously as the ratio \(a/f\) increases. The tangential specific forces are also considerably greater than on the rake face of an ordinary tool. All this is consistent with the high degree of deformation of the lower layers of the built-up edge and is explained by the fact that the comparatively large forces arising during deformation of thick cut layers are here necessarily distributed over the limited area of the chamfer.

Table 1

Let us idealize the scheme of the chip-formation process on a tool with a chamfer as shown in Fig. 9, that is, let us replace the actual contours of the built-up edge by a right triangle. Suppose further that the built-up edge is rigidly connected with the tool and that the forces “on the rear face of the built-up edge” are not transmitted into the cutting zone. Then, by the usual method, one may consider the equilibrium of a chip element and write the following equations of static equilibrium:

\[ \Sigma Z = N_\gamma \cos \gamma_0 + F_\gamma \sin \gamma_0 - N_\beta \sin \beta - F_\beta \cos \beta = 0; \]

\[ \Sigma X = N_\gamma \sin \gamma_0 - F_\gamma \cos \gamma_0 + N_\beta \cos \beta - F_\beta \sin \beta = 0; \]

\[ \Sigma M_A = N_\beta ml - N_\gamma nc = 0, \]

where \(N_\beta\) and \(F_\beta\) denote the normal and tangential forces in the shear plane, and \(N_\gamma\) and \(F_\gamma\) the forces on the contact surface of the chip

with the built-up edge; by \(l\) and \(c\), respectively, the length of the shear plane and the length of the chip contact surface; and, finally, by \(m\) and \(n\), the relative distances of the points of application of the normal forces from the apex of the built-up edge.

Obviously, one may take \(m=0.5\). Further, one may substitute:

\[ l=\frac{a}{\sin\beta} \]

and

\[ c=\frac{f}{\cos\gamma_0}. \]

Finally, on the basis of experimental data, we shall also take the shear angle to be equal to the chip-flow angle: \(\beta=\gamma_0\). Experiments show that this condition is satisfied with an accuracy of \(\pm 5^\circ\), and for an approximate estimate of the interrelation between the parameters of the chip-formation process it may be accepted.

Fig. 9.

Taking all these restrictions into account, we obtain:

\[ N_{\gamma}=F_{\beta}; \qquad F_{\gamma}=N_{\beta}; \qquad N_{\beta}a\cos\gamma_0-2N_{\gamma}nf\sin\gamma_0=0, \]

whence

\[ \tg\gamma_0= \frac{1}{2n}\cdot\frac{a}{f}\cdot\frac{F_{\gamma}}{N_{\gamma}} = \frac{1}{2n}\cdot\frac{a}{f}\cdot\mu_{\gamma}. \]

In the last formula, \(\mu_{\gamma}\) is the “coefficient of friction” of the chip against the built-up edge, i.e., a certain conditional quantity determining the ratio of the normal and tangential forces on the contact surface of the chip with the built-up edge.

Since along the entire, or almost the entire, contact surface there occurs plastic flow passing into fracture, it may be considered that the tangential stress on this surface, in contrast to the contact zone of an ordinary tool, is approximately constant at all points and is equal to the shear strength limit of the material being machined. Then the tangential force \(F_{\gamma}\) must be proportional to the length \(c\) of the contact surface and, consequently, must increase with the growth of the ratio \(a/f\) and of the chip-flow angle. And since the normal force \(N_{\gamma}\) will also increase in this case, for the chip thickness \(a\) increases (Fig. 8), the coefficient \(\mu_{\gamma}\) should ultimately change only slightly.

Taking in the last formula \(\mu_\gamma = \mathrm{const}\) and \(n = \mathrm{const}\) and substituting \(\dfrac{1}{2n}\mu_\gamma = B\), we obtain: \(\operatorname{tg}\gamma_0 = B\dfrac{a}{f}\), that is, the tangent of the chip-flow angle is proportional to the parameter \(a/f\). This relation, derived from the equilibrium condition for a chip element, is qualitatively fully confirmed by the experiments (Fig. 4), but it cannot be used for quantitative calculations, chiefly because the derivation did not take into account the forces acting on the built-up edge from the side of the cutting surface.

Conclusions

1. The built-up edge on a cutter with a shortened rake face is characterized by high stability; at the same time, however, a continuous exchange of material takes place between the built-up edge and the surrounding media.

2. In the built-up edge, especially in its layers adjacent to the cutter, high pressure prevails; these layers are extremely strongly deformed and have increased microhardness.

3. The chip shrinkage when cutting with a chamfered cutter does not depend on the material being machined, but is determined only by the parameter \(a/f\).

4. The direction of chip flow (the flow angle) is determined by the equilibrium conditions of a chip element and, in this connection, is a function of the parameter \(a/f\).

In conclusion, it should be noted that the use of a chamfered cutter for investigating contact phenomena on the rake face is legitimate only under conditions in which there is no built-up edge, that is, for a definite combination of the parameters \(\gamma_\phi\) and \(a/f\), which is not taken into account in all of the cited studies [1, 2, 3].

REFERENCES

1. Zorev N. N. Problems in the mechanics of the metal-cutting process. Mashgiz, 1956.

2. Takeyama N. — The effect of tool–chip contact area in metal machining. — “Paper Amer. Soc. Mech. Engrs.,” No. A--45, 1957.

3. Chao B. T., Trigger K. G. — Controlled contact cutting tools. — “Paper Amer. Soc. Mech. Engrs.,” No. SA--42, 1958.

4. Poletika M. F. Investigation of the cutting process with a tool having a double rake face. Tomsk, 1959.

5. Rozenberg A. M., Poletika M. F. Features of the cutting process with a chamfered tool in high-speed turning. Izvestiya TPI, vol. 75, 1954.

6. Poletika M. F. Microstructure and microhardness in the cutting zone when working with a chamfered cutter. Izvestiya TPI, vol. 85, 1957.

7. Klushin M. I. New investigations of the metal-cutting process. “Stanki i instrument,” No. 1, 1947.

8. Klushin M. I. Metal Cutting. Mashgiz, 1958.

9. Eremin A. N. The physical essence of phenomena in the cutting of steel. Mashgiz, 1951.