PROCEEDINGS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR POLYTECHNIC
INSTITUTE named after S. M. KIROV

Vol. 133 1965

CONTACT PHENOMENA IN METAL CUTTING

M. F. POLETIKA

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

The processes occurring in the zone of contact between the chip and the cutter play a decisive role in cutting. The contact zone is, in essence, the channel through which such most important factors as cutting temperature, the properties of the cutting-tool material, the properties of the medium, etc., act on the chip-formation process. The conditions in the contact zone determine the character and intensity of tool wear.

With the aim of studying the features of contact phenomena on the rake face of the cutter in connection with the process of chip formation when cutting various metals, we carried out investigations with 14 work materials. In the experiments all the principal characteristics of chip formation were measured: chip shrinkage, cutting temperature, the length of contact between the chip and the cutter, and cutting force. From the experimental data, the average contact stresses in cutting, the stresses in the shear zone, and other quantities were calculated. Some results of these experiments are presented below.

Figure 1 shows the dependence of chip shrinkage on cutting speed when machining various metals in the region of relatively high cutting speeds. We see that the decrease in shrinkage with increasing speed is a general law, valid for all the metals investigated. However, the intensity of this decrease, as well as the absolute magnitude of shrinkage for different work materials, is far from the same. Moreover, as can be seen from the same Fig. 1, shrinkage is determined not only by the mechanical properties of the work material, but also by other factors. Thus, for example, the chip shrinkage in cutting commercially pure titanium (VT1) and cadmium is approximately the same, although in their mechanical properties these metals differ greatly from one another.

The length of contact between the chip and the cutter as a function of cutting speed changes analogously to chip shrinkage. There must be a close connection between these most important parameters of chip formation, which follows logically already from the condition of equilibrium of the moments of the forces in the cutting zone, obtained by N. N. Zorev [1], and is confirmed by our theoretical and experimental investigations.

The existence of such a connection is illustrated by Fig. 2, in which the relative contact length $c/a$ is presented as a function of chip shrinkage. A cursory glance at this graph suggests the idea of a uni-

Fig. 1.

Vertical axis: Chip shrinkage

Horizontal axis: Cutting speed, m/min

Legend: Work material

• ■ — Brass L62
• △ — Annealed copper
• ♦ — St 10
• ✛ — Armco iron
• □ — Aluminum alloy D1
• ◭ — Lead
• ◊ — Annealed St 12KhN3
• ● — Annealed St 9KhS
• ▲ — Cadmium
• ○ — Tin
• × — Titanium alloy VT-1

Fig. 2.

Vertical axis: %

Horizontal axis: \(\xi_a\)

Legend: Work material

• ● — Armco iron, \(\gamma = 10^\circ\)
• ○ — Steel 12KhN3, \(\gamma = -10^\circ, 0^\circ, 10^\circ, 20^\circ\)
• ♙ — Steel U12 (annealed), \(\gamma = 10^\circ\)
• △ — Copper M, VT2 tool, \(\gamma = 25^\circ\)
• ◭ — Copper M, BrB2 tool, \(\gamma = 25^\circ\)
• ▲ — Copper V, R9 tool, \(\gamma = 10^\circ\)
• × — Bronze BrB2, \(HB = 110\), \(\gamma = 10^\circ\)
• • — Bronze BrB2, \(HB = 200\), \(\gamma = 10^\circ\)
• ◐ — Bronze BrB2, \(HB = 320\), \(\gamma = 10^\circ\)

significant relationship between the value of \(c/a\) and shrinkage, especially since the scatter of the experimental points is explained to a considerable extent by the inaccuracy of the method we used for measuring the contact length (from the visible wear mark on the rake face).

A more careful analysis shows, however, that this is not so, and that the dependence obtained can be considered unambiguous only as a very rough approximation. The curves \(c/a=f(\zeta)\) for different machined materials and cutting conditions do not coincide, and the reason for their noncoincidence lies in the absence of an unambiguous relationship between the shear-plane angle \((\beta_1)\) and the angle of action \((\omega)\), which determines the position of the resultant force on the rake face.

Figure 3 gives some results of an investigation of the mean tangential contact stress (specific friction force) \(q_F\) in the cutting process. They further convince us that

Fig. 3.

the constancy of the value \(q_F\), first discovered by N. N. Zorev in the cutting of steels [1] and confirmed by our other experiments for some nonferrous metals, is a sufficiently general law of the chip-formation process.

We found a different regularity for the specific friction force only for titanium alloys [2]; moreover, the possibility is not excluded that the decrease in \(q_F\) observed in this case with increasing cutting speed is a consequence of the imperfection of the adopted method for measuring the contact length. When titanium alloys are cut, the wear mark on the rake face increases rapidly immediately after the tool enters the cut, and at high cutting speeds, despite the short duration of the experiment, we obtain overestimated values of the contact length.

For different machined materials the magnitude of the contact stress \(q_F\) is not the same. From an analysis of Fig. 4, where the dependence of this stress on the actual ultimate strength of the machined metal is presented, it is not difficult to conclude that the mechanical properties of the machined material play here the role, if not of the only, then in any case of the principal determining factor.

We shall show that this interrelation is not accidental, but is due to the specific features of the contact between the chip and the tool.

It has been proved by numerous studies that the contact zone on the rake face consists of two regions: a plastic region and an elastic region. Within the first of these, the contact layer of the chip undergoes deep plastic deformation. Within the second, elastic deformations predominate, while plastic deformations are localized in surface asperities and seizure points; that is, phenomena typical of dry friction are observed.

It is natural to suppose that in the region of plastic contact, where the strongly deformed chip material receives additional deformation over the thickness of the contact layer, the tangential contact stress is either approximately constant along the entire length of the plastic region (strain hardening is insignificant), or increases somewhat with distance from the cutting edge (owing to strain hardening).

Fig. 4.

In the region of elastic contact, the tangential stress decreases continuously and smoothly to zero at the point where the chip separates from the tool.

The assumption made is confirmed by the results of studies of the stress distribution on the contact area of the tool, carried out by various methods, including our results obtained by the photoelastic-polarization method [3].

Consequently, the average tangential contact stress must be determined by the magnitude of the tangential stress in the plastic region and by the ratio between the length of this region and the total contact length. Since this ratio, depending on the cutting conditions, varies within comparatively narrow limits (this has been proved experimentally), there must be a definite relation between the average contact stress \(q_F\)

and the tangential stress \(\tau_1\) (also average) on the plastic region there must exist a proportional relation.

The magnitude \(\tau_1\), in turn, is a function of the mechanical properties of the material being machined and of the degree of its hardening in the contact layer. Since the degree of deformation here is extremely high and the hardening is close to the limiting value, the principal factor affecting the contact tangential stress must be the strength of the material being machined, which is also confirmed by the graph in Fig. 4.

In the chain of reasoning presented, two of the most important factors of chip formation are absent: cutting speed as the rate of deformation, and the average contact temperature. As regards the first of these, the work of A. M. Rozenberg and A. N. Eremin has shown the insignificance of its effect on stresses at ordinary cutting speeds for most metals [4]. Concerning the influence of the average contact temperature on the contact stresses, there is no consensus in the literature. Some believe that, as the speed increases, the material in the contact zone should soften. Others assume that, owing to the short time for which particles of the contact layer remain within this zone, the softening process will not have time to occur. It seems to us that the results we obtained experimentally confirm the second point of view.

Since, for a given material being machined, the specific friction force on the rake face does not depend on the cutting conditions, remaining constant over a wide range of their variation, the average coefficient of friction of the chip on the tool is a function of the average contact pressure on the rake face and does not have the meaning of a physical constant. The specificity of the concept of the coefficient of friction in cutting has repeatedly been pointed out in the literature [1, 8]. Our investigations [5, 6, 7] speak of the same thing with complete conviction.

Despite the obviousness of these considerations for most investigators, in the existing schemes explaining the interrelation of the factors of chip formation, the average coefficient of friction on the rake face still plays the role of the principal controlling factor. It seems to us that the experimental material accumulated to date is sufficient to advance certain new assumptions in this regard and thereby to introduce the necessary changes into the scheme of interaction of factors in cutting, eliminating from it the coefficient of friction as a certain independent factor.

To do this, let us turn to the scheme of chip formation (Fig. 5) and consider the phenomena occurring in the region of plastic contact. Near the cutting edge, newly formed (juvenile) surface layers of the chip enter onto the rake face of the tool. The very high normal pressure at this point ensures the plastic state of the contact layer and, consequently, a high contact density, and prevents particles of the surrounding medium from penetrating onto the contact surface. Here seizure of the contacting surfaces develops fully, impeding further advance of the chip.

The continuity of the process, however, does not allow the chip to be held up. But its further displacement must be accompanied by shear along the contact surface, which will be preceded by deep plastic deformation of the contact layer.

Since this plastic deformation occurs over the entire width of the contact layer, the condition for its occurrence will be expressed by the inequality:

\[ \Delta f_{\mathrm{n}}\cdot \tau < \Delta f \sigma \tau_c, \tag{1} \]

where \(\Delta f_{\mathrm{n}}\) is the nominal contact area on some elementary segment;

\(\Delta f_{\partial}\) is the actual contact area on this same segment;

\(\tau\) is the shear resistance of the chip material;

\(\tau_c\) is the resistance to cutting the bonds between the contacting metals.

If, near the cutting edge, the actual contact area is equal to the nominal one, then, as the distance from the edge increases, the normal contact pressure decreases, and it becomes less than nominal. Contact no longer occurs over the entire visible area of contact, but only over its separate portions. The imbalance in expression [1] is thereby reduced. Finally, at a certain point \(K\), inequality (1) becomes an equality:

Fig. 5.

\[ \Delta f_{\mathrm{n}}\cdot \tau = \Delta f_{\partial}\cdot \tau_c . \tag{2} \]

With a further decrease in the normal pressure, the area of actual contact will no longer be sufficient to provide plastic deformations in the contact layer. Consequently, point \(K\) lies on the boundary of the plastic contact region. The actual contact area (more precisely, the ratio \(f_{\partial}/f_{\mathrm{n}}\)) is a function of the normal contact pressure, increasing as it rises. Therefore, for a given pair of contacting materials and for a given state of the medium, point \(K\) will correspond to a definite value \(p_k\) of the contact pressure.

Since

\[ \frac{\Delta f_{\partial}}{\Delta f_{\mathrm{n}}}=\varphi(p_k), \tag{3} \]

and from (2) it follows that

\[ \frac{\Delta f_{\partial}}{\Delta f_{\mathrm{n}}}=\frac{\tau}{\tau_c}, \]

then it is not difficult to conclude that the indicated pressure \(p_k\)—let us call it the limiting pressure—is determined by the ratio of the shear resistance in the chip material to the shear resistance at the contact point:

\[ p_k = \psi \left(\frac{\tau}{\tau_c}\right). \tag{4} \]

The greater the strength of the bonds \(\tau_c\), which depends on the chemical properties of the tool material and the material being machined relative to one another, the lower the limiting pressure. As the strength of the chip material increases, on the contrary, it rises. The medium exerts a chemical (oxidizing) action on the contacting metals and therefore contributes to a reduction in the strength \(\tau_c\) of the bonds. In this case the limiting pressure will increase. The average contact temperature determines the intensity of the chemical interaction between the medium and the contacting metals. Therefore an increase in the cutting temperature must always lead to an increase in the limiting pressure \(p_k\).

Since the fundamental character of the envelope of contact pressures on the rake face does not depend on any of the factors indicated, any increase in the pressure \(p_k\) must lead to a decrease in the length \(c_p\) of plastic contact, and vice versa.

On the other hand, as noted above, the ratio between the length \(c_p\) of plastic contact and the length \(c\) of full contact depends only weakly on cutting factors. Therefore any change in the length of plastic contact will be accompanied by an approximately proportional change in the full contact length.

Fig. 6.
Labels in the diagram: properties of the machined material; properties of the tool metal; properties of the medium; thermal conductivity; chemical; mechanical; heat capacity; limiting pressure; average contact stress; cutting temperature; contact length; friction force; normal force in the shear plane; chip shrinkage; cutting speed; chip thickness; cutting width; rake angle.

Further. Since the specific friction force is practically independent of cutting conditions, the friction force \(F\) on the rake face will change in proportion to the contact length. All factors that cause an increase in contact length will lead to an increase in the friction force. Factors acting in the opposite direction will contribute to its decrease.

If we now consider the cutter as a single whole together with the chip, likening it to a die pressing on the plastic region in the cut layer ahead of the cutter, then the friction force $F$ will be the principal component determining the force taken up by this “die.” The shrinkage of the chip, being a certain average estimate of the degree of deformation of the metal under the “die,” is a function of the force $F$.

The chain of interrelations described above is illustrated by the diagram in Fig. 6.

REFERENCES

1. N. N. Zorev, Problems in the Mechanics of the Metal-Cutting Process. Mashgiz, Moscow, 1956.

2. M. F. Poletika. Investigation of the cutting process of titanium alloys. In the collection Machinability of Heat-Resistant and Titanium Alloys, Kuibyshev, 1962.

3. M. F. Poletika, M. Kh. Uteshev. On the strength calculation of the cutting part of a cutter. In the present collection.

4. A. M. Rozenberg, A. N. Eremin. Elements of the Theory of the Metal-Cutting Process. Mashgiz, 1956.

5. M. F. Poletika, M. Kh. Uteshev. Investigation of the cadmium-cutting process. Izv. TPI, vol. 109, 1963.

6. M. F. Poletika. Investigation of the process of cutting beryllium bronze. In the present collection.

7. M. F. Poletika. Influence of the material of the cutting tool on the cutting process. In the present collection.