FRICTION WORK IN THE PROCESS OF METAL CUTTING

T. M. SEDOKOV

Various, including directly opposing, opinions have been expressed about the role of friction in the process of metal cutting. L. S. Murashkin [1], G. N. Epifanov [2], and others believe that in the process of chip formation the coefficient of friction on the rake face has ordinary values (0.1–0.2). N. N. Zorev [3] experimentally showed a substantial change in the coefficient of friction under variable cutting conditions. In machining 35Kh3MN steel with a cutter having a rake angle \(\gamma = 10^\circ\), the coefficient of friction, according to his data, is equal to 0.8; 1.1; 0.5 if the temperature on the rake face is respectively 300, 500, and \(1000^\circ\)C.

M. I. Klushin and M. B. Gordon [4] came to the conclusion that the friction force, referred to the shear area, is the decisive factor determining the course of the entire chip-formation process. In contrast to this, Lowen, in a discussion of the work of Ling and Saibel [5], noted that it is better not even to regard the coefficient of friction as a fundamental factor in the cutting process.

On the basis of numerous experiments [3, 6] it has been established that an increase in the average coefficient of friction leads to an increase in the degree of plastic deformation of the layer being removed.

Earlier, a relationship was proposed between the angles of friction, cutting, and shear [7]:

\[ \mu = 1 - \operatorname{tg}(\beta_1 - \gamma). \tag{1} \]

Here \(\beta_1\) is the shear angle, determined from chip shrinkage, which, together with the rake angle of the cutting element \(\gamma\), determines the magnitude of the relative shear in the metal transformed into chips. Figure 1 gives an experimental verification of dependence (1) based on the experiments of a number of investigators [3, 6, 8].

The good experimental confirmation of dependence (1) over the entire range of variation of the principal parameters of the mechanics of chip formation agrees with I. V. Kragelsky’s opinion that, in the general case, the friction force is determined by resistance to volumetric deformation of the metal and by the destruction of contact films, and also that “the nature of the materials has less effect on the coefficient of friction than external conditions” [9].

The existence of a single relationship between the angles of friction, shear, and cutting for the materials investigated and for all cutting regimes, with the exception of those in which it is difficult to establish a common shear plane, reflects

features of friction in the cutting process. Friction has a substantial influence on the process of plastic deformation also in pressure working. But the nature of this influence is different. In the upsetting of solid bodies between rough plates, the upsetting force depends on friction on the contact surfaces. But, despite this, in upsetting it is possible to obtain any degree of plastic deformation (if the material is sufficiently plastic) at any value of the coefficient of friction at the ends of the body being deformed. In metal cutting, the friction conditions, determining the direction of the resultant force, at the same time determine the direction of the shear plane and, consequently, the degree of plastic deformation of the metal transformed into chip. Thus, the coefficient of friction in metal cutting manifests itself as a kinematic parameter of the chip-formation process, which is reflected by dependence (1).

Fig. 1. Experimental verification of the relation between the angles of friction, cutting, and shear

Applying dimensionless parameters to analyze the mechanics of chip formation—parameters which represent the corresponding specific cutting forces under the condition that the cutting resistance of the metal being machined, expressed by the magnitude of the shear stresses acting in the shear plane, is always equal to unity—on the basis of (1) it was established [10] that

\[ K_1 = \varepsilon + 1. \tag{2} \]

Here

\(K_1\) is a dimensionless parameter numerically equal to the specific work of chip formation under the condition that the cutting resistance of the machined metal is equal to unity,

\(\varepsilon\) is the relative shear, which is determined by the formula

\[ \varepsilon = \operatorname{ctg}\beta_1 + \operatorname{tg}(\beta_1 - \gamma). \tag{3} \]

Figure 2 shows an experimental verification of dependence (2), which relates the work of cutting to the degree of plastic deformation. All experimental results known in the literature fall on the straight line (2). Figure 2 gives only part of these results. No limits to the applicability of dependence (2) have yet been found.

Taking into account that the work of cutting consists of two principal parts: the work of plastic deformation \(A_{\text{pl}}\), which is proportional to the magni

value of the relative shear (3), and the work of friction—\(A_{\mathrm{fr}}\), one can establish the relationship between the component parts of the cutting work

\[ \frac{A_{\mathrm{fr}}}{A_{\mathrm{pl}}}=\frac{1}{\varepsilon}. \tag{4} \]

Relation (4) is confirmed by the data presented in Fig. 2. It agrees with the experimental conclusion that the specific weight of the work of friction decreases with increasing degree of deformation.

Fig. 2. Calculated and actual relationship between cutting force and chip deformation

Sometimes doubts are expressed as to whether the quantity obtained from the results of measuring cutting forces with a three-component dynamometer is in fact the coefficient of friction. Might this quantity, in addition to the coefficient of friction, include some other parameters reflecting the specific character of the cutting process? How can one explain the high values of the coefficient of friction in the cutting of ordinary metals?

If the coefficient of friction is regarded as a characteristic of the direction of the resultant interaction force between two solid bodies sliding relative to one another—and this is precisely how the coefficient of friction is regarded in the general theory of friction [9, 11]—then, taking into account the scheme of forces arising on the rake face, which is shown in Fig. 1, there are no grounds for the doubts indicated.

A high value of the coefficient of friction in metal cutting does not always occur (Fig. 1). Equally high values of the coefficient of friction are also observed in other types of friction, for example, when particles of very fine powders slide along an inclined plane [11]. With regard to the cutting process, B. V. Deryagin’s opinion [11] concerning the substantial influence of molecular interaction forces acquires the greatest credibility, since in the chip-formation process juvenile, newly formed surfaces come into contact, while the forces normal to the rake face of the cutter are very small.

Undoubtedly, dependences (1), (2), and (4), which relate friction to the deformation occurring in the cutting process, do not reveal the physical nature of friction, but they do make it possible, from the final result, to assess the role of friction in the process under study. Here it must also be borne in mind that in the cutting of metals the average coefficient of friction is determined by dynamometric measurement, and that the ratios between tangential and normal stresses at different points of the contact area between the chip and the tool will differ substantially from one another.

However, these relationships make it possible to calculate cutting forces on the basis of the actual nature of the phenomenon; they make it possible to calculate the coefficient of friction from chip shrinkage, and to determine the ratio of the component parts of the cutting work without recording the forces that arise in the cutting process. This latter circumstance may serve as a basis for developing a method for studying the complex laws of friction in metal cutting without dynamometry.

REFERENCES

1. L. S. Murashkin. Some questions concerning the process of chip formation in high-speed cutting of steel. In: Progressive Technology of Mechanical Engineering, part II, Mashgiz, 1952.

2. G. N. Epifanov. On two theories of metal cutting. Journal of Technical Physics, vol. 22, issue 3, USSR Academy of Sciences, 1952.

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

4. M. I. Klushin. Metal Cutting. Mashgiz, 1953.

5. F. F. Ling, Saibel Edward. Interaction of friction and temperature at the chip-tool interface in metal machining. Trans. ASME, 77, No. 5, 1954.

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

7. L. M. Sedokov. Calculation of the coefficient of friction in metal cutting. Machine Tools and Tooling, No. 2, 1958.

8. G. Altmeyer, H. Kranf. Über Schnittkraftmessungen beim Drehen mit Aluminiumoxydschneidplatten. Werkstattstechnik, 51, Heft 9, 1957.

9. I. V. Kragelskii, I. E. Vinogradova. Coefficients of Friction. Mashgiz, 1962.

10. I. A. Nemirovskii et al. Increasing the productivity of large metal-cutting machine tools. Mashinostroenie, 1965.

11. B. V. Deryagin. What Is Friction? Publishing House of the USSR Academy of Sciences, Moscow, 1963.