STUDY OF THE DYNAMICS OF THE CUTTING PROCESS OF GRAY AND DUCTILE CAST IRONS AT MICROSPEEDS

Yu. A. ROSENBERG, I. B. FILIPCHENKO

(Submitted by Prof. Dr. A. M. Rosenberg)

The study of the cutting process of “brittle” metals has been addressed in the works of I. A. Time [1], K. A. Zvorykin [2], Ya. G. Usachev [3], S. F. Glebov [4], I. M. Besprozvanny [5], A. M. Rosenberg [6, 13], A. M. Danielyan [7], V. A. Krivoukhov [8], I. Ya. Aizenshtok [9], M. I. Klushin [10], N. N. Zorev [11], and Yu. A. Rosenberg [12]. In these works, various analytical and graphical relationships for calculating cutting forces have been developed in sufficient detail.

However, all these relationships are given for medium and high cutting speeds, i.e., for cases in which temperature has a substantial influence on the cutting process. In addition, at such speeds the inertia of the measuring apparatus is of great importance.

During the formation of elemental chips, successive shear of individual elements takes place. Consequently, the cutting forces vary from some minimum to a maximum.

Which forces, then, were recorded by the measuring apparatus—having relatively large inertia—used by the above-mentioned authors in their works: maximum, minimum, or some average forces remains unknown. To this day, the character of the variation of forces, the coefficient of friction, and other quantities in the process of formation of a single element also remains unclear. In connection with this, it is natural to consider carrying out a study of the cutting process of “brittle” metals under conditions in which the influence of temperature and the inertia of the apparatus are absent.

One such method is the study of the cutting process at microspeeds. The use of microspeeds considerably facilitates the study of the cutting process and makes it possible to obtain a number of relationships in a “pure” form, without the influence of temperature. The influence of the inertia of the apparatus at these speeds is very small, which permits the use of simpler and more accurate apparatus for measuring forces.

The practical absence of tool wear ensures the obtaining of more accurate experimental results.

Methodology of the work, equipment, and tool

The study was carried out on a horizontal milling machine by the planing method.

To obtain low cutting speeds, the machine table was equipped with a special reduction gear that reduced all longitudinal table feeds by a factor of 60. The cutting forces were measured with a two-component elastic dynamometer with inductive sensors, which was mounted, by means of a special base, on the cross slide of the machine.

As the first experiments showed, the use of ordinary dial instruments is completely ruled out because of the very large changes in force during the formation of a single element.

Therefore, a loop oscillograph, MPO-2, was used to record them.

For cutting, plates measuring \(3 \times 50 \times 70\) mm were made from ductile cast iron with hardness \(130 \, \text{HB}\) and from gray cast iron with hardness \(200 \, \text{HB}\).

The high-speed steel cutters used in the experiments had rake angles from \(+30^\circ\) to \(-11^\circ\).

After each pass, the front and rear faces of the cutter were carefully honed with a fine-grained stone. The chip thickness was varied from \(0.1\) to \(0.8\) mm. The cutting speed was varied within the range \(0.0093\)—\(0.76\) m/min.

Results Obtained

As a result of the work carried out, a large number of curves recording the forces were obtained (Fig. 1). These curves, with the aid of a large projector of the BP type, were processed at tenfold magnification. On the basis of the data obtained, graphs were plotted of the dependence of the cutting forces on chip thickness, as well as graphs of the variation of the force, the coefficient of friction, and the angle \(\omega\) (the angle between the direction of velocity and the resultant acting on the front face) along the path of element formation.

Fig. 1. Oscillograms of forces in cutting:
a) ductile cast iron, \(V = 9\) mm/min, \(a = 0.7\) mm,
\(\gamma = 0^\circ\), recording speed \(4\) mm/sec;
b) gray cast iron, \(V = 9\) mm/min, \(a = 0.5\) mm,
\(\gamma = +11^\circ\), recording speed \(10\) mm/sec.

Figures 2 and 3 present the dependences of the forces \(P_{z \max}\) and \(P_{x \max}\) on chip thickness and on the rake angle of the cutter for gray and ductile cast irons at the cutting speed \(V = 0.0093\) m/min. Similar dependences were obtained

and for all other cutting speeds. In addition, similar dependences were also obtained for the minimum values of the forces. Since the character of variation of the latter does not differ from the character of variation of their maximum values, they are not presented in this article. Upon careful consideration of the dependences of the forces on the chip thickness, one can see that, for gray cast iron, for all rake angles they are expressed by straight lines that do not pass through the origin. The intercepts cut off by these lines on the force axis are the forces on the flank face.

For ductile cast iron these dependences are represented by straight lines only up to a chip thickness, definite for each rake angle, after which a noticeable deviation from linearity begins.

As can be seen from Fig. 3, with a decrease in the rake angle of the cutter, the rectilinearity of this dependence improves.

A legitimate question arises: how can such a difference in the dependences for gray and ductile cast irons be explained? On the basis of the data obtained, it may be assumed that such a discrepancy in the character of the dependence of the cutting force on the chip thickness is rooted in the difference in the plastic properties of these metals. Confirmation of this may be

Fig. 2.

Fig. 3.

the fact that, when cutting ductile cast iron, the cutting force is somewhat higher than that obtained on gray cast iron, despite the considerably greater hardness of the latter. Experiments on the investigation of strain hardening, carried out by the method of hardness measurement, showed that the limiting strain hardening of gray cast iron does not exceed 10%, whereas for ductile cast iron it reaches 40%.

A consequence of the latter is the different type of chip obtained at different thicknesses and rake angles.

Analyzing the chip obtained in each experiment, the authors observed that when gray cast iron is cut, the chip has the form of separate elements, only slightly or not at all connected with one another, regardless of the rake angle and the thickness of cut.

In ductile cast iron, however, at small thicknesses and large rake angles, it comes off as a continuous ribbon. As the thickness increases, this ribbon separates into individual elements.

With a decrease in the rake angle, the division of the chip into individual elements begins at smaller thicknesses. At the same time, it was noted that with increasing thickness and decreasing rake angle, the bond between the elements weakens and, at a given rake angle, beginning with a certain thickness, disappears completely.

What influence the thickness of cut has on the type of chip obtained is not yet known. An increase in the rake angle, however, promotes the formation of a continuous chip. This ability of the cutter rake angle, as is known, is associated with a reduction in the degree of plastic deformation of the layer being cut. It may be assumed that, when brittle metals are cut, a continuous chip can also be obtained, but only under the condition that the degree of deformation of the layer being cut is below the maximum permissible for the given metal. In this connection, the smaller the permissible degree of deformation, the larger the rake angle of the cutter must be in order to obtain a continuous chip.

The disruption of the bond between elements during cutting leads to the fact that the forces during the formation of a single element do not remain constant, but continuously vary from a minimum to a maximum corresponding to the given cutting speed, thickness of cut, and rake angle.

A detailed analysis of the data obtained showed that with a change in cutting speed not only do the extreme values of the forces change, but their difference also changes; moreover, the greater the cutting speed, the smaller this difference.

Comparing the obtained graphs of “cutting force—thickness of cut” for various speeds, it is easy to see that as the cutting speed increases, the maximum force values increase relatively little, especially at high speeds. It is sufficient to point out that for ductile cast iron, when the speed changes from 0.0093 to 0.76 m/min, the angle of inclination of the tangent to the curve for a cut thickness of 0.5 mm changes by only 10° (from 43 to 53°), whereas for the minimum force values this change is 25° (from 20 to 45°). Thus, with increasing cutting speed, the minimum force value comes closer and closer to the maximum.

As follows from the foregoing, in the process of cutting “brittle” metals the forces do not remain constant, but change continuously. Moreover, this change, as various authors indicate, is associated with the formation of individual elements.

In this connection, there naturally arises a desire to study the mechanism of formation of an individual element, to determine the regularities that occur in this process, and so forth.

Of greatest interest are the cutting forces and the factors affecting them. Therefore the authors attempted, first of all, to determine how the forces change during the formation of one element, and how the coefficient of friction \(\mu\) on the rake face of the cutter and the angle \(\omega\) change in this process.

Figure 4 shows the variation of the force \(P_z\), the coefficient of friction \(\mu\), and the angle \(\omega\) along the path of formation of an element for ductile cast iron. As can be seen from this graph, the coefficient of friction and the angle \(\omega\) vary according to a cri-

... having a minimum approximately at the middle of the path; however, the force \(P_z\) in this case varies along a curve having a maximum. In addition, the graph shows that the maximum value of the force does not coincide with the minimum values of the angles \(\omega\) and \(\gamma\).

The graph presented above also shows that the increase in force at the initial moment of element formation proceeds considerably faster than at the final moment. The same can also be seen in the oscillogram (Fig. 1, a), obtained at a cutting speed \(V = 0.0093\ \text{m/min}\), chip thickness \(a = 0.7\ \text{mm}\), and rake angle of the cutter \(\gamma = 0^\circ\).

At first glance, the data presented seem somewhat unusual. And indeed, where the coefficient of friction decreases, the force

Fig. 4.

increases rather rapidly; and, conversely, where the coefficient of friction increases, the increase in force slows considerably, and at the end of the element path its magnitude even decreases.

Calculation of the resultant \(R\) of the forces on the rake face for these cases (Table 1) also shows that its variation is analogous to the variation of the force \(P_z\).

A careful analysis of the data obtained shows that, for the given tool geometry, the following factors influence the cutting force during formation of a single element:

1. Variability of chip thickness.
2. Coefficient of friction on the rake face.
3. Strain hardening of the metal.

It is not yet possible to say how large the influence of each of these factors is.

At present one can only suppose that, as the mov—

Table 1

[[unclear: beginning of word]]tion of the cutter (Fig. 5), the increase in chip thickness that results from this causes an increase in the cutting force. However, this increase cannot be proportional to the chip thickness because, on the one hand, the coefficient of friction decreases, and, on the other, the degree of deformation of the element increases. The arguments concerning the regularities that occur in the formation of a single element apply mainly to the results obtained on ductile cast iron; nevertheless, as can be seen from Fig. 6, similar relationships also occur in cutting gray cast iron, although they are less pronounced. At the same time, in the course of the investigation the authors verified a formula relating shear stresses to hardness for ductile cast iron as well.

As is known, this relation, established in the cutting laboratory of the Tomsk Polytechnic Institute [13], considerably simplifies and accelerates the calculation of shear stresses and, consequently, of forces in metal cutting.

To calculate shear stresses by this formula it is sufficient to know the hardness of the cut chip, i.e., it is sufficient to establish the hardening that the chip has undergone in the deformation process.

In this connection, for gray cast iron, as a material that is limitingly hardening and has a very low percentage of hardening (not more than 10%), it proved possible to calculate the stresses not from the hardness of the chip, but directly from the hardness of the initial metal [4].

However, for ductile cast iron, as a material that also has limiting hardening, the latter formula is unsuitable, since it gives results 30–50% below the actual ones. Analysis shows that this underestimation is due to the fact that, at the same hardness, ductile cast iron has a considerably higher percentage of hardening (up to 50%) than gray cast iron, i.e., ductile cast iron possesses considerable plasticity in comparison with gray cast iron. Measurement of the chip hardness shows that it remains constant under all investigated cutting conditions, and the magnitude of this hardness is greater than the hardness of the initial metal by the hardening coefficient (the hardening coefficient is understood as the ratio of the hardness of the specimen deformed to fracture to the initial hardness of that specimen). This provision makes it possible, in cutting ductile cast iron as well, to calculate shear stresses not from the chip hardness but from the initial hardness of the metal, but with allowance for the hardening coefficient. In this case the formula will have the form:

\[ \tau = 0.185 \cdot C \cdot H_B,\ \text{kg/mm}. \]

where \(C\) is the hardening coefficient,
\(H_B\) is the initial Brinell hardness of the cast iron.

Path of cutting during the formation of one element

Fig. 5.

\(P\)

gray cast iron, \(v = 93\ \text{mm/min}\)
\(a = 0.4\ \text{mm}\)
\(\bullet\) — \(\gamma = -11^\circ\)
\(\times\) — \(\gamma = 0^\circ\)
\(\Delta\) — \(\gamma = 16^\circ\)
\(\circ\) — \(\gamma = 30^\circ\)

Path of element formation, in mm

Fig. 6.

Verification of this formula shows that the results obtained from it are very close to the actual ones. For example, for ductile cast iron having an initial hardness \(H_b = 140\) and a maximum strain hardening of 40%, this formula gives \(\tau = 36.2\ \mathrm{kg/mm^2}\). In cutting, the shear stresses have the value \(\tau = 35\ \mathrm{kg/mm^2}\). This formula also proves valid for gray cast iron, with the value of the stress obtained being closer to the actual one.

LITERATURE

1. Time, I. A. Resistance of metals and wood to cutting. Gornyi zhurnal, 1871.

2. Zvorykin, K. A. Work and forces necessary for removing metal chips. Moscow, 1893.

3. Usachev, Ya. G. Phenomena occurring in the cutting of metals. Izvestiya SPB, Polytechnic Institute, vol. XXIII, no. 1, 1915.

4. Fedorov, S. F. Theory of the Most Advantageous Cutting of Metals, Book One, Laws of Cutting. ONTI, 1933.

5. Besprozvannyi, I. M. Fundamentals of the Theory of Metal Cutting. Mashgiz, 1948.

6. Rosenberg, A. M. Dynamics of Milling. Sovetskaya nauka, 1945.

7. Danielyan, A. M. Dynamics of Milling. ONTI, 1936.

8. Krivoukhov, V. A. Metal Cutting. ONTI, 1938.

9. Aizenshtok, I. Ya. Basic Problems in the Mechanics of the Metal-Cutting Process. Mashgiz, 1950.

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

11. Zorev, N. N. Study of Elements of the Mechanics of the Cutting Process. Mashgiz, 1952.

12. Rosenberg, Yu. A. Study of the cutting process of gray cast iron. Author’s abstract, Tomsk, 1952.

13. Rosenberg, A. M.; Eremin, A. N. Elements of the Theory of the Metal-Cutting Process. Mashgiz, 1956.

14. Rosenberg, Yu. A.; Sedokov, L. M. On calculating the cutting force in turning and milling gray cast iron. Vestnik mashinostroeniya, no. 12, 1957.