THE CHIP FORMATION ZONE IN METAL CUTTING

G. L. Kufarev, V. A. Govorukhin, M. G. Goldshmidt

(Presented by the scientific seminar of the Departments of Machine Tools and Metal Cutting and of Mechanical-Engineering Technology)

Studies of metal deformation in the cutting zone during operation at microspeeds, carried out with the use of dividing grids [1, 2], have convincingly shown that the thickness of the plastically deformed zone in this case is 2–3 times greater than the thickness of the layer being cut.

The opinions of various researchers concerning the magnitude of the chip-formation zone during cutting at high speeds are contradictory. Thus, for example, N. N. Zorev [3] believes that, “since at high cutting speeds the chip-formation zone narrows considerably, the width of the chip-formation zone may, to a good approximation, be regarded as a quantity of the second order of smallness in comparison with the chip thickness.” However, apart from a reference to a microphotograph of the chip root, N. N. Zorev substantiates this proposition with nothing. At the same time, in analyzing P. Oxley’s work on determining the thickness of the chip-formation zone, N. N. Zorev [4] criticizes his method, rightly pointing out that determining the thickness of the chip-formation zone from the distortion of the microstructure of the chip root gives a substantial underestimation of the former because noticeable distortion of the microstructure occurs only at significant deformations.

D. Kececioglu [5], and subsequently P. Oxley and W. Palmer [6], used the metallographic method indicated above to determine the thickness of the chip-formation zone. Later P. Oxley applied scratches to the surface of the workpiece and observed the path of displacement of material particles during deformation, photographing them with a motion-picture camera. Processing the motion-picture frames enabled him to judge the thickness of the shear zone. It should be noted that the possibilities of this method are very limited because of the difficulty of providing satisfactory illumination during filming at high speeds and because of the possible shrinkage of the chip, which does not allow the pattern of the trajectory of motion to be seen clearly enough.

In cutting at high speeds P. Oxley came to the conclusion that the initial and final boundaries of the chip-formation zone are parallel and that the ratio of the thickness of the deformation zone to its length is approximately 0.1. However, it is noted that this deviation may vary somewhat with changes in feed and rake angle. By the thickness of the chip-formation zone P. Oxley understands the thickness of the plastic region between the initial boundary \(FE\) and the final boundary \(CD\), in the direction perpendicular to the conventional shear plane \(OB\) (Fig. 1).

To investigate the thickness of the chip-formation zone during cutting at high speeds, the present work used the method of coordinate division grids. The experiments were carried out on a 1K62 lathe in free turning with transverse feed of a composite specimen consisting of two disks, the inner surfaces of which were carefully lapped to a tight fit. A coordinate grid in a polar coordinate system was applied to one of the specimens. One system of lines of the coordinate grid was an Archimedean spiral with a pitch of 0.05 mm; the second system consisted of rays emanating from the center of the workpiece at an angle of 5 minutes to one another. The cutting speeds were varied from \(V = 5\) m/min to \(V = 250\) m/min, the feeds from \(S = 0.1\) mm/rev to \(S = 0.39\) mm/rev, and the rake angle from \(\gamma = +5^\circ\) to \(\gamma = +22^\circ\). Brass L62, steel 2Kh13,

Fig. 1

Fig. 2

steel ShKh15, and steel 40 were selected as the work materials. An “instantaneous” stopping of the cutting process at any speed at the point where the division grid had been applied was performed by means of a special device with an electrical-contact arrangement. After the cutting process was stopped, the resulting chip root was photographed on a PMT-3 instrument; a photograph of the chip “root” was made at an overall magnification of 220–270 times, and the distorted cells of the division grid were measured. The calculation of all components of the strain tensor and of the strain intensity \(e_i\) was carried out by a specially developed procedure [7] on the Minsk-1 digital computer.

From the results of calculating the strain intensity in each cell of layer \(AB\) of the division grid (Fig. 2), graphs were plotted of the variation in strain intensity along the deformation path \(dS\), enclosed between points 1 and 2 of the initial and final boundaries of the plastic region. Hereafter the quantity \(dS\) is called the thickness of the chip-formation zone. From the graphs \(e_i = f(dS)\), the thickness of the deformation zone was determined. The end point of the plastic zone of the given layer was taken to be the point at which the magnitude of the strain intensity \(e_i\) no longer changed. The initial boundary of the plastic region was taken to be the line on which the strain intensity was equal to \(e_i = 0.2\). This value of \(e_i\) was adopted as a conditional initial boundary because calculation of \(e_i\) shows instability of the solution when \(e_i < 0.2\), owing to the existing inaccuracy in measuring the distortions of the division grid. As a result of taking the line \(FE\) with \(e_i = 0.2\) as the initial boundary of the plastic region, the actual thickness of the chip-formation zone was obtained somewhat underestimated.

It turned out that the thickness of the chip-formation zone over the thickness of the removed layer \(a\) is a variable quantity. It is minimal at

of the tool tip and increases somewhat when moving toward the free boundary of the chip. Near the free boundary of the chip, as a result of deformation from the preceding pass, the thickness of the chip-formation zone again decreases somewhat. The upper boundary of the chip-formation zone is approximately parallel to the assumed shear plane.

In what follows, the thickness of the chip-formation zone for each root is understood as the arithmetic mean thickness of the zone for all layers of the dividing grid. Figure 3 shows the change in the thickness of the chip-formation zone for all the materials investigated as a function of cutting speed. The feed and rake angle of the tool were kept constant in these experiments. As follows from the graph presented, the thickness of the chip-formation zone decreases with increasing cutting speed, but even at \(V=250\ \text{m/min}\), when cutting brass, it amounts to more than half the thickness of the cut.

Fig. 3. Dependence of the thickness of the chip-formation zone on cutting speed and on the properties of the metal being machined

The thickness of the chip-formation zone depends substantially on the strength properties of the material being machined. Thus, for example, the stress intensity \(\sigma_i\) in compression of specimens of these materials up to \(e_i=1\) was: for brass L62—\(\sigma_i=67\ \text{kg/mm}^2\); for steel ShKh15—\(\sigma_i=124\ \text{kg/mm}^2\); for steel 2Kh13—\(\sigma_i=104\ \text{kg/mm}^2\); for steel 40—\(\sigma_i=76\ \text{kg/mm}^2\), i.e., the thickness of the chip-formation zone at constant cutting speed was arranged in approximately the same order as the strength properties of the materials being machined.

With an increase in the thickness of cut from \(a=0.1\ \text{mm}\) to \(a=0.39\ \text{mm}\), the thickness of the chip-formation zone increased from \(dS=0.06\ \text{mm}\) to \(dS=0.27\ \text{mm}\). These experiments were conducted on steel 2Kh13 at a cutting speed \(V=100\ \text{m/min}\) and rake angle \(\gamma=17^\circ\).

Thus, an almost proportional increase in the thickness of the chip-formation zone is observed with increasing thickness of cut. However, the obtained relation is not entirely exact, since the thickness of the chip-formation zone could have been independently affected by the degree of deformation of the material in the chip, which, as is known, when working at speeds exceeding the built-up-edge region, decreases with increasing thickness of cut.

To determine the influence of the rake angle on the thickness of the chip-formation zone, experiments were conducted in cutting steel 2Kh13 at a cutting speed \(V=55\ \text{m/min}\), with a thickness of cut \(a=0.31\ \text{mm}\). These experiments showed that at \(\gamma=+5^\circ\), \(dS=0.16\ \text{mm}\); at \(\gamma=+17^\circ\), \(dS=0.145\ \text{mm}\); and at \(\gamma=+22^\circ\), \(dS=0.2\ \text{mm}\), i.e., no substantial change in the thickness of the chip-formation zone with increasing rake angle was detected, although some increase in \(dS\) with an increase in the rake angle does occur.

The results of the investigation thus show that:

1) the thickness of the chip-formation zone is comparable with the thickness

cut when machining all the materials studied at speeds up to \(V=250\ \text{m/min}\);

2) determination of the plastic-deformation zone from the distortion of the microstructure [5], as well as from the distortion of scratches parallel to the direction of the cutting speed [6], gives underestimated values of its dimensions.

The magnitude of the chip-formation zone is assessed most fully from the distortion of scratches perpendicular to the direction of the cutting speed. Thus, the difference in the estimates of the size of the deformation zone obtained by various authors is explained by differences in, and the imperfection of, the research methods they used.

It should be noted that the existence of a significant deformation zone does not call into question the relationship for determining chip shrinkage obtained by I. A. Time in analyzing a cutting scheme with a single shear plane, since, as shown in the work of V. I. Sadchikov [8], this relationship reflects the condition of continuity of the chip material, which is certainly satisfied even in the presence of a substantial chip-formation zone. Studies have also shown [9] that the final degree of deformation of the chip metal, calculated from its shrinkage using the relationship obtained from analysis of the scheme with a single shear plane, numerically coincides with the final degree of deformation of the chip metal determined experimentally from the distortion of a dividing grid. Thus, the scheme with a single shear plane makes it possible to correctly estimate the final degree of chip deformation.

Knowledge of the actual dimensions of the plastically deformed chip-formation zone is necessary when calculating the strain rate, which is one of the principal conditions governing the deformation process and predetermines the final relation between stresses and strains.

Thus, for example, P. Oxley, proceeding from a chip-formation zone with parallel boundaries, the thickness of which is

\[ dS=\frac{a}{10\cdot \sin\Phi}, \]

determines the average shear rate by the formula [10]

\[ \dot{\varepsilon}_{\text{av}}= \frac{V\cdot \cos\gamma}{dS\cdot \cos(\Phi-\gamma)} \cdot 16.65\ \text{s}^{-1}, \]

where

\[ \begin{aligned} \dot{\varepsilon}_{\text{av}} &\text{— shear rate, in } \text{s}^{-1},\\ V &\text{— cutting speed, in } \text{m/min},\\ dS &\text{— thickness of the chip-formation zone, in mm},\\ a &\text{— depth of cut, in mm},\\ \Phi &\text{— angle determining the position of the conditional shear plane, in degrees},\\ \gamma &\text{— tool rake angle, in degrees}. \end{aligned} \]

For plane deformation, the shear rate is converted into the strain-intensity rate by the formula:

\[ \dot{e}_{i\text{av}}=\frac{1}{\sqrt{3}}\,\dot{\varepsilon}\ \text{s}^{-1}. \]

In processing the results of our experiments, we had all the necessary data for calculating the average deformation rate by P. Oxley’s formula and were able to calculate the actual average deformation rate \(\dot{e}_{i\phi.\text{av}}\). A comparison of these results is presented in Table 1.

Table 1

The data presented in Table 1 were obtained when cutting L62 brass with a feed \(S = 0.31\) mm/rev and a rake angle \(\gamma = 17^\circ\).

As follows from Table 1, the formula proposed by P. Oxley for determining the thickness of the chip-formation zone requires correction, since the resulting values of the average strain rate are, on average, overstated by a factor of 5 relative to the actual value. Hence it follows that, for calculating the average strain rate in the cutting process, one may use the approximate relation

\[ dS = \frac{a}{2 \cdot \sin \Phi}. \]

References

1. G. L. Kufarev. Deformation of metal in the cutting zone during the formation of continuous chips. Candidate dissertation, Tomsk, 1958.

2. M. G. Goldshmidt. Investigation of the stress–strain state in the cutting zone. Candidate dissertation, Tomsk, 1966.

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

4. N. N. Zorev. Investigation of the process of cutting metals in the USA, issue 1, NIIMASH, Moscow, 1965.

5. D. Kececioglu, “Sher-Strain Rate in Metal Cutting and Its Effects on Shear-Flow Stress,” Trans. ASME, vol. 80, 1958, pp. 158–168.

6. W. B. Palmer and P. L. B. Oxley. The Mechanics of Orthogonal Machining, Proceedings, The Institution of Mechanical Engineers, vol. 173, 1959.

7. V. A. Govorukhin, G. L. Kufarev. Calculation of deformations in the cutting process, Izvestiya TPI, vol. 188, in press.

8. V. I. Sadchikov. On the theory of continuous-chip formation. Candidate dissertation, Tomsk, 1962.

9. V. A. Govorukhin. The stress–strain state when cutting ductile metals at high speed. Candidate dissertation, Tomsk, 1968.

10. P. Oxley. Strain rate in metal cutting. Design and Technology of Machine Building, Mir Publishing House, No. 4, Moscow, 1963.