FEATURES OF CHIP FORMATION IN RESTRICTED CUTTING WITH A TOOL HAVING A POINT ANGLE GREATER THAN 90°

G. L. KUFAREV, K. B. OKENOV

(Presented by the scientific seminar of the Department of Machine Tools and Metal Cutting)

The study of the process of chip formation in restricted cutting began comparatively recently [1, 2, 3, 4, 5]. Most of these works relate to investigation of force cutting, which is characterized by a small ratio of the width of the layer being cut to its thickness and is carried out with a tool of special geometry. The simplest and at the same time the most widespread case of restricted cutting is cutting by two conjugate cutting edges of the layer being cut, with \( b/a = 1 \). This case of the restricted-cutting process is the least studied. A correct understanding of the scheme of chip formation and of the mechanism of deformation on the auxiliary cutting edge of the tool makes it possible, to a considerable extent, to predetermine the roughness, the degree and depth of work hardening of the machined surface, since the latter are closely connected with the phenomena occurring on the auxiliary cutting edge of the tool.

Investigations carried out in recent years in the metal-cutting laboratory of the Tomsk Polytechnic Institute have shown that the geometry of the tool, especially its point angle \(\varepsilon\), has a significant influence on the process of chip formation in restricted cutting. It has been found that the angle \(\varepsilon\) affects the character and degree of deformation on the auxiliary cutting edge of the tool, the shape of the transverse section, and the angle of chip flow, etc.

In the present work, the case of chip formation in restricted cutting by a tool with a point angle \(\varepsilon > 90^\circ\) is analyzed.

The study of the process of chip formation was carried out by a detailed investigation of the chip roots obtained with the use of a special device that permits the tool to be instantaneously withdrawn from under the chip, while preserving the undeformed chip-deformation zone.

The investigations were performed in machining various materials. Their results are illustrated by the example of cutting annealed steel 20 with a tool fitted with a T15K6 hard-alloy insert and having the following geometrical parameters: rake angle \(\gamma = 10^\circ\), inclination angle of the main cutting edge \(\lambda = 0\), auxiliary cutting-edge angle in plan \(\varphi_1 = 8^\circ\), main and auxiliary clearance angles respectively \(\alpha = 10^\circ\) and \(\alpha_1 = 8^\circ\), and tool-nose radius \(r = 0\). The values of the main cutting-edge angle in plan \(\varphi\), the point angle of the tool \(\varepsilon\), and the cutting conditions are given in Table 1.

Cutting in this series of experiments was carried out at a cutting speed of 85 m/min, ensuring the absence of a built-up edge on the cutter. The adopted values of the angles in the cutter plane are those recommended in production and provide a fairly wide variation of the point angle.

Table 1

Each chip root was photographed from the side of the rake face of the cutter, which made it possible to determine the direction of chip flow. Then polished sections were prepared and analyzed:

a) of the transverse section of the chip (Fig. 1); on them the chip thickness was measured at various points across its width, as well as the angles of inclination of its side surfaces;

Fig. 1

b) of the chip root in a section parallel to the rake face of the cutter (Fig. 2), analysis of which made it possible to assess the nature of deformation of the chip metal;

c) of the chip root in sections parallel to the principal cutting plane, on which the angle $\Phi$, determining the position of the conventional shear plane in each of the sections, was measured;

d) of the chip root in sections parallel to the auxiliary cutting plane, on which the angle $\Phi'$, determining the direction of shear in the process of deformation of the chip metal from the side of the auxiliary cutting edge, was measured.

Processing and analysis of the information obtained from several analogous series of experiments, performed under different cutting conditions for different metals, made it possible to establish a number of features of chip formation in restricted cutting with a cutter having $\varepsilon > 90^\circ$ and to develop a scheme of the chip-formation process (Fig. 3).

Fig. 2

Fig. 3

The proposed scheme of chip formation reflects the following experimentally established regularities:

1. The chip shrinkage in section \(A'C'\) (Fig. 3) is constant; in section \(C'K'\) it decreases, and then again (in section \(K'E'\)) remains unchanged.

2. Deformation of the chip metal occurs in section \(A'K'\) by shear along the surface \(OABD\), and in section \(K'E'\)—along the plane \(OED\).

3. The direction of chip flow within the contact of the chip with the cutter deviates from the perpendicular to the main cutting edge by the angle \(\eta\), whose value changes depending on the ratio \(\frac{b}{a}\) and on the change in the angle \(\varepsilon\). Subsequently, the decrease in shrinkage along the main cutting edge toward the tool tip \((\xi_a > \xi_k\) or \(a_c > a_k\) and \(V_A < V_E)\) leads to curling of the chip in the plane of the rake face of the cutter.

Analysis of the scheme (Fig. 3) makes it possible to establish functional relationships between the chip parameters, the cross-section of the cut, and the cutter angles measured in the principal plane.

The width of the removed metal layer, measured in the direction perpendicular to the direction of chip flow,

\[ b_g=\left\{\frac{t}{\sin\varphi}+a\left[\operatorname{tg}\eta+\operatorname{ctg}(\varphi+\varphi_1)\right]\right\}\cdot\cos\eta= \]

\[ =\left\{\frac{t}{\sin\varphi}+a\left[\operatorname{tg}\eta-\operatorname{ctg}\varepsilon\right]\right\}\cdot\cos\eta. \tag{1} \]

The inclination angle of the free lateral side of the chip

\[ \operatorname{tg}\rho=\frac{a}{a_c}(\operatorname{tg}\eta+\operatorname{ctg}\varphi)\cdot\cos\eta =\frac{1}{\xi_c}(\operatorname{tg}\eta+\operatorname{ctg}\varphi)\cdot\cos\eta. \tag{2} \]

The inclination angle of the inner lateral side of the chip

\[ \operatorname{tg}\rho_1=\frac{a}{a_k}\left[\operatorname{tg}\eta+\operatorname{ctg}(\varphi+\varphi_1)\right]\cdot\cos\eta =\frac{1}{\xi_k}\left[\operatorname{tg}\eta-\operatorname{ctg}\varepsilon\right]\cdot\cos\eta. \tag{3} \]

The angle determining the position of the conditional shear plane \(OED\)

\[ \operatorname{tg}\Phi'=\frac{1}{\xi_k}\left[\operatorname{tg}\eta+\operatorname{ctg}(\varphi+\varphi_1)\right]\cdot\sin(\varphi+\varphi_1) =\frac{1}{\xi_k}\left[\operatorname{tg}\eta-\operatorname{ctg}\varepsilon\right]\cdot\sin\varepsilon. \tag{4} \]

To verify the validity of the expressions derived on the basis of the proposed scheme of chip formation, the calculated values of the parameters determined by equations (1), (2), and (3) were compared with the actual values; the results are given in Table 2. The data of Table 2 confirm the validity of the derived relationships and, consequently, the proposed scheme of chip formation realistically reflects the process of non-free cutting by a cutter with a point angle greater than \(90^\circ\).

The experimental materials presented (Figs. 1 and 2) and the data of the tables, in combination with dependencies (1)—(4), make it possible to draw the following conclusions, revealing the mechanism of chip formation at \(\varepsilon > 90^\circ\).

When analyzing the deformation of the chip metal, three sections along its width should be distinguished: \(A'C'\), \(C'K'\), and \(K'E'\). The variation in chip thickness in the first section is determined by the variation in the thickness of the removed layer within it. The magnitude of this section is determined

Table 2

first of all by the angle \(\varphi\). At \(\varphi=90^\circ\), the angle \(\eta=0\) [6]; the angle \(\rho\), in accordance with equation (2), is also equal to zero, which leads to the disappearance of the segment \(A'C'\). On the segment \(K'E\), the thickness of the layer being cut is also variable, but its magnitude is determined not by the angle \(\varphi\), but by the angle \(\varepsilon\). The angle \(\rho_1\) and the segment \(K'E\) will be equal to zero at \(\varepsilon=90^\circ\), independently of the magnitude of the angle \(\varphi\). In this case, in accordance with equation (4), the angle \(\Phi'\) will also be equal to zero, i.e., the auxiliary cutting edge will deform the metal according to the cutting scheme [6].

The segment \(C'K'\) is characterized by constancy of the thickness of the layer being cut. The decrease in shrinkage from point \(C'\) to point \(K'\) is explained by the constrained conditions of metal deformation at the tool point. The relative decrease in shrinkage in this segment usually increases with an increase in the feed and in the absolute value of chip shrinkage.

A decrease in the angle \(\varepsilon\) and an increase in the thickness of cut at constant depth of cut lead, as follows from the scheme (Fig. 3) and formula (4), to difficulty in deformation in sections parallel to the auxiliary secant plane. This leads, at small values of the angle at the point (experiments 7, 8 in Fig. 2) and small ratios

\[ \frac{b}{a} \]

(experiments 4, 7 in Fig. 2), to a periodic displacement of the chip metal along the auxiliary cutting edge and to the formation, on the inner side surface of the chip, of elements whose dimensions are determined by the length of the working segment of the auxiliary cutting edge.

The very slight widening of the chip (Table 2) makes it possible to say that the deformation scheme in restricted cutting is considerably closer to plane deformation than in free cutting.

The concepts developed concerning the scheme of deformation of the chip metal in restricted cutting make it possible correctly to describe also the mechanism of formation of the machined surface, the roughness, degree, and depth of deformation of which are to a considerable extent predetermined by the conditions of deformation of the chip metal within the working segment of the auxiliary cutting edge.

LITERATURE

1. G. N. Loladze. Chip Formation in Cutting Metals. Mashgiz, Moscow, 1950.

2. S. F. Glebov. Operation of the auxiliary blade. Stanki i instrument, No. 8, Moscow, 1950.

3. N. I. Reznikov. Theoretical Justification of Sharpening with Large Feeds by the Kolesov Method. Mashgiz, Moscow, 1953.

4. P. N. Obukhov. Investigation of the Process of Power Cutting of Steels. Dissertation, Tomsk, 1955.

5. N. N. Zorev. Problems in the Mechanics of the Process of Cutting Metals. Mashgiz, Moscow, 1956.

6. G. L. Kufarev, K. B. Ozhenov. Chip formation in the process of restricted cutting of plastic metals (present collection).