EFFECT OF THE INCLINATION ANGLE OF THE TOOL’S MAIN CUTTING EDGE ON CHIP DEFORMATION

V. M. MOSTOVOI, I. M. PAZNIKOV

(Presented by Prof. A. M. Rozenberg, Doctor of Technical Sciences)

Introduction

The question of the influence of the inclination angle of a tool’s main cutting edge on the cutting process has not yet been studied in sufficient detail. Usually, in all literary sources, especially in textbooks on metal cutting, it is stated that the position of the tool’s main cutting edge (Fig. 1) affects only the direction of chip flow. On the basis of observations, we suppose that the inclination angle of the main cutting edge has a substantial influence on the plastic deformation of the chip, and consequently on the cutting forces as well. The aim of the present work is to determine the influence of the inclination angle of the tool’s main cutting edge on chip shrinkage and on the cutting temperature in combination with other geometric parameters, in particular with the cutting angle.

Fig. 1

The determination of the influence of the inclination angle of the cutting edge has been undertaken by: Sellergren, Glebov, Pankin, Zorev, and A. M. Rozenberg. In 1896, Sellergren, with the cutting edge inclined to the direction of motion, proposed measuring the cutting angle in a plane deviating from the normal to the blade by the same angle $\lambda$ by which the blade deviates from the perpendicular to the direction of motion (Fig. 2). Glebov called the position advanced by Sellergren the “Sellergren law” and gave the following formulation [1]: “The angle of deviation of the chip from the perpendicular to the blade is equal to the angle of deviation of the blade from

Fig. 2

perpendicular to the direction of motion.” Thus, according to Selengren, Glebov, and Pankin, the cutting angle must be measured not in the plane \(AOB\), but in the plane \(COD\) (Fig. 3). In the triangles \(AOB\) and \(COD\), the side \(AB\) is perpendicular to the side \(AO\), and \(CD\) is perpendicular to \(CO\); hence the cutting angle is determined as:

\[ \tg \delta_T=\frac{CD}{OC}=\frac{CD}{\frac{AO}{\cos \lambda^\circ}}=\tg \delta_N \cdot \cos \lambda^\circ . \]

From this calculation it follows that the inclination of the main cutting edge decreases the cutting angle. However, Professor A. M. Rozenberg believes that the inclination of the cutting edge does not decrease the cutting angle but, on the contrary, increases it [2].

Fig. 3

Research Methodology

The first part of the experimental work was carried out beginning in 1953 on a type 1616 screw-cutting lathe of the Kuibyshev Plant. Steel 30 was machined in free and constrained cutting. Chemical composition of the steel machined: \(C = 0.33\%\); \(Mn = 0.79\%\); \(Si = 0.15\%\). Mechanical characteristics: ultimate strength \(\sigma_{vr}=54\ \frac{kg}{mm^2}\), yield strength \(\sigma_s=27.2\ \frac{kg}{mm^2}\), relative elongation \(\delta=24\%\). In order to eliminate the influence of built-up edge on chip shrinkage, the experiments were repeated on red copper. The cutters were fitted with T15K6 cemented-carbide inserts. The geometry of the experimental cutters is given in the table. The cutting speed was varied from 8 to 200 \(m/min\) at a feed of \(S=0.21\ mm/rev\), cutting depth \(t=2\ mm\).

The remaining angles were kept as follows: $\beta = 62^\circ$, $\alpha = 5^\circ$, $\gamma = 23^\circ$.

The relative temperature was measured by a tool–workpiece thermocouple and recorded by a galvanometer.

The second part of the experimental work was carried out on a 1A62 screw-cutting lathe, machining carbon steel 45 with a high-speed steel R9 cutter, at a cutting speed $V = 72\ \text{m/min}$, cutting depth $t = 1.6\ \text{mm}$, and feed $S = 0.2\ \text{mm/rev}$.

In carrying out the experiments, the inclination angle of the main cutting edge and the cutting angle were varied over a wide range. Of all the experimental cutters, the greatest durability was shown by the cutter with an inclination angle of the main cutting edge $\lambda = +32^\circ$, a rake angle (in the direction of chip flow) $\gamma = 50^\circ$, and a plan angle $\varphi = 50^\circ$.

Results of the investigations

Figure 4 presents curves of the dependence of chip shrinkage on speed for various inclination angles of the main cutting edge. With an inclination angle of the main cutting edge $\lambda = 0^\circ$ (curve $a$), in the speed range

Fig. 4. Machined material: steel 30

from 8 to 25 m/min, shrinkage decreases sharply under the action of the growing built-up edge. With a further increase in speed from 25 to 120 m/min, shrinkage increases owing to the gradual decrease of the built-up edge. From numerous studies by other authors it is known that the change in cutting force follows shrinkage; this gives grounds to believe that the cutting forces will change according to the same law as chip shrinkage. Curve $b$ corresponds to the angle $\lambda = +3^\circ$. At this inclination angle of the main cutting edge, shrinkage has higher values. With a further increase of this angle, chip shrinkage increases continuously (curves $v$, $g$, $d$). With a negative value of the inclination angle of the main cutting edge, i.e., at $\lambda = -12^\circ$ (curve $e$), shrinkage is less than in all the preceding cases (curves $d$, $g$, $v$, $b$, $a$). The reduction of shrinkage when chips are removed by a cutter having a negative value of the inclination angle of the main cutting edge of the cutter,

is explained by the less constrained cutting conditions; in this case, the tool tip (Fig. 5a) is located above any point of the cutting edge and, because of this, the normal force and the friction force will have smaller values. With positive values of the angle \(\lambda\) (Fig. 5b), the conditions of chip separation are made more difficult, as a result of which the normally acting force and the friction force will have higher values. In addition, in this case

Fig. 5

the chip being separated is not pushed away from the machined surface, as occurs for negative values of the angle, but, on the contrary, is pressed in the direction of the chip root. In this case the angle between the auxiliary cutting edge and the direction of chip flow decreases.

To confirm the above, we carried out an experiment in free cutting while maintaining the same conditions as in constrained cutting. As follows from Fig. 6, the curves of the dependence for inclination angles of the main cutting edge \(\lambda = -12^\circ\) and \(\lambda = +12^\circ\) are superimposed on one another. In these two

Fig. 6. Free cutting of steel 30

cases under consideration, equality of shrinkages is preserved as a result of the equality of the cutting angles in the direction of chip flow and of identical chip-formation conditions. For positive values of the angle \(\lambda\), the chip flows along the rake face toward the smaller cutting angle, i.e., toward the machined surface of the part, and for negative values

of the angle $\lambda$ the chip also moves in the direction of the smaller cutting angle, but to the opposite side, i.e., away from the machined surface (Figs. 5a and b). The angles of chip flow relative to the normal to the main cutting edge are equal, but oppositely directed. Oblique cutting is characterized by large shrinkages and temperatures when cutting with tools having a positive value of the inclination angle of the main cutting edge, and conversely. The cutting process with a positive angle $\lambda$ proceeds under more complex conditions: chip formation takes place under constrained conditions. In order to neutralize the harmful influence of a positive value of the inclination angle of the main cutting edge on the cutting process, in our opinion, one may proceed by increasing the rake angle.

The arrangement of the curves of the dependence of chip shrinkage on cutting speed at different values of the inclination angle of the main cutting edge (Fig. 4) indicates that, as the positive values of the inclination angle $\lambda$ increase, the curves shift into the zone of lower speeds. Thus, for example, the minimum value of shrinkage at $\lambda=+12^\circ$ corresponds to the speed $V=20$ m/min (curve d), while at $\lambda=-12^\circ$ the minimum shrinkage corresponds to the speed $V=30$ m/min (curve e). Such an arrangement of the curves of the dependence $\xi=f(V)$ is in good agreement with notions concerning the thermal processes occurring in the cutting of steel. In addition, from Fig. 4 the speed becomes clear at which, for the given specific conditions, the inclination angle of the main cutting edge does not exert a substantial influence on the cutting process. The validity of what has been stated is well confirmed in Fig. 7; here the character of the variation of the relative

Fig. 7. Work material: steel 30

temperature (galvanometer divisions) on the rake face of the tool is preserved for all inclination angles of the main cutting edge. At the same time it is also found that the temperature rises sharply up to a cutting speed equal to 70 m/min. With a further increase in speed, the rise in temperature lags sharply. In Fig. 7, curve a was obtained at an inclination angle of the main cutting edge $\lambda=0^\circ$; b) $\lambda=+3^\circ$; c) $\lambda=+6^\circ$; d) $\lambda=+9^\circ$; e) $\lambda=+12^\circ$; f) $\lambda=-12^\circ$. At the same time, a fan-shaped arrangement of the curves is clearly observed here. Curve f, obtained at the negative value of the angle $\lambda=-12^\circ$, is located in the zone of lower temperatures, and, conversely, with an increase in the positive value of the cutting-edge inclination angle from 0 to $+12^\circ$, curves b, c, d, e shift into the zone of higher temperatures. Here the influence of the constrained conditions during chip formation is well illustrated.

In Fig. 4 the character of the change in the curves is determined by the action on the cutting process of two factors: the presence of a varying built-up edge and the dif-

...with different inclination angles of the main cutting edge. Both factors, acting together, change the direction of chip flow (Figs. 5a and 6).

In order to eliminate the influence of built-up edge on chip shrinkage and to reveal only the influence of the inclination angle of the main cutting edge, we carried out experiments on red copper, during the machining of which built-up edge is absent. In Figs. 8 and 9 the curves are arranged in the same order as in Figs. 4 and 7, but their character in the case under consideration differs sharply from the curves obtained for steel in the presence of built-up edge on the tool.

Fig. 8. Work material: red copper

Experiments on red copper convincingly show that the inclination angle of the main cutting edge has a direct and rather substantial effect on the cutting process.

Fig. 9. Work material: steel 30

When machining steel 45 with a cutter made of high-speed steel R9 and with the above-indicated geometry, a tool life 25% higher was obtained in comparison with a tool of normal geometry, with a considerable reduction in power.

On the basis of the investigations carried out, the following conclusions may be drawn:

1. With an increase in the positive value of the inclination angle of the main cutting edge, the temperature on the contact surface of the chip and the tool and the chip shrinkage increase, which is confirmed by experiments both on steel and on red copper.

1. With a negative value of the inclination angle of the main cutting edge, chip shrinkage and cutting temperature have lower values.

2. With equal values of the positive and negative inclination angles of the main cutting edge (in free cutting), the chip will come off in the direction of equal cutting angles, and in this case the chip shrinkages in both cases will be the same (Fig. 6).

In constrained cutting, chip shrinkage increases with an increase in the positive values of the inclination angles of the main cutting edge, and vice versa.

1. The adverse effect of a positive value of the inclination angle of the main cutting edge on the cutting process (increase in shrinkage, cutting temperature, and power) can be neutralized by reducing the cutting angle.

2. The results of these preliminary investigations show that the inclination angle of the main cutting edge has a substantial effect on the cutting process.

REFERENCES

1. Glebov, S. F. — Theory of the Most Advantageous Cutting of Metals. Book I. Laws of Cutting. Gosmashmetizdat, 1933.

2. Rosenberg, A. M. — Dynamics of Milling. Moscow, Soviet Science Publishing House, 1945.