STUDY OF THE BRASS CUTTING PROCESS

Yu. A. Rozenberg, V. I. Karnov

Presented by Prof., Doctor A. N. Eremin

One of the most important problems in the theory of metal cutting, on which the solution of other problems is based, is the study of the dependence of the magnitude of cutting forces on various conditions, i.e., the dynamics of the cutting process. Most of the work carried out both in our country and abroad has been devoted to the cutting process of ductile metals, although a large group of low-ductility (brittle) metals is also subjected to cutting. A special place in this group is occupied by low-ductility brass LS-59-1; studying the cutting process of this material makes it possible to reveal a number of regularities that are difficult to detect when cutting such a complex metal as steel. There are comparatively few studies on the dynamics of the cutting process in general, and on brass LS-59-1 in particular. Various authors [1, 2], in cutting brass, have studied some single particular question within the general complex of problems of cutting dynamics; consequently, they do not explain all the phenomena arising when cutting such a distinctive metal as brass LS-59-1.

In the metal-cutting laboratory of the Tomsk Polytechnic Institute, a study was carried out of the brass cutting process, covering a wide range of questions: the dynamics of the cutting process, wear of the cutting tool, the process of chip formation, the distribution of deformations and stresses in the cutting zone, the roughness of the machined surface, etc. This article considers the principal regularities in the influence of various factors on cutting forces.

For preliminarily compressed specimens having different degrees of deformation, hardness and effective axial stress were determined. Dynamic experiments in cutting brass were carried out on lathes 163, 1K62, and 1D63A; the cutting forces were measured on three different dynamometers: one hydraulic and two electric, with inductive and wire sensors. Although all three dynamometers have different designs and different stiffnesses, the forces measured under identical cutting conditions on these three dynamometers agree quite satisfactorily in magnitude (the difference does not exceed 5%).

Brass was cut with tools having mechanical clamping of VK-8 grade hard-alloy inserts, with different rake angles $\gamma$ ($-2^\circ$, $-13^\circ$, $16^\circ$, $30^\circ$). For measurement during the cutting process

To measure the shear angle \(\beta_1\), an instrument was used—an “optical angle indicator,” designed and manufactured by Prof. A. N. Eremin. Measurement of the amount of wear of the cutting tool on the flank face, as well as of the width of contact between the chip and the rake face of the cutting tool, was carried out with a portable Brinell microscope at 10-fold magnification. The values of the forces in the cutting process were calculated from the readings of microammeters, or from recordings on the tape of a loop oscillograph, or on the paper of the recording device of a hydraulic dynamometer.

The cutting conditions used were:

\[ \begin{aligned} \text{cutting speed } & V = 5\text{--}522\ \text{m/min},\\ \text{feed } & S = 0.1\text{--}0.61\ \text{mm/rev},\\ \text{depth of cut } & t = 1\text{--}5\ \text{mm}. \end{aligned} \]

One of the interesting features of LS-59-1 brass is that, when it is cut, no built-up edge appears on the cutting tool, and none is formed in any ranges of cutting speeds.

As a result of the experiments performed, it was established that the cutting forces do not depend on the cutting speed. This constancy of forces, when measured on three dynamometers and with the cutting speed varied by more than a factor of one hundred, was observed when cutting brass with tools having four different rake angles. The values of the main component of the cutting force as a function of speed and feed for one of the rake angles \(\gamma = -13^\circ\) are given in Fig. 1.

The independence of the force values from the cutting speed is apparently explained by the absence of a built-up edge in the process of cutting brass. As is known, only the presence of a stagnation zone explains the existence of a dependence of forces on cutting speed according to the typical curve, which has a maximum and a minimum. And since no built-up edge is present in any ranges of speeds when cutting brass, this circumstance leads to the independence of the forces from the cutting speed.

Fig. 1.

The experiments carried out to determine the influence of depth on the cutting forces showed a linear dependence, as can be seen from the graphs inನ್

Fig. 2. In the cutting process, in addition to the forces acting on the rake face of the cutting tool, forces also arise on the flank face; in our experiments these were determined by the method developed by A. M. Rozenberg [3]. Since, when cutting brass, the cutting forces do not depend on speed, then at identical speeds (which is the same as at identical temperatures) the forces on the rake face of the tool must be directly proportional to the chip thickness. The total forces measured in the experiments with a dynamometer and representing the sum of the forces acting on the rake and flank faces of the cutter are shown on the feed–force graph \((s—P)\) as straight lines that do not pass through the origin of coordinates.

Fig. 2.

Visible labels in the figure:

\[ P \text{ kg} \]

\[ \gamma = -13^\circ,\qquad \alpha = 12^\circ,\qquad \varphi = 70^\circ,\qquad \varphi_1 = 15^\circ,\qquad \lambda = 0^\circ,\qquad S = 0.61\ \mathrm{mm/rev} \]

Curves:

\[ P_z,\qquad P_x,\qquad P_y \]

Horizontal axis:

\[ t\ \mathrm{mm} \]

In Figs. 3 and 4 the forces \(P_z\) and \(R_{xy}\) for various rake angles were expressed by straight lines cutting off segments of definite length on the ordinate axis.

If the forces on the flank face were absent, then the force lines would have to pass through the origin of coordinates. Therefore the segments on the ordinate axis are the forces on the flank face. Analysis of the graphs presented shows that the forces on the flank face do not depend on the rake angle of the tool, on the chip thickness, or on the forces on the rake face. Although these forces are small for a sharp cutter, they must necessarily be taken into account when calculating the coefficient of friction on the rake face, which is obtained as independent of chip thickness. If, however,

force on the flank face from the dynamometer readings, then the coefficient of friction on the rake face of the cutter decreases with an increase in chip thickness, which contradicts elementary notions of the mechanics of the cutting process.

Having experimental data on the cutting forces and the shear angle \(\beta_1\) measured in the course of the experiments, one can calculate the angle of inclination of the resultant \(\omega\), the friction angle \(\eta\), the coefficient of friction \(\mu\),

Fig. 3.

the shear stress in the shear zone \(\tau_p\) from the formulas given by A. M. Rozenberg [3].

\[ \operatorname{tg}\omega=\frac{P_z-F_1}{R_{xy}-N_1}, \qquad \eta=\omega+\gamma, \qquad \mu=\operatorname{tg}\eta=\operatorname{tg}(\omega+\gamma), \]

\[ \tau_p=\frac{P_z-F_1}{s\cdot t}\cdot \frac{\sin\beta_1\cdot\cos(\omega+\beta_1)}{\cos\omega}, \]

where \(P_z\) is the principal component of the cutting force,
\(R_{xy}\) is the resultant of the forces \(P_x\) and \(P_y\),
\(F_1=14\) kg is the friction force on the flank face,

Fig. 4.

Fig. 5.

\(N_1 = 18\ \text{kg}\) — normal force on the flank face,
\(s\) — feed,
\(t\) — depth of cut.

The values calculated from the indicated formulas are summarized in Table 1, from which it is evident that the shear stress in the shear plane does not depend on the tool rake angle, the dimensions of the layer being cut, or the cutting speed, and is on average equal to \(24\ \text{kg}/\text{mm}^2\).

Table 1

The condition of constancy of the maximum shear stress makes it possible to reduce the formulas for calculating the cutting forces with a sharp tool to

\[ P_z = k_1 \cdot \tau_p \cdot s \cdot t + c_1 \frac{t}{\sin \varphi},\ \text{kg}, \qquad R_{xy} = k_2 \cdot \tau_p \cdot s \cdot t + c_2 \frac{t}{\sin \varphi}\ \text{kg}, \]

where

\[ \tau_p = 24\ \text{kg}/\text{mm}^2, \]

\[ c_1 = 4.4, \]

\[ c_2 = 2.5; \]

the coefficients \(k_1\) and \(k_2\) are determined as a function of the rake angle of the tool from the graphs in Fig. 5.

This form of the structural formulas is physically justified, since their first term represents the part of the force applied to the rake face of the tool, while the second term represents the part of the force applied to the flank face. The feed is not included in this second term, since the forces on the flank face do not depend on the thickness of the cut.

To determine the influence of the degree of wear of a carbide tool on the cutting forces, special experiments were carried out. Even during the dynamic experiments it was observed that, when cutting brass at all speeds, a wear crater does not form on the rake face; wear on the rake face is so insignificant that its influence on the cutting forces may be neglected. Wear occurs mainly on the flank face in the form of a chamfer, which leads to a considerable increase in the force of elastoplastic contact between the wear chamfer and the cutting surface. On VK-8 carbide inserts, wear was obtained on the flank face with various wear-chamfer widths, namely: \(h = 0.2;\ 0.5;\ 0.8;\ 1.0\ \text{mm}\).

Figure 6 presents graphs of the dependence of all three components \(P_z\), \(P_x\), \(P_y\) on the degree of tool wear for \(\gamma = -13^\circ\) and \(s = 0.11\ \text{mm/rev}\). From the graphs it is evident that the forces increase significantly as flank-surface wear increases. With increasing wear-chamfer width, the horizontal components of the force, \(P_x\) and \(P_y\), increase especially strongly. The observed increment of the cutting forces, which in the experiments is recorded from the dynamometer readings, must be attributed to the increase in the force acting on the flank face. It is precisely for this reason that, with tool wear, the components \(P_x\) and \(P_y\) increase considerably more than \(P_z\), since in the components \(P_x\) and \(P_y\) the share of the forces on the flank face is greater than in the component \(P_z\). For the same reasons, when

when cutting with small feeds, the forces increase with wear relatively more than when cutting with large feeds.

In most cases, when brass is cut, an elemental chip of trapezoidal or triangular shape is obtained. During the formation of a chip element, its plastic deformation occurs, encompassing a certain volume that is located both behind the surface of final shear and below the cutting line. Plastic deformations in the element do not lead to its destruction; it is a whole solid body, making it possible to measure its hardness. The hardness of the chips obtained in all experiments is the same and is equal to the hardness of a specimen under limiting compressive stress, i.e., at the moment of its failure.

Fig. 6.

As the rake angle and cutting speed are increased, and also as the cut thickness is decreased, the sliding of the elements becomes incomplete; adjacent elements remain connected with one another and form a more or less strong ribbon. However, in the resulting ribbon of metal the individual elements are very sharply delineated, and the entire chip takes on the appearance of a sort of curved saw. Only when the cut thickness is less than \(0.1\) mm and the rake angle is greater than \(30^\circ\) does the chip come off in the form of a continuous ribbon in which the individual elements cannot be distinguished; traces of the elements remain in the form of slight strokes on the outer surface of the chip. A peculiarity of the brass-cutting process is the impossibility of characterizing the degree of its plastic deformation by chip compression. The “continuous chip” obtained when cutting brass is easily broken into separate elements, so that compression in this case is only an indirect expression of the degree of its deformation.

REFERENCES

1. A. I. Isaev. The Process of Formation of the Surface Layer in Machining Metals by Cutting. Mashgiz, 1950.

2. A. V. Rudnev, A. P. Dobychina. Turning of nonferrous alloys and fiberglass laminate with diamond cutters. Stanki i instrument, No. 10, 1961.

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