On the Intensity of Cutter Wear in Turning Gray Cast Iron

A. M. Rozenberg, A. K. Baikalov

In the wear of metal-cutting tools, the work of the frictional forces on the faces of the tool is expended in abrading a certain volume of hard alloy, as a result of which a crater is produced on the rake face, and a wear land is formed on the flank face.

The intensity of abrasion of the tool with time may be expressed by the relation:

\[ I=\frac{W}{\tau}. \tag{1} \]

Here:
\(I\) — absolute wear intensity, in \(\mathrm{mm^3/min}\),
\(W\) — volume of hard-alloy wear, in \(\mathrm{mm^3}\),
\(\tau\) — tool operating time, in min.

For cutters that wear on the flank face, the wear volume (Fig. 1) is expressed by the formula:

\[ W=\frac{1}{2}\,\tg\alpha\,\frac{t}{\sin\varphi}\,(1+\tg\alpha\cdot\tg\gamma)\,h^2\ \mathrm{mm^3}. \tag{2} \]

In the formula: \(\alpha,\gamma,\varphi\) — geometry of the tool sharpening,
\(t\) — depth of cut, in mm,
\(h\) — averaged width of the wear land on the flank face, in mm.

Fig. 1

For a given cutting regime and tool geometry:

\[ I=C\frac{h^{2}}{\tau}, \tag{3} \]

where

\[ C=\frac{1}{2}\tan\alpha\ \frac{t}{\sin\varphi}(1\pm \tan\alpha \tan\gamma)=\text{const}. \]

Let us express the wear intensity in relative form:

\[ i=\frac{I}{\Delta}=\frac{W}{\Delta\tau},\quad \frac{\mathrm{mm}^{3}}{\mathrm{mm}^{2}\,\mathrm{min}}, \tag{4} \]

\[ \Delta=b\cdot h(1\pm \tan\alpha \tan\gamma)\ \mathrm{mm}^{2}. \]

In formula (5)

\[ b=\frac{t}{\sin\varphi}. \tag{5} \]

Here: \(\Delta\) is the actual area of the wear land, in \(\mathrm{mm}^{2}\);

\(i\) is the relative wear intensity, in \(\dfrac{\mathrm{mm}^{3}}{\mathrm{mm}^{2}\,\mathrm{min}}\).

Solving equations (2), (4), and (5), we obtain:

\[ i=\frac{1}{2}\tan\alpha\ \frac{h}{\tau}. \tag{6} \]

The intensity of volumetric wear of cutters on the flank face depends both on the sharpening geometry of the flank face and on the intensity of the linear change in the width of the wear land with time. Expression (6) is more convenient for analysis and is widely used for investigating the laws governing the wear of metal-cutting tools.

Often, wear intensity is understood simply as the ratio \(\dfrac{h}{\tau}\). Such an expression is used, for example, by Prof. I. M. Besprozvannyi in establishing cutting regimes on the basis of determining the degree of wear of the cutting edge of the tool [1], and by a number of other authors.

The formula \(i=\dfrac{h}{\tau}\) reflects, strictly speaking, the intensity of the change in the width of the wear land with time and cannot, strictly speaking, be identified with the intensity of volumetric wear of the tool itself. The identification of these two concepts is permissible insofar as, at \(\alpha=\text{const}\), the intensity of volumetric wear of the cutter is proportional to the intensity of the linear change of the wear land with time. With a variable clearance angle (for example, in experiments to determine the optimum value of the clearance angle), as will be shown below, cutter wear intensity must be characterized by expression (6).

If in formula (6) \(i=\text{const}\), then when working with a tool of constant geometry the ratio \(\dfrac{h}{\tau}=\text{const}\) must also hold. In this case, the increase in the width of the wear land with time is represented graphically by a straight line. Numerous studies show that tool wear—

under constant experimental conditions does not obey this elementary relationship.

The most typical case of wear on the flank face is shown in Fig. 2. The curve is divided into 3 zones: the zone of initial wear, or the “running-in” zone of the tool; the normal zone; and the accelerated-wear zone.

Fig. 2

In the experiment, the only variable, if the wear on the rake face is small, is the wear land \(h\), or, more precisely, the area of contact of the cutter along the flank face with the material being machined. It should be expected that an increase in the contact area will lead to an increase in the forces on the flank face and to a change in the heat balance in the contact zone. Figures 3 and 4 show the nature of the change in the friction force and the normal force on the flank face of the cutter as a function of the wear of alloy VK8 when turning gray cast iron of hardness \(H_B = 190\ \mathrm{kg/mm^2}\). (Experimental graphs Nos. 3 and 4 and the subsequent experimental data are taken from work [7]. The forces on the flank face were determined according to the method of [4].)

It is seen from Figs. 3 and 4 that, as the tool becomes dull, the absolute magnitude of the forces on the flank face increases monotonically. If, for a sharp cutter, the friction force and the normal force are \(10\text{–}20\ \mathrm{kg}\), then when wear reaches \(h = 1.05\ \mathrm{mm}\) these forces increase to \(40\text{–}80\ \mathrm{kg}\). For individual feeds at certain cutting speeds, an increase in the force on the flank face by a factor of 5–10 is observed. Similar relationships were also obtained for other feeds in the range from \(S = 0.059\ \mathrm{mm/rev}\) to \(S = 0.43\ \mathrm{mm/rev}\).

An increase in the work of the friction forces on the flank face with increasing dulling of the tool should cause additional heat generation in the contact zone and an increase in cutting temperature. However, a considerable increase in temperature, as follows from Figs. 5 and 6, is not observed (the temperature was measured in divisions of the galvanometer of the natural thermocouple cast iron–hard alloy VK8). For heavy cuts \((S = 0.291\ \mathrm{mm/rev},\ \text{Fig. 6})\), the temperature on the faces of the tool remains practically constant over the entire range of dulling. This is evidently explained by the fact that, when working with large feeds, the cutting temperature is determined mainly by the quantity—

Fig. 3

by the amount of heat entering the cutter through the rake face; the magnitude of the latter predominates over the quantity of heat generated directly on the wear land. The additional release of frictional heat on the wear land is not capable of substantially changing the heat balance on the faces of the tool, especially since, along with blunting, the heat removal from the cutting edge of the cutter improves; the “cooling” influence of the wear land becomes apparent.

Fig. 4

When thin chips are removed \((S \leq 0.1\ \mathrm{mm/rev},\ \text{Fig. 5})\), the principal source of heat generation shifts to the flank face. In this case the temperature on the faces of the tool (and therefore also the integral temperature recorded by a natural thermocouple) is determined by the quantity of heat released on the wear land.

For illustration, a calculation is given of the work of friction on the faces of a worn cutter \((h = 1.05\ \mathrm{mm})\) under the cutting conditions \(t = 2\ \mathrm{mm},\ S = 0.054\ \mathrm{mm/rev},\ V = 120\ \mathrm{m/min}\). The friction force on the rake face for these conditions was \(6\ \mathrm{kg}\), and the friction force on the flank face was \(40\ \mathrm{kg}\). The minute work of friction on the rake face (without taking chip shrinkage into account) is

\[ A_{\mathrm{rf}} = 6 \times 120 = 720\ \mathrm{kg\,m/min}, \]

and the work of friction on the flank face is

\[ A_{\mathrm{ff}} = 40 \times 120 = 4800\ \mathrm{kg\,m/min}. \]

The ratio of the works of friction indicates that, in cutting with thin chips, the principal source of heat generation is located in the zone of contact of the flank face with the workpiece. Naturally, the change in the work of friction in the contact zone in this case is noticeably reflected in the thermal

Fig. 5

balance at the tool faces and on the readings of the thermocouple galvanometer. It must be noted that the increase in temperature in connection with the growth of the wear land occurs more slowly than would be expected on the basis of an analysis of the friction work on the flank face, owing to the ever-improving conditions of heat removal from the cutting edge of the tool. In those cases when the friction work on the flank face is not sufficiently great (\(V < 80\ \mathrm{m/min}\), Fig. 5), the “cooling” effect of the wear land not only compensates for the rise in temperature, but even causes a certain decrease in it.

In general, the change in cutting temperature on a worn tool as compared with a sharp tool is small. For the majority of cutting speeds and feeds practically used in machining cast iron, it may be assumed that blunting of the tools occurs at a constant temperature.

Fig. 6

Thus, in the cutting of gray cast iron, tool wear on the flank face occurs with a continuous increase in the forces on the flank face and under more or less constant temperature conditions. It is quite clear that the change in the intensity of wear in the various blunting zones (Fig. 2) is connected with the magnitude of the forces on the flank face and with the character of their variation. To analyze the intensity of tool wear from this point of view, the mean values of the specific forces on the flank face were determined for different wear lands (Figs. 7 and 8).

The character of the variation of \(n\) and \(f\), presented in Figs. 7 and 8, agrees well with the curve of the intensity of tool wear with time (Fig. 2). For a sharp tool, the specific forces on the flank face are very considerable and are the principal cause of the accelerated wear of the tool in the “running-in” zone. If it is assumed that the contact area of the sharp edge of the tool with the workpiece is less than \(0.1\ \mathrm{mm}^2\), then the specific forces \(n\) and \(f\) must exceed \(100\ \mathrm{kg/mm}^2\). The “running-in” zone, as follows from Figs. 7 and 8, will be determined by the time necessary for wear of the tool on the flank face up to \(h = 0.2\text{–}0.3\ \mathrm{mm}\), after which the “normal” blunting process will begin, with more or less constant specific forces \(n\) and \(f\). Zone III (the zone of accelerated wear) will begin upon reaching \(h = 0.8\text{–}0.9\ \mathrm{mm}\), since at this contact area an increase in the specific forces on the flank face begins again.

Fig. 7

The contact area of the cutter with the material being machined does not remain indifferent in the process of tool wear.

Its influence on wear is manifested in the fact that, first, it determines the absolute and relative magnitude of the forces on the rear face of the cutter that arise as a result of the elastic-plastic contact of the rubbing pair cutter–workpiece, and, second, it improves the conditions of heat removal and, to a certain extent, slows the rise of temperature in the friction zone.

Thus, in turning cast iron, the character of the wear curve and the nonconstancy of its intensity in the different periods of tool dulling are qualitatively explained quite satisfactorily by the dynamics of the forces on the rear face. As applied to cast iron, as a brittle material, in the cutting of which the abrasive, mechanical type of wear of metal-cutting tools plays the principal role, such a simplified representation of the wear mechanism is fully justified.

For hard alloys possessing high wear resistance, i.e., low sensitivity to changes in the wearing forces, the wear curve (Fig. 2) differs only slightly from a straight line. Then, for a given dulling criterion \(h\), one may operate with the mean value of the wear intensity

\[ i_{\mathrm{cp}} = \frac{1}{2}\,\tg \alpha \,\frac{h}{T}, \]

which differs little from the individual values:

\[ i = \frac{1}{2}\,\tg \alpha \,\frac{h}{\tau} \]

for the current change of the coordinates \(h\) and \(\tau\) (here \(T\) is the tool life for the selected dulling criterion \(h\)).

Fig. 8

In conducting tool-life tests to determine the optimum geometry, interest is directed first of all to the magnitude of the rear angle, which most substantially affects the life of a tool wearing mainly on the rear face.

Experiments in these investigations are carried out at a constant cutting regime and work material, with a cutter having a variable rear angle while the remaining geometrical parameters are unchanged. Obviously, if one neglects the inequality of temperatures on the tool faces due to the variable included angle, then it may be assumed that both the magnitude of the specific forces in the contact zone and their change as dulling proceeds will be the same for all cases of sharpening. In that case the mean wear intensity for all sharpening variants must be constant, i.e., \(i_{\mathrm{cp}1} = i_{\mathrm{cp}2} = i_{\mathrm{cp}3} = \ldots = i_{\mathrm{cp}k}\), where \(1, 2, 3, \ldots, k\) are the indices of cutters with different rear angles. According to formula (6), it should be:

\[ \frac{1}{2}\operatorname{tg}\alpha_1\,\frac{h}{T_1} = \frac{1}{2}\operatorname{tg}\alpha_2\,\frac{h}{T_2}, \quad \frac{1}{2}\operatorname{tg}\alpha_3\,\frac{h}{T_3} = \ldots = \frac{1}{2}\operatorname{tg}\alpha_k\,\frac{h}{T_k} \tag{7} \]

or, taking into account the inequality of temperatures on the tool faces,

\[ \frac{\operatorname{tg}\alpha_1}{T_1} \leqslant \frac{\operatorname{tg}\alpha_2}{T_2} \leqslant \frac{\operatorname{tg}\alpha_3}{T_3} \leqslant \ldots \leqslant \frac{\operatorname{tg}\alpha_k}{T_k} \tag{7a} \]

under the condition \(\alpha_1 < \alpha_2 < \alpha_3 \ldots < \alpha_k\).

Expression (7a) is valid for all values of clearance angles up to \(\alpha_{\mathrm{opt}}\), determined experimentally.

Inequality (7a) loses its meaning for clearance angles exceeding the optimum value of the clearance angle, since at \(\alpha > \alpha_{\mathrm{opt}}\) the cutting wedge is insufficiently strong and the wear of the cutter will already be determined by the forces acting on the rake face.

Proceeding to compare the wear intensity of cutters with clearance angles \(\alpha_2 > \alpha_1\), we have:

\[ \frac{T_2}{T_1} \leqslant \frac{\operatorname{tg}\alpha_2}{\operatorname{tg}\alpha_1} \tag{7б} \]

or, taking (1) into account:

\[ \frac{T_2}{T_1} \leqslant \frac{W_2}{W_1}. \tag{7в} \]

It follows from formulas (7б) and (7в) that the gain in life due to the clearance angle is proportional to the increase in the volume of wear of the cemented carbide and numerically coincides with the increase in the tangent of the clearance angle. It is obvious that the gain in life cannot exceed the ratio \(\dfrac{\operatorname{tg}\alpha_2}{\operatorname{tg}\alpha_1}\). With an increase in the clearance angle, an increase in the intensity of volumetric wear should be expected, since both the conditions of heat removal from the cutter tip and the mechanical strength of the cutting edge deteriorate.

Table 1 gives the results of tool-life tests for determining \(\alpha_{\mathrm{opt}}\) in turning gray cast iron, showing the validity of inequalities (7б) and (7в).

Table 1

If, in experiments to determine the optimum relief angle, formula (7b) is not confirmed, then it is necessary to look for an error in the experiment. D. K. Margulis [3], in milling gray cast iron, obtained an optimum relief angle \(\alpha = 10^\circ\). The wear graphs show that a cutter with \(\alpha = 14^\circ\) has practically the same tool life. It would be more correct to regard \(\alpha = 14^\circ\) as the optimum relief angle, which would correspond to the data of Prof. M. N. Larin [2] on milling the same cast iron \((\alpha_{\mathrm{opt}} = 15^\circ)\) and would not disagree with relation (7a). It should be noted that in [2] there are also contradictions. Thus, when the relief angle is changed from \(\alpha = 5^\circ\) to \(\alpha = 15^\circ\), an increase in tool life by a factor of 5 is obtained, and not by a factor of 3, as would be expected from formula (7b)

\[ \left( \frac{\operatorname{tg} 15^\circ}{\operatorname{tg} 5^\circ} \simeq 3 \right). \]

There are no grounds for a decrease in the intensity of wear when passing to larger relief angles. A shortcoming of tool-life tests is the singularity of the results, which does not make it possible to establish the experimental error. The greatest errors are associated with the nonconstancy of the mechanical properties of the cast iron being machined and of the cutting qualities of the carbide inserts. The use of formula (7b) will, to a certain extent, make it possible to judge the reliability of the experiment and to detect an erroneous result easily.

Let us return again to formulas (7b and 7c). A consequence of their analysis is the conclusion that, first, increasing the relief angle gives a proportional gain in tool life. The limit to increasing the relief angle from this point of view is only the mechanical strength of the cutting edge. In this connection the tendency to design tools with the maximum possible relief angles is quite understandable. Secondly, the gain in tool life due to the relief angle does not lead to a saving in the consumption of carbide over time, since the intensity of wear for all sharpening variants is approximately the same (strictly speaking, greater for larger relief angles). Nevertheless, the use of tools with large relief angles, since they provide a considerable gain in tool life, is expedient both from the point of view of the productivity of the cutting process and from the point of view of the cost of production. When working with economic tool life, the increase in cutting speed for the new sharpening variant is determined by the equality:

\[ V_2 = V_1 \left( \frac{\operatorname{tg} \alpha_2}{\operatorname{tg} \alpha_1} \right)^m , \tag{8} \]

where: \(\alpha_1, V_1\) and \(\alpha_2, V_2\) are the relief angle and the cutting speed corresponding to the optimum tool life for two variants of sharpening of the flank face.

Experiments [7] have established that when turning gray cast iron with hardness \(H_B = 190\text{–}220\ \mathrm{kg/mm^2}\), the optimum value of the relief angle is \(20^\circ\), and the exponent of the degree of relative tool life is \(m = 0.38\). In comparison with the relief angle \(\alpha = 8^\circ\) recommended by the standards, the increase in cutting speed will be:

\[ \frac{V_2}{V_1} = \left( \frac{\operatorname{tg} 20^\circ}{\operatorname{tg} 8^\circ} \right)^{0.38} = 1.4 \text{ or } 140\%. \]

Along with the increase in cutting speed, the consumption of carbide per workpiece will increase.

In comparison with the former cutting condition \((V_1)\), the consumption of carbide will be (in %):

\[ K_W = \left( \frac{\operatorname{tg} \alpha_2}{\operatorname{tg} \alpha_1} \right)^{1-m} \times 100\% = \left( \frac{\operatorname{tg} 20^\circ}{\operatorname{tg} 8^\circ} \right)^{0.62} \times 100 = 180\%. \]

The actual consumption of hard alloy will be somewhat higher, since the conclusions do not take into account the increase in wear intensity due to the deterioration of heat removal for a tool with a large clearance angle.

The increased consumption of hard alloy at higher cutting speeds is fully compensated by the growth in labor productivity and by the final cost of metalworking. This is indicated by the entire practice of introducing high-speed cutting conditions.

Conclusions

1. In turning gray cast iron, the character of the tool-wear curve and the change in wear intensity are qualitatively explained quite satisfactorily by the dynamics of the cutting forces on the flank face of the tool.

The cause of the initial wear of tools should be considered to be the high values of the specific forces \(n\) and \(f\), whose magnitude on a sharp tool may exceed \(100\ \text{kg}/\text{mm}^2\). To reduce initial wear, a land should be ground on the flank face, \(0.1\)—\(0.2\ \text{mm}\) wide, with zero clearance angle. The zone of normal blunting of the tool is characterized by a moderate and more or less constant value of the specific forces on the flank face \((10—30\ \text{kg}/\text{mm}^2)\). When a certain amount of wear of the cutting edge is reached, the forces on the flank face increase, which again leads to accelerated blunting of the tool.

1. To characterize the intensity of blunting of tools wearing on the flank face, the relative intensity of volumetric wear of tools is proposed:

\[ i = \frac{1}{2}\,\operatorname{tg}\alpha \cdot \frac{h}{\tau}, \]

which takes into account the geometry of the tool and the linear intensity of growth of the wear land over time.

The transition from the linear wear intensity to volumetric wear may be useful for studying the mechanism of wear and questions of tool life by the radioactive-isotope method, as well as in analyzing the wear intensity of tools with variable sharpening geometry.

1. The increase in tool life due to the clearance angle is associated with a proportional increase in the volume of wear of the hard alloy and is limited by the ratio

\[ \frac{\operatorname{tg}\alpha_2}{\operatorname{tg}\alpha_1}. \]

The latter expression may serve as a criterion of the reliability of the experiment in determining the optimum clearance angle.

1. In designing tools that wear on the flank face, one must strive for the maximum possible values of the clearance angles. The necessary mechanical strength of the cutting blade should be created by the shape of the rake face and by other geometrical parameters \((\gamma,\varphi,\lambda,r\ \text{etc.})\), which affect tool life to a considerably lesser degree than the clearance angle.

Literature

1. Besprozvannyi I. M. Establishing cutting conditions on the basis of determining the gradual wear of the tool cutting edge. Collection “Metal Cutting,” Bauman Moscow Higher Technical School. Mashgiz, 1951.

2. Larin M. N. High-speed milling of cast-iron blanks. Collection on the exchange of technical experience “High-Speed Metal Cutting.” Issue IV. Chelyabgorizdat, 1950.

3. Margulis D. K. High-speed metal cutting at the Chelyabinsk Tractor Plant named after V. I. Stalin. Collection on the exchange of technical experience “High-Speed Metal Cutting,” issue IV, Chelyabgorizdat, 1950.

1. Rosenberg A. M.—Determination of forces on the rear face of a cutter. Collection of Notes of the Siberian Branch of the Academy of Sciences of the USSR, “Problems of Mechanical Engineering and Machine Building.” Novosibirsk, 1941.

2. VNII—Designs of carbide tools, edited by I. I. Semenchenko, Mashgiz, 1951.

3. MSS—High-speed cutting regimes for metals, part 1, Mashgiz, 1950.

4. Baikalov A. K.—Optimal geometry of cutters in high-speed turning of gray cast iron, dissertation, Tomsk, 1952.