WEAR OF A CARBIDE CUTTING TOOL ON THE FLANK FACE AND ITS INFLUENCE ON CUTTING FORCE

G. L. KUFAREV, V. A. NAUMOV

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

Tool wear and its consequences attract the close attention of many researchers. This is understandable. In the national economy, an enormous range and quantity of cutting tools are used, and even a small increase in their wear resistance promises great savings of public funds.

An important section in the study of wear mechanics is the establishment of the relationship between wear and the forces acting on the faces of the tool.

The reasons for the lag in the study of the dynamics of a worn cutter are the complexity of the process and the difficulty of separating the forces acting on the different faces of the tool.

Even for a sharply ground cutter, methods for isolating the forces on the flank face [1, 2, 3] are laborious and not beyond reproach with respect to accuracy.

A number of works [4, 5] are devoted to studying the influence of wear on force characteristics; they do not claim to provide a complete treatment of the question under investigation.

The cutting tool wears on all surfaces of its cutting part, and the wear of each of the surfaces—the rake face, the flank face, and the auxiliary flank face—affects the cutting forces in different ways.

Because of the complexity of the phenomenon, it is impossible to study the complex influence of tool wear on cutting forces. It is simplest and most expedient to analyze the change in cutting forces when one of the indicated surfaces wears.

The present work solves the problem of the influence on the cutting forces of wear only of the principal flank surface of the cutter.

Research methodology. As preliminary studies showed, wear of the rake face is practically absent, within fairly wide limits of variation of the parameters of the cutting process, when turning titanium alloy VT-6, which also determined the choice of the work material in these studies. The frequently observed intensive wear of the flank surface at the cutter tip was eliminated by giving the cutter a positive cutting-edge inclination angle \((\lambda = +11^\circ)\).

Thus, the adopted tool geometry: \(\gamma = +10^\circ\), \(\varphi = 70^\circ\), \(\varphi_1 = 20^\circ\), \(\lambda = +11^\circ\), and \(\alpha = 10^\circ\), as well as the choice of VT-6 alloy as the work material, made it possible to reproduce such

a cutting process in which the principal and practically the only type of wear was wear on the main flank face of the tool.

The experiments were carried out on a model 1D3 lathe equipped with a rigid three-component dynamometer with inductive sensors.

The influence of wear on the cutting forces was studied at different cutting speeds and with different feeds. In each of the experiments the tool was brought to optimal wear; moreover, over the period of its life the following were repeatedly measured:

1. The actual geometry of the worn tool (the width of the wear land on the flank face \(h_{\text{fl}}\) and the actual clearance angle on the wear chamfer \(\alpha_0\)).

2. The components of the cutting force \(P_x;\ P_y;\ P_z\).

The geometry of the worn tool during the experiment was recorded by the imprint method [7] and by photographing polished sections of a replica of the tool on a metallographic microscope. Recording of the tool profile was carried out on a special instrument developed in the cutting laboratory of TPI [6].

A special procedure was also developed for determining the actual clearance angle of the tool on the wear chamfer. After the tool was mounted in the dynamometer, the angle in the main cutting plane between the main flank surface and a plumb line was photographed. From the photograph obtained, this angle could be determined with an accuracy of up to \(\pm 3\%\). Thus, in the subsequent processing of the profilograms and photographs of the polished sections of the tool replicas, the flank face served as the reference for measuring the actual clearance angle on the wear chamfer.

The components of the cutting force \(P_x,\ P_y,\ P_z\) were recorded on paper tape by a reequipped BB-662 self-recording instrument from the Kalibr plant.

In addition, during the experiments the temperature in the cutting zone was recorded by the natural-thermocouple method using a KVT6/EN—MAW (GDR) recorder and a millivoltmeter.

Results of the investigation. In the course of the study, two series of experiments were carried out.

In the first series, at a constant feed \(S = 0.2\ \text{mm/rev}\), the tools were successively brought to optimal flank wear at speeds \(V = 106;\ 68.1;\ 38.2\ \text{m/min}\).

The second series was conducted at a constant cutting speed \(V = 38.2\ \text{m/min}\) with feeds \(S = 0.4;\ 0.3;\ 0.2\ \text{mm/rev}\).

From the experimental results, graphs were plotted for the variation, along the cutting path, of the flank wear chamfer \(h_{\text{fl}}\), the actual clearance angle on it \(\alpha_0\), the chip compression \(\xi\), and the three components of the cutting force. These graphs for the second series of experiments are given in Fig. 1.

Comparison of the curves of variation of the cutting forces with the actual geometry of the cutting part of the tool makes it possible to establish the causes and explain the nature of the change in forces with increasing operating time of the tool or cutting path.

It is assumed here that the change in forces with the growth of tool flank wear is determined only by the change in the force components acting on the flank face of the tool, while the force components on the rake face remain unchanged.

As follows from the graphs presented, the chip compression remained constant as the tool became dull. When cutting titanium alloys and, in particular, alloy VT-6, the chip is elemental, i.e., the chip compression in this case does not reflect the degree of its plastic deformation. But the constancy of the shape and dimensions of the chip elements,

as a result of which the constancy of chip shrinkage is ensured, makes it possible to state with sufficient certainty the constancy of the forces involved in the formation of this chip, i.e., the forces acting on the rake face of the cutter. This was also to be expected, since in machining the alloy VT-6, wear of the rake face was practically absent.

Additional confirmation of the constancy of the forces on the rake face is the absence of a rounding radius of the cutting edge of the cutter even at large values of wear on the flank face of the cutter. This fact was established experimentally from a large number of photographs of microsections.

The actual clearance angle \(\alpha_{э}\) varied from the setting angle \(\alpha\) to negative values. Cutting speed has no effect on the change of this angle; therefore all the points satisfactorily lay on a single curve.

Conversely, increasing the feed shifts the \(\alpha_{э}—L\) curve toward larger negative angles (Fig. 1).

The reasons for the formation of a negative clearance angle on the wear land are apparently the difference in the temperatures of the contact surfaces near the tool tip and away from it, as well as the nature of microchipping of the cutting edge. The relatively rapid wear of the cutter material at points close to its tip leads to the formation of a wear land with a negative angle.

The formation of a wear land with a negative clearance angle is also promoted by the kinematic reduction of the clearance angle. This may explain the fact that in Fig. 1 the \(\alpha_{э}—L\) curves are located lower, the larger the feed value and, consequently, the larger the inclination angle of the helical cutting surface.

Fig. 1

The obtained results of studying the change in the geometry of the worn part make it possible to refine the general picture of wear on the flank face.

The existing conception of the wear mechanism [8] amounts to the following (Fig. 2a): wear occurs in uniform layers parallel to the cutting plane. On this basis, the formula for radial wear (wear in the principal cutting plane) was given:

\[ \Delta = h_{zg}\tan\alpha . \tag{1} \]

Fig. 2

The refinement of the wear mechanism concerns the circumstance that, in the process of wear, not only does the contact area increase according to the typical curve (Fig. 2b), but it also rotates, i.e., the actual clearance angle \(\alpha_e\) changes from a positive value \(\alpha\) to some particular value \(\alpha_e\), which has a negative value in the case of machining VT6 titanium.

The good reproducibility of the geometric form of the \(\alpha_e - L\) curve makes it possible to regard it as a typical wear curve, which must necessarily be taken into account along with the curve \(h_{zg}=f(L)\); \(f_{zg}=f(L)\), where \(f_{zg}\) is the magnitude of the contact area on the flank face.

The change in \(\alpha_e\), especially in the negative region, has a decisive influence on the redistribution of the values of the cutting-force components.

On the \(\alpha_e - e\) curve, three stages of rotation of the area are clearly distinguishable: the first stage, corresponding to the running-in of the cutter (a rapid decrease in \(\alpha_e\), leading to self-strengthening of the cutting wedge); the second stage, corresponding to normal wear (a smooth decrease in \(\alpha_e\) with transition into the negative region); the third stage, corresponding to accelerated wear (the wear land increases sharply and the negative value of the angle \(\alpha_e\) increases). In our experiments the negative value of \(\alpha_e\) reached \(-10^\circ\), \(-12^\circ\); therefore formula (1) is inaccurate, and the error may reach 100% or more.

The new conception of the mechanism of wear of the cutter flank face makes it necessary to introduce the corresponding corrections into the scheme of forces acting on the flank face.

In the proposed scheme (Fig. 3a), the friction force \(F_1\) is directed not opposite to the direction of the cutting speed, but along the wear land; the force \(N_1\) is perpendicular to it, since within the contact with the cutter the points of the machined surface move along the flank face, and not in the direction of the cutting speed. They acquire the component perpendicular to the speed within the contact as a result of elastic

Fig. 3

a
Labels in the diagram: \(O\), \(N\), \(F\), \(N'\), \(R_n\), \(R_z\), \(R_{z}^{e}\), \(R_{z}^{c}\), \(P_z\), \(V_{\mathrm{result}}\), \(V_{\mathrm{el}}\), \(V_{\mathrm{pl}}\).

b
Labels in the diagram: \(O\), \(O'\), \(O''\), \(F'\), \(N'\), \(N''\), \(V_{\mathrm{result}}\), \(V_{\mathrm{el}}\), \(V_{\mathrm{pl}}\), \(V_{\mathrm{result}}'\), \(V_{\mathrm{el}}'\), \(V_{\mathrm{pl}}'\).

restoration of the metal deformed by forces from the flank face in the primary deformation zone.

A similar scheme for an ideal sharp cutter was proposed by K. A. Zvorykin in 1893, but was later rejected by a number of researchers.

Some of them [10] experimentally proved that the contact area on the flank face already at the first moment of cutting has a finite value. Experiments carried out on titanium VT6 confirmed this fact. The assumption that \(\alpha_3 = 0^\circ\) was erroneous.

Others [9] asserted that the direction of the forces proposed by K. A. Zvorykin contradicts the principles of theoretical mechanics. This is a misconception. In Fig. 3a, point \(O\) moves to \(O^1\) along the flank face with velocity \(V_{\mathrm{sum}}\), which is the sum of the vectors of the cutting velocity \(V\) and the velocity of elastic recovery of the deformed material \(V_{\mathrm{el}}\); therefore the direction of the friction force must be opposite to the resultant-velocity vector, and not to the cutting-velocity vector, as O. K. Zvorykin does. The contact area at the first moment may have finite dimensions, since the elastic displacement \(V_{\mathrm{el}}\) has a finite value.

Figure 3b gives the real scheme of deformation and friction on the flank face under the condition \(\alpha_3 < 0^\circ\). Two contact regions are visible: the elastic-plastic region \(OO'\) and the elastic region \(O'O''\).

In the region \(OO'\), point \(O\) participates simultaneously in two motions: along the cutting-velocity vector \(V\) and in elastic-plastic crushing \(V_{\mathrm{pl}}\).

In the region \(O'O''\), point \(O'\) likewise participates in two motions: along the cutting-velocity vector \(V\) and at the velocity of elastic recovery \(V_{\mathrm{el}}\). Accordingly, two normal forces \(N'_1\), \(N''_1\) and two friction forces \(F'_1\) and \(F''_1\) act. Here, too, there is no contradiction with the principles of theoretical mechanics.

The technological components of the cutting force (from Fig. 3a and b) will be expressed by the formulas:

a) For the case when \(\alpha_3 > 0^\circ\),

\[ P_z = N \cos \gamma + F \sin \gamma + F_1 \cos \alpha_3 - N_1 \sin \alpha_3, \tag{2} \]

\[ R_{\mathrm{n}} = -N \sin \gamma + F \cos \gamma + N_1 \cos \alpha_3 + F_1 \sin \alpha_3. \tag{3} \]

b) For the case when \(\alpha_3 < 0^\circ\),

\[ P_z = N \cos \gamma + F \sin \gamma + F'_1 \cos \alpha_3 + N'_1 \sin \alpha_3 + F''_1 \cos \alpha - N''_1 \sin \alpha, \tag{4} \]

\[ R_{\mathrm{n}} = -N \sin \gamma + F \cos \gamma - F'_1 \sin \alpha_3 + N'_1 \cos \alpha_3 + F''_1 \sin \alpha + N''_1 \cos \alpha. \tag{5} \]

In formulas (4) and (5), the components \(N'_1\) and \(F'_1\) are the result of elastic-plastic contact on the flank face, while the components \(N''_1\) and \(F''_1\) are the result of elastic contact on the flank face. Analyzing the curves \(\alpha_3 - L\), \(f_{3\mathrm{g}} - L\), as well as formulas (2, 3, 4, 5), one can foresee the qualitative change in the components of the cutting force. The reasoning is based on the fact that when \(\alpha_3 = f(L)\) changes, the scheme of deformations and friction on the contact area along the flank face changes. A change in the deformation scheme leads to a change in temperature and in the coefficient of friction. The transition of \(\alpha_3\) into the negative region, in addition to all that has been said earlier, causes the appearance of new components \(F'_1\) and \(N'_1\).

Briefly, the nature of the change in cutting forces with the path traveled by the cutter during wear on the flank face can be reduced to the following.

The change in forces follows a curve resembling the character of the change

\[ f_{3\mathrm{g}} = f(L). \]

In the region of initial wear there follows a sharp increase in the cutting force, which is explained by the rapid increase in the contact area \(f_{з}\) and by the decrease in the actual angle \(\alpha_{з}\).

The region of steady wear corresponds to the region of steady increase of the components \((P_z;\ R_{\text{н}})\). In the region of forced wear, one should expect a sharp increase in the magnitude of the components of the cutting force.

The arguments presented are valid only for titanium, for which the steady region of the curve \(\alpha_{з}\) lies in the region of negative values. The same character of the curve should occur if the region of steady wear lies in the positive region \(\alpha_{з} > 0^\circ\) throughout the experiment.

The experimental data presented in Figs. 1 and 2 confirm the considerations expressed above concerning the relation between the components of the cutting force and wear on the flank face.

Considering the graphs \((P_x;\ P_y;\ P_z) = f(L)\) together with the graphs \((\alpha_{з};\ h_{з}) = f(L)\), one can detect the regions of initial and steady wear and the corresponding increase in them.

Conclusions

1. The investigations carried out made it possible to clarify the concept of the mechanism of wear on the flank face of the tool.

2. The actual angle \(\alpha_{з}\) on the wear land does not remain constant and equal to \(0^\circ\). It changes from \(\alpha\) (the grinding and setting angle) to negative values reaching \(-10^\circ;\ -14^\circ\).

3. The negative wear land causes an additional interference fit of the machine–fixture–tool–workpiece system. Its appearance is an inevitable regularity of the cutting process. It is especially characteristic of difficult-to-machine materials. Therefore it is necessary in every way to increase the rigidity of metal-cutting machine tools intended for machining these materials.

4. The phenomenon discovered (the nonconstancy of \(\alpha_{з}\)) makes it possible satisfactorily to explain the character of the change in the components of the cutting force during wear on the flank face.

5. In studying force relationships on a worn tool, it is necessary to take into account the phenomena of rotation of the friction area on the flank face and to take them into account accordingly (formulas 2; 3; 4; 5).

REFERENCES

1. N. N. Zorev. Questions of the Mechanics of the Metal-Cutting Process. Mashgiz, 1956.

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

3. M. E. Itkin. Investigation of the forces acting on the faces of a tool. In: Machinability of Heat-Resistant and Titanium Alloys, Kuibyshev, 1962.

4. A. K. Baikalov. Optimal Geometry of Cutters in High-Speed Turning of Gray Cast Iron. Dissertation, Tomsk, 1952.

5. Yu. A. Tolokov. Change in cutting forces during tool wear. Machine Tools and Tooling, No. 10, 1960.

6. M. F. Poletika, V. A. Naumov. An instrument for investigating the wear of a cutting tool. Izv. TPI, vol. 147, 1966.

7. G. L. Kufarev, V. A. Naumov. Influence of wear on cutting forces in turning. Izv. TPI, vol. 147, 1966.

8. M. I. Danielyan. Tool Wear and Thermal Phenomena in Metal Cutting. Mashgiz, 1954.

9. O. K. Zvorykin. On the direction of the forces acting on the rear surface of a cutting tool. Questions of Mechanics and Machine Building, Publishing House of Kiev University, Kiev, 1964.

10. N. N. Zorev. Investigation of Elements of the Mechanics of the Metal-Cutting Process. Mashgiz, 1952.