Dependence of Cutting Forces on Tool Wear

G. L. Kufarev, A. A. Kozlov

(Presented by the scientific seminar of the Departments of Machine Tools and Metal Cutting and of Mechanical-Engineering Technology)

It has been established that, in the general case, two groups of forces act on a tool—forces on the rake and flank surfaces. For a given work material and constant tool geometry, the forces on the rake surface are determined primarily by the dimensions of the cross section of the layer being cut and by the degree of its plastic deformation. The forces on the flank surfaces are the forces of elastic-plastic contact between the flank surface of the tool and the machined surface, and are determined mainly by the conditions of this contact and by its dimensions.

As observations have shown, face mills, when machining nonferrous metals, wear mainly on the flank surfaces. As wear increases, the area of contact between the flank surface of the tool and the machined surface increases and, consequently, the forces on the flank surfaces also increase. Do the forces on the rake surface change in this case?

Since these forces, for a constant section of the layer being cut, are determined by the degree of its deformation, it was necessary to determine whether the degree of deformation of the layer being cut changes as the tool wears. For this purpose, special experiments were carried out. The materials machined were brass L62, bronze BrAZh9-4, and duralumin D1. In the course of the experiments, the chip shrinkage $\xi$, the circumferential force $P$, the feed force $P_s$, and the cutting temperature $T$ were measured.

The cutting speed and feed were varied within the ranges $V = 9 \div 970\ \text{m/min}$, $S_z = 0.02 \div 0.503\ \text{mm/tooth}$. The milling depth remained constant and equal to $t = 3\ \text{mm}$.

The experiments were conducted on a 6N13G vertical milling machine with face mills equipped with VK8 cemented-carbide inserts of constant geometry: rake angle $\gamma = +10^\circ$; clearance angle $\alpha = 10^\circ$; approach angle $\varphi = 90^\circ$. Processing of the experimental results showed that, when milling duralumin, the dependences $\xi = f(v)$, as wear increases, shift into the region of lower cutting speeds without changing their extreme values. This is caused by the fact that, as wear increases, the cutting temperature, owing to additional heat sources on the side of the flank surfaces at constant cutting speed, rises; this leads to the disappearance of the built-up edge at lower cutting speeds, the greater the amount of wear, and consequently to the corresponding shift of the curves $\xi = f(v)$.

If all the experimental points of shrinkage for different degrees of wear are plotted on a graph with shrinkage–temperature coordinates, they reliably fall on a single curve.

In milling brass and bronze, chip shrinkage decreases as tool wear increases. The decrease in shrinkage cannot be explained solely by a rise in temperature (as was done for duralumin), since even under the condition of constant temperature (Fig. 1) the shrinkage proves to be the smaller, the greater the tool wear.

It is all the more impossible to speak of the influence of temperature on shrinkage in the milling of bronze, since for it the chip shrinkage practically does not depend on the cutting temperature (Fig. 1).

Fig. 1

The main reason leading to a reduction in chip shrinkage when milling brass and bronze with a blunted tool is, in our opinion, the significant plastic deformation to which the metal layers located both beneath the machined surface and beneath the cutting surface are subjected, i.e., work hardening of the surface layer.

Specially conducted experiments showed that, with increasing tool wear, the main characteristics of work hardening increase [1], and since with increasing work hardening the plastic properties decrease, consequently, with increasing wear the chip shrinkage should decrease.

To verify this proposition, we carried out experiments to investigate the influence of work hardening on chip shrinkage in free planing of L62 brass with different degrees of preliminary work hardening of the machined surface. To avoid the influence of cutting temperature on chip shrinkage, the experiments were carried out at a speed of \(v = 98\) mm/min.

Analysis of the results obtained showed that, with an increase in the degree and depth of work hardening, chip shrinkage decreases. Since the cutting temperature during all experiments remained approximately constant and close to room temperature, the decrease in shrinkage may be...

is caused only by a decrease in the plasticity of the surface layer due to its work hardening.

In addition to the factors indicated, chip shrinkage is also affected by the radius of rounding of the cutting edge of the milling-cutter tooth, which increases as it wears. An increase in the rounding radius leads, on the one hand, to a decrease in the effective rake angle and, consequently, to an increase in shrinkage, and on the other hand, to an increase in the basic characteristics of work hardening and, consequently, to a decrease in shrinkage. As a result, shrinkage will vary depending on which of these parameters predominates.

In the general case, chip shrinkage when cutting with a tool worn on the flank face will be determined by the combined influence of the factors indicated above.

Let us now turn to the cutting forces when working with a dulled tool.

Fig. 2 presents a graph of the dependence of the circumferential force and the feed force when machining brass with milling cutters having different amounts of wear on the flank surface. The plot was constructed under the condition of constant chip shrinkage.

It is evident from the figure that when milling with a sharp cutter ($\delta = 0$), the circumferential force and the feed force vary in direct proportion to the increase in feed. The segments cut off by the straight lines $P, P_s = f(S_z)$ on the ordinate axis at $\delta = 0$ represent the forces on the flank surfaces of the sharp cutter.

When working with a cutter having wear on the flank surfaces of $\delta = 0.09 \text{ mm}$, the proportional dependence of the forces on feed is not disturbed. The straight lines $P, P_s = f(S_z)$ for the sharp cutter and for the cutter with wear $\delta = 0.09 \text{ mm}$, while remaining parallel, cut off different segments on the ordinate axis. The parallelism of the straight lines indicates that slight wear of the cutter on the flank surfaces does not change the forces on the rake surface over the entire range of feed variation.

The different segments cut off by the straight lines $P, P_s = f(S_z)$ for the sharp cutter and the cutter with the first stage of wear on the ordinate axis show that, with the appearance of wear, the forces on the flank surfaces increase.

With a further increase in wear, the proportional dependence of the force on feed is no longer maintained for all feeds. The points corresponding to small feeds lie above the straight line $P, P_s = f(S_z)$ drawn through the experimental points corresponding to medium and large feeds; moreover, as wear increases, both the value of the feed at which deviation from the proportional dependence $P, P_s = f(S_z)$ begins and the absolute displacement of the experimental points from the straight line $P, P_s = f(S_z)$ increase; and this displacement proves to be the greater, the larger the amount of wear on the flank surfaces and the smaller the feed.

When milling BrAZh9-4 bronze, a similar phenomenon is still more pronounced, while when milling duralumin no noticeable deviation from the proportional variation of cutting forces with feed was found for all degrees of wear. Such an anomaly in the dependence of cutting forces on feed when milling with a dulled tool at small feeds is explained by the influence of the radius of rounding of the cutting edges, the magnitude of which increases as tool wear increases. An increase in the radius of rounding of the cutting edges leads to the fact that, when working with small feeds, i.e., with small thicknesses of the layer being cut, the effective rake angle becomes so small that the cutting process practically ceases—

creases. Experiments show that in this case the metal is removed from the cutting zone not in the form of chips, but, undergoing large plastic deformation, is extruded toward the machined surface, forming on it a peculiar “build-up.”

Fig. 2

The process of extrusion of metal from the cutting zone leads to a sharp increase in the cutting forces, especially the feed force \(P_s\).

With an increase in feed, the actual mean rake angle becomes larger and the extrusion process gradually changes...

to normal chip formation, which leads to a decrease in the feed force. With a further increase in feed, the circumferential force \(P\) and the feed force \(P_s\) increase in proportion to the increase in feed.

The transition from extrusion to the normal chip-formation process is explained by the formation, in front of the tip of the milling-cutter tooth, of a stagnant zone; for the metals studied, the region in which it exists is determined by the thickness of the layer being cut and by the properties of the material being machined.

Chip roots obtained with the aid of the “falling tool” device showed that when turning brass with a tool having flank-surface wear \(\delta = 0.32\) mm and a cutting-edge rounding radius \(\rho = 50 \div 60\) μm, at a feed of \(S = 0.035\) mm/rev, no stagnant zone is formed. As the thickness of the layer being cut increases, a stable stagnant zone appears, whose radius of curvature is considerably smaller than the rounding radius of the dulled milling-cutter tooth; this leads to an increase in the effective rake angle and, as a result, to a transition from the extrusion process to the normal chip-formation process. A similar picture is observed in the machining of BrAZh-4 bronze. In the machining of duralumin, the stagnant zone proves stable over the entire range of feed variation; extrusion of metal from the cutting zone is not observed, and the cutting forces, both with a sharp and with a dulled tool, increase in proportion to the increase in feed, while wear affects only the forces acting on the flank surfaces. The forces on the rake surface over the entire range of feed variation in this case are practically independent of tool wear.

Conclusions

1. In milling with a dulled tool, chip shrinkage generally changes owing to the variability of three main factors:

a) cutting temperature;
b) the radius of curvature of the cutting edges;
c) preliminary work hardening of the cutting surface.

1. An increase in cutting temperature and in the preliminary work hardening of the cutting surface reduces chip shrinkage; an increase in the radius of curvature of the cutting edge increases it. A decrease in shrinkage with increasing work hardening of the layer being cut is characteristic only of strain-hardening metals. The final change in chip shrinkage is determined as the result of the simultaneous action of all factors.

2. When metals are machined with a tool having wear on the flank surfaces, owing to the increasing radius of curvature of the cutting edge, a stagnant zone is formed in front of the tool tip and takes an active part in the cutting process. The region of existence of the stagnant zone and its stability for the work materials studied are determined by the thickness of the layer being cut and by the properties of the material being machined.

Literature

1. G. L. Kufarev, A. A. Kozlov. Machinability of nonferrous metals in face milling. Vestnik mashinostroeniya, No. 3, 1965.