Study of Cutters to Determine Their Rational Geometry

V. I. Zvarygin, S. S. Sulakshin

(Presented by the scientific seminar of the Department of Exploration Technology)

The effectiveness of hard-alloy core bits in rotary drilling with an annular face depends to a large extent on the geometric form of the cutters and their arrangement in the bit crown ring. In order to determine the most rational geometry of certain types of cutters, studies were carried out under laboratory conditions to reveal the influence of a number of factors on cutting forces, depth of penetration, and cutter durability. For this purpose, a setup was used consisting of a hydraulic machine with a horizontally positioned cylinder. To record the cutting forces and the depth of cutter penetration on an N-700 oscillograph, the setup was equipped with a specially designed dynamometer with inductive transducers. The studies were conducted on samples of medium-grained sandstones taken from deposits of the Kuzbass. The main task of the investigations was to determine the influence on cutting forces and cutter penetration depth of the following parameters:

a) cutter width;
b) shape of the cutter cutting edge;
c) cutter clearance angle;
d) cutter rake angle;
e) magnitude of cutter protrusion;
f) orientation of the cutter in the bit crown ring.

Influence of Cutter Width on Cutting Forces and Cutter Penetration Depth

The cutters studied had widths of 2.5 mm, 4.5 mm, and 8 mm, with a rake angle \(\gamma\) equal to zero and a clearance angle \(\alpha = 20—30^\circ\).

Cutting with narrow cutters was carried out with a gradual increase in load until chipping or breakage of the cutters occurred. In this case, wear of the cutting edges was practically not observed. Cutting with wide cutters was carried out until a wear land, visible to the eye and about 0.1 mm wide, appeared. For each type of cutter, a series of tests was conducted on 15–20 cutters. The results of processing the oscillographic records are presented in the form of graphs in Fig. 1. These graphs show the dependence of the penetration depth and the forces acting on the cutter on its width. Analysis of the data obtained makes it possible to draw the following conclusions.

1. The dependence of the cutting forces on the width of the cutters is linear in character; moreover, the straight lines of dependence do not pass through the origin, but cut off a certain segment on the ordinate axis (Fig. 1, c).

2. The cutting forces, at the same depth of penetration of the cutter, increase more slowly than the cutter width.

Thus, at a cutter penetration depth equal to 1 mm and with an increase in cutter width by a factor of 3.2, the horizontal forces increase only by a factor of 1.86 (Fig. 1, b), and the axial forces by a factor of 2.3 (Fig. 1, a).

1. At a small cutting depth (up to 0.2 mm), the growth of the axial forces is proportional to the growth of the cutter width. This is apparently explained by the fact that

Fig. 1, a. Graph of the dependence of cutter penetration depth on axial forces for various cutter widths.
b. Graph of the dependence of horizontal forces on penetration depth for various cutter widths.
c. Graph of the dependence of cutting forces on cutter width.

at small axial forces, insufficient for penetration of the cutter into the rock, there occurs not volumetric destruction of the rock, but its abrasion.

1. With an increase in cutter width at one and the same penetration depth, the specific load decreases, but its absolute value increases. Therefore the leading “kerfing” cutters should be made of the smallest possible width.

Influence of the Shape of the Cutter Cutting Edge on Cutting Forces and Depth of Penetration

For the purpose of selecting the optimal shape of the cutting edge of cutters, experiments were carried out on cutting rocks with cutters of rectangular cross section with a cutting edge in the form of a straight line (No. 1), a semicircle (diameter 2.5 mm—No. 2 and diameter 10 mm—No. 3), and a wedge-shaped form. In addition, the cutters with a wedge-shaped cutting edge had a rake face of two types: flat (No. 4) and double-beveled (No. 5). In all cases the cutters were installed vertically.

The results of processing the oscillographic records are presented in the form of graphs (Fig. 2a, b).

From the graphs obtained it is evident that the best indices are possessed by cutters No. 1, No. 2, and No. 4, and the worst by cutters No. 3 and No. 5. At the same depth of penetration of the cutter, the minimum cutting forces (axial and horizontal) occur when cutting with cutters having a wedge-shaped cutting edge with a flat rake face (No. 4) and a cutting edge in the form of a semicircle Ø 2.5 mm (No. 2).

Fig. 2. Graphs of the dependence of the cutting conditions and cutter penetration depth for cutters with different shapes of the cutting edge.

However, when considering the cutting efficiency of cutters with different shapes of the cutting edge, one must also take into account the strength of the cutter in fracture. In the course of the experiments, along with recording the cutting forces and the depth of penetration of the cutters, we also recorded the critical forces at which breakage of cutters with different cutting-edge shapes occurred. Below is given a table of the critical horizontal cutting forces.

From Table 1 it is evident that the most stable cutter forms are wedge-shaped cutters with a double-beveled rake face (No. 5), and the least stable are cutters with a cutting edge in the form of a semicircle Ø 2.5 mm (No. 2). High strength was also shown by wedge-shaped cutters with a flat rake face (No. 4).

Thus, on the basis of the foregoing, the most rational form of the cutting edge of the cutter is wedge-shaped (No. 4). But, on the other hand, it should be expected that wear of cutters with a wedge-shaped cutting edge will occur more rapidly and that the cutter will therefore operate effectively only at the initial moment of drilling.

Table 1

Influence of the rear angles of the cutter on cutting forces and penetration depth

Experiments to determine the influence of rear angles on the effectiveness of cutting were carried out with cutters 2.5 mm wide, with front angle \(\gamma=0\) and rear angles \(\alpha\) equal to 30, 45, and 60°, on specimens taken from the Anzhero deposit: sandstones and siltstones. The results of processing the records of cutting forces and cutter penetration depth are presented in the graphs (Fig. 3, a and b). Each curve was plotted from the results

Fig. 3. Graphs of the dependence of cutting forces on the penetration depth of the cutter for cutters with different values of the rear angle.

of measurements of 7—20 cutters. It is evident from the graphs that the curves obtained when cutting with cutters having different rear angles are located very close to one another and intersect one another. Consequently, it may be considered that, within the range of the angle values investigated, the magnitude of the rear angle does not affect the penetration depth of the cutter or the cutting forces.

Influence of Rake Angles on Cutting Forces and the Depth of Penetration of the Cutter

In order to determine the influence of the rake angle on the cutting forces and the depth of penetration of the cutter, investigations were carried out over a wide range of variation of the rake angles, from \(-60^\circ\) to \(+60^\circ\).

On the basis of the oscillograms obtained, graphs were constructed showing the dependence of the depth of penetration and of the cutting forces on the magnitude of the rake angle (Fig. 4, a, b, c).

The graph (Fig. 4, a) shows the dependence of the axial cutting forces \(P\) on the depth of penetration for various values of the rake angle \(\gamma\). In Fig. 4, b, a graph is given of the dependence of the horizontal forces

Fig. 4.
a. Graph of the dependence of the axial force on the depth of penetration of the cutter for various values of the rake angle.
b. Graph of the dependence of the horizontal forces on the depth of penetration of the cutter for various values of the rake angle.
c. Graph of the dependence of the cutting forces on the rake angle of the cutter.

on the depth of penetration for different \(\gamma\). Finally, Fig. 4, c shows the dependence of the cutting forces \((P\) and \(F)\) on the magnitude of the rake angle.

The graphs obtained make it possible to draw the following conclusions:

1. The dependence of the cutting forces on the depth of cutter penetration is linear.

2. As the rake angle increases, at the same depth of cutter penetration, the axial forces grow faster than the horizontal ones.

3. For positive and negative angles, the growth of the cutting forces occurs according to different laws:

a) when the rake angle is varied within the range \(+60 \div 0^\circ\), the axial forces fluctuate within very narrow limits;

b) when the rake angle is varied from \(0\) to \(-60^\circ\), the cutting forces increase more intensively than at \(\gamma = 0 \div 60^\circ\).

Thus, cutters with positive rake angles operate most effectively. However, in evaluating the operating effectiveness of cutters with positive rake angles, their strength should also be taken into account. Table 2 gives the critical force values recorded in the experiments, at which fracture of the cutters occurs.

It is evident from the table that the greatest durability of the cutters occurs at an angle \(\gamma\) equal to \(+(30 \div 45^\circ)\).

Table 2

Consequently, the investigations carried out make it possible to recommend, for cutting certain types of rock, the most optimal values of rake angles within the range \(+30 \div +45^\circ\).

Influence of Cutter Projection from the Crown Body on Cutting Effectiveness

The very fact of the cutters projecting from the crown body during the cutting of hard rocks, when the depth of penetration of the cutters reaches fractions of a millimeter, would seem not to play a substantial role. On the contrary, with a large cutter projection the durability of the cutters decreases, which compels a reduction in the cutting forces. However, it is important here to note the fact that, with

Fig. 5.

limited projection of the cutter from the core-bit ring, in the process of cutting rock an indurated mass is formed in front of it under the end face of the core-bit ring; this mass changes the cutting angle and, consequently,

and the cutting force. As a result of this circumstance, we may fail to obtain the expected effect when increasing the rake angle.

The phenomenon of formation of compacted rock in front of cutters with limited protrusion is observed most intensively at large positive angles.

To eliminate this defect, the protrusion of the cutters should be increased by lengthening the cutters and by making a special cutout in the body of the crown in front of the cutters (Fig. 5).

Effect of the orientation of the cutter in the crown body on cutting forces and depth of penetration

To determine the dependence of cutting forces on the orientation of the cutter in the body of the crown, studies were carried out on cutting sandstones at the following values of the cutting angles in the plane \((\delta)\): \(90, 60, 30\), and \(0^\circ\). On the basis of the results of the investigations, graphs were prepared (Fig. 6). From the graphs it is evident that, at the same depth of penetration of the cutter, the axial forces at different angles \(\delta\) differ little from one another. A noticeable reduction in the axial forces is observed only at \(\delta = 0\).

Fig. 6. Graphs of the dependence of cutting forces on the angle in the plane.

Horizontal forces decrease more distinctly as the angle \(\delta\) is reduced. But with a reduction of forces at small values of \(\delta\), the volume of rock chipped off also decreases. Therefore, cutters with small \(\delta\) can be recommended only as “scoring” cutters.

Conclusions

1. The increase in cutting forces at a penetration depth of more than \(0.2\) mm occurs more slowly than the increase in cutter width; therefore, when designing crowns, the “scoring” (front) cutters should be installed with the smallest width. The subsequent cutters will operate under more favorable conditions, and the smaller the number of cutters across the width of the borehole groove, the less force will be expended on cutting the rock. Consequently, the subsequent cutters, in order to overlap the groove completely, should be made of greater width.

2. At a small depth of penetration of the cutter (less than \(0.2\) mm), the increase in cutting forces occurs in proportion to the increase in cutter width.

1. The most rational shape of the cutting edge of a cutter from the series of cutters tested is a wedge-shaped form with a flat front face of the cutter.

2. The clearance angle of the cutter when cutting rock does not affect cutting efficiency.

3. The cutters with a rake angle of \(30—45^\circ\) proved to be the most durable and effective in operation. Therefore, when designing crowns, it may be recommended to install cutters with the indicated rake angles.

4. With a limited projection of the cutters from the body of the crown ring, a compacted mass of rock forms in front of them, which changes the rake angle of the cutter, as a result of which the cutting forces increase. To eliminate this defect, the projection of the cutters should be increased by lengthening the cutters and by making a special cutout in the body of the crown in front of the cutters.

5. As the cutting angle in plan \(\delta\) decreases, the cutting forces decrease; however, with the decrease in forces the volume being chipped off also decreases. Therefore, cutters with small values of \(\delta\) can be recommended only as “undercutting” cutters.