At present, the most widely used drill matrix shapes are circular arc with chamfer and flat bottom. However, under complex geological conditions, their wear is very serious.
Many researchers try to calculate the best cross-sectional shape of the end of diamond bit according to the research results of diamond drilling mechanism, so as to ensure constant working pressure, friction or pulsating pressure on the working diamond layer.
A historical review of (1) optimization of end face shape of diamond bit.
As early as 1960s, впп Onishen studied the wear problem of impregnated diamond bit when drilling into diabase, and on this basis, put forward a model to keep its cross-sectional shape unchanged and maintain the equal strength wear at the end of the bit (that is, the end width should be reduced in a balanced way). The model puts forward the following assumptions:
(1) load is evenly distributed along the whole end zone;
(2) The wear of the end face of the drill bit is directly proportional to the specific work (unit area) of the friction force.
Results The following equation was obtained:
Application of synthetic diamond superhard material in drilling
Where: z is the height of the matrix (a function of the distance from the bit axis); R is the radius of the end element; D and D 1 are the outer diameter and inner diameter of the bit, respectively.
According to this equation, the curve expression of the optimal section can be obtained (Figure 5-9), which is a parabola. впп Onishen also pointed out that more than 80% of worn bits have a profile close to parabola. According to the author, this shows that it is the best shape.
нееееееееееееееееееее??еее??10777 The shape of the diamond bit shall conform to the following formula:
Application of synthetic diamond superhard material in drilling
Where: φi is the included angle between the tangent of the section shape and the plane perpendicular to the rotary shaft of the drill bit; Ni and Nm are axial forces determined according to experimental data; Ri is the instantaneous radius of the drill bit; Rmax(min) is the outer (inner) diameter of the drill bit (consider rmax when Ni >: 0, and when Ni
According to the formula (5-58), the cross section of the diamond drill (Figure 5- 10) can have different shapes, even in the opposite direction.
Figure 5-9 Ends of drill bit with equal strength wear (according to впппп)
Fig. 5-Equal wear-resistant end face shape of10 bit (former Soviet national standard A.C.1170109)
There are other calculation methods, which do not consider the performance of the drilled rock when calculating the optimal cross-sectional shape of the drill bit. For example, in order to keep the pulsating pressure constant, it has been proposed to establish the bit profile according to the following formula:
Application of synthetic diamond superhard material in drilling
Where: βi is the included angle between the axial load direction and the tangent of its curve segment.
The optimum profile form established by this formula is shown in Figure 5- 1 1.
There are some other programs that are obviously different from the above opinions. For example, врр Puniak once established the curve equation (Equation 5-60) of the optimal cross section of the impregnated drill bit end according to the research results of the drill bit wear process. In the author's opinion, this cross-sectional shape will ensure balanced wear when drilling holes in broken rocks (Figure 5- 12):
Application of synthetic diamond superhard material in drilling
Fig. 5- Cross-sectional shape of diamond bit (A.C.1201511).
Where: x is the existing coordinate of the drill radius; Y is the existing coordinates of the diamond layer of the profile.
One of the effective methods to strengthen the drilling process of impregnated drill bit is to make its rock-breaking part into a right-angled trapezoidal section inclined to the core.
The role of axial force is to help the diamond protruding from the matrix eat into the rock. Torque ensures that the eaten diamond moves under the tangential force. Under the combined action of these two forces, the micro-cutting process of rock at the bottom of the hole is produced.
We can divide the working lip of the drill bit into several rings with equal width. Under the condition of the same moving distance, the diamonds near the inner ring surface must cut deeper into the rock than the diamonds in the outer ring under the load. Therefore, the phenomenon of premature wear of the matrix often occurs in the inner diameter part of the drill bit. In order to improve the service life, people try to overcome the above shortcomings by improving the bit structure. One solution is to use an inwardly inclined wedge-shaped matrix on the drill bit.
(2) New research progress on the relationship between drilling power consumption and bit lip shape.
For superhard materials research? 46 mm drill bit for drilling test. Five drills with different inclination angles (α = 30, 45, 60, 90) and semi-chamfer profiles are used (Figure 5- 13).
In order to determine the pressure on the contact surface with rocks, the researchers established a corresponding relationship. For the contact surface S90 of the flat bottom drill, there is the following expression.
Application of synthetic diamond superhard material in drilling
The expression can be simplified to:
Application of synthetic diamond superhard material in drilling
Where: d and d are the outer diameter and inner diameter of the drill bit respectively; M is the number of sector blocks; Is the width of the nozzle.
For bits with other inclination angles on the working lip, contact area:
Application of synthetic diamond superhard material in drilling
Fig. 5- 12 Equal Wear Profile of Diamond Bit (according to впп Puniak)
Fig. 5- 13 schematic diagram of bit wear test with different working inclination angles.
Contact area of drill bit with semi-circular chamfer part
Application of synthetic diamond superhard material in drilling
Where r0 is the chamfer radius of the section.
The pressure of the drill bit on the inclined bottom lip and the flat bottom lip has the following relationship.
Application of synthetic diamond superhard material in drilling
Where σ 1 and σ2 are the normal loads applied to the unit cross-sectional area of the flat bottom lip and inclined bottom lip at the end of the drill bit, respectively.
This ratio can be obtained with the help of Figure 5- 14, where: p is the total axial load acting on the drill bit; P 1 is the partial axial load acting on the working lip surface S 1, that is, the flat bottom end of the bit; P2 is the partial axial load acting on the working lip S2, that is, acting on the inclined surface of the drill bit or its projection (S-S 1), where S is the projection of the working end face of the drill bit on the plane perpendicular to the rotation axis of the drill bit.
Obviously, P=P 1+P2, but the surface area
Fig. 5- 14 schematic diagram for determining lip pressure distribution of inclined flat-bottom bit.
Application of synthetic diamond superhard material in drilling
Stress, thus
Application of synthetic diamond superhard material in drilling
Where ρ2 is the total stress in S2 plane.
Therefore, the normal load acts on the S2 plane.
Application of synthetic diamond superhard material in drilling
under the circumstances
Application of synthetic diamond superhard material in drilling
It shows that we can get the relationship between the pressure ratio on the inclined plane and the flat bottom surface and the angle value, which refers to the included angle between the working lip surface of the bit formed by the inclined plane and its rotating shaft. If the bit surface pressure is a constant value, then the load to ensure the pressure value can be determined according to the following formula.
For drill bits with semi-circular chamfers
Application of synthetic diamond superhard material in drilling
In this case, the σ value should be an average value, because it varies with the curvature of the bit part. Fig. 5- 15 (curve 1) shows the relationship between drilling power consumption and inclination angle of bit working lip.
Fig. 5- 15 Relationship curve between relevant parameters and working face inclination angle α.
As can be seen from the figure, with the increase of working lip inclination angle, drilling power consumption decreases, that is, under the same drilling regulations, the power consumption of wedge-section bit is greater than that of flat-bottomed bit. This can be explained by more diamonds in contact with rocks.
When the angle is increased from 30 to 90 (three times the original), the drilling power consumption is reduced by 42% (from 5.5kW to 3.2kW). A similar relationship also appears in curve 2 reflecting ROP.
When the projected area of the end face on the plane perpendicular to the rotation axis is the same, the larger the contact area, the more obvious the advantage of penetration rate.
Because there are few diamond particles on its contact surface, the drilling speed of flat-bottomed bit is lower than that of wedge-shaped bit. When α = 30, the ROP of the bit is 4.5m/h, while when α = 90, the ROP is 2.25m/h. ..
The relationship between specific work of rock breaking (work required for rock breaking per unit volume) and angle α is shown in curve 3 in figure 5- 15.
This relationship curve is increasing function, and the function value increases with the increase of angle. This relationship is contrary to the drilling power consumption reflected by the curve 1 When the drill bit breaks the same volume of rock at the same angle, we can see that the drilling speed and drilling time are different by comparing the correlation between the parameters, which shows that there is a direct proportional relationship between the rock breaking work and them. The absolute value of the product of power consumption and drilling time is also smaller than that of the drill with small working lip inclination. Therefore, the former drilling time decreases significantly faster than the drilling power consumption increases. It has been proved that the rock-breaking efficiency of small inclination (α) bit is high, and its characteristic is low specific energy consumption.
In order to optimize the above parameters, we studied the relationship between bit wear resistance and different α angles. Obviously, the smaller the specific work of rock breaking, the better the cutting ability of the end face of the bit, which also means the stronger the wear resistance of the bit. When the specific work is large, if the contact surface between the drill bit and the rock is not well run-in, the cutting ability of the drill bit cannot be exerted. At this time, the rock fragmentation is not mainly the result of micro-cutting, but by grinding. In this case, the wear resistance of the drill bit decreases. This situation is truly reflected in the relationship between bit wear and α angle (curve 4) in Figure 5- 15. The wear of drill bit varies from 30 ~ 120 mg, which is almost three times different.
Fig. 5- 16 shows the derived curves of drilling power (curve 1) and wear weight loss (curve 2) in the contact area between bit lip and rock.
The contact area is inversely proportional to the α angle. The larger the α angle, the smaller the contact area. This can be seen from the data listed in Table 5-6.
Table 5-6 Relationship between Contact Area and α Angle
With the increase of contact area, drilling power increases linearly, while the wear weight loss of drill bit decreases hyperbolic. This relationship can be obtained through experiments, in which the drilling rules are 630r/min and 10kN (provided that the rock can be cut smoothly).
Under the given drilling specifications, the drilling power is increased by 30%, while the wear is reduced to 1/3. During this drilling period, the total contact area increased by 1 times.
Fig. 5- 17 shows the relationship among drilling power, rock breaking specific work, bit wear weightlessness and axial load when α angle increases from 30 to 90, in order to keep the drilling speed and the inclination angle of bit end face unchanged.
Fig. 5- 16 Relationship between drilling power, matrix wear and contact area Sk between bit and rock.
Figure 5- 17 Relationship between related parameters and working face inclination angle α
The curve 1 reflects the law of drilling power changing with the independent variable α, which is a straight line and presents the function characteristic of monotonic growth along the ordinate in the whole α range. At this time, the drilling power changed from 0.8 to 1.7kW, which increased by more than 1 times, while the dip angle of working face increased by 2 times. In our observation range, the drilling power is increasing. However, it must be noted that the variation trend of drilling power of drills with different working face inclination angles is opposite under the conditions of free feed and forced feed, that is, with the increase of α angle, the power consumption decreases under the condition of free feed and increases under the condition of forced feed. This view proves that there are different contact mechanisms between the end face of diamond bit and the rock surface.
The first case is to maintain a constant pressure on the tool, and the second case is to maintain a constant penetration rate. Obviously, in the second case, when the working face inclination is constant, the axial load is not only related to the working face inclination, but also depends on the cutting state of the working face.
In the problem studied, when the α angle increases, in the same range (as mentioned above), the drilling power increases by 1 times in the case of Vm=const, while the drilling speed and drilling power of the drill bit decrease by 42% at the same time in the case of free feed. In this case, the absolute value of the corresponding power is related to the drilling and cutting parameters.
The relationship between rock breaking specific work and α angle is shown in figure 5- 17 curve 2.
It can be seen that this relationship conforms to the changing law of drilling power. Under the conditions of this study, the volume crushing speed of rock is constant, and the drilling power depends on the state of cutting surface. As mentioned earlier, the power consumption of small inclination drilling rig is higher. Therefore, the rock breaking effect of the bit with this inclination angle is better. The measured power value is not large, which also reflects this characteristic. It can be seen that the product of power and drilling time increases with the increase of α angle.
From the point of view of energy consumption, the drilling effects of two feeding methods are studied. The results show that the bit with large wedge section is more effective than the flat-bottomed bit.
Curve 3 of fig. 5- 17 shows the wear resistance of the drill bit determined by the wear weight loss. As shown in the figure, under the condition of forced feed, the wear weight loss of the drill bit changes with α angle, and it also has the same characteristics under the condition of free feed.
This is consistent with the rock-breaking specific work curve of impregnated diamond bits with different inclination angles under the conditions of free feed and forced feed.
As mentioned earlier, the wear resistance of the drill bit is a function of the specific work of rock breaking. At this time, the greater the specific work of rock crushing, the smaller the wear resistance of tools in this rock. In other words, the wear resistance of the drill bit depends not only on the structural parameters and drilling regulations of the drill bit, but also on the physical and mechanical properties of the drilled rock. In this regard, Figure 5- 17 shows the relationship between the axial force obtained from the experiment and the inclination angle of the working face. The condition of forced feed is that the feed rate per turn is 80 μ m under the premise of bit speed of 630r/min.
When the feed rate is 80 μ m, the penetration rate is 3.02m/h. Therefore, the axial pressure must be ensured by the hydraulic system of the test bench. The principle of selection is to ensure that the penetration rate reaches 3.02m/h, and the appropriate axial load is automatically selected through the instantaneous penetration rate detected by the sensor instrument.
The axial force obtained by this method shows that it increases with the increase of α angle, that is, the axial force is the largest when the bit section is close to the flat bottom.
Whether the constant penetration rate is achieved by forced feed or optimization of WOB, the measured penetration power consumption is actually the same in both cases.
As can be seen from the figure, when the drill bit transits from the wedge-shaped section (α = 30) to the flat-bottomed section (α = 90), the required axial load increases by 70% when the feed per turn is 80μ m. From the point of view of dynamic load and energy consumption, it can also be seen that the wedge-shaped section drill bit has more drilling advantages.
Figure 5- 18 shows the relationship between drilling power consumption, wear weight loss and contact area when the diamond bit rubs against the rock.
Fig. 5- 18 Relationship between related parameters and contact area between bit and rock
Table 5-6 shows the contact areas with different inclination angles. In the case of forced feed, the drilling power consumption decreases hyperbolic with the increase of contact area, while it increases in the case of free feed (see Figure 5- 16). This change is reflected in the reduction of drilling power consumption by 55%.
As we all know, the larger the contact area, the more diamonds will be involved in crushing rocks with the same volume. In this case, the cutting function of the end face has been obviously improved, which is reflected in the actual process. Under certain footage conditions, the axial force is reduced and the same power consumption is also reduced. The wear weight loss of the drill bit also presents hyperbolic characteristics, which has nothing to do with the feeding mode to ensure the diamond to eat into the rock. Under these two feeding conditions, the wear weight loss of the drill bit decreases with the increase of contact area. Thus, as shown in Figure 5- 18, the wear amount decreased from 100mg to 25mg, a decrease of 75%.
Fig. 5- 19 describes the relationship between drilling power and wear weight loss under the condition of forced feed (80μm per revolution) and the pressure value on the contact surface between the bit and the rock. The pressure on the working lip surface is determined according to Formula (5-7 1) and Formula (5-72). Table 5-7 lists the relationship between these values and the working lip inclination.
The curve 1 is directly proportional, and the drilling power increases with the increase of specific pressure. When the specific pressure is increased from 0.22 to 1.46kN/cm2 (an increase of 6 times), the drilling power is increased by 1. 1 times, from 0.8kW to 1.7kW, and this linear growth law also exists in the wear weight loss of the drill bit. When the specific pressure changes in the same range, the wear weight loss of the bit increases by 5 times. When the axial load is 10kN, we can observe a similar relationship to the specific pressure. Therefore, the wear weight loss of the drill bit also has a functional characteristic independent of the feed form and the inclination angle of the working lip.
Fig. 5- 19 Relationship between related parameters and bit face pressure
Table 5-7 Relationship between Pressure and Angle of Working Lip
Figure 5-20 shows the relationship among absolute drilling power, rock breaking specific work, axial load and working lip inclination. The curve 1 shows that there is a hyperbolic relationship between the calculated axial force and α angle.
Figure 5-20 Relationship between working lip inclination and related parameters of carcass.
Increasing the contact area or decreasing the α angle will increase the axial force. When the α angle increases from 45 to 90 (increasing 1 times), the axial load decreases from 13.6kN to 6.8kN (decreasing by the same number of times). Because the axial load decreases with the increase of α angle, and the drilling power is always proportional to the load, the hyperbolic relationship between drilling power and α angle (curve 2) is credible, and it does exist. That is, with the increase of α angle, the drilling power also decreased from 2.25kW to 1.35kW.
The straight line 3 shows that the relationship between the specific work of rock breaking and the different inclination angles of the working lip has little change under the condition of constant pressure.
Therefore, it is not certain that the rock-breaking specific work of different α-angle bits presents the characteristics of increasing function under the conditions of free feed and forced feed.
Figure 5-2 1 (curve 1) describes the functional relationship between penetration rate and α angle.
Fig. 5-2 1 relationship between penetration rate (1) and matrix wear (2) and working lip inclination.
It can be seen that ROP decreases with the increase of α angle. This relationship is consistent with the test results under constant axial load (curve 2) (Figure 5- 15). In the observed case, the axial load decreases with the increase of α angle.
Curve 2 determines the wear resistance of drill bits with different working lip inclination angles through the loss of wear weight.
Under the conditions of forced feed and free feed, with the increase of α angle, the pressure required for each rotation of the working lip surface also increases. Therefore, high pressure will inevitably lead to great grinding loss. This has been confirmed in curve 3 of figure 5- 15 and curve 4 of figure 5- 15.
In the above experiment, the pressure is constant, but the area is variable, which is inversely proportional to the α angle. Obviously, under the condition of constant pressure, the wear weight loss increases with the increase of friction surface, and vice versa.
Related to this, the flat bottom drill has great wear resistance. Curve 2 also shows the same regularity. The experimental relationship obtained under the condition of constant bit face pressure shows that the wear amount decreases by n times with the increase of α angle.
This regularity is more obvious than the similar relationship obtained under the condition of constant axial pressure or forced feeding.
In order to understand the rock breaking process at the bottom of the hole more deeply, Table 5-8 supplements the relationship between the critical load and the inclination angle and rotation speed of the bit working lip through a batch of data.
When the critical load threshold is exceeded, the peak power consumption will appear on the automatically recorded wattmeter paper tape.
It can be seen from Table 5-8 that the critical values of drilling power and ROP increase with the increase of rotating speed and the decrease of working lip inclination angle, but the specific work of rock breaking reaches an extreme value.
Table 5-8 Critical Load Values of Bits with Different Working Face Inclinations
See Table 5-9 for the drilling effect of the drill bit with the rock-breaking part (profile) made into a right-angled trapezoid.
Table 5-9 Different working lip shapes? Comparative test results of 59 mm bit
One fact is very obvious. When designing the structure of diamond bit, it is necessary to avoid sharp corners and sharp edges in its working unit, because there will be a high concentration of stress in these places, and at the same time, its friction and wear will consume a lot of energy. In addition, it is necessary to consider the installation position of the rock breaking unit on the working lip surface. We have analyzed before that the specific contact load of a single diamond on the inner lip surface of the carcass section is obviously higher than that on the outer lip surface.
Obviously, there is a higher contact load on this group of diamonds near the inner side, which makes their penetration depth per revolution greater. Therefore, large debris will be formed near the inner side of the fan-shaped block during drilling. The specific contact load Pk in the first half of the hole bottom rock breaking process increases because the cutting depth per revolution and the cuttings particles near the inner side of the hole bottom increase (Figure 5-22 (a)). In order to ensure the uniform wear of the first half of the sector block, it should be arc-shaped. For this reason, people have developed various cutting unit layout schemes to eliminate the abnormal wear of the first half of the diamond bit.
Figure 5-22 Wear of the Front Half of Sector Block
(3) Measures to solve the abnormal wear of the front half of the sector block
As shown in Figure 5-22 (b), in order to solve the abnormal wear problem of the front half of the sector block, the cutting unit can move forward a certain distance relative to the bisector of the sector block.
Therefore, the following methods are adopted to solve the problems of reasonable selection of section shape and uniform wear of the front half of the sector block:
(1) suppose that the rock breaking volume of the cutting unit is proportional to the distance from the center of the drill bit.
(2) Assume that the volume wear of the work unit is directly proportional to the volume of the broken rock.
According to the scheme adopted in profile design (Figure 5-23), these conditions can be written as follows:
Figure 5-23 is a schematic diagram of calculating the cross section of the first half of the sector block.
Application of synthetic diamond superhard material in drilling
In ...
Application of synthetic diamond superhard material in drilling
Where: I is the height wear of the sector; B is the radial width of the sector; αi is the width of the sector in the radial vertical direction.
According to Formula (5-73) and Formula (5-74):
Application of synthetic diamond superhard material in drilling
At this time, the instantaneous width of the sector is perpendicular to the radial direction.
Application of synthetic diamond superhard material in drilling
If the angle β takes polar coordinates, the midline equation of the sector block can be written as:
Application of synthetic diamond superhard material in drilling
Where φ is the angle between the radius passing through the point and the tangent to the point.
At this time, cosφ≈t/αi, and t is the sector width.
Consider Formula (5-75):
Application of synthetic diamond superhard material in drilling
now
Application of synthetic diamond superhard material in drilling
Transformation (5-79), we can draw:
Application of synthetic diamond superhard material in drilling
Rewrite (5-80) into a more convenient form:
Application of synthetic diamond superhard material in drilling
or
Application of synthetic diamond superhard material in drilling
Sequence and split conversion, including:
Application of synthetic diamond superhard material in drilling
In order to integrate Equation (5-83), we substitute according to the known method:
Application of synthetic diamond superhard material in drilling
. So:
Application of synthetic diamond superhard material in drilling
The integral of Equation (5-84) is:
Application of synthetic diamond superhard material in drilling
Where: c is a constant depending on the condition. β=0 under initial conditions.
Application of synthetic diamond superhard material in drilling
At this moment
Application of synthetic diamond superhard material in drilling
Substitution and a series of transformations, and finally:
Application of synthetic diamond superhard material in drilling
Calculate the beta angle according to Formula (5-88), which is expressed as:
Ri = 20mmβ=0 ;
ri = 2 1mm； β=5.7 ;
Ri = 25mmβ= 14.3 ;
Ri = 30mmβ=28.7 。
If a section is formed along these points, its shape is close to the original shape, as shown in Figure 5-23.
Therefore, we suggest that the front segment of the diamond bit sector should ensure that the bit has a uniform wear-resistant structure.
Table 5- 10 lists the matrix shapes of the most widely used mass-produced diamond bits in Russia.