The new design scheme of drilling rock cutting tools, working in rotation mode pairs

. The article describes the dynamics of drill bits, drilling modes, distribution of resistance forces when drilling with bits. The theory of drilling a well of arbitrary shape, possible shapes of contacting figures at the bottom hole and the type of drill bit operating in the rotation pair mode are considered. This type of bit has the properties of a double center of rotation, which results in attrition drilling. At the same time, during drilling, the load on the bit will be located the same throughout the working part, it is also theoretically shown that the specific volumetric and contact work of the cutting parts will be the same, which leads to the same wear of the bit. It also discusses the issues of improving the flushing and blowing of wells when drilling with rotary steam bits.


Introduction
Practice shows that the dynamics of all types of drill bits at the bottom of the well is unstable. They always strive to get out of the rotation mode around the borehole axis, but, having acquired an abrupt inter-axial eccentricity, they minimize it. This chaotic process is ultimately stabilized when a drill bit with a variable centerline eccentricity is operating, i.e. in the mode with a non-fixed axis of rotation. Hence, multifaceted cross-sections of wellbores are obtained [1]. The nature of this phenomenon is currently theoretically substantiated by the dependence of power consumption on the forces of resistance to motion [2]. When the drill bit is operating in the mode with a non-fixed axis of rotation, the ROP increases, and in the mode of a couple of rotations, in addition, wear of the cutting structure at the end of the bit becomes uniform.
The main goal in the creation of new generation rock cutting tools is to calculate the limits of variation of the centerline eccentricities at which the operation of drill bits in the mode of a pair of rotations will be stable. Let us prove that any end face of the bit has a range of setting the centerline eccentricities for self-reproducing and stable operation in the mode of a pair of rotations, that it linearly depends on the values of the geometric shapes.

Methods
We solve the set tasks by comparing the energies performed by the working protrusions per unit time (one revolution) in the modes of rotation around one given center and a pair of rotations. Let the forces of resistance to motion at each point of their trajectories and the contact areas of the working protrusions be constant, the number of points of the lines is identically determined by their lengths. In this case, a comparative analysis of the powers from the forces of resistance to movement in different modes of rotation of the end of the bit is admissible in terms of the values of the contact paths of its working protrusions.
Choose a system of n points, are in contact during rotation at a distance from the rotational center R1 <R2 <... <Rn. We get the sum of the contact paths: In the rotation mode couples to the same points of the system: where ε -eccentricity between the axles, mm. If we take ε = RJ, then if ε = Rn, then . (4) It is natural to assume that there is a value of the eccentricity of the axle, in which . (5) Consequently, for a system of points rigidly connected with a given center of rotation, there is such an inter-axial eccentricity at which the powers from the forces of resistance to motion in the modes of rotation around this center and a pair of rotations are equal. We will call this value balancing. An eccentricity greater than the balancing one gives a stable rotation around a given center, the smaller one -a pair of rotations.
Since no restrictions are imposed on the coordinates of the selected system of points, it can be argued that for any surface in contact there is a whole region of inter-axial eccentricities that provide a stable mode of a pair of rotations.
Further, when determining the balancing eccentricities, we selected a point, a circle, a radial line, a circle and an arbitrary geometric shape ( Fig.1), for which the following dependencies were obtained.
1.For a system of points located on a circle with radius R '(as a special case, this includes one point remote from the center of rotation by the value R): = .
To circle completely filled with points of concentric circles: For a freeform geometric shape: Where Rj -the radii of the corresponding concentric circles, mm; lj -the number of missing points (length of arcs) on them, mm.
The obvious linear dependence of formulas (6), (7), (8), (9) allows us to assert that the larger the geometric figure, the greater the balancing eccentricity, therefore, the range of setting the real value for the self-reproducing mode of a pair of rotations. In this case, the balancing value cannot exceed the radius of the circumscribed circle of any geometric Figure of any shape ( fig.1).
Excluding from a given geometric figure the points located between the center of rotation and the calculated balancing eccentricity, we thereby increase its value. It will decrease when excluding points located between its value and the radius of the circumscribed circle. It does not change in three cases: with symmetrical exclusion of points relative to the middle on the radial line; any number of points from a circle; sectors from a circle.
Note that we assumed geometrical figures, to one degree or another, comparable to the possible surfaces of the ends of rock cutting tools in the plan, for which the considered dynamics is identical to the dynamics of plane figures.
Creation of rock cutting drilling tools based on new more efficient dynamics of their working surfaces is an objective reality today.
The designed tool has the ability to work in the mode of a pair of rotations due to the introduction of a second parallel axis of rotation into the structure. In this case, the axial eccentricity does not go beyond the radius of the circumscribed circle of the working surface of the tool in plan; the given surface of the well bottom is completely covered.
In addition to existing rock cutting drilling tools with a solid bottom and core drills, it is possible to create core bits for coring with any cross section, with natural wedge formation for directional and exploration drilling, etc.
The development of a drill bit working in the steam rotation mode is possible. At the same time, the possible limits of variation of the center-to-center distances of the parallel axes of rotation in this mode are determined, which are in the limit 0 <ε <εcr for different schemes of placing weapons on the working matrices.
We had to make such a device, as already noted, for convincing proof not only of the possible design of drilling tools with working matrices operating in the mode of rotation pairs, but also for optimizing the cutting structure on the surfaces of the bottom holes and indicating ways to optimize other components of the overall dynamics of such tools. This design of drill bits belongs to the cutting-abrasive type and can be used when drilling blast holes. All of these bits, as a rule, have one axis of rotation aligned with the axis of the borehole.  But there is a known device for drilling wells in which, in order to ensure the effective operation of the drill bit in the mode of a pair of rotations with a given eccentricity, the drill bit body is made conical, and the top of the cone is directed towards the opposite side of the working end [3].

Point
The disadvantage of this device is that both the layout of the cutting structure on the working surface of the bit and the layout of the flushing channels are unknown. In this device, the flushing channels are located above the working part of the device, which does not allow us to confidently assert the efficiency of such designs of drilling tools.
The disadvantage of such designs of drill bits is that its working matrices are made in the form of annular matrices along the periphery and a circular cylinder in the center of the bit. In this case, when drilling wells in soft formations, the circular cylinder has the ability to overwrite the central region of the well, which will lead to a sharp decrease in ROP. The second disadvantage of this bit design is that the diameters of the inlet and outlet channels for the flushing holes are not matched. At the same time, it is difficult to design a bit with an enlarged diameter and with several annular matrices of the working surface of the bit [4]. This goal is achieved by the fact that the working surfaces of such bits are made entirely only by annular dies, and the inlet and outlet flushing channels should be equal in crosssectional areas, and the areas of each of them should not be less than the cross-sectional area of the central flushing channel. In other words, the condition must be satisfied.
where rj in are the radii of the inlet holes, mm; rj out -radii of outlet openings, mm; Rc -radius of the central flushing channel, mm; n -is the number of inlet or outlet openings, pcs. This applies to both horizontal and downward and upward outlets. And this is done in order to create energetically equal-cost conditions at the bottom of the well during the destruction of rocks and to eliminate accelerations in the flushing channels (holes), which are the primary causes of vortex flows, and, consequently, the conditions for gland formation.
All this makes it possible to design drill bits that effectively operate in the rotation pairs mode, of any diameter for drilling wells in any rock hardness, varying the number and parameters of annular dies and channels, both for flushing fluids and with air blowing (Fig.2).
Possible execution options for various conditions at the bottom of the well, depending on the physicomechanical properties of rocks, are represented by varying eccentricities -ε, strength and abrasive properties of the working matrix armament from bit steel to diamondcontaining elements. In this case, we will rely on a comparative analysis of the general scheme of a drilling tool, which we assumed, programmed to operate in a pair of rotation mode with the dynamics of existing and most widely used bits in the practice of bit building: with cutting-abrasive bits (PDC) and roller cone bits.
At this stage, it is necessary to identify not only all the advantages of the proposed general structures, but also possible disadvantages in optimization for all components of the general dynamics of their operation in real conditions of well drilling, i.e. taking into account their type and dimension [5].
When drilling with roller-cone bits, both three-cone and single-cone bits, very favorable conditions are created for this process.
In our case, bottomhole flushing is limited to closed targeted jet streams in the form of round holes, which practically excludes the process of gland formation. At the same time, the outlets from the surface of the bits into the annulus have almost laminar upward flows. At least this can be achieved anyway.
Thus, the issue of combating the process of gland formation in our case has been resolved positively and finally.
To everything that has been said regarding the functioning of drill bits operating in the rotation pairs mode, one more important aspect should be noted, concerning the temporal durability of the axes of the working matrices.

Conclusion
The abrasive and strength resistance of the axial assemblies of drill bits operating in pairs of rotation, other things being equal, will have a significant advantage over those in the roller cone version, this advantage is obvious and lies in the fact that, firstly, the axles will depend to a much lesser extent on the axial loads on the drilling bit, and secondly, the axle loads will change in time along the next axes over the entire surface. In roller cone bits, the loads on the cone axes are always and constantly concentrated in one-sided order, as a result of which the contact loads on the axles create one-sided thermal overloads and will wear out much faster.