Design features of drilling equipment elements using materials with shape memory effect

Alloys exhibiting thermoelastic phase transformations are getting more and more used in different industries. This is due to the shape memory effect and pseudo-elasticity (sometimes termed “superelasticity”) they exhibit, which can considerably improve the performance characteristics of various technical systems. One of the highest reliability and durability criterias are applied to equipment for drilling oil and gas wells, and according to this the above-described smart materials and the phenomena they exhibit have been gradually implemented in the oil and gas industry. This article analyzes the developed design of roller cone bits elements and proposes its assembly method, and presents its comparison with currently existing designs. Computational research and computer analysis of a drilling equipment assembly containing parts made of shape memory materials were performed, these studies showed significant advantages of the proposed method.


Introduction
The modern process of drilling oil and gas wells is a complex multi-step process.Safety requirements for various technological operations, used in the development of oil and gas fields, depend on the high reliability level of all technical systems.Any emergency situation leads to increased costs, as well as to possible personnel injuries, in some cases fatal, associated with uncontrolled energy releases.Also, increasing the reliability of drilling equipment is important due to the complexity of the drilling process, in which it is of great importance to prevent emergency situations that lead to a significant increase in the number of repair and maintenance activities and related costs.One of the most critical components of drilling equipment are drill bits.While estimating the reliability and operating safety of drilling rigs, most attention is paid exactly to it.Primarily, this is due to the fact that all drill bits have a complicated structure with parts, operating under complex loadings.Since it is impossible to take into account all the aspects affecting the materials resistance during drilling, it is necessary to increase the safety factor to ensure the overlap of all errors that may occur.It also matters that drill bits are located at the very bottom of the drillstring at the well bottom.If it's broken it is necessary not only to stop the drilling process, but also to back off the drill string fully, to disassemble it, to eliminate the accident consequences and to assemble the drillstring with new drill bits again -that causes high economic and time losses.From all has been said it follows that reliability of drill bit designs is a relevant issue and the efficiency and safety of drilling equipment depends on it.
Currently roller cone drill bits are most widely used while drilling wells.Every year bits of this particular group are used in about 90% of the drilling wells volume in the world [1,2].

Justification of the proposed solution
Alloys exhibiting thermoelastic phase transformations are alloys that exhibit polymorphism under both thermal and mechanical stresses.The phase transformation in such material occurs without diffusion at the speed of spreading of atomic displacements lower than the speed of sound in the given environment.Both the location of atoms and the positions of dislocation structures are preserved due to the ordered collective displacement [3,4].This is the source of such important phenomena as shape memory effect and pseudoelasticity (superelasticity), the application of which can significantly improve the design of parts and mechanisms.The tests show a sufficient level of durability of this type of smart materials in environments typical for the oil and gas industry.And the existence of a wide variety of alloys with shape memory effect allows to select the necessary compositions depending on the specifics of operation [5,6].All the above factors show a high potential in the application of alloys with thermoelastic phase transformations in order to increase the reliability and service life of oil and gas equipment.
As it was mentioned above, tooth loss during drilling is a frequent and harmful incident.Fallen out teeth, getting under the teeth of rotary bits, lead to their breakage, thereby reducing the bit's rockcutting ability.For efficient and trouble-free operation of subsequent bits, thorough bottom-hole cleaning is required.Therefore, any costs associated with increasing the reliability of teeth fixation on the bit body can't be compared to the losses that occur when teeth fall out.The interference fit does not provide the necessary force sufficient to hold the teeth in the bit body, and a significant increase in the difference between the linear dimensions of the bit body and tooth base contributes to stresses that can lead to the destruction of both the teeth and the bit body itself, as well as cause premature initiation and rapid propagation of cracks from the mating point in both the bit body and the tooth.The most efficient method of tooth mounting at the moment remains the method of selective selection (group selection) [7], which requires a lot of time and does not solve the problem of rapid tooth fallout from the roller cone body.Increasing the reliability of fixation of the teeth in the body of the cone can be provided by the shape of the seating hole in the cone body and the shape of the base of the teeth.
Thus, by making the teeth in the form of a cone (truncated cone), it is possible to ensure their holding not by the force of a static friction ("interference fit"), but by the geometric shape itself, which prevents them from falling out, so the loss of teeth is possible only when the tooth itself is destroyed [8].
In the case of interference fit, the tooth is held in the seating hole by friction forces, which are directly proportional to the force of tooth compression by the seating cylindrical surface.In the case of fixation by means of the geometric shape of the tooth, the tooth and the seating hole in the cone are sheared or cut when breaking out.Thus, in order to break out a tooth, it is necessary to shear the material layer of either the tooth or the cone around the seating hole.Typically, the force required for this shear is much greater than the force required to press the tooth in and out when using an interference fit.
The connection of teeth with cone-shaped seating surface to the cone-shaped bit body with corresponding cone-shaped holes is currently only possible by casting or by using a material with shape memory effect.In case of casting, the resulting product has defects that cause premature failure of the roller cone bit.Also the presence of metal sections of different thickness in the casting mold leads to the occurrence of sinks, shrinkages and undercastings in the places of mating of the teeth and the bit cone body.When casting the bit body, exposure of the teeth to hot casting alloy leads to changes in the structure of the material from which the teeth are made, which causes reduction of physical and mechanical characteristics of the teeth.At the same time, it should be noted that when parts are assembled using their geometric shape in the surface layers of the seating hole there are no stresses and deformations in contrast to the interference fit, where there are stresses and deformations that provide the necessary force for reliable fixation of the tooth in the bit seating hole.
The assembly sequence according to the proposed assembly principle consists of the following steps: the sleeve to be installed, made of material with shape memory effect, is cooled to a temperature corresponding to the low-temperature phase state of the material (martensite), after which the shape is set to ensure its free installation in the seating hole in the body of the cone.Then it is heated to the temperature corresponding to the high-temperature phase state of the material (austenite), thanks to which it acquires its original shape, self-centering and self-fixing into the seating hole in the body, providing a tight mating on all external surfaces.Dismantling or replacement is carried out in reverse order.
Thus, the proposed solution [8] can considerably increase the duration of trouble-free operation by increasing the reliability of the main connecting assemblies, which can greatly reduce the economic and time losses associated with the failure of drilling roller cone bits.

Used methods and software systems
In order to prove the advantages of the proposed bit assembly method with elements made of materials with shape memory effect, two methods were used to model the processes associated with the operation of the described equipment.The obtained conclusions are a direct proof of increase in reliability and service life of roller cone bits.
Computer modeling was carried out using CAD software complex "SolidWorks" for automation of industrial enterprise work at the stages of design and technological preparation of production.For this purpose nonlinear static analysis of the calculation module "SolidWorks Simulation" was used, which allowed to take into account the features of deformation behavior of alloys with shape memory effect.Three-dimensional models of assemblies of both currently used bits and bits corresponding to the proposed technical solution were created.They were subjected to virtual tests, which demonstrated the safety margin of these structures.Mathematical modeling was also carried out for different technical solutions in order to demonstrate the advantages of the proposed design and method.For this purpose, classical formulas for strength calculation as well as principles of strength theory were used [9].

Modeling the process of pulling out the tooth of a cone bit
The process of axial breakout load on the tooth of a roller cone bit was taken as a basis for modeling the process of tooth breakout from the cone body.It is assumed that this load arises from the crushing and shearing action of the teeth on the rock.Both the currently used design and the one developed by the author's team were subjected to computer and mathematical analysis, which can fairly reliably determine the advantages of the new method.In all calculations the following is accepted: the material of the cone is 14Х2Н3МА according to GOST 4543-71, the material of the tooth is a structural tungsten alloy, the material of the sleeve is titanium nickelide containing 55 % (wt.)Ni and 44,2 % (wt.)Ti, with the temperature of the end of austenitic transformation Af 5-18 °С.
To confirm the higher reliability of the proposed solution, we will use computer modeling.Figure 2 shows a three-dimensional model of a tooth pressed into a roller cone bit.This assembly unit was not subjected to any external influence, and all the observed stresses occurred only as a result of pressing.The maximum stresses in the tooth are 1070.3MPa, which is an acceptable value for a hard alloy and the maximum stresses in the cone are 873 MPa.Since the yield strength of 14Х2Н3МА is 980 MPa, it can be concluded that the interference fit initially significantly limits the mechanical properties of materials, which leads to the conclusion that such a design is unreliable.As can be seen from the stress diagram in Figure 2, the stress extremes shown in red occur abrupt changes in the part's geometry, around sharp corners, grooves, which are stress concentrators.This problem is solved by design elements such as tangles and chamfers, but they also remain the places where crack initiation is most likely to occur.
It is worth noting that if you reduce the maximum value of stresses located abrupt changes in the part's geometry, then on the cylindrical surface of the seating hole for the tooth there are stresses in the range of 500-700 MPa, while the yield strength of material 14Х2Н3МА is equal to 980 MPa.This indicates that during drilling, the load taken on the tooth at an angle is significantly limited, as the total stresses may exceed the yield strength, the result of which will be plastic deformation of the seating hole with subsequent tooth breakout or change in its orientation and positioning, which will also lead to tooth loss.
It is also evident from the resulting stress diagram that the tooth also has stresses near the base of the foundation.This is due to the fact that the tooth material has nowhere to be displaced in depth and at the base the tooth experiences a complex stressed state, in which stresses occur in all three directions, and as more far away from the base, the material along the axis of symmetry can deform more (the farther away from the base, the greater the deformation in the direction along the axis), which reduces the stresses that occur.The presence of stresses in the tooth in the layers located at the base also reduces the value of the perceived load on the tooth, in particular, the contact load, because in these sections it is possible to nucleate and propagate a crack, which will lead to the destruction of the tooth at the base and further tooth protrusion.Thus, the interference fit significantly reduces the permissible load absorbed by the bit tooth and the bit cone during drilling, and, as a consequence, requires taking into account this circumstance when selecting drilling modes.
In Figure 3 we can see that at a force of 120 kN the onset of plastic deformation and tooth fall-out occurs (the onset of change in the slope of the graph corresponds to the time interval of 1.17-1.25 sec).Thus, the model confirms the correctness of calculating the amount of load allowed by the sleeve.This method of holding the tooth in the seating hole does not lead to the occurrence of stresses both in the tooth body and in the near-surface layers of the cone in the seating hole.According to the graph and features of alloys with shape memory effect [10], a part of the deformation exceeding the elastic deformation value can be restored by the phenomenon of pseudoelasticity/"superelasticity", which increases the value of allowable load and also provides resistance to overloads during drilling.According to the stress diagram, the critical stresses leading to the failure of the structure occur mainly in the tooth and partially in the bit seating hole, but not in the sleeve, because in shear those deformations that occur in the tooth and in the bit seating hole are irreversible, as they exceed the limit of proportionality and yield strength and lead to shear with subsequent cutting.Due to the phenomenon of pseudoelasticity/"superelasticity", the deformation occurring in the sleeve and exceeding the limit of proportionality is reversible, which is associated with the occurrence of deformation martensite, and when the load is removed, leads to the formation of the austenitic phase by the reverse transformation mechanism.

Conclusion
The issue of ensuring reliability of connecting elements of roller cone bits is relevant, it is justified by high safety requirements and high economic and time costs of technological processes of drilling oil, gas and gas condensate fields.The proposed technical solution changes not only the design of drilling equipment, but also the technology of its assembly/disassembly by using materials with shape memory effect, this solution is quite relevant and justified from the economic point of view.The results of mathematical calculations and computer modeling, having a convergence rate of 90-95 %, allow us to assert that the design and method of tooth fixation proposed by the authors provides a high degree of reliability.Taking into account the increased resistance of materials with thermoelastic phase transformations to abrasive [11][12][13] and corrosive [14] effects, as well as to fatigue failure and constant dynamic loads [15,16], it can be confidently claimed that this research has a high potential for application in the design of roller cone bits.

Figure 1 .
Figure 1.The computer model of the proposed design of the roller cone drill bit, tooth and intermediate element (sleeve).

Figure 2 .
Figure 2. Three-dimensional stress diagram of a pressed tooth.