## Abstract

Drilling systems that use downhole rotation must react torque either through the drill-string or near the motor to achieve effective drilling performance. Problems with drill-string loading such as buckling, friction, and twist become more severe as hole diameter decreases. Therefore, for small holes, reacting torque downhole without interfering with the application of weight-on-bit, is preferred. In this paper, we present a novel mechanism that enables effective and controllable downhole weight on bit transmission and torque reaction. This scalable design achieves its unique performance through four key features: (1) mechanical advantage based on geometry, (2) direction dependent behavior using rolling and sliding contact, (3) modular scalability by combining modules in series, and (4) torque reaction and weight on bit that are proportional to applied axial force. As a result, simple mechanical devices can be used to react large torques while allowing controlled force to be transmitted to the drill bit. We outline our design, provide theoretical predictions of performance, and validate the results using full-scale testing. The experimental results include laboratory studies as well as limited field testing using a percussive hammer. These results demonstrate effective torque reaction, axial force transmission, favorable scaling with multiple modules, and predictable performance that is proportional to applied force.

## 1 Introduction

Small diameter boreholes, such as those less than 120.7 mm (4.75 in.) in diameter, have the potential to significantly enhance geothermal energy extraction, exploration, and monitoring [13]. The small diameter of the holes enables lower costs, the use of more compact equipment, smaller environmental costs, and easier handling [4]. We are particularly interested in decreasing the cost and time to drill exploratory holes by creating compact, portable, small-diameter drilling systems. Replacing heavy drill pipe with more flexible tubing can dramatically reduce system footprint, particularly for deeper holes, but necessitates downhole rotation.

However, a common challenge associated with downhole rotation in drilling is achieving sufficient reaction torque while simultaneously delivering controlled weight on bit (WOB) [1]. Drilling dysfunction can be caused by drill string twist and the inability to manage WOB. This is especially true when drill string torsional stiffness is low (i.e., long drilling distances, small diameter drill pipe, etc.). Cable-suspended drilling systems such as wireline-deployed designs can simplify drilling operations and have emerged as an approach for Arctic ice and bedrock drilling [5,6]. Such cable-suspended systems cannot rely on surface-derived torsional stiffness and therefore require downhole torque reaction systems [7]. The small borehole diameter, combined with the large drilling depths (∼ 5000 m), makes it desirable to perform drilling using a cable-suspended downhole rotation/drilling system such as the one illustrated in Fig. 1. This figure shows how the drilling and rotation motor are configured at the bottom of the drill-string. To drill, the downhole rotation motor generates considerable torque, and this must be reacted. In addition, proper downhole WOB must be maintained: if too low, drilling performance tends to be poor; if too high, the drill motor may stall.

Some approaches to react torque in cable-suspended drilling systems include friction blades [7], leaf springs [8,9], side milling cutters [10], and U-shaped blades [11]. Comparative studies of various techniques have shown that achieving a good combination of high torque reaction and low axial resistance remains challenging [7]. Techniques from coiled tubing and wire line drilling can also be used to provide downhole forces and torques. Options include downhole tractors using a variety of mechanisms including wheeled approaches, inchworm-type configurations, and corkscrew drives [12,13]. For example, the MaxTRAC downhole tractor uses toothed cams to adaptively grip the borehole wall for inchworm-like motions [12]. The ReSolve device uses a hydraulically powered tractor in combination with a drilling module to resist torque and provide downhole WOB [14].

In this work, we outline a novel mechanical module that can be deployed above the downhole motor. This design differs from previous tractor, centralizer, and cable-suspended approaches through its use of mechanical advantage, anisotropic friction, and modularity to achieve continuous motion, effective WOB transmission, and scalable torque reaction capacity. The contributions of this work are the description of the new design, the performance analysis for single and multiple units, the bench-level measurement of performance with multiple modules, and the validation in percussive drilling systems.

Our design, shown in Fig. 1, uses the vertical force from dead weight to create frictional forces for gripping the walls of the borehole and reacting the torque from the downhole motor. The design uses mechanical advantage to produce large radial forces at the borehole wall. Rolling elements that contact the borehole wall provide vastly different coefficients of friction for different directions of motion. This enables torque reaction (high friction against rotation) while still allowing WOB transmission and continuous penetration (low friction against vertical motion). Increased reaction torque can be achieved by using multiple modules in series without a substantial WOB penalty. The reaction torque limit is proportional to WOB, which is valuable because drilling torque generally increases with WOB. The design shown in Fig. 1 has been experimentally validated in both hard and soft rock samples and has been shown to effectively react torques while transmitting WOB under continuous motion. The techniques outlined in this work have applicability beyond micro-hole drilling. For example, this design approach could hold particular promise for drilling approaches that involve down-hole rotation and effective torque control such as directional or cable-suspended drilling [15,16].

This paper begins by outlining the unique and challenging requirements that stem from small borehole drilling. We then introduce our mechanism design and describe the kinematic and static performance of the design. We demonstrate how multiple modules provide favorable scaling, enabling the system to react large torques with relatively modest forces. Our custom dynamic test-bed is described in detail, and experimental results are used to illustrate the promise and effectiveness of our design. Results of further testing indicate how the friction properties change in the presence of vibration due to percussive drilling. Field drilling experiments are also described along with preliminary field testing results. This paper concludes with a discussion of potential applications of the mechanism.

## 2 Small Diameter Drilling Overview

Scaling analysis reveals the need for new approaches to microhole drilling when the borehole diameter is very small. Specifically, using drill pipe to transmit or resist torsional loads creates a high risk of large torsional wind-up. If we model drill pipe as a solid cylinder, we can examine the torsional stiffness in relation the hole radius. We use D to denote the hole diameter, L to denote the whole depth, and G to denote the shear modulus.
$Ktorsion=GπD432L$
(1)
Torsional stiffness, Ktorsion, for a solid cylinder is proportional to D4. This means that torsional deformations become much larger when drilling smaller holes. Therefore, we seek a new solution such as the one shown in Fig. 1, which reacts torque near the downhole motor, uses dead-weight to generate WOB, and uses flexible tubing rather than continuous lengths of drill-pipe. Based on our downhole motor design and prior drilling experiences, we seek a torque reaction and WOB transmission system that meets the following functional requirements:

1. System has torque reaction capacity for resisting up to 450 Nm (300 ft-lbs) torque at the downhole motor. This prevents any large rotations of the components above the downhole motor.

2. System achieves torque reaction capacity while achieving nominal downhole WOB of 2225–4450 N (500–1000 lbs).

3. System is capable of continuous drilling in order to improve drilling speed and simplify operations.

Our survey of existing literature and techniques did not provide a solution that combines large downhole torque resistance at relatively low WOBs, and continuous motion. Therefore, we developed a mechanism module that can be used independently or combined in series to better meet the unique needs of small diameter drilling.

## 3 Modular Torque Reaction System

This section provides force calculations, scaling analysis, and performance predictions for the proposed torque reaction system. A sketch of one mechanism module is shown in Fig. 2. The unique performance of this design stems from four key features: mechanical advantage, anisotropic friction, modular scalability, and proportionality of WOB and maximum reaction torque to applied axial force.

The ability to react torque is derived from the application of WOB forces. Based on the coordinate system shown in Fig. 2, this entails producing radial (r) normal forces and corresponding frictional holding forces from applied vertical (z) forces. The mechanism shown in Fig. 2 uses geometry to convert z direction forces into r direction forces. The mechanism can have two or more linkages that transmit vertical forces to the borehole. We use n to denote the number of linkages. The net radial force, Fr, is the scalar sum of the force across all linkages. This can be determined from the configuration of the mechanism. In this analysis, we assume that the revolute joints are frictionless and that the system is quasi-static (not accelerating). We also assume the applied loads are far larger than any internal gravitational loads on the links/wheels. The applied force Fin,z is controlled via the drilling rig, and Fout,z is the actual WOB.
$Fr=∑i=1n1nFin,ztanϕ=Fin,ztanϕ$
(2)

The expressions in Eq. (2) reveal three important features. First, the ratio between the radial force, Fr, and the applied vertical force, Fin,z, is dependent on the engagement angle $ϕ$. Since the nominal borehole diameter is known (equal to the bit diameter), the design can be tuned to give a specific ratio of forces. Second, for angles $ϕ<π/4$, the radial force will exceed the applied force. For example, if $ϕ=π/6$, Fr = 1.73 Fin,z. This mechanical advantage is particularly relevant for cases where the applied force, Fin,z, is relatively low. Lastly, the net radial force is independent of the number of linkages.

### 3.2 Anisotropic Friction.

The outlined mechanism can produce radial forces at the borehole wall per the preceding section. As Fig. 3 shows, when the wheels contact the borehole wall, these radial forces act as normal forces for friction in the z and $θ$ directions. The net radial force, Fr, can be used to find the net vertical friction force, Ff,z and the net tangential friction force, $Ff,θ$. Note that all the net forces are scalar quantities.
$Ff,z=Frμz$
(3)
$Ff,θ=Frμθ$
(4)
The tangential friction force, $Ff,θ$, reacts the torque from the downhole motor, and the translational friction force, Ff,z, resists the transmission of force from Fin,z to Fout,z. A force and torque balance analysis of the mechanism produces the following expressions. We use the variables μz, $μθ$ to represent the coefficients of friction for motions in the axial and tangential directions, respectively.
$τin≤Fin,ztanϕD2μθ$
(5)
$Fout,z=Fin,z−Fin,ztanϕμz$
(6)

In order to effectively transmit WOB to the bit while simultaneously reacting torque, a design objective is $μz<<μθ$. Rolling contact may be used to enable this direction-dependent behavior. The wheels shown in Fig. 3 employ rolling contact when moving in the z-direction, but use sliding motion to move in the $θ$ direction. With this design, we anticipate that $μθ$ may be tailored to be roughly an order of magnitude larger than μz.

### 3.3 Modular Scaling.

If low rolling friction, μz, can be achieved, very favorable scaling can be achieved by using multiple modules in series. This concept, highlighted in Fig. 4, can enable increased torque reaction and robustness with only small reductions in output force, Fout,z. As long as μz is small (e.g., 0.1), most of the vertical force will be transmitted to the next module. Therefore, each set of rollers pushes out with only slightly reduced radial force. In the case of multiple modules, we use the nomenclature shown in Fig. 4(a). In this case Fin,z is still applied at the top, but Fout,z is the output force through all the modules. Similarly, the tangential friction force, $Ff,θ$, is the net force associated with all the modules. The performance of a system with N modules is predicted by the following expressions that‘ consider the forces at each module.
$Fout,z=Fin,z(1−μztanϕ)N$
(7)
$Ff,θ=∑i=1NμθFin,ztanϕ(1−μztanϕ)i−1$
(8)
The torque needed to induce the start of slipping, $τslip$, can be computed from the net tangential friction force.
$τslip=Ff,θD2$
(9)

We visually demonstrate the favorable scaling performance of multiple modules by predicting nominal performance based on a desired output force, Fout,z. We use coefficients of friction of 0.1 and 1 for μz and $μθ$ respectively. In Fig. 4(b), we show how the normalized predicted input force, Fin,z, and slip torque, $τslip$, scale with multiple modules. The input force and slip torque are normalized by dividing by the value associated with the one-module case. The plot clearly illustrates how the torque reaction capacity increases at a far faster rate than the applied load. Use of multiple modules also affords greater performance in boreholes with deviations or blowouts. Multiple modules spaced apart can still react torque even if a single module does not perform well due to local problems in the hole.

### 3.4 Torque Reaction and Downhole Weight on Bit Proportional to Applied Load.

A key advantage to this approach is the fact that torque reaction capacity, $τin$, and downhole WOB, Fout, are both proportional to the force applied at the top, Fin. This remains true even when multiple modules are used (Eqs. (7) and (8)). This behavior enables the mechanism performance and downhole WOB to be simply controlled by modulating the loads at the top. A common way to achieve this is to pull up on the weight above the bottom-hole-assembly. Thus, the reaction torque capacity may be increased by increasing the WOB. This generally aligns well with drilling, wherein torque and WOB for effective drilling generally scale together. However, there could be conditions in which it is desired to drill with high torque and modest WOB. This condition could be accommodated at the design stage, by using a small value of $ϕ$, or at drilling time by using a separate actuator to create an additional internal force in the module without impacting WOB.

## 4 Nominal Design

### 4.1 Predicted Performance.

The analysis outlined in the previous section was used to design a system for drilling ∼108 mm (4.0 in.) diameter holes. As per Sec. 2, it is required to react up to 450 Nm (300 ft-lbs) with 2225 N (500 lbs) WOB applied at the bottom of the hole to a downhole motor and hammer drill. The design is conservative in that the maximum torque is reacted using the minimum WOB; additional force can be applied at the top if torque-reacting friction, $μθ$, is less than expected. Coefficients of friction of $μθ=1$ (steel on rough rock) and μz = 0.1 (rolling contact with high-load bushings) were used for design.

Two free variables are available to tune the design: the engagement angle, $ϕ$, and the number of modules, N. The design problem can be approached in two ways: (a) determining the number of modules and using this to select the engagement angle or (b) first choosing the engagement angle and then calculating the number of required modules. For our design, we used approach (b) and chose the engagement angle. We attempted to maximize the mechanical advantage while still providing some robustness through the ability to expand into slightly larger holes. We achieve an engagement angle of $ϕ=0.7$ (40 deg) for a 102 mm (4.0 in.) hole, and can expand to a maximum hole diameter of 108 mm (4.25 in.). Beyond 108 mm diameters, the links will collide and contact with the borehole wall is no longer ensured. We choose to utilize three linkages per module (n = 3). Two axially symmetric linkages/wheels produce no radially induced moment on the drill string. Thus, two rollers are the minimum when assuming axial symmetry. Additional linkages offer no additional net torque gain but do reduce contact forces. However, additional linkages also add complexity and reduce the annular area for cuttings evacuation. A three-linkage/roller design was chosen to provide robustness to linkage/roller failure, contact force reduction, and maximization of annular area. The wheel diameter was chosen based on packaging constraints and was not optimized for cuttings evacuation or resistance to material accumulation.

The predicted performance with this design is shown in Fig. 5. The dashed horizontal line represents the amount of tangential force at the borehole wall that is required to resist the design torque, $τin$. The circles denote the predicted tangential frictional force, $Ff,θ$. To achieve our desired performance, a design using four modules provides sufficient reaction torque and gives a 5000 N safety margin. The use of four modules increases $Ff,θ$ from 3470 N (780 lbf) (one module) to 14720 N (3308 lbf) (four modules). The required input force to achieve the downhole WOB of 2225 N (500 lbf) is shown with diamond markers and increases far more slowly from 2526 N (568 lbf) to 3697 N (831 lbf). This illustrates the favorable scaling behavior of our approach.

### 4.2 Prototype Design.

A prototype design for laboratory evaluation and field testing was developed. This design, shown in Fig. 6, uses three sets of nested links to achieve the desired strength and kinematics. This design is intended for use in a nominally 108 mm (4.0 in.) borehole and features a clear central space for 25.4 mm (1 in.) tubing to supply the downhole components with pressurized air. Mounting features enable multiple modules to be placed in series.

All components are made of 4340 steel alloy. Originally, all bearings were high-load, high-temperature bushings made from PTFE or PEEK. The plastic bushings were used for the majority of experiments described in this work. Field testing demonstrated durability issues, and metal bushings were used for the full system tests. Thrust loads are managed using high-load thrust washers (shown in Fig. 6 on each side of the wheels). This is essential to our design because the wheels are required to roll while subject to large thrust loads resulting from the downhole motor moment. A variety of wheel geometries can be used. In this work, we focus primarily on smooth wheels where the edges have a radius to match that of the nominal borehole (Fig. 6(b)). This geometry minimizes the effect of wear and relies solely on friction rather than cutting into the borehole wall.

Stress analysis was performed on the critical components such as the shafts and the links. The stress on the shafts stems from the transmission of the vertical and radial forces. A conservative analysis assumes that the bottom-most module (closest to motor) bears the full motor torque until it slips slightly, allowing torque to be shared with the module above it. Under this assumption, the worst-case loading condition is when a single module is subjected to ∼ 4450 N (1000 lbf) axial load and 270 Nm (199 ft-lbs) of torque. Components that are most likely to fail are the shafts and the outer links.

We assume that the vertical load is transmitted to the walls uniformly through all three links. The smaller shafts at each end of the mechanism see a peak stress of roughly 109 MPa (15.8 ksi), giving a 7.6 safety factor when using 4340 steel (σyield = 710 MPa).

The loading on the inner and outer links is more complex and stems from resisting torque. If we assume a worst-case scenario where the torque is uniformly resisted by each of the three linkages on only two modules (i.e., the load is shared equally by only half of the total linkages), each link sees a tangential force of 1500 N (337 lbf). Finite element analysis results are shown in Fig. 7. Even with these extremely conservative assumptions, the peak stresses remain below the yield strength for 4340 steel. The arrows illustrate the tangential and radial loads on the system. The boundary conditions are stationary shaft constraints on the ends of the inner and outer links.

### 4.3 Practical Considerations.

The spacing between modules depends on many application specific conditions such as the borehole geometry. Larger spacing increases robustness to borehole geometry deviations, but placing the modules too far apart may introduce additional effects such as compliance. In this work, a small spacing is used for lab testing, and a larger spacing is used for field tests. Cuttings present another practical concern. If allowed to accumulate, the cuttings could obstruct free operation of the linkages. The bearing blocks are designed to close and leave only a small gap for cuttings to enter (Fig. 12(c)). In addition, positive pneumatic pressure from the central tube can be used to prevent cutting accumulation.

## 5 Laboratory Experimental Evaluation

### 5.1 Dynamic Torque Reaction Simulator.

In order to quantitatively validate the performance and models for our torque reaction mechanism, we constructed a new laboratory test-bed focused on dynamically evaluating torque reaction and WOB transmission. This system, known as the Dynamic Torque Reaction Simulator, is part of Sandia National Laboratories’ geothermal engineering facilities. The torque reaction simulator is illustrated in Fig. 8 and is designed to emulate the physics of vertical WOB transmission and torque reaction. A schematic diagram shown in Fig. 8 shows how the torque reaction mechanism sits within a rock sample. Weights are placed above the mechanism to simulate the use of drill collars to create downhole WOB. Axial forces and torques can be measured with each of the two force/torque sensors (Interface 2816 Axial Torsion Load Cell). Force/torque sensor 2 is connected to a pneumatic motor (Rad Torque 10GX), which is used to impart torques onto the torque reaction mechanism. The thrust bearing above force/torque sensor 1 allows the system to rotate if the torque reaction mechanism slips, without moving the weights. The rotary position of the torque reaction mechanism and pneumatic motor can be measured using a US Digital MAE3 encoder system (not shown). Finally, a linear actuator (Firgelli Automation) is used move the whole assembly up and down. This setup enables testing while allowing the system to move downwards (like in real drilling) and allows measurement of both above-hole and down-hole forces and torques.

#### 5.1.1 Single Module Tests.

Initial tests utilized one module and were performed in a concrete block. The tests consisted of moving the mechanism to the top of the block, placing a set amount of weights, then moving the linear actuator downwards while commanding increasing torques. Due to limited stroke, the torques were started at a value known to not cause slip but only slightly below the slip torque. The pneumatic motor does not act as an ideal torque source so the applied torque fluctuates. A typical set of experimental data is shown in Fig. 9. Initially, the rotation angle, $θ$, remains flat and then sharply increases as the motor torque reaches the slip levels and the module slips. Since the torque fluctuates, slipping often stops when the torque relaxes. The occurrence of slip is denoted with the dashed vertical lines.

For the case shown in Fig. 9, the amount of weight added to the top of the system was 2136 N (480 lbf). The other components weigh 400 N (90 lbf) resulting in a total applied force of 2537 N (570 lbf). The measured forces in the z-direction using both force/torque sensors are shown in Fig. 9(a). The input force, measured by force/torque sensor 1, is relatively constant and matches our estimate for total applied force (Fin,z). The force measured by force/torque sensor 2 is the force transmitted through our torque reaction mechanism (Fout,z) and is representative of the downhole WOB. As Fig. 9 shows, while this force fluctuates as the mechanism moves downwards, the average force for this trial is within a $28%$ deviation of the input force. It is hypothesized that many of the fluctuations stem from irregular surfaces in the concrete borehole. It is important to note that the downhole WOB tracks within variations typical of drilling despite the fact that the mechanism is simultaneously moving downwards (Fig. 9(c)) and subject to substantial twisting torques.

The torque applied by the pneumatic motor is shown in Fig. 9(d). The torque command is increased until frequent slipping occurs. Examples of slipping are illustrated in Fig. 9(b), which shows the measured rotation angle, $θ$. Note that this is a highly dynamic process that depends on friction and involves the transition from static conditions to motion. As a result, the slip does not always occur at consistent torque levels. Therefore, we estimate the slip torque threshold, $τslip$, using a statistical approach based on aggregate data for each trial. The angular velocity, $θ˙$, is first filtered to reduce effects of sensor quantization. Then, the instances where nonzero $θ˙$ occurs are recorded along with the corresponding measured “motion torque.” These torques are compiled and sorted, and a set of the lowest 10 motion torque points (roughly bottom quartile of data) is used. Specifically, we use the median of this set to determine the actual slip threshold. We believe this is a conservative estimate for $τslip$ because it uses the lowest slip levels (which may be indicative of small motions and compliance rather than full slipping). The estimate for $τslip$ for this particular trial is highlighted with a horizontal line in Fig. 9(d).

Similar data were taken at three other top weight settings: 846 N (190 lbf), 1268 N (280 lbf), and 1669 N (370 lbf) and demonstrate similar results. Three trials were performed at each top weight setting. The one-module data is summarized in Fig. 10. The axial force data was compiled by averaging the measured downhole force over the trial, and the slip torque was estimated using the approach described earlier. The best-fit lines are forced to intercept (0, 0) in order to match the structure of our analytical models.

The slopes of the best-fit lines can be used to estimate frictional properties using Eqs. (5) and (6). Using this approach, we get the following estimates: μz = 0.18, $μθ=1.9$. These values are higher than expected, but their ratio is very close to the design conditions. This is most likely due to the concrete rock sample being relatively soft, which causes the wheels to bite into the material. This higher friction assists torque reaction, and the axial friction remains relatively low, enabling good force transmission.

#### 5.1.2 Two Module Tests.

A similar battery of tests was performed using two modules. This was to evaluate the performance of using multiple modules in order to increase torque reaction capacity. Time series data from a sample trial are shown in Fig. 11. The aggregated data over several applied weight settings are shown in Fig. 12.

While the structure of the dual module data is very similar to the single module data, there are two clear differences. First, the two module trials had reduced axial force transmission. This is illustrated most clearly in Fig. 12(a), which shows that the slope of the line of best fit has decreased from 0.79 to 0.673. We hypothesize that this is mainly due to the increased axial friction from the additional module. This behavior is in line with our theoretical predictions for performance.

The second difference is that the two-module case achieves higher torque reaction per unit input force than the single-module case. If the best-fit slopes of the slip torque versus applied load plots are compared, this gives a prediction for the relative performance of one-module versus two-modules. Based on comparing the slopes, the slip torque per applied weight is 1.44X higher with two modules than with one module. This is a clear increase in torque reaction capacity.

In theory, two modules should provide a 1.78X improvement, which is $24%$ larger than what we observed. We believe there are two sources of this discrepancy. First, as described above, the slipping behavior is inherently dynamic and stochastic and therefore difficult to estimate precisely. Second, we hypothesize that the two-module system undergoes asymmetric loading, with the bottom module taking the full torque load until it slips slightly and begins loading the top module. This process is difficult to predict and may cause premature detection of slip. While we remain confident in the overall benefits of using multiple modules, it may be advisable to use conservative safety factors with a design that utilizes multiple modules.

Again, the best-fit lines can be used to estimate the frictional behavior. This time, we have to use the expressions for multi-module systems (Eqs. (7) and (8)). Using these expressions, we get μz = 0.15 and $μθ=1.53$. These differ from the single module predictions by about $20%$; however, the 10 : 1 ratio of friction from the $θ$ to z directions is remarkably consistent across tests.

### 5.2 Discussion.

The test-bed results demonstrate the four key attributes associated with our proposed modular torque reaction system. Specifically, the results in this section illustrate (1) that mechanical advantage can be used to resist large torques within a small borehole, (2) that rolling contact creates direction dependent behavior (axial translation versus rotation), (3) that the modular design enables scalable performance, and (4) that torque reaction and downhole WOB are proportional to applied load.

## 6 Testing At the Sandia High Operating Temperature Percussive Drilling Facility

An additional set of validation experiments were performed at Sandia’s High Operating Temperature (HOT) percussive drilling facility to simulate more realistic drilling conditions. The HOT drilling facility is an instrumented drilling system built to test down-the-hole hammers (DTHH) at high temperatures simulating downhole geothermal conditions. This facility consists of a percussive hammer, pneumatic weight on bit, and a large top hole pneumatic rotation motor. Hammer pressures up to 2078 kPa (300 psi) can be achieved along with WOBs ranging from 445–26700 N (100–6000 lbf). The top hole motor can produce torques in excess of 1355 Nm (1000 ft-lbs). WOB is measured using pressure transducers in the pneumatic cylinders, and motor rotation is measured using a magnetic counter. The motor torque was characterized prior to experiments by comparing input commands with the measured load on a load cell. The motor torque was most consistent at a setting of 312 Nm (230 ft-lbs).

While we did not utilize the high-temperature capability, the HOT facility enabled testing under realistic forces and torques. Most importantly, it allowed realistic testing of system durability during hammering. The large forces and vibrations caused by hammering are difficult to model and replicate in a laboratory environment. A photograph of the HOT drilling facility is shown in Fig. 13(a).

The HOT experiments were performed with two modules (as shown in Fig. 13). The test protocol involved first spinning the motor with a nominal torque output (∼ 312 Nm) and then steadily increasing the applied axial force, Fin,z, until the spinning was completely halted by torque reacted by the module. This was done with and without hammering, and the results are shown in Fig. 14. The experimental results show that once a certain threshold WOB is achieved, the rotation angle (blue line) stops increasing. The axial force to react the torque was about $40%$ greater with hammering than without. This is likely due to the vibrations creating a dither-like effect that prevents static friction to engage. This is an important factor that must be taken into account for field drilling. Two options for dealing with this effect are adding more modules or increasing the applied force, Fin,z. Based on the limited HOT data, we still anticipate that a percussive system with four modules will still provide roughly 450 Nm (300 ft-lbs) of torque reaction while achieving a downhole WOB of ∼ 2200 N (500 lbf).

During testing at the HOT facility, the module was exposed to torques of up to approximately 500 Nm and applied load of approximately 160, 000 N (3600 lbf). The modules survived these loads without visible damage other than slight wear on the wheels and cracking to plastic bushings. All plastic components were replaced with metal ones for future systems and experiments.

## 7 Field Drilling

Four of the torque reaction modules outlined in this work were deployed as part of a full microhole drilling system. This wireline-deployed system uses a downhole motor and percussive hammer to drill 101.6 mm (4 in.) diameter holes. Drill collars were used to apply WOB. The bottom hole assembly consisted of (bottom to top) percussive hammer, downhole motor, torque reaction modules, and 1800 lbs of drill collars. The system was tested on the Blue Canyon Dome at the New Mexico Institute of Mining and Technology in Socorro, New Mexico. A photograph of the full system is shown in Fig. 15. When deployed in drilling, visual inspection is used to assess the performance of the torque reaction modules. The downhole motor caused the cable to twist when the torque reaction mechanism was not engaged with the formation. When engaged, the torque reaction mechanism prevented twisting of the cable suspension and allows the drilling assembly to advance as intended. Performance was qualitatively evaluated by drilling a short distance with the modules engaged ∼ 0.5 m.

## 8 Conclusions

This paper has presented a novel modular mechanism that simultaneously reacts torque and transmits axial forces to a drill bit. We have described the conceptual design, provided mathematical analysis, physical designs, and experimental results. Our results illustrate that this approach enables continuous drilling motion and is capable of scalable performance. Additionally, this system provides force transmission and torque reaction capabilities that are proportional to applied force. Therefore, the resulting physical systems are simple to control and can be used in a manner similar to traditional drilling systems.

In this work, we provided a case-study example based on drilling of very small (101.6 mm) diameter holes. The design was formulated using the analytical tools proposed in this work and was then validated both on a controlled laboratory test-bed and under realistic drilling conditions at the Sandia HOT facility. These experimental results illustrate that our proposed design has four valuable attributes: mechanical advantage for resisting large torques with friction (∼ 340 Nm), anisotropic frictional behavior using rolling elements (∼ 10x), scalable performance through multiple modules, and load capacity that scales linearly with applied force. The mechanism was also used within a wireline-deployed drilling system where it enabled drilling and prevented twisting of the cable.

We believe the principles outlined in this work have broad applicability beyond microholes. For example, other systems that require downhole rotation such as directional drills could benefit from the ability to react torque near the motor rather than with the drill string. Similarly, the mechanical advantage principles can be used to create other types of relevant devices such as inchworm type devices that lock within the borehole, or cutting tools that exploit mechanical advantage to apply large radial loads to the borehole wall.

## Acknowledgment

Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia LLC, a wholly owned subsidiary of Honeywell International Inc. for the U.S. Department of Energy’s National Nuclear Security Administration under Contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. SAND2020-14277 J.

The authors thank Elton Wright, Dennis King, and Michael Kuehl for their assistance with fabrication, prototyping, and testing. This work was funded by the United States Department of Energy, Office of Science, GTO WBS – 3.2.1.4.

## Conflict of Interest

There are no conflicts of interest.

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