Research on Fidelity Performance of Coring Bits during Drilling and Cutting in Deep Extreme Environments

Abstract

Deep rock formations in extreme environments are characterized by complex working conditions, various structures, high hardness, and high resistance to compression. However, existing coring techniques leave the cores of deep rock formations vulnerable to residual stresses, resulting in poor fidelity during deep coring. This paper develops a rock-breaking model for the structural parameters of drill bits. It proposes that a drill bit’s structural parameters in terms of back-rake and side-rake angles will affect the core’s fidelity performance. In addition, the core’s mechanical specific energy and maximum stress will reflect the fidelity effect. The accuracy of the theoretical model was verified via simulation analysis. The simulation results show that the tool’s average cutting force and Standard deviation of cutting force increase as the drill bit’s back-rake and side-rake angles vary. This leads to increased shear friction on the core, which affects the maximum stress and mechanical specific energy, and, subsequently, the fidelity of the core. The back-rake angles ranged from 15° to 25°, with the optimum back-rake angle of 21° producing a maximum stress and a mechanical specific energy that were 0.69 and 0.85 times higher than the highest point, respectively. The side-rake angles range from 5° to 15°, with the optimum side-rake angle of 10° producing a maximum stress and a mechanical specific energy that were 0.76 and 0.96 times higher than the highest point, respectively. The finite element method error was 1.21%. This work’s main results will help reveal the fidelity mechanisms of the drilling process and contribute to the development of fidelity drill bits for complex surface drilling processes.

1. Introduction

As traditional energy sources, such as oil and coal, in the shallow parts of the Earth are gradually depleted, mining deep resources is a strategic, scientific, and technological issue that we must address [1,2,3]. Deep rock formations in extreme environments are characterized by complex working conditions, various structures, high hardness, and high resistance to compression. Moreover, traditional drilling and coring techniques encounter challenges related to poor core fidelity and low rock-breaking efficiency [4,5]. New fidelity drilling and coring techniques aim to obtain complete rock samples, explore in situ stratigraphic information, investigate the in situ characteristics and physical and mechanical properties, and analyze the rock mechanical behavior of deep rocks within high-hardness rock formations at different depths exceeding 1000 m [6]. Core fidelity refers to the accuracy and integrity of the core samples obtained during drilling or coring operations. It measures how well the extracted core samples retain the original characteristics of the subsurface formations. Minimizing the stress impact on the core samples during the drilling process is essential, as residual stresses within the core can influence its physical and mechanical properties. Furthermore, maintaining residual stresses within the linear elastic range after drilling and cutting the core ensures the fidelity of the core samples. As the drilling depth increases, the pressure required to break the core during bit cutting also rises, thus presenting a more significant challenge in achieving core fidelity. By using appropriate coring bits and minimizing disturbances or damage to the core during extraction, fidelity coring enables researchers to obtain samples that accurately reflect the characteristics of subsurface rock formations [7]. The structural parameters of the drill bit used in this process directly affect the magnitude and distribution of stresses within the core, thereby impacting the fidelity of coring performance. Therefore, selecting appropriate drill bit structural parameters can optimize the breaking effect, reduce stress impact on the core, and enhance core fidelity performance. Conducting in-depth research on the influence of core drilling bit parameters on fidelity coring performance holds significant importance for comprehensively understanding the drilling and cutting mechanisms of core drilling bits.

In the field of fidelity coring, Xie et al., introduced the concept of in situ insulation and pressure-holding coring principles and techniques. They developed a coring device to achieve fidelity coring under in situ pressure and temperature conditions, allowing for the characterization of deep rocks at various depths [8]. Gao et al., proposed a coring principle and technique for in situ pressure-holding coring in deep coal mines. They also developed an in situ pressure controller to ensure high coring efficiency and stable pressure holding [9,10]. Wan et al., addressed the limitations of insulated coring and proposed an innovative design of an active insulation system for accurate temperature retention in in situ fidelity coring of deep rock formations [11]. He et al., developed an in situ fidelity coring system and designed pressure controllers for different coring formations to minimize disturbance during drilling [12,13]. In the past, limited research has been conducted to develop fidelity coring tools. Most research in the field of fidelity has primarily concentrated on the temperature and pressure control of cores that have already been drilled by corers. Since a drill bit’s cutting teeth directly contacts the core, ensuring fidelity control during the drilling process is crucial. However, very few previous research studies have explored the relationship between the structural parameters of drill bits and fidelity performance.

In the field of rock drilling and cutting, Zhu et al., utilized the Drucker–Prager criterion for orthogonal cutting based on three-dimensional mechanical modeling of rocks, incorporating weights on intermediate principal stresses, and proposed an analytical model [14]. Gao et al., studied the effect of drilling parameters on rock-cutting efficiency, developing a cutting temperature model, and discussed the sensitivity of cutting tooth temperature to different parameters using orthogonal analysis [15]. Xi et al., conducted dynamic experiments and numerical simulations on a hard rock to quantify the influence of various impact parameters on rock-breaking efficiency [16]. Zhang et al., performed finite element simulations to analyze the thermal–structural coupling during rock breaking using a full-size Polycrystalline Diamond Compact (PDC) bit, optimizing the bit’s life through the distribution of contact stresses on the PDC cutting teeth [17]. Chen et al., conducted PDC single-tooth cutting experiments considering rock material properties and studied the rock-breaking mechanism of cutting teeth at high temperatures [18]. While coring bits’ drilling and cutting mechanism significantly impacts fidelity performance during coring, research in this area is relatively limited compared to the extensive studies on rock fragmentation during drilling. And existing studies primarily focused on rock fragmentation mechanisms and did not specifically address the effects of drill bits’ structural parameters on fidelity performance. Therefore, further research is necessary to understand the relationship between drill bits’ structural parameters and fidelity performance during coring operations.

Theoretical research on drill bits’ fidelity coring must catch up with engineering applications. In the oil and gas industry, new coring tools and in situ simulation devices can help improve resource exploration and production efficiency and safety in deep and ultra-deep areas. An in-depth study of the influence of the structural parameters of drill bits on fidelity coring performance during the drilling and cutting process is of great value for the application of fidelity coring technology to coring bits. This paper analyzes the influence of back-rake and side-rake angles as a drill bit’s structural parameters on fidelity performance. We discuss the drilling and cutting mechanism of the core drill bit, adopt the Drucker–Prager criterion as the rock-yielding criterion, and conduct 3D finite element analysis on the drilling and breaking process of the core drill bit. This analysis helps identify the relationship between core drill bit parameters and fidelity coring performance. Furthermore, optimizing the design of core drill bits’ structural parameters and improving the effect of deep in situ coring is of great significance. This research provides theoretical support for deep fidelity coring. The specific arrangement of this article is as follows: Section 2 establishes an analytical model of the fidelity performance of a drill core; Section 3 explains the failure criteria of rocks and the various parameters of the simulation model; Section 4 verifies the influence of the rear and side camber angles on fidelity performance through simulation experiments; and the fifth section provides the conclusions.

2. Drill Core Fidelity Performance Model

The cutting action of a Polycrystalline Diamond Compact (PDC) coring bit is performed by multiple cutting teeth [19]. Therefore, studying the structural parameters of individual cutting teeth is essential for understanding the rock-breaking mechanism and drill bit fidelity. Through extensive theoretical analysis and experimental studies, we have discovered that the shear strength of rock is significantly lower than its compressive strength. Additionally, we have identified critical zones within the rock that are particularly prone to shear stress. The torque generated by the rotating bit of the PDC drill used in this paper supplies the shear force required to break the rock, causing the cutting teeth to be pressed into the rock and induce shear fracture.

2.1. Effect of Back-Rake and Side-Rake Angle on Fidelity Performance

The back-rake angle, θ, represents the angle at which the PDC bit presses into the rock vertically along the coring bit. It is a crucial design parameter for the coring bit, as it affects the contact angle between the cutting edge and the rock and the transmission of forces, Physical view of the deep coring drill bit is shown in Figure 1. A suitable back-rake angle not only increases drilling pressure and cutting speed but also reduces the retention time of rock chips on the cutting-edge surface, preventing a decline in cutting performance due to frictional heat generated between the rock chips and the PDC piece. The literature [20] shows that the back-rake angle is generally designed to be 0–30°.

When the back-rake angle is slight, the contact area between the rock and the drill bit decreases, resulting in larger cutting forces, leading to the poorer surface quality of the rock sample and reduced fidelity performance. On the other hand, a larger back-rake angle provides a larger contact area. It reduces cutting forces, making it easier to maintain the straight movement of the core barrel during coring, thus achieving better core fidelity [21,22,23]. However, an excessively large back-rake angle can increase friction and heat generation during coring, affecting drilling and breaking efficiency.

The side-rake angle, β, refers to the counterclockwise rotation of the PDC drill bit when positioned horizontally, as shown in Figure 2. The side-rake angle directly affects the magnitude and direction of the lateral forces acting on the cutting chips. During the rock-breaking process, the side-rake angle of the cutting teeth primarily operates in the radial direction, exerting thrust on the rock chips and preventing their accumulation at the bottom of the hole. This preservation of chip accumulation affects the quality of the drilled core and the efficiency of drilling and coring. From the literature [24], the side-rake angle is generally designed to be 0–25°.

When the side-rake angle is slight, the contact area between the cutting tooth and the rock diminishes, making the cutting tooth more susceptible to lateral forces from the rock. This can result in excessive lateral vibration of the cutting tooth during rock breaking, thereby affecting the fidelity performance of the core. Conversely, when the side-rake angle is large, the cutting teeth are more prone to rock impact, leading to increased tooth wear and a higher amount and retention time of rock chips. These factors negatively impact the surface quality of the core, ultimately reducing core fidelity.

Therefore, when designing a fidelity core drill bit, it is essential to consider the characteristics of the actual rock sample and structural parameters, such as the back-rake and side-rake angles. This approach ensures the acquisition of the best fidelity core and improves the fidelity performance of the core.

2.2. Analysis of Forces on Cutting Teeth

As the drill bit continues to drill downwards, the damage of the cutting force of the cutter is gradually transmitted to the core part. With increasing stress inside the rock, when these stresses surpass their tolerance limits, the rock fractures, forming a core. The core created during the drill bit’s cutting process is therefore influenced by the cutting forces exerted by the drill bit and the rock damage mechanism.

For the sake of calculation convenience, the fracture surface of the rock is simplified as a plane. It can be deduced from force analysis that the stress distribution on this fracture is maximum at the bottom edge and zero at the free surface. Based on this boundary condition, let us assume that the stress distribution on the fracture follows Equation (1) [25].

$$p=p_0{(\frac{d}{\sin \alpha }-r)}^n$$

(1)

In the provided equation, “r” represents the distance from any point on the fracture face to the tip of the cutting tooth; “d” is the depth of cut; “α” is the angle between the fracture face of the rock and the cutting plane of the PDC piece; and “n” is the stress distribution coefficient, which is influenced by the back-rake angle θ and the geometry and size of the drill bit. By integrating the above equation, the force acting on the cut core can be simplified as shown in Figure 3 without considering the motion effect. The resultant external load on the fracture surface should be equal to the external force of the PDC acting on the cut core, that is, the average cutting force, as shown in Equations (2) and (3).

$$p_0{\displaystyle {\int }_0^{d/\sin \alpha }{(\frac{d}{\sin \alpha }-r)}^n}dr=P_N$$

(2)

$$p_0=\frac{(n+1)P_N}{{(d/\sin \alpha )}^{n+1}}$$

(3)

Bringing the stress distribution of the structure into Equation (1) above, this results in a maximum stress for the tip of the rupture face as shown in Equation (4).

$$p_{\max }=\frac{(n+1)P_N\sin \alpha }{d}$$

(4)

At this point the direction of the maximum stress p_max load is parallel to the cutting surface and the angle γ is the shear fracture angle forming the rupture surface, then the positive and tangential stresses σ and τ on the shear breaking surface of the rock, where:

$$\sigma =p_{\max }\sin \alpha =p_{\max }\sin \left(\frac{\pi }{2}-\theta -\gamma \right)=p_{\max }\cos (\theta +\gamma )$$

(5)

$$\tau =p_{\max }\cos \alpha =p_{\max }\cos \left(\frac{\pi }{2}-\theta -\gamma \right)=p_{\max }\sin (\theta +\gamma )$$

(6)

The damage analysis of the rock is based on the M-C shear damage theory, which takes into account the effects of positive and shear stresses [26]:

$$\tau =\sigma \tan \phi +c$$

(7)

where φ is the angle of internal friction, c is the cohesive force, and the simplification gives:

$$P_N=d\cdot c\cdot \frac{\cos \phi }{(n+1)\cdot \cos (\theta +\gamma )\cdot \sin (\theta +\gamma -\phi )}$$

(8)

The relationship between the cutting force and the structural parameters of the drill bit is shown in Equation (8), and the core’s shear strength and the drill bit’s structural parameters are shown in Equation (9).

$$\tau =\sin (\theta +\gamma )\cdot c\cdot \frac{\cos \phi }{\sin (\theta +\gamma -\phi )}$$

(9)

Based on the analysis presented above, it is demonstrated that the shear stress distribution in the PDC drill core depends not only on the axial and tangential loads, as well as the internal friction angle and cohesion of the rock, but also on factors such as the back-rake and side-rake angles of the drill bit’s structural parameters. Since the internal friction angle and cohesion of the rock remain constant during the cutting process, this paper proceeds with simulation experiments to analyze the impact of the back and side rake angles of the drill bit’s structural parameters on the fidelity performance of the drill bit.

2.3. Mechanical Specific Energy

The mechanical specific energy (MSE) refers to the amount of energy consumed in breaking a unit volume of rock. More detailed work indicates a more significant energy input per unit volume when a drill bit breaks rock. This increased energy input results in more substantial core damage and rock fracture. As a result, the core becomes less capable of accurately representing the mechanical and physical properties of the rock in its original position, leading to a decrease in fidelity. Therefore, the mechanical-specific energy is a crucial indicator for evaluating fidelity performance.

Calculating the actual volume of crushing is complex, but Zhou et al., found through simulation and experimental studies that the results were similar when comparing the existing and projected crushing volume [26]. For the sake of convenience in the calculation, this paper characterizes the rock-crushing ratio based on the projected volume of crushing using the following equation:

$$MSE=\frac{W}{V}=\frac{F_{h}d}{Ad}=\frac{F_h}{A}$$

(10)

MSE is required to break the rock. The work (W) represents the energy consumed in breaking the rock, while the volume of rock broken (V) corresponds to the amount of rock that has been fragmented. The work (W) can be calculated by multiplying the average cutting force (F) by the cutting stroke (d). Similarly, the volume of rock broken (V) is determined by multiplying the projected area (A) of the cutting surface by the cutting stroke (d)

$$A=\left[r^2{\cos }^{-1}\left(\frac{r-d/\cos \theta }{r}\right)-r\left(r-\frac{d}{\cos \theta }\right)\sin \left({\cos }^{-1}\left(\frac{r-d/\cos \theta }{r}\right)\right)\right]\cos \beta$$

(11)

In this paper, the radius of the cutting tooth (r) and the cut’s (d) depth are considered fixed parameters. The projected area of the cutting surface, which determines the rock-breaking ratio work, is primarily influenced by the back-rake angle (θ) and the side-rake angle (β). To achieve a high-fidelity performance, controlling the magnitude of the rock-breaking specific work is crucial. This can be achieved by carefully designing and selecting drill structure parameters, aiming to minimize core damage and fragmentation.

3. Finite Element Analysis of Processes

3.1. Cutting Model Establishment

To validate the accuracy of the cutting analysis model for the drill bit’s cutting teeth, the fidelity performance of the cutting teeth was simulated and analyzed under various structural parameters of the drill bit. This paper investigates the impact of cutting teeth on the fidelity performance of a full-size PDC bit during the rock-breaking process. A three-dimensional model of the PDC bit was created using Solidworks 2021, as depicted in the figure below. The following hypothesis is made for the calculation model:

• The cutting teeth and the PDC coring bit are set as rigid bodies during the simulation;
• The rock is set up as a continuous homogeneous medium with constant velocity and drilling pressure acting on the cutting teeth and bit;
• The helical motion of the cutting teeth is replaced by a linear motion in the single tooth force simulation, and the effect of tooth wear on the fidelity of the core drill bit is not considered.

The 3D model and Boundary conditions for a single cutting tooth are shown in Figure 4, with a single cutter composite sheet evenly distributed on the bit. The drill-rock breaking model was simplified to optimize computational efficiency and reduce the number of meshes, allowing for the analysis of stress variation in individual cutting teeth under different drill structure parameters.

The finite element analysis of the cutting tooth-rock model was conducted using the abaqus2021 program. The individual cutting tooth of the drill has a diameter of 5 mm and a height of 3 mm. Following the Saint Venant principle [27], the size of the rock model is typically 3–5 times larger than the cutting tool, resulting in a rock size of 40 × 30 × 20 mm. The dimensions of the cutting tooth composite and the rock model can be seen in Figure 5 below. The boundary conditions for the 3D cutting diagram and simulation are shown in Figure 5.

3.2. Rock Strength Criterion and Failure Criterion

Selecting an appropriate rock constitutive model is crucial for simulating rock fracture. This paper chooses the Drucker–Prager criterion as it considers the rock’s shear expansion, the influence of stress on yield, and the effect of intermediate principal stresses [28]. The expressions for the D–P criterion are as follows:

$$f(\sigma )=\alpha I_1+\sqrt{J_2}-K=0$$

(12)

$I_1$ is the first invariant of stress, $J_2$ is the second invariant of stress bias:

$$I_1={\sigma }_1+{\sigma }_2+{\sigma }_3$$

(13)

$$J_2=\frac{1}{6}\left[{\left({\sigma }_1-{\sigma }_1\right)}^2+{\left({\sigma }_1-{\sigma }_1\right)}^2+{\left({\sigma }_1-{\sigma }_1\right)}^2\right]$$

(14)

σ1, σ2 and σ3 are the principal stresses of the effective stresses, and α and K are experimental constants related only to the angle of internal friction and cohesion forces in the rock. ${\epsilon }^{pl}$ is the equivalent plastic strain of the rock and ${\epsilon }_f^{-pl}$ is the equivalent plastic strain when the rock is completely destroyed [28].

$$\alpha =\frac{2\sin \varphi }{\sqrt{3}(3-\sin \varphi )}$$

(15)

$$K=\frac{6c\cos \varphi }{\sqrt{3}(3-\sin \varphi )}$$

(16)

$${\epsilon }^{pl}\le {\epsilon }_f^{-pl}$$

(17)

As rocks fracture primarily through shear damage, the shear damage criterion determines rock fracture. Rock damage begins when the rock’s plastic strain value approaches the material’s plastic strain value, separating the rock unit from the rock mass. The material begins to fail when the rock nodes’ equivalent plastic strain value reaches the material’s equivalent plastic strain value.

3.3. Simulation Conditions and Cutting Characteristics

In terms of hardware, the simulation was performed on a PC with an 11th Gen Intel(R) Core(TM) i5-11260H processor running at a base frequency of 2.60 GHz (with a maximum turbo frequency of 2.61 GHz)—the simulation utilized 8 processors running in parallel to enhance computational efficiency.

In the simulations, the dynamic constitutive model of the rock is implemented using the D-P criterion. The analysis does not consider the effect of cutting tooth wear. The rock body and the cutting teeth are represented using an 8-node linear hexahedron element with hourglass control. The specific element used is the C3D8R cell with reduced integration. Additionally, a mesh refinement technique is applied to the rock body in the region where cutting occurs to capture the details accurately. The cutting tooth is treated as a separate rigid body and anchored at a reference point RP1 to enable the application of cutting speed to the tool. The composite material can only move in a straight line along the x-axis. The mesh and boundary conditions are depicted in Figure 4 provided. Considering the impact of computer performance on simulation efficiency, the simulation time is set to 0.125 s, and the cutting speed is specified as 400 mm/s. An elastic slip penalty friction formula is employed for the contact between the cutting tooth and the rock, with a tangential friction coefficient of 0.4. A “hard contact” formula is adopted for the regular contact relationship between the contact surfaces. The material parameters in the core are shown in

Table 1. Relevant material parameters used in the finite element analysis.

	Density/kg m−3	Elasticity Modulus/Gpa	Poisson Ratio	Shear Strength/MPa	Cohesion/MPa	Internal Friction Angle/°	Flow Stress Ratio
Cutter	3510	890	0.077
Rock	2250	27.1	0.29	17.3	27.2	46.934	0.8

.

The results of the grid independence study are presented in Figure 6. As the number of grids increases, the stress distribution values tend to stabilize, and the difference between adjacent data points decreases. Specifically, the difference between adjacent data from grid 82,046 to grid 12,550 is approximately 2.9%, and the difference from grid 12,550 to grid 170,054 is about 1.21%. This suggests that the numerical simulation results have converged, indicating the completion of the verification of grid independence. In other words, when the number of grids exceeds 170,054, the simulation solution is considered to be grid-independent.

4. Simulation Experiments and Results

4.1. Effect of Back-Rake Angle

This paper uses simulation to analyze the fidelity of the cutting teeth of PDC drills under different cutting structure parameters and to obtain the corresponding laws. The depth of cut is 2 mm, the side-rake angle is 0°, and the back rake is 5.0°, 10.0°, 15.0°, 20.0°, 25.0°, and 30.0°, respectively. The simulated cutting forces with time at a back-rake angle of 15° are shown in Figure 7:

As can be observed from the graph, the cutting forces exhibit significant fluctuations over time. This is attributed to the rock reaching its yield limit, leading to fracture damage. Specific units fail to absorb plastic deformation energy, resulting in a rapid decrease in cutting force. However, to proceed with the cutting process for the subsequent division, the cutting force experiences a rapid increase once again. Throughout the cutting process, while maintaining a constant depth of cut, the tangential and axial forces fluctuate within a specific range. Nonetheless, there is an underlying stable average value. By utilizing this average value as the representative tangential and axial forces, the average cutting force at a back-rake angle of 15° is determined to be 822.5 N. In the ABAQUS 2023 post-processing, the X-directional support force C_FN2 at the RP point, which is attached to the rigid body, is extracted [29,30]. This force represents the tangential force exerted by the cutting tooth on the rock, reflecting the cutting force of the cutting tooth under actual working conditions. C_FN2 values are extracted at various time points (i) after contact between the tooth and the rock to determine the average cutting force. The average cutting force is then calculated using the following equation:

$$F_h=\overline{C_{FN2}}=\frac{1}{n}\sum _{i=1}^n{C}_{FN2i}$$

(18)

$${\sigma }_X=\sqrt{\frac{{\displaystyle \sum _{i=1}^n{(C_{FN2i}-\overline{F_h})}^2}}{n}}$$

(19)

Figure 8 below shows the simulated cutting forces followed by the change in back-rake angle.

When the rear back-rake angle ranges from 5° to 15°, the average cutting force increases as the angle risk increases. Within this range, the standard deviation of the cutting force initially increases and then decreases, with an overall minimal difference. This behavior is attributed to the fact that as the back-rake angle increases, the contact area between the cutting teeth and the rock also increases. Consequently, the rock becomes more tightly compressed, increasing friction between the cutting teeth and the rock. With the same cutting speed and depth of cut, more excellent cutting and axial forces are required to break the rock, leading to a natural increase in the cutting force. Within the 5–15° range, the back-rake angle causes more significant fluctuations in the cutting forces when the cutting teeth of the drill break the rock. Although the rock becomes easier to break, the cutting teeth are subjected to more severe impact loads. This scenario is not conducive to drilling and coring stability. Therefore, a back-rake angle within this range is not recommended, despite the lower average cutting force and higher efficiency it may offer under the same rock-breaking conditions.

Within the 15° to 25° range, the average cutting force increases slower, even though the axial and frictional forces continue to grow with the angle. However, due to the elastic nature of the rock and the mechanical properties of rock damage, the standard deviation of the cutting force exhibits a fluctuating pattern. This indicates that using a back-rake angle within this range under the same rock-breaking conditions will lower output torque and reduce disturbances caused by drilling cuts, thereby improving core stability [31]. After the back-rake angle exceeds 25°, both the standard deviation of cutting forces and the cutting forces increase rapidly. This is likely due to the increased contact area and a shift in the rock-crushing mode from shear crushing to impact crushing. It should be noted that the shear strength of the rock is significantly lower than its compressive strength. As a result, the cutting force required to crush the rock gradually increases.

Therefore, choosing the optimal back tilt angle within the 15° to 25° is recommended to achieve better core fidelity, as it balances cutting force, output torque, and drilling stability.

4.2. Optimum Back-Rake Angle

Based on the discussions presented above, it is evident that the optimal back-rake angle for the rock falls within the range of 15–25°. Therefore, simulation tests are conducted with a gradual increase in the back-rake angle, specifically in increments of 1° within the 15–25° range. This allows for a more precise examination of the stress distribution and the cutting tooth contact stress diagram during a single tooth drilling cut.

For instance, the stress diagram and the cutting tooth contact stress diagram for a single tooth drilling cut at a 15° back-rake angle are displayed below:

During the vibration of the drill cutting corer, the core experiences stress that does not meet the fidelity performance requirements. The cutting teeth create localized force concentrations near the contact points during cutting, leading to plastic deformation of the rock, mostly at the point where the cutting teeth are in direct contact with the core, which is consistent with the results of the theoretical model. To enhance core fidelity, it is crucial to identify the area where the maximum stress point is located and minimize the peak value of this stress point, as shown in Figure 9.

By utilizing the post-processing function in ABAQUS 2023, the stresses at the outermost edge of the core were derived for different inclination angles, and the variation of residual stresses with the cutting path for different inclination angles is shown in Figure 10. Different colours represent different cutting angles. As observed in Figure 10, the area of direct contact with the cutting teeth experiences the highest stress levels. Furthermore, the cores obtained after cutting display a concentration of residual stresses at the edges, which consequently impacts the fidelity of the cores [32,33]. These findings align with the residual stress patterns identified in the theoretical analysis.

As observed in Figure 11, the back inclination angle is in the range of 15° to 21°, as the angle increases, the specific work of breaking the rock gradually decreases, and the maximum stress first increases and then decreases. This is because a smaller back inclination angle can produce a greater concentration of stress on the cutting edge and cutting surface, making it easier for the cutting teeth to enter the rock, giving full play to the advantages of shear breaking and improving the breaking efficiency, but also leading to a sharp increase in the maximum stress. As the back inclination angle gradually increases from 17° to 21°, the breaking area of the cutting tooth in contact with the rock slowly increases, and as shown above, the standard deviation of the cutting force gradually decreases at this time. The fluctuation of the cutting force decreases, which improves the stability of drilling and coring, gradually decreases the maximum stress and attains the lowest at the back inclination angle of 21°. Between 21° and 25°, there is a rapid increase in the MSE and maximum stress. In this case, it is due to the increase in the back inclination angle to the cutting teeth compacting the rock and the increase in friction between the cutting teeth and the rock as the angle increases. The rock-breaking mode transitions from shear crushing to shear-impact crushing. As a result, higher mechanical energy is required to break the rock under the same cutting speed and depth. This leads to increased MSE and a significant fluctuation in cutting force during impact crushing, which is consistent with the conclusions of Zhang et al. [28], consequently increasing maximum stress within the core.

The x-axis represents the standard deviation of the cutting force at a back-rack angle of 15–25°, while the y-axis represents the stress at the outermost edge of the core at different dip angles. The z-axis corresponds to various cutting angles’ MSE values. These variables are used to create a scatter plot, and a surface is fitted to the data in the XYZ-axis.

From Figure 12, it is evident that the back-rake angle of the drill has an impact on the maximum stress and MSE, aligning with the findings of the theoretical model. As the back-rake angle increases, the standard deviation of the mean cutting force exhibits a decreasing and then increasing trend. Based on the distribution and aggregation of points, when the standard deviation of the cutting force is at large, the maximum stress in the core also becomes larger, inferring that there is a relationship between the maximum stress in the core and the standard deviation of the cutting force. Furthermore, the back-rake angles ranged from 15° to 25°, with the optimum back-rake angle of 21° producing a maximum stress and mechanical specific energy that were 0.69 and 0.85 times higher than the highest point, respectively. Based on the simulation results, the optimal back-rack angle is 21°, considering the maximum stress, MSE, and average cutting force.

4.3. Effect of Side-Rake Angle

In this section, the simulation considers a back tilt angle of 21°and side tilt angles of 0°, 5.0°, 10.0°, 15.0°, 20.0°, and 25.0°, respectively. Figure 13 illustrates the variation curve of the simulated cutting force with the side-rake angle.

In the side-rake range from 0° to 25°, it is observed that the average cutting force tends to decrease and then increase as the angle increases, with minimal overall variation. This indicates that a smaller lateral back rake is advantageous for rock breaking, but its impact on the cutting force is limited. However, the standard deviation of the mean cutting force shows a linear decrease from 0° to 10°. This is attributed to the reduced lateral vibration of the cutting teeth during the breaking process, which enhances the stability of the drilling cut. In the range of 10° to 25°, the standard deviation of the cutting forces increases rapidly, and the rate of change exhibits a fluctuating pattern of increase and then decrease. This phenomenon results from gradually enlarging the contact area between the cutting teeth and the rock, leading to increased wear between them. The wear between the cutter face and the rock intensifies, increasing rock chip production and retention time. Therefore, choosing a side-rake angle of approximately 5–15° is optimum for the rock-breaking process. Because of the continuity of the simulation results, the standard deviation of cutting forces shifts significantly when the lateral inclination angle is around 10° and is the smallest standard deviation of cutting forces, so the optimum side-rake angle during rock breaking should be in the range of 5–15°.

4.4. Optimum Side-Rake Angle

Based on the previous findings, the optimal side-rake angle for rock breaking falls within the range of approximately 5–15°. Therefore, simulation tests were conducted with side-rake angles ranging from 5° to 15° in increments of 1°. The experimental results are presented in Figure 14.

In the 5° to 15° of the side-rake range, the MSE required to break the rock slightly increases with increasing the side-rake range. Still, the increase is relatively small, and the cutting area tends to grow more slowly, which is broadly consistent with the findings of Zhu et al. [24]. on the predicted trend of the effect of lateral dip angle on the specific work of breaking rock. When the side-rake range is between 5° and 10°, increasing the angle makes it easier for the cutting teeth to penetrate the subsurface rock and exert cutting forces. Furthermore, as the side-rake range increases, it induces shear deformation of the rock in specific areas during the cutting process. This shear deformation reduces the stress transfer within the cutting area, resulting in a lower overall stress level within the core. On the other hand, when the side-rake angle exceeds 10°, the contact area between the cutting teeth and the rock gradually increases, causing the rock to transition from pure shear crushing to shear-impact crushing. This results in more direct contact between the rock and the cutting teeth and causes more friction. The increased friction increases the resistance of the cutting teeth in the rock, making it more difficult to break the rock. As a result, the maximum stress in the core increases as the angle increases.

As shown in Figure 15, the x-axis represents the standard deviation of the cutting force at a side-rack angle of 5–15°, while the y-axis represents the stress at the outermost edge of the core at different dip angles. The z-axis corresponds to various cutting angles’ MSE values. These variables are used to create a scatter plot, and a surface is fitted to the data in the XYZ-axis.

From Figure 15, it is evident that the side-rake angle of the drill has an impact on the maximum stress and MSE, aligning with the findings of the theoretical model. As the side-rake angle increases, the standard deviation of the mean cutting force exhibits a decreasing and then increasing trend. Based on the distribution and aggregation of points, MSE values vary slightly between lateral dips, with adjacent angles often clustered together, and the large differences in maximum stress in the core may be due to a shift in the cutting and crushing method [15]. Based on the simulation results, the optimal back-rack angle is 10°, considering the maximum stress, MSE, and average cutting force. Furthermore, The side-rake angles ranged from 5° to 15°, with the best side-rake angle of 10° producing a maximum stress and mechanical specific energy of 0.76 and 0.96 times higher than the highest point, respectively.

5. Conclusions

This paper presents a new concept that a drill bit’s backward and sideways inclination angles affect the core’s fidelity and analyzes the influence of backward and sideways inclination angles on the fidelity of the core through theorical modeling and simulation. The optimum backward and sideways inclination angles were found from the simulation results. The improved core drill bit has a better fidelity performance. The following conclusions are drawn:

(1)

A parametric analytical model of the drill bit’s structure was established by studying the influence of cutting tooth structural parameters on core fidelity performance. Additionally, a three-dimensional finite element analysis of the rock-breaking process was conducted to validate the accuracy of the parametric analytical model.

(2)

The theoretical model and simulation experiments revealed that in deep extreme environments with varying back-rake and side-rake angles as the drill bit structural parameters, increasing the horizontal mean cutting force and the standard deviation of the cutting force resulted in more severe shear friction on the drill bit. This friction impacted the maximum stress of the core and the specific work of breaking, ultimately affecting the fidelity performance of the core. Therefore, it is crucial to carefully select appropriate back-rake and side-rake angles during the design phase to enhance core fidelity performance.

(3)

The back-rake angles ranged from 15° to 25°, with the optimum back-rake angle of 21° producing a maximum stress and a mechanical specific energy that were 0.69 and 0.85 times higher than the highest point, respectively. The side-rake angles ranged from 5° to 15°, with the optimum side-rake angle of 10° producing a maximum stress and a mechanical specific energy that were 0.76 and 0.96 times higher than the highest point, respectively. The FME method error was 1.21%.

In future research, the comprehensive influence of additional drill bit structural parameters on cutting tooth fidelity performance will be considered. Weighting analysis will also be conducted on factors such as core stress in the fidelity evaluation model.