Numerical Analysis of the Stress Distribution and Concentration Factors of the Tool Joint of the Directional Drill Pipe

Shu, Jiangjun; Zhang, Yu; Zhao, Zhiqiang; Mei, Anping; Liu, Li

doi:https://doi.org/10.1155/2023/8106535

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2023 | Article ID 8106535 | https://doi.org/10.1155/2023/8106535

Numerical Analysis of the Stress Distribution and Concentration Factors of the Tool Joint of the Directional Drill Pipe

Jiangjun Shu,^1,2Yu Zhang,^1,2Zhiqiang Zhao,^1,2Anping Mei,^1,2and Li Liu^1,2

Academic Editor: Libor Pekař

Received18 Oct 2022

Revised20 Mar 2023

Accepted29 Mar 2023

Published17 Apr 2023

Abstract

With the wide application of directional drilling technology in coal mine predraining boreholes, the failure problem of the tool joint of the directional drill pipe has become one of the main factors restricting the drilling efficiency. The main reason for the failure problem of the tool joint of the directional drill pipe is the stress concentration. The stress test rig for the tool joint of the directional drill pipe is designed based on the resistance strain measurement method, and the stress of the tool joint of the directional drill pipe is tested. The tool joint’s 3D finite element model was established based on nonlinear contact theory. The experiment verified the accuracy of this model. The stress distribution of the tool joint of the directional drill pipe was obtained. The research shows that the stress of the tool joint of the directional drill pipe is concentrated at the root between the third and the fourth turn of the engaged thread. The work presented in this study is a reliable guide to the design and field use of the tool joint of the directional drill pipe.

1. Introduction

With the increase in coal mining intensity and the rapid growth of mining depth, the problems of gas outbursts are becoming more serious [1–3]. Therefore, the predraining boreholes are required to prevent gas outbursts [4–6]. Directional drilling technology (DDT) has the advantages of a controllable track, a long effective extraction distance, multiple branch holes, and a large concentrated extraction area, as well as the advantages of a lower drilling construction cost and high-efficiency gas extraction [7]. Therefore, many coal mines have adopted DDT to drill predraining boreholes, as shown in Figure 1.

The diameter of the directional drill pipe is small, and a cable is installed inside the drill pipe. Therefore, the tool joint of the directional drill pipe is designed with a thin-walled thread [8–10]. The tool joint of the directional drill pipe is easy to fracture. The most common reason for joint failure [11] is stress concentration [12–14]. The Mises stress of the FEM results is closely related to the failure of the tool joint [15].

Many drill pipes are connected through threaded tool joints to form the drill string [16]. The tool joint of the directional drill pipe is the weakest link in the whole drill string [17, 18]. Statistics show that tool joint failure accounts for 70% of all drill string failures.

According to the statistics, in 2020, during the construction process of the predraining boreholes, in Huainan City, Anhui Province, China, for every 20,000 meters of the predraining boreholes, there will be about ten drilling accidents, among which the box fracture accounts for 16%, the pin fracture accounts for 72%, and other accidents account for 12%. Figure 2 shows the failure characteristics. The box fractures between the thread’s third and fourth turns. The pin fractures or cracks between the thread’s third and fourth turns. Therefore, it is crucial to study the stress distribution in the tool joint of the directional drill pipe.

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In recent years, a great deal of research has been carried out on drill pipe tool joints. Several research studies conducted experiments to analyze the fatigue life of drill pipe tool joints according to a quasi-static scheme, such as Miscow et al. [16] used a resonance test bench to analyze the fatigue life of drill pipe tool joints. Bertini et al. [17] showed two types of resonance testing of the drilling elements: plane bending and rotating bending rigs. Wittenberghe et al. [18] determined the crack propagation in a threaded pipe with bend experiments. Several research studies use FEM to analyze drill pipe failure from specific aspects based on the stress clouds of the drill pipe tool joint. Knight and Brennan [19] determined the maximum stress at the first thread tooth of the large-end with a 2D axisymmetric finite element analysis model. Zhu et al. [20] established a 3D drill pipe thread finite element model and analyzed the mechanical properties of double shoulder tool joints. Dong et al. [21] analyzing the relationship between thread and shoulder with a 3D finite element model, they proposed a new type of thread structure for drill pipe tool joints. Guo et al. [22] analyzed the influence of the internal and external thickening transition zones on the stress of the drill pipe tool joint, and concluded the reason for the failure of the external thread joint. Yu Wang et al. [14] studied the stress distribution in the joint threaded by analyzing under axial tension and optimized the threaded structure of the joint. Wittenberghe et al. [23] used finite element analyses of conical threaded API line pipe couplings to quantify the influence of their contact parameters (coefficient of friction, preload, and taper angle).

In summary, the existing research has mainly carried out the experimental study of drilling pipe fatigue. The experiment of drill pipe stress distribution is rare in the literature report. None of the existing FEMs has been verified by relevant experiments. As a result, the results of the stress distribution in drill pipe tool joints cannot be uniformly concluded by different research studies at present. Therefore, the experiment of stress distribution in drill pipe is carried out in this paper.

In order to accurately study the stress distribution of the directional drill pipe tool joint, a nonlinear FEM of directional drill pipe tool joints was established for mechanical analysis in harsh environments. An experiment was conducted to compare the results and verify the correctness of the analysis model.

2. The FEM of the Tool Joint

2.1. The Tool Joint Structure

The connected tool joint of the directional drill pipe is shown in Figure 3. The tool joint consists of a box, a pin, and a tube. The box and the pin have the same thread structure. The directional drill pipe must ensure that the internal space is as large as possible, so the thin-walled thread structure is used for the directional drill pipe. The tooth angle and the taper are the main parameters of the thin-walled thread structure.

For ease of analysis, the thread’s sections are numbered, as shown in Figure 4. The stress value of the FEM results was extracted to calculate the average value of each half-turn thread.

2.2. Material Parameters and Mesh

The material of the tool joint is 42CrMo, the yield stress is 851 MPa, the tensile strength is 1,010 MPa, the elastic modulus E is 208,000 and the Poisson’s ratio is 0.28. The isotropic bilinear elastic-plastic material model is established. The FEM is shown in Figure 5. The model is meshing using the 10-node modified quadratic tetrahedron (C3D10). The mesh is reasonably refined at the thread turns. The Johnson–Cook failure model is used in the FEM.

2.3. Process Simulation

The model’s initial state is that the tooth of the external thread and the tooth of the internal thread are correctly engaged. The surface-surface contact approach has been used to model the contact between the engaging tooth pairs on both sides of the thread. Coulomb’s law of friction is used between them, and the coefficient of friction is 0.15 [24]. Due to the nonlinear nature of the contact phenomena [25, 26], an explicit method has been chosen to solve the problem. A reference point is set at the center of the end face, which is coupled to the end face. According to the drilling machine and the borehole trajectory, the theoretical loads of the drill pipe tool joint are obtained. Considering the extreme conditions in the hole, the theoretical load was multiplied by a safety factor [27] of 1.2. Tension, bending, and torque loads are applied to the coupling point, as shown in Table 1.

2.4. Mesh Independence Verification

Fine mesh (the mesh size is 1 mm around 711,545 cells), medium mesh (the mesh size is 1.5 mm around 320,004 cells), and coarse mesh (the mesh size is 2 mm around 180,864 cells) have been created to investigate mesh independence. The result is most accurate when the joint is subjected to tension. Therefore, the mesh independence analysis was carried out at 160,000 N tension. As shown in Figure 6, when defined as the medium mesh and the fine mesh, the stress of the tooth is a minimal difference. The maximum difference was found in the tail of the thread, with a maximum difference of 4%. Considering the reasonable computational time and the satisfactory model accuracy, the medium mesh is applied to the analysis model of this paper.

3. FEM Verification and Computation Result Analysis

3.1. The FEM Validation

Figure 7 shows the comparison of the results obtained by FEM simulation and experimental testing. The main error occurs at the beginning and end of the thread. This error is mainly due to the incomplete tooth shape at the beginning and end of the thread. The mesh distortion causes the FEM simulation error at the beginning and end of the thread. Except for the beginning and end positions of the thread, it can be found that the result data obtained by FEM simulation agrees well with the result of the experiment. Therefore, it is demonstrated that the computational accuracy of this FEM is sufficient to analyze the tool joint of the directional drill pipe.

3.2. Effects Analysis of Tension

The calculation results under the tension forces are shown in Figure 8. As shown in figures 8(a) and 8(b), the pin and the box show the same stress variation tendency. As shown in figures 8(c) and 8(d), the stress of the tool joint is extremely uneven under the tension forces, and the stress concentration phenomenon is evident at the 3.5 turns. The slight stress changes from 1-2.5 turns. After 2.5 turns, the stress distribution increases sharply, and the maximum stress is found in the thread turns of 3.5 turns. The main reason is that the joint is subjected to unidirectional force, so the stress of the small numbered tooth is superimposed on the large-numbered tooth. The fourth turn of thread engagement is incomplete, so the maximum stress is at the position of 3.5 turns. These analysis results identify positions of maximum stress. Therefore, the strength of these positions can be increased in the design.

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3.3. Effect Analysis of Bending

The calculation results under the bending are shown in Figure 9. The stress distribution of the box and the pin is quite different. The pin stress distribution under the bending is shown in Figures 9(a) and 9(c). The pin stress increases when the number of thread turns is less than 3.5. The maximum stress in the pin is 690 MPa at 3.5 turns. The box stress distribution under the bending is shown in Figures 9(b), and 9(d). The compressive stress of the box is greater than the tension stress. The maximum stress in the box is 760 MPa. As shown in figures 9(c), and 9(d), during the bending processes, the tool joint of the directional drill pipe has immense stress, which is caused by deformation. In the design and use process, the life of the tool joint of the directional drill pipe can be improved by reducing the deformation.

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3.4. Effect Analysis of Torque

The calculation results of the tool joint under the torque are shown in Figure 10. As shown in Figure 10(d), the stress in the box is mainly concentrated in the front position of the thread. As shown in Figures 10(a) and 10(b), the stress value difference between the pin and the box is slight. As shown in Figure 10(c), the bin stress concentration at the shoulder. The stress value increases when the torque increases, but the stress concentration factor decreases. The torque enables better engagement of the thread, which reduces the stress concentration. It can be concluded that proper torque can improve the stress distribution in a drill pipe tool joint. The joint must be pretightened before drilling construction.

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3.5. Orthogonal Analysis and Result Analysis

According to previous research, the stress distribution of the tool joint is highly uneven. It is necessary to study the stress concentration of different teeth. A stress concentration factor is defined as shown in formula (1) to quantify the stress concentration. In the present article, K is defined as the ratio of the maximum Mises stress at the root of the tooth () to the average stress of the tooth ()

In Figure 11, T_h is the tooth angle, and T_a is the taper. In order to study the influence of parameter changes in T_a and T_h on the stress concentration factor, a factor-level table of orthogonal analysis was established, as shown in Table 2.

According to previous research, when the tool joint is subjected to tension, bending, and torque, the stress distribution trend of the tool joint is consistent. Considering the feasible workload, the stress distribution of tension is applied to the orthogonal analysis. According to Table 2, T_a and T_h were selected as two factors, and each factor has three levels. The two factors and three levels (of the L9 (3²)) orthogonal analysis were applied. The orthogonal table and calculation results are shown in Table 3. Ta and T_h have little effect on the maximum stress. The change in maximum stress is less than 2%. The combination of Ta and T_h affects the stress concentration factor. Therefore, the stress concentration factor should be given priority in the optimal selection. The optimization scheme uses a Ta of 1 : 22 and a T_h of 34°. The thin-walled threads of the tool joint of directional drill pipe structural parameters are strongly correlated. The stress concentration factor is affected by several parameters.

4. Experimental Test of Tool Joint

4.1. Experimental Scheme

The tension stress test of the tool joint of the directional drill pipe is carried out, as shown in Figure 12, to study the stress variation of each tooth and verify the accuracy and reliability of the simulation results by the FEM analysis. The pin and the box connected correctly to form a test joint. One end of the test joint is connected to the hydraulic cylinder, and the other is connected to the experimental platform. Both ends of the test joint are connected to the experimental platform by a hinge to ensure that the test joint only bears tension. As shown in Figure 12, the foil gauges are pasted on both the inner and outer surfaces at the position of thread engagement. The shielded wire was applied to data transmission. A static stress and strain acquisition instrument (DH3816N) was used to process the data.

The static stress and strain acquisition instrument’s main parameters are shown in Table 4. Acquisition frequency is a crucial parameter of the test process. The acquisition frequency leads to too much data, but the acquisition frequency slowly leads to experimental error. This testing studies the stress distribution of the tool joint of a directional drill pipe in the elastic deformation range. The hydraulic cylinder runs very slowly during testing, and the deformation is minimal. By way of testing, the data acquisition frequency of 5 Hz can meet the test requirements. The foil gauge’s main parameters are shown in Table 5.

4.2. Experimental Process

The foil gauges are pasted on the inner and outer surfaces of the thread engagement to test the stress distribution at the thread engagement position of the tool joint of the directional drill pipe. The acquisition instrument measures the stress value of each foil gauge. The tension stress test experiment is shown in Figure 13. The tension strength of the joint material is 1,010 MPa. This paper studies the stress distribution of the tool joint in the elastic deformation range. Considering that the stress at the tooth’s root is much greater than stress on the inner and outer surfaces, stop increasing tension when the test stress reaches 400 MPa. The test procedure is as follows:(1)A section of the test joint convenient for measurement is chosen. The marker is on the tooth position of the box and the pin.(2)Wiping the surface of the paste position and cleaning it with anhydrous alcohol to help the foil gauges stick firmly(3)Marking the position of the tooth and pasting the foil gauges at the marked tooth position(4)The shielded wire connects the foil gauge and the static stress and strain acquisition instrument(5)The test joint, which has been pasted with the foil gauge, is installed on the experimental platform(6)A tension force of 5 KN is applied to the drill pipe tool joint to check each foil gauge for the output signal(7)The hydraulic cylinder shrinks slowly. The tension value of the hydraulic cylinder increases by 50,000 N every time, then keep it for two minutes until the stress reaches 400 MPa.

4.3. Experimental Results and Discussion

In the tool joint of the directional drill pipe tension test, the stress curves of each foil gauge on the pin are shown in Figure 14. The stress of each tooth is proportional to the tension. The stress change of each tooth is consistent with the tension change, but the stress change rate of each tooth is different. The stress on the third tooth is the greatest. The stress on the first tooth is the least. When the joint is stretched, the stress in order from maximum to minimum is as follows: tooth 3, tooth 4, tooth 2, and tooth 1. The stress distribution of the test joint is consistent with the FEM analysis results, so the correctness of the analysis result is verified.

In the tool joint of the directional drill pipe tension test, the stress curves of each foil gauge on the box are shown in Figure 15. The stress of each tooth is proportional to the tension. The stress on the tooth 3 is the greatest. The stress on the tooth 1 is the least. The stress on tooth 2 is slightly higher than that on tooth 1. The stress in order from maximum to minimum is as follows: tooth 3, tooth 4, tooth 2, and tooth 1. By comparing Figures 14 and 15, it can be found that the stress on each tooth of the box is smaller than that on the pin. This law explains that the pin is more likely to fracture than the box in actual construction.

5. Conclusions

In this research, a 3D FEM of the tool joint of the directional drill pipe was established to analyze the influence of various loads on the stress distribution. The tension experiment on the tool joint of the directional drill pipe was conducted. The strain method was used to determine the stress distribution on the tool joint of the directional drill pipe. The agreement between the numerical and the experimental data are quite good. Therefore, the following conclusions were obtained:(1)In this study, the stress distribution of the tool joint of the directional drill pipe was obtained for the first time by an experimental method. The FEM established in this paper is consistent with the experimental results, so our research provides a correct FEM, which can guide drill pipe design.(2)Compared with the stress distribution of the tool joint of directional drill pipe subjected to tension, torque, and bending, the stress of the tool joint is the largest in the bending process. The bending process causes the most damage to the tool joint of the directional drill pipe.(3)The maximum stress value of the tool joint of the directional drill pipe occurs at the root between the engaged thread’s third and fourth turns. Therefore, these positions should be strengthened to prevent fractures due to excessive stress.

In summary, the FEM analysis method established in this study is correct and effective. So, we can directly use this study FEM method and experimental data to analyze a similar tool joint of the drill pipe. It should be noted that we have not optimized the drill pipe tool joint, but the research results of this study provide a direction for the subsequent structural optimization.

Data Availability

Data used to support the findings of this study are available from the corresponding authors upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work reported in this study was supported by self-supporting research project of the Chongqing Institute (2017ZDXM11/2022YBXM59), and special project of the Tiandi Science and Technology Innovation and Entrepreneurship Fund (2019-TD-MS018).

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Copyright © 2023 Jiangjun Shu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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