A drill string axial-torsional coupled vibration analysis method and device

Abstract

The present invention proposes a drill string axial-torsional coupled vibration analysis method and device, which relate to the field of drilling engineering. In view of the physical and mechanical properties of the PDC drill bit in crushing rocks, a drill bit-rock interaction model considering friction and cutting is established; considering the multi-degree-of-freedom characteristics of the drill string system and the action of the near-bit power tool, a drill string concentrated parameter dynamic model with the action of the ground and near-bit power tools is established; combined with the drill bit-rock interaction model considering friction and cutting, an axial-torsional coupled vibration model of the drill string considering the action of the near-bit power tool is obtained; and then using actual data, the axial-torsional coupled vibration characteristics of the drill string under different power tool outputs are analyzed. The beneficial effect of the present invention is that the model can effectively characterize the dynamics of the drill string system during drilling, and provides a feasible solution for in-depth understanding of the axial-torsional coupled vibration characteristics of the drill string and conducting research on drill string vibration analysis and suppression during drilling, which is practical and applicable.

Description

Technical Field

[0001] The present invention relates to the field of drilling engineering, and in particular to applications in drill bit-rock interaction modeling, multi-dimensional coupled drill string vibration modeling and analysis, and more particularly to a drill string axial-torsional coupled vibration analysis method and device. Background Art

[0002] Drilling technology plays a key role in exploration operations. The drill string system, the core of drilling technology, typically consists of a drive unit, drill pipe, and drill bit, all connected in a spiral pattern, and can extend for thousands of meters. Polycrystalline Diamond Compact (PDC) drill bits are the most commonly used drill bits. As drilling depth increases, the external forces acting on the drill string become more intense, making various types of drill string vibrations highly likely to occur, reducing drilling efficiency and damaging the wellbore structure.

[0003] Drill string vibration occurs primarily in three forms: lateral, torsional, and axial. During actual drilling, the drill string system is subject to complex external forces, resulting in the interaction of various drill string motion dimensions. These vibrations often occur simultaneously and are coupled to each other. As drilling depth increases, operating parameters and the overall stiffness of the drill string system continuously change, leading to different characteristics of drill string vibration. Lateral and torsional vibrations are the most common, while axial vibration is more pronounced at greater drilling depths or when encountering alternating soft and hard formations. Because the rock reaction forces acting on the drill string are primarily axial and torsional, axial-torsional drill string vibration has attracted considerable attention.

[0004] Conventional rotary drilling techniques suffer from low penetration rates when encountering hard or fractured formations. To address hard formations and reduce resistance during drilling, power tools are often deployed near the drill bit to provide axial or torsional power. In the axial dimension, near-bit tools such as hydraulic vibrators and downhole hammers are commonly deployed near the drill bit. These near-bit tools apply axial weight-on-bit (WOB) to the drill bit, causing it to impact the rock and advance through a rotary percussion process, accelerating rock fragmentation. In the torsional dimension, the most commonly used near-bit power tool is the screw motor. The screw motor is a positive displacement downhole power tool. By installing a screw motor in the drill bit assembly, adjusting the flow and pressure of the drilling fluid delivered by the mud pump further controls the screw motor's torque and speed, achieving dual surface and near-bit power. However, current drill string vibration models lack consideration of downhole power tools, and there is a lack of a multi-dimensional coupled drill string vibration model foundation for downhole power tool validation.

[0005] In summary, the research on the drill string axial-torsional coupled vibration analysis method and device considering the action of near-bit power tools is of great significance for ensuring the safety and efficiency of the drilling process.

[0006] The above content is only used to assist in understanding the technical solution of the present invention and does not constitute an admission that the above content is prior art. Summary of the Invention

[0007] The present invention aims to solve the problem that the existing drill string vibration analysis method lacks consideration of the effect of near-bit power tools, and provides a solution: a drill string axial-torsional coupled vibration analysis method and device are proposed.

[0008] According to a first aspect of the present invention, a drill string axial-torsional coupled vibration analysis method comprises the following steps:

[0009] S1: Establish a drill bit-rock interaction model considering friction and cutting effects;

[0010] S2: Considering the multi-degree-of-freedom characteristics of the drill string system and the effects of near-bit power tools, a lumped parameter dynamic model of the drill string is established with the effects of both the surface and near-bit power tools. Combined with the drill bit-rock interaction model that considers friction and cutting, an axial-torsional coupled vibration model of the drill string is obtained that also considers the effects of near-bit power tools.

[0011] S3: Based on the established drill string axial-torsional coupled vibration model, actual data is used to consider the effects of near-bit power tools in the axial and torsional dimensions. The influence of near-bit power tool outputs in different dimensions on the drill string axial-torsional coupled vibration is analyzed through numerical simulation.

[0012] According to a second aspect of the present invention, a drill string axial-torsional coupled vibration analysis device includes the following units:

[0013] The first modeling unit is used to establish a drill bit-rock interaction model considering friction and cutting effects;

[0014] The second modeling unit is used to consider the multi-degree-of-freedom characteristics of the drill string system and the effects of the near-bit power tool, and establish a concentrated parameter dynamic model of the drill string with the effects of the ground and near-bit power tools. Combined with the drill bit-rock interaction model that considers friction and cutting effects, an axial-torsional coupled vibration model of the drill string is established that considers the effects of the near-bit power tool.

[0015] The vibration analysis unit is used to analyze the impact of the output power of near-bit power tools in different dimensions on the multi-dimensional vibration of the drill string system based on the established axial-torsional coupled vibration model of the drill string, using actual data and considering the effects of near-bit power tools in the axial and torsional dimensions.

[0016] According to a third aspect of the present invention, an electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the steps of the drill string axial-torsional coupled vibration analysis method are described.

[0017] According to a fourth aspect of the present invention, a storage medium stores a computer program thereon, which, when executed by a processor, implements the steps of the drill string axial-torsional coupled vibration analysis method.

[0018] The technical solution provided by the present invention has the following beneficial effects:

[0019] The present invention provides a drill string axial-torsional coupled vibration analysis method and device. First, based on the physical and mechanical properties of the PDC drill bit in crushing rocks, a drill bit-rock interaction model that takes into account friction and cutting is established; considering the multi-degree-of-freedom characteristics of the drill string system and the action of the near-bit power tool, a drill string concentrated parameter dynamic model with the action of the ground and near-bit power tools is established; combined with the drill bit-rock interaction model that takes into account friction and cutting, an axial-torsional coupled vibration model of the drill string that takes into account the action of the near-bit power tool is obtained; on this basis, actual data is used to analyze the axial-torsional coupled vibration characteristics of the drill string under different power tool outputs. The beneficial effects of the present invention are: an axial-torsional coupled vibration model of the drill string that takes into account the action of the near-bit power tool is established, and the influence of different power tool outputs on the axial-torsional coupled vibration of the drill string is analyzed. The model can effectively characterize the dynamics of the drill string system during drilling, and provides a feasible solution for in-depth understanding of the axial-torsional coupled vibration characteristics of the drill string and conducting research on drill string vibration analysis and suppression during drilling. It is practical and applicable. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments, in which:

[0021] Figure 1 This is a flow chart of a drill string axial-torsional coupled vibration analysis method according to an embodiment of the present invention;

[0022] Figure 2 This is a simplified schematic diagram of the axial-torsional coupled dynamic model of the drill string in an embodiment of the present invention;

[0023] Figure 3 It is the drill bit speed when the axial and torsional outputs of the near-bit power tool are both 0;

[0024] Figure 4 It is the drill bit speed when the axial dimension output of the near-bit power tool is 20 kN;

[0025] Figure 5 It is the drill bit speed when the axial dimension output of the near-bit power tool is 40 kN;

[0026] Figure 6 is the drill bit speed when the near-bit power tool torsional dimension output is 3000 N·m;

[0027] Figure 7 is the drill bit speed when the near-bit power tool torsional dimension output is 5000 N·m;

[0028] Figure 8 1 is a structural diagram of a drill string axial-torsional coupled vibration analysis device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, specific embodiments of the present invention are now described in detail with reference to the accompanying drawings.

[0030] Example 1:

[0031] Figure 1 This is a flow chart of a drill string axial-torsional coupled vibration analysis method according to an embodiment of the present invention, which specifically includes the following steps:

[0032] S1: Establish a drill bit-rock interaction model considering friction and cutting effects.

[0033] Depending on the drilling purpose, different drill bits will be selected during the drilling process, and PDC drill bits are the most commonly used drill bits in drilling. Based on the physical and mechanical properties of PDC drill bits in crushing rocks, a drill bit-rock interaction model considering friction and cutting effects is established.

[0034] The rock breaking process of a PDC drill bit mainly includes two processes: friction and cutting. The drill bit-rock interaction force and torque are the superposition of the friction component and the cutting component. Under normal circumstances, the calculation formula of the friction component and the cutting component is as follows:

[0035]

[0036] Where W bf and T bf are the force and torque of the friction process respectively; W bc and T bc are the force and torque of the cutting process respectively; ε is the inherent specific energy of the rock, which is related to the hardness of the rock; R b is the drill bit radius, λ is a constant that characterizes the blade inclination, σ is the rock contact strength, l is the length of the drill bit wear surface, μ is the contact friction coefficient between the drill bit and the rock, γ is a parameter that describes the direction and spatial distribution of the drill bit blade friction contact surface, and d(t) is the sum of the cutting depth of each blade during one rotation of the drill bit.

[0037] Since each blade of the drill bit is basically the same, the instantaneous cutting depth d of each blade is n Basically the same, the axial position z of the blade at the current moment n (t) minus a time period τ n Previous axial position z n (tt τ ) can get the instantaneous cutting depth d n and the total cutting depth d(t), the formula is as follows:

[0038] d(t)=n b d n , d n =z n (t)-z n (t-τ n ) (2)

[0039] Where t is the current time, n b is the number of blades of the drill bit, τ n is a rotation of 2π / n b Time required, 2π / n b is the angular distance between two adjacent blades, which can be numerically solved according to the following implicit equation:

[0040]

[0041] Where Φ n (t) represents the torsional position of the drill bit at the current moment, Φ n (t-τ n ) represents a time period τ n Previous twist position of the drill bit.

[0042] According to the calculation formula of friction component and cutting component in normal drilling mode in formula (1), the drill bit-rock interaction model considering the combined effect of friction and cutting can be expressed as follows:

[0043]

[0044] In the formula and sgn(·) are the Heaviside function and sign function, respectively, which are used to judge different operating modes of the drill bit-rock interaction.

[0045] S2: Establish an axial-torsional coupled vibration model of the drill string considering the effects of near-bit power tools. Considering the multi-degree-of-freedom characteristics of the drill string system and the effects of near-bit power tools, a lumped parameter dynamic model of the drill string is established, which incorporates the effects of both the surface and near-bit power tools. Combined with the drill bit-rock interaction model that considers friction and cutting, a coupled axial-torsional vibration model of the drill string is obtained, also considering the effects of near-bit power tools.

[0046] refer to Figure 3 This is a simplified schematic diagram of the drill string axial-torsional coupled dynamic model, treating the system as a mass-spring-damper system consisting of n units. In this system, each concentrated mass unit has axial and torsional motion, and the lateral motion of the concentrated mass unit is ignored. The force conditions of each concentrated mass unit are considered segment by segment. The axial bit weight W0 and torsional torque T0 of the drill string system are applied to the well drive unit. The axial reaction force W caused by the drill bit-rock interaction is considered in the near-bit drill bit assembly. b and reaction torque T b .

[0047] The established drill string axial-torsional coupled dynamic model considering the action of the near-bit power tool is as follows:

[0048]

[0049] Where J = diag{J1, J2, L, J n} and M=diag{M1,M2,L,M n} are the n-row and n-column diagonal real moment of inertia matrix and mass matrix respectively; is the displacement state vector in the axial dimension, Φ(t)=col{Φ1(t),Φ2(t),L,Φ n (t)} represents the displacement state vector in the torsional dimension; C α and K α are the damping coefficient matrix and stiffness coefficient matrix of each dimension, respectively. The subscript α∈{a,t} represents the axial dimension and the torsional dimension, respectively. The stiffness coefficient matrix and damping coefficient matrix of the axial dimension and the torsional dimension have the same form. The specific forms of the stiffness coefficient matrix and damping coefficient matrix of each dimension are as follows:

[0050]

[0051] The right side of formula (6) is the external force acting on each unit, which can be written in vector form as follows:

[0052]

[0053] According to the structural parameters of the drill string system, the moment of inertia J of the above units is i 、Quality M i , axial damping coefficient c ai and the torsional damping coefficient c ti The calculation formula is as follows:

[0054]

[0055] Where L i is the length of each unit, Roi and R ni are the outer and inner diameters of each unit, ρ i is the density of each element, η and ξ are the damping coefficients in the axial and torsional dimensions, respectively;

[0056] Let the state vector be According to equations (6) and (7), we can obtain the following state space equation:

[0057]

[0058] Where F(t) is the external force vector, u(t) is the input vector of the wellbore, and U T (t) is the downhole power input vector provided by the power tool in the near-bit drill tool assembly.

[0059] For ease of analysis, the power input vector of the drill string system is divided into the ground power tool input vector and the near-bit power tool input vector. The axial weight on bit and torsional torque provided by the near-bit power tool only act on the near-bit drill tool assembly unit, and its form is as follows:

[0060]

[0061] Where W0 and T0 are the axial weight on bit and torsional torque provided by the uphole part respectively; W TOOL and T TOOL are the axial weight on bit and torsional torque provided by the near-bit power tool. The external force vector F(t) is in the form of

[0062]

[0063] In the formula and are the axial and torsional force vectors of the drill string system, J n 、M n The reciprocal of .

[0064] A is the system matrix, which is in the following form:

[0065]

[0066] In the formula is a matrix consisting of the inverse of the moment of inertia, is a matrix consisting of the inverse of the mass

[0067]

[0068] At this point, the drill string vibration model can be established according to different drill string system structures and transformed into the state space equation shown in formula (9) for subsequent numerical simulation analysis.

[0069] S3: Analyze drill string vibration under different near-bit power tool outputs. Based on the established drill string axial-torsional coupled vibration model, using actual data and considering the effects of the near-bit power tool in both axial and torsional dimensions, numerical simulations were performed to analyze the impact of different near-bit power tool output dimensions on the drill string axial-torsional coupled vibration.

[0070] For a drill string system equipped with near-bit power tools, we deployed near-bit power tools in both the axial and torsional dimensions. We used numerical simulation to analyze the impact of the near-bit power tool outputs in different dimensions on the multidimensional vibration of the drill string system. The simulation parameters are listed in Table 1.

[0071] Table 1 Simulation parameters

[0072]

[0073] According to the structure of the drill string system, the drill string system is divided into two concentrated mass units. According to formula (9), let the state vector The matrix forms of the state space equations of the axial-torsional coupled vibration model of the drill string system are as follows

[0074]

[0075] First, the influence of different outputs of the axial near-bit power tool on the vibration characteristics is analyzed. Different near-bit axial forces are applied to the drill string system to analyze the influence of the near-bit power tool on the axial-torsional coupled vibration of the drill string. The axial near-bit power tool is installed on the drill string system, and axial drilling pressures of 0KN, 20KN, and 40KN are applied respectively to observe its influence on the axial and torsional vibration of the drill string system. The experimental results are as follows. Figures 3 to 5 shown.

[0076] Depend on Figures 3 to 5 It can be seen that when the axial weight on bit output by the near-bit power tool is 0, the drill string system experiences periodic synchronous sticking in both the axial and torsional dimensions. However, when the near-bit power tool outputs axial weight on bit to the drill bit, the sticking phenomenon in both the axial and torsional dimensions gradually weakens and disappears, and the greater the output power, the faster the sticking phenomenon weakens.

[0077] Secondly, the influence of different outputs of the torsional near-bit power tool on the vibration characteristics is analyzed. Different near-bit torsional forces are applied to the drill string system to analyze the influence of the near-bit power tool on the axial-torsional coupled vibration of the drill string. The torsional near-bit power tool is installed on the drill string system, and torsional torques of 0 N·m, 3000 N·m, and 5000 N·m are applied respectively to observe its influence on the torsional and axial vibration of the drill string system. Figure 3 、 Figure 6 and Figure 7 shown.

[0078] Figure 3 This is the drill bit speed when the torsional dimension output of the near-bit power tool is 0. At this time, the drill string system experiences periodic torsional-axial coupled vibration. When the output torque of the near-bit power tool is increased to 3000N·m and 5000N·m, the axial and torsional vibration of the drill string system are as follows: Figure 6 and Figure 7 By comparison, it was found that when the near-bit power tool began to continuously output constant torsional power, the duration of the drill bit's axial viscosity gradually decreased, and the greater the output power, the faster the viscosity phenomenon weakened. This is consistent with the results shown by the near-bit power tool in the axial dimension.

[0079] In summary, deploying a near-bit power tool that can output axial weight-on-bit and torsional torque on the drill string system and controlling the output of the near-bit power tool can effectively reduce the severity of the drill string axial-torsional coupled vibration. The greater the output of the near-bit power tool, the weaker the axial-torsional coupled vibration of the drill string.

[0080] Example 2:

[0081] refer to Figure 8 This embodiment provides a drill string axial-torsional coupled vibration analysis device, comprising the following units:

[0082] The first modeling unit 1 is used to establish a drill bit-rock interaction model considering friction and cutting effects;

[0083] The second modeling unit 2 is used to combine the drill bit-rock interaction model considering friction and cutting effects, establish the drill string axial-torsional coupled vibration model considering the action of the near-bit power tool, and convert it into a state space equation form;

[0084] The vibration analysis unit 3 is used to analyze the impact of the near-bit power tool output in different dimensions on the multi-dimensional vibration of the drill string system.

[0085] Example 3:

[0086] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer program is characterized in that when the processor executes the program, the steps of the drill string axial-torsional coupled vibration analysis method described in Example 1 are implemented. The effects achieved are the same as those of Example 1 and are not further described herein.

[0087] Example 4:

[0088] This embodiment provides a storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the drill string axial-torsional coupled vibration analysis method are implemented. The effects achieved are the same as those of the first embodiment and are not described again here.

[0089] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or system comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or system. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or system comprising the element.

[0090] The serial numbers of the embodiments of the present invention are for descriptive purposes only and do not represent superiority or inferiority of the embodiments. In a unit claim that lists several means, several of these means may be embodied by the same item of hardware. The use of the terms first, second, and third, etc., does not denote any order and should be construed as identifiers.

[0091] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A drill string axial-torsional coupled vibration analysis method, characterized in that The following steps are involved: S1: Establish a drill bit-rock interaction model considering friction and cutting effects; S2: Considering the multi-degree-of-freedom characteristics of the drill string system and the effects of near-bit power tools, a lumped parameter dynamic model of the drill string is established with the effects of both the surface and near-bit power tools. Combined with the drill bit-rock interaction model that considers friction and cutting, an axial-torsional coupled vibration model of the drill string is obtained that also considers the effects of near-bit power tools. The process of establishing the drill string axial-torsional coupled vibration model includes: The drill string system is considered as a mass-spring-damper system with n degrees of freedom, and the dynamic equations in axial and torsional dimensions are established; Consider the axial and torsional motions of each concentrated mass unit, and ignore the lateral motion of the concentrated mass unit; The power input vector of the drill string system is divided into the surface power tool input vector and the near-bit power tool input vector. The effect of the near-bit power tool on the drill string system in the lateral dimension when in operation is ignored. The axial weight on bit and torsional torque provided by the near-bit power tool are considered to act only on the near-bit drill tool assembly unit. Establish a concentrated parameter dynamic model of the drill string with the effects of surface and near-bit power tools; The drill bit-rock interaction model considering friction and cutting is used to describe the coupling relationship between the axial and torsional motions of the drill string. The axial-torsional coupled vibration model of the drill string considering the action of the near-bit power tool is obtained. S3: Based on the established drill string axial-torsional coupled vibration model, actual data is used to consider the effects of near-bit power tools in the axial and torsional dimensions. The influence of near-bit power tool outputs in different dimensions on the drill string axial-torsional coupled vibration is analyzed through numerical simulation.

2. The drill string axial-torsional coupled vibration analysis method according to claim 1, wherein in step S1: In step S1, based on the physical and mechanical properties of the PDC drill bit in crushing rocks, a drill bit-rock interaction model is established that takes into account friction and cutting effects; Where W b and T b are the reaction force and reaction torque caused by the interaction between drill bit and rock; W bc and T bc are the force and torque during the cutting process respectively; W bf and T bf are the force and torque of the friction process respectively; d(t) is the sum of the cutting depth of each blade during one rotation of the drill bit; represents the first derivative of the torsional position of the drill bit at the current moment; Represents the first derivative of the axial position of the blade at the current moment; and sgn(·) are the Heaviside function and the sign function, respectively, which are used to judge the different operation modes of the drill bit-rock interaction; x represents d(t), one of the.

3. The drill string axial-torsional coupled vibration analysis method according to claim 2, characterized in that: In step S2, the formula of the drill string axial-torsional coupled vibration model is: Where, J=diag{J1,J2,…,J n } and M=diag{M1,M2,…,M n } are respectively the diagonal real moment of inertia matrix and mass matrix with n rows and n columns; Z(t)=col{Z1(t),Z2(t),…,Z n (t)} is the displacement state vector in the axial dimension, is the first derivative of the displacement state vector in the axial dimension, is the second derivative of the displacement state vector in the axial dimension; Φ(t)=col{Φ1(t),Φ2(t),…,Φ n (t)} represents the displacement state vector in the torsional dimension, The first derivative of the displacement state vector representing the torsional dimension, The second derivative of the displacement state vector representing the torsional dimension; C α and K α are the damping coefficient matrix and stiffness coefficient matrix of each dimension, respectively. The subscript α∈{a,t} represents the axial dimension and torsional dimension, respectively. W(t) and T(t) are the vector forms of the external forces in the axial and torsional dimensions, respectively.

4. A drill string axial-torsional coupled vibration analysis device, characterized in that: The following units are included: The first modeling unit is used to establish a drill bit-rock interaction model considering friction and cutting effects; The second modeling unit is used to combine the drill bit-rock interaction model considering friction and cutting effects to establish the drill string axial-torsional coupled vibration model considering the action of the near-bit power tool; In the second modeling unit, the process of establishing the drill string axial-torsional coupled vibration model includes: The drill string system is considered as a mass-spring-damper system with n degrees of freedom, and the dynamic equations in axial and torsional dimensions are established; Consider the axial and torsional motions of each concentrated mass unit, and ignore the lateral motion of the concentrated mass unit; The power input vector of the drill string system is divided into the surface power tool input vector and the near-bit power tool input vector. The effect of the near-bit power tool on the drill string system in the lateral dimension when in operation is ignored. The axial weight on bit and torsional torque provided by the near-bit power tool are considered to act only on the near-bit drill tool assembly unit. Establish a concentrated parameter dynamic model of the drill string with the effects of surface and near-bit power tools; The drill bit-rock interaction model considering friction and cutting is used to describe the coupling relationship between the axial and torsional motions of the drill string. The axial-torsional coupled vibration model of the drill string considering the action of the near-bit power tool is obtained. The vibration analysis unit is used to analyze the impact of near-bit power tool output in different dimensions on the axial-torsional coupled vibration of the drill string.

5. The drill string axial-torsional coupled vibration analysis device according to claim 4, wherein in step S1: In the first modeling unit, based on the physical and mechanical properties of PDC drill bits in crushing rocks, a drill bit-rock interaction model considering friction and cutting was established. The formula is as follows: Where W b and T b are the reaction force and reaction torque caused by the interaction between drill bit and rock; W bc and T bc are the force and torque during the cutting process respectively; W bf and T bf are the force and torque of the friction process respectively; d(t) is the sum of the cutting depth of each blade during one rotation of the drill bit; represents the first derivative of the torsional position of the drill bit at the current moment; Represents the first derivative of the axial position of the blade at the current moment; and sgn(·) are the Heaviside function and the sign function, respectively, which are used to judge the different operation modes of the drill bit-rock interaction; x represents d(t), one of the.

6. The drill string axial-torsional coupled vibration analysis device according to claim 5, wherein in step S1: The formula of the drill string axial-torsional coupled vibration model is: Where, J=diag{J1,J2,…,J n } and M=diag{M1,M2,…,M n } are respectively the diagonal real moment of inertia matrix and mass matrix with n rows and n columns; Z(t)=col{Z1(t),Z2(t),…,Z n (t)} is the displacement state vector in the axial dimension, is the first derivative of the displacement state vector in the axial dimension, is the second derivative of the displacement state vector in the axial dimension; Φ(t)=col{Φ1(t),Φ2(t),…,Φ n (t)} represents the displacement state vector in the torsional dimension, The first derivative of the displacement state vector representing the torsional dimension, The second derivative of the displacement state vector representing the torsional dimension; C α and K α are the damping coefficient matrix and stiffness coefficient matrix of each dimension, respectively. The subscript α∈{a,t} represents the axial dimension and torsional dimension, respectively. W(t) and T(t) are the vector forms of the external forces in the axial and torsional dimensions, respectively.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the drill string axial-torsional coupled vibration analysis method according to any one of claims 1 to 3 are implemented.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the drill string axial-torsional coupled vibration analysis method according to any one of claims 1 to 3 are implemented.

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