Modeling method and effectiveness verification method of special thread joint considering roughness

Abstract

This invention discloses a modeling method for special threaded joints that considers roughness. It employs WM fractal functions to describe the contour of the rough surface of the special threaded joint, imports the contour coordinate data of the fractal curves into ANSYS finite element analysis software, and constructs a three-dimensional solid model of the special threaded joint containing the rough fractal contour. This invention also discloses a method for verifying the effectiveness of the above three-dimensional model. Using ANSYS finite element analysis software, material and interface properties are defined, the three-dimensional model is meshed and refined, assembly properties are defined, loads and constraints are applied according to boundary conditions, and structural nonlinear static analysis is performed to obtain equivalent stress contour maps and contact pressure curves of the special threaded joint, thereby verifying the model's effectiveness. The modeling method using fractal functions to characterize the rough surface of special threaded joints not only possesses determinism and uniqueness but also accurately describes the morphology of the rough surface, providing an effective and accurate method for refined solid modeling of special threaded joints.

Description

Technical Field

[0001] This invention belongs to the field of mechanics, specifically relating to a modeling method for special threaded joints that takes roughness into account, and also relating to a method for verifying the effectiveness of special threaded joints that take roughness into account. Background Technology

[0002] In high-temperature, high-pressure gas wells, special threaded joints are used to connect the downhole casing and tubing strings, forming a channel for fluid transport from the bottom of the well to the wellhead. With advancements in oil and gas exploration technology and the continuous development of ultra-high-production, ultra-high-temperature, ultra-high-pressure, and ultra-corrosive oil and gas wells, the downhole operating conditions for special threaded joints are becoming increasingly harsh. Under complex loads, the special threaded joints at the casing and tubing string connection points are prone to sealing or connection failure, compromising well integrity and potentially leading to safety accidents. Unlike traditional API (American Petroleum Institute) joints that rely on threaded sealing, special threaded joints have an independent sealing structure, achieving sealing through an interference fit of the sealing surface.

[0003] In reality, no metal processing technique can achieve a perfectly smooth sealing surface; all always possess a certain degree of roughness. Existing methods for modeling the rough surfaces of special threaded joints primarily focus on statistical methods. These methods treat the height distribution at various points on the rough surface as a random process, using a distribution function and autocorrelation function to determine the surface profile. Statistical models rely heavily on the statistical parameters of the rough surface, which are influenced by the resolution of the measuring instrument and the sampling length, thus failing to accurately reflect all the characteristics of the rough surface. Therefore, constructing a solid model of a special threaded joint that considers roughness is crucial for accurately analyzing the stress and contact pressure distribution on the sealing surface and evaluating its sealing performance. Summary of the Invention

[0004] To address the issue that statistical parameters of rough surfaces cannot accurately reflect all the characteristics of rough surfaces, the purpose of this invention is to provide a special threaded joint modeling method that takes roughness into account.

[0005] Another objective of this invention is to provide a method for verifying the effectiveness of special threaded joints that takes into account roughness.

[0006] The technical solution adopted in this invention is a special threaded joint modeling method considering roughness, which includes the following steps: Step 1: Construct the WM fractal function using the fractal dimension of the fractal surface and the characteristic coefficients of the special threaded joint as parameters. The characteristic coefficients include fractal roughness, surface profile spectral density related parameters, and frequency exponent. Step 2: Draw the fractal contour curve of the rough surface of the special threaded joint according to the WM fractal function, and export it as a script; Step 3: Use finite element analysis software to construct the geometric model of the special threaded joint. Import the script into the software to construct a solid three-dimensional model of the special threaded joint containing a rough fractal profile.

[0007] The invention is further characterized by: The WM fractal function in step 1 is specifically given by equation (1). (1).

[0008] In step 2, the fractal contour curve of the rough surface of the special threaded joint is plotted in MATLAB, and the contour coordinate data of the fractal curve is exported as a script.

[0009] Step 3 specifically involves: Using the finite element analysis software ANSYS and its parametric design language, a parametric geometric model of the special threaded joint was built from the bottom up. The script was then imported into ANSYS, and spline curves were used to fit the coordinates. Fractal curves from the script were introduced from the sealing surface of the geometric model to simulate the rough surface, thus establishing a solid three-dimensional model of the special threaded joint containing a rough fractal profile.

[0010] Another technical solution of the present invention is a method for validating the effectiveness of special threaded joints considering roughness. This method verifies the effectiveness of the solid 3D model established by the aforementioned method for modeling special threaded joints considering roughness, specifically including the following steps: Step 1: Define the assembly, material properties, and interface properties of the 3D solid model of the special threaded joint with a rough fractal profile, and then mesh and refine it. Step 2: Apply load and displacement constraints according to the assembly boundary conditions, perform nonlinear static analysis on the boundary of the three-dimensional model, obtain equivalent stress cloud diagram and contact pressure distribution curve, and verify the effectiveness of the model.

[0011] Another feature of the technical solution of the present invention is that: Step 1 specifically involves: defining the contact between the special threaded joint coupling and the tubing body, establishing four contact pairs: the torque shoulder surface, the conical sealing surface, the threaded bearing surface, and the guide surface, and setting the interference fit of the contact pairs; setting the material properties as follows: elastic modulus of 2.06×10⁵ MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, tensile strength of 862 MPa, and selecting the bilinear elastoplastic strengthening model; setting the mesh size of the tubing body to 0.5; refining the mesh size of the torque shoulder and tubing end sealing surface to 0.1; and refining the mesh size of the rough micro-protrusions on the coupling end sealing surface to 0.001.

[0012] The Coulomb friction model was chosen to simulate the friction between the main sealing surface of the special threaded joint and the contact surface of the thread teeth of the oil pipe body.

[0013] Using the Newton-Raphson principle, nonlinear static analysis was performed on four contact pairs to obtain equivalent stress contour plots and contact pressure distribution curves for the four contact pairs of the special threaded joint. The effectiveness of the model was verified based on the equivalent stress and contact pressure of the four contact pairs.

[0014] Compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention proposes a fractal theory-based microscopic morphology model for rough surfaces of special threaded joints, based on the self-similarity and scale-independent characteristics of such surfaces. Fractal theory, with its self-similarity, continuity, scale independence, and non-integer dimensions, can objectively describe the structure of rough surfaces of special threaded joints. First, the WM fractal function is used to characterize the microscopic rough surface profile of the sealing surface of the special threaded joint. Then, the coordinate parameters of the rough surface profile are extracted to construct a finite element solid model of the special threaded joint containing its rough surface features, enabling accurate analysis of the stress and contact pressure, and other mechanical properties, of the special threaded joint.

[0015] 2. This invention uses the WM fractal function, which has more explicit parameter meaning, to describe the contour of the rough surface of a special threaded joint. This not only accurately describes the morphology of the rough surface, but also ensures that the morphology is deterministic and unique. This invention provides an effective and accurate method for refined solid modeling of special threaded joints. Attached Figure Description

[0016] Figure 1(a) shows the fractal dimension of Embodiment 3 of the present invention. D A three-dimensional fractal model of a rough surface at a value of 2.1; Figure 1(b) shows the fractal dimension of Embodiment 4 of the present invention. D A three-dimensional fractal model of a rough surface at a value of 2.3; Figure 1(c) shows the fractal dimension of Embodiment 5 of the present invention. D A three-dimensional fractal model of a rough surface at a value of 2.5; Figure 1(d) shows the fractal dimension of Embodiment 6 of the present invention. D A three-dimensional fractal model of a rough surface at a value of 2.7; Figure 2 This is the assembly geometric model of the special threaded joint in Embodiment 3 of the present invention; Figure 3(a) shows the finite element mesh generation model of the special threaded joint considering roughness in Embodiment 3 of the present invention; Figure 3(b) is a partial enlarged view of the contact surface in Figure 3(a); Figure 3(c) is a magnified view of the fractal surface after mesh refinement in Figure 3(b); Figure 4 This is a diagram showing the boundary conditions and loading of the special threaded joint of the present invention; Figure 5(a) is the Mises stress nephogram of the optimal make-up torque when Ra = 0.4 μm in Embodiment 3 of the present invention; Figure 5(b) is the Mises stress nephogram of the optimal make-up torque when Ra = 0.8 μm in Embodiment 4 of the present invention; Figure 5(c) is the Mises stress nephogram of the optimal make-up torque when Ra = 1.2 μm in Embodiment 5 of the present invention; Figure 5(d) is the Mises stress nephogram of the optimal make-up torque when Ra = 1.6 μm in Embodiment 6 of the present invention; Figure 6 is the contact pressure curve graph of the optimal make-up torque for Embodiments 3-6 of the present invention; Figure 7(a) is the contact pressure distribution curve graph along the sealing surface when Ra = 0.4 μm in Embodiment 3 of the present invention; Figure 7(b) is the contact pressure distribution curve graph along the sealing surface when Ra = 0.8 μm in Embodiment 4 of the present invention; Figure 7(c) is the contact pressure distribution curve graph along the sealing surface when Ra = 1.2 μm in Embodiment 5 of the present invention; Figure 7(d) is the contact pressure distribution curve graph along the sealing surface when Ra = 1.6 μm in Embodiment 6 of the present invention; Detailed implementation manners The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0017] Embodiment 1 A modeling method for a special thread joint considering roughness specifically includes the following steps: Step 1. Use the characteristic coefficient of the special thread joint as a parameter and consider the fractal dimension to construct a Weierstrass-Mandelbro (WM) fractal function as shown in Equation (1), (1) In the formula: z ( x , y ) is the height of the rough surface profile; L is the sampling length; G is called the amplitude coefficient or fractal roughness; D is the fractal dimension of the fractal surface, 2 < D < 3 for the three-dimensional fractal function, and 1 < D < 2 for the two-dimensional fractal function; r ( r > 1) is the surface profile spectral density correlation parameter; M is the overlapping number of surface wrinkles; m For scale parameters; n The frequency index is 0 for the lowest frequency and 0 for the highest frequency. ; L s This is the cutoff length; θ m,n The phase is random, and its value ranges from [0, 2π]. Step 2: Based on equation (1), plot the fractal profile curve of the rough surface of the special threaded joint in MATLAB. When plotting, avoid... x =0, a MATLAB script to create a curve; Step 3: Use ANSYS finite element analysis software to construct the geometric model of the special threaded joint. Import the script into the finite element analysis software to establish a solid three-dimensional model of the special threaded joint containing a rough fractal profile. The validity of the above-mentioned 3D solid model of a special threaded joint with a rough fractal profile is verified by the following steps: Step 1: Define the assembly, material, and interface properties of the 3D solid model of the special threaded joint with a rough fractal profile, and assign values ​​to the interface properties. Then, perform mesh generation and refinement on the 3D solid model of the special threaded joint with a rough fractal profile. Step 2: Apply load and displacement constraints according to the boundary conditions, perform nonlinear static analysis on the boundary of the three-dimensional model, obtain equivalent stress cloud diagram and contact pressure distribution curve, and verify the effectiveness of the model.

[0018] Example 2 A special threaded joint modeling method considering roughness includes the following steps: Step 1. Use the characteristic coefficients of special threaded joints as parameters. The characteristic coefficients include fractal roughness, surface profile spectral density related parameters and frequency index, and consider the fractal dimension to construct the Weierstrass-Mandelbro (WM) fractal function, as shown in Equation (1).

[0019] Step 2: Based on equation (1), plot the fractal profile curve of the rough surface of the special threaded joint in MATLAB. When plotting, avoid... x =0, a MATLAB script to create a curve; Step 3: Using the finite element analysis software ANSYS and its APDL parametric design language, a parametric geometric model of the special threaded joint is established from the bottom up. The script is then imported into ANSYS, and spline curves are used to fit the coordinates. Fractal curves from the script are introduced from the sealing surface of the geometric model to simulate the rough surface, thus establishing a solid three-dimensional model of the special threaded joint containing a rough fractal profile.

[0020] The validity of the above-mentioned 3D solid model of a special threaded joint with a rough fractal profile is verified by the following steps: Step 1: Define the contact between the special threaded joint coupling and the tubing body, establishing four contact pairs: the torque shoulder surface, the conical sealing surface, the threaded bearing surface, and the guide surface. Set the interference fit for each contact pair. Set the material properties as follows: elastic modulus of 2.06 × 10⁵ MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, and tensile strength of 862 MPa. Select the bilinear elastoplastic strengthening model. Set the tubing body mesh size to 0.5. Refine the mesh size of the torque shoulder and tubing end sealing surface to 0.1. Refine the mesh size of the rough micro-protrusions on the coupling end sealing surface to 0.001. Select the Coulomb friction model to simulate the friction between the main sealing surface of the special threaded joint and the surface of the threaded contact point of the tubing body.

[0021] Step 2: Apply load and displacement constraints according to the assembly boundary conditions, and perform nonlinear static analysis on the four contact pairs using the Newton-Raphson principle to obtain the equivalent stress cloud diagram and contact pressure distribution curve of the four contact pairs of the special threaded joint. Verify the effectiveness of the model based on the equivalent stress and contact pressure of the four contact pairs.

[0022] Example 3 Based on fractal theory, the WM fractal function is derived from fractal parameters. D , G , r , n Therefore, the WM fractal function method of equation (1) is adopted to simulate the contour curve of the rough sealing surface of the special threaded joint, wherein the parameters of the WM fractal function are as follows: G =1*10 -13 ; M =10; r =1.5; L =1*10 -19 ; L s =5*10 -9 fractal dimension D =2.1; at the same time, avoid x =0 point, take n =10~70, xThe value is taken in the range [0.6, 0.7]. The fractal curve is plotted using MATLAB software, and Figure 1(a) shows the three-dimensional fractal model of the curve.

[0023] Using the finite element analysis software ANSYS and its APDL parametric design language, a bottom-up parametric geometric model of the special threaded joint was established. First, the coordinates of key points in the model were determined based on the dimensional parameters of the special threaded joint. Lines were generated from these key points, and surfaces were created from these lines. Then, by using loop commands and adjusting the corresponding pitch, the contour model of the special threaded joint was established. Similarly, by using loop commands and controlling the corresponding pitch, the contour model of the coupling was established. The key coordinate points of the sealing surface and torque shoulder were determined by combining the Get and Do loop commands, and then the sealing surface and torque shoulder structures were established using these key coordinate points. For example... Figure 2 As shown, the special threaded connector has the following specifications: Φ88.9mm×6.45mm, P110 steel, 4.234mm pitch, 1 / 2 taper of sealing surface, 1 / 16 taper of thread, -10° shoulder angle, 10° guide surface angle, and -3° bearing surface angle.

[0024] The contour coordinate data of the fractal curve with a roughness Ra=0.4μm plotted in MATLAB software was used to create a script. This script was then imported into ANSYS, and spline curves were used to fit the coordinates. A fractal curve with a length of 0.6mm was introduced from the sealing surface to simulate the rough surface, establishing a solid 3D model of a special threaded joint containing a rough fractal contour. A model with large deformation and large strain analysis capabilities was selected, and the elastic modulus of the material was defined as 2.06x10⁻⁶. 5 MPa, Poisson's ratio is 0.3, yield strength is 758 MPa, tensile strength is 862 MPa, and a bilinear elastoplastic strengthening model is selected. The solid 3D model of the special threaded joint with rough fractal contour is meshed, and the mesh of key parts is refined. The mesh size of the tubing body is set to 0.5, as shown in Figure 3(a); the mesh size of the torque shoulder and the sealing surface of the tubing end is refined to 0.1, as shown in Figure 3(b); the mesh size of the rough micro-protrusions on the sealing surface of the coupling end is refined to 0.001, as shown in Figure 3(c).

[0025] ANSYS finite element software was used to simulate the connection between the internal thread of the coupling and the external thread of the pipe body through surface-to-surface contact analysis. Specifically, the contact between the special threaded joint coupling and the pipe body was defined, establishing four contact pairs: a torque shoulder surface, a tapered sealing surface, a thread bearing surface, and a guide surface. The contact stiffness of each pair was set to 1.0, and the interference fit of the contact pairs was also set. The Coulomb friction model was selected to simulate the friction between the main sealing surface of the special threaded joint and the surface at the contact point of the thread teeth. Loads and constraints were added to the above finite element model, such as... Figure 4As shown, an axial concentrated load (displacement load x) is applied to the cross-section at the distal end of the pipe, while a radial uniformly distributed load is applied to the inner walls of the pipe and the coupling. Structural nonlinear static analysis is performed on the four contact pairs to obtain equivalent stress contour maps and contact pressure distribution curves for the special threaded joint, thus verifying the effectiveness of the model.

[0026] Considering that stress concentration and plastic deformation may occur at local locations of the joint, large deformation is selected in the ANSYS solution settings. At the same time, the number of load steps and iterations are increased to improve the convergence of the nonlinear analysis.

[0027] The Newton-Raphson method is used to calculate the residuals. The residuals are expressed by equation (2): (2) In the formula: R (u) For residuals; P These are the observed values; I These are predicted values.

[0028] Nonlinear analysis of equation (2), R (u) ≠0, therefore a displacement correction value needs to be found. c u , so that: (3) Taylor expansion of equation (3) is shown in equation (4): (4) Ignoring higher-order terms, let's denote... R right u The partial derivative is - K tangent Then the above equation can be transformed into equation (5): (5) At this point, the residual is transformed into a computable quantity. First, the residual is... P Divide into several incremental steps, with the load of each incremental step being Δ. P The equilibrium solution of the previous increment step is P 0 load U 0, the objective equilibrium solution for this incremental step is P 0+△ P = P Displacement solution under load U 1. Based on U 0, residual updated to: (6) In the formula: c 1 represents the displacement correction value; K 0 represents tangential stiffness; I 0 represents internal force.

[0029] The average force at all nodes within this incremental step is calculated as shown in equation (7): (7) The default convergence tolerance is 0.005 times the average force. If... (8) This satisfies the equilibrium condition. Generally, further verification of the displacement equilibrium condition is also required. (9) If either the force equilibrium condition or the displacement condition is not met, the iteration will not converge, and the process will proceed to the next iteration step. u 1. Establish a new tangential stiffness K 1. When adding a displacement correction c At time 2, configuration update: (10) (11) The residual can be expressed as (12) Continue to determine whether the residual meets the tolerance requirements. If not, continue with a new iteration.

[0030] Example 4 The WM fractal function method of equation (1) is used to simulate the profile curve of the rough sealing surface of the special threaded joint. The parameters of the WM fractal function are as follows: G =1*10 -13 ; M =10; r =1.5; L =1*10 -19 ; L s =5*10 -9 fractal dimension D =2.3, and at the same time avoid x =0 point, take n =10~70, x The value is taken in [0.6, 0.7]. The fractal curve is plotted using MATLAB software. Figure 1(b) shows the three-dimensional fractal model of the fractal curve.

[0031] The fractal curve characterizes the fractal profile of a rough surface with a roughness of 0.8 μm. A MATLAB script was created to import the coordinate data of the fractal profile with a roughness of 0.8 μm, constructed using the WM fractal function, into the ANSYS finite element analysis software. Spline curves were used to fit the coordinates, and a fractal curve with a length of 0.6 mm was introduced onto the sealing surface to simulate the rough surface. A material with an elastic modulus of 2.06 × 10⁻⁶ was selected, possessing large deformation and large strain analysis capabilities. 5 With a strength of MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, and tensile strength of 862 MPa, a bilinear elastoplastic strengthening model was selected. Surface-to-surface contact analysis using ANSYS finite element software was employed to simulate the connection between the internal thread of the coupling and the external thread of the pipe. Four contact pairs were defined between the coupling and the pipe: a torque shoulder surface, a conical sealing surface, a bearing surface, and a guide surface. The contact stiffness was set to 1.0, and the interference fit of the contact pairs was also set. A Coulomb friction model was selected to simulate the friction between the main sealing surface and the surface at the thread tooth contact point of the special threaded joint. Structural nonlinear static analysis was performed on the four contact pairs to obtain equivalent stress contour plots and contact pressure distribution curves of the special threaded joint, thus verifying the effectiveness of the model.

[0032] Example 5 The WM fractal function method of equation (1) is used to simulate the profile curve of the rough sealing surface of the special threaded joint. The parameters of the WM fractal function are as follows: G =1*10 -13 ; M =10; r =1.5; L =1*10 -19 ; L s =5*10 -9 fractal dimension D =2.5; at the same time, avoid x =0 point, take n =10~70, x The value is taken in the range [0.6, 0.7]. The fractal curve is plotted using MATLAB software, and Figure 1(c) shows the three-dimensional fractal model of the curve.

[0033] The fractal curve characterizes the fractal profile of a rough surface with a roughness of 1.2 μm. A MATLAB script was created to import the coordinate data of the fractal profile with a roughness of 1.2 μm, constructed using the WM fractal function, into the ANSYS finite element analysis software. A spline curve was then used to fit the coordinates, and a fractal curve with a length of 0.6 mm was introduced onto the sealing surface to simulate the rough surface. A material with an elastic modulus of 2.06 × 10⁻⁶ was selected, possessing large deformation and large strain analysis capabilities. 5With a strength of MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, and tensile strength of 862 MPa, a bilinear elastoplastic strengthening model was selected. Surface-to-surface contact analysis using ANSYS finite element software was employed to simulate the connection between the internal thread of the coupling and the external thread of the pipe. Four contact pairs were defined between the coupling and the pipe: a torque shoulder surface, a conical sealing surface, a bearing surface, and a guide surface. The contact stiffness was set to 1.0, and the interference fit of the contact pairs was also set. A Coulomb friction model was selected to simulate the friction between the main sealing surface and the surface at the thread tooth contact point of the special threaded joint. Structural nonlinear static analysis was performed on the four contact pairs to obtain equivalent stress contour plots and contact pressure distribution curves of the special threaded joint, thus verifying the effectiveness of the model.

[0034] Example 6 The WM fractal function method of equation (1) is used to simulate the profile curve of the rough sealing surface of the special threaded joint. The parameters of the WM fractal function are as follows: G =1*10 -13 ; M =10; r =1.5; L =1*10 -19 ; L s =5*10 -9 fractal dimension D =2.7; at the same time, avoid x =0 point, take n =10~70, x The value is taken in the range [0.6, 0.7]. The fractal curve is plotted using MATLAB software, and Figure 1(d) shows the three-dimensional fractal model of the curve.

[0035] The fractal curve characterizes the fractal profile of a rough surface with a roughness of 1.6 μm. A MATLAB script was created to import the coordinate data of the fractal profile with a roughness of 1.6 μm, constructed using the fractal WM function, into the ANSYS finite element analysis software. Spline curves were used to fit the coordinates, and a fractal curve with a length of 0.6 mm was introduced onto the sealing surface to simulate the rough surface. A material with an elastic modulus of 2.06 × 10⁻⁶ was selected, possessing large deformation and large strain analysis capabilities. 5With a strength of MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, and tensile strength of 862 MPa, a bilinear elastoplastic strengthening model was selected. Surface-to-surface contact analysis using ANSYS finite element software was employed to simulate the connection between the internal thread of the coupling and the external thread of the pipe. Four contact pairs were defined between the coupling and the pipe: a torque shoulder surface, a conical sealing surface, a bearing surface, and a guide surface. The contact stiffness was set to 1.0, and the interference fit of the contact pairs was also set. A Coulomb friction model was selected to simulate the friction between the main sealing surface and the surface at the thread tooth contact point of the special threaded joint. Structural nonlinear static analysis was performed on the four contact pairs to obtain equivalent stress contour plots and contact pressure distribution curves of the special threaded joint, thus verifying the effectiveness of the model.

[0036] The Mises stress clouds of the special threaded joints in Examples 3 to 6 under the optimal threading torque are shown in Figures 5(a), 5(b), 5(c) and 5(d), respectively. The Mises stress on the sealing surface under the optimal threading torque is greater than 758 MPa. The interference fit of the micro-protrusions on the fractal surface at the sealing surface leads to stress concentration, and some micro-protrusions undergo plastic deformation.

[0037] Examples 3-6 illustrate the contact pressure of special threaded joints with different roughnesses under optimal threading torque, such as... Figure 6 As shown, the sealing surface with the longest contact length and best sealing performance is at Ra=0.4μm. Due to the presence of micro-protrusions, the contact pressure on the sealing surface exhibits a discrete distribution, resulting in stress concentration. The sealing surface contact pressures of the special threaded joints in Examples 3-6 under different threading torques are shown in Figures 7(a), 7(b), 7(c), and 7(d). The fractal rough surface causes the contact pressure distribution at the sealing surface to be a non-smooth curve, and local stress concentration occurs. Under the same roughness, the sealing surface contact pressure distribution is more uniform under the optimal threading torque.

Claims

1. A special threaded joint modeling method considering roughness, characterized in that, Includes the following steps: Step 1: Construct the WM fractal function using the fractal dimension of the fractal surface and the characteristic coefficients of the special threaded joint as parameters. The characteristic coefficients include fractal roughness, surface profile spectral density related parameters, and frequency exponent. Step 2: Draw the fractal contour curve of the rough surface of the special threaded joint according to the WM fractal function, and export it as a script; Step 3: Use finite element analysis software to construct the geometric model of the special threaded joint. Import the script into the software to construct a solid three-dimensional model of the special threaded joint containing a rough fractal profile.

2. The method for modeling special threaded joints considering roughness according to claim 1, characterized in that, The WM fractal function in step 1 is specifically given by equation (1). （1）。 3. The special threaded joint modeling method considering roughness according to claim 1, characterized in that, In step 2, the fractal contour curve of the rough surface of the special threaded joint is plotted in MATLAB, and the contour coordinate data of the fractal curve is exported as a script.

4. The method for modeling a premium thread connection considering roughness according to claim 1, characterized in that, Step 3 specifically involves: Using the finite element analysis software ANSYS and its parametric design language, a parametric geometric model of the special threaded joint was built from the bottom up. The script was then imported into ANSYS, and spline curves were used to fit the coordinates. Fractal curves from the script were introduced from the sealing surface of the geometric model to simulate the rough surface, thus establishing a solid three-dimensional model of the special threaded joint containing a rough fractal profile.

5. A method of verifying the effectiveness of a premium threaded connection taking into account roughness, characterized in that, The effectiveness verification of the solid 3D model established by the special threaded joint modeling method considering roughness as described in any one of claims 1-4 includes the following steps: Step 1: Define the assembly, material properties, and interface properties of the 3D solid model of the special threaded joint with a rough fractal profile, and then mesh and refine it. Step 2: Apply load and displacement constraints according to the assembly boundary conditions, perform nonlinear static analysis on the boundary of the three-dimensional model, obtain equivalent stress cloud diagram and contact pressure distribution curve, and verify the effectiveness of the model.

6. The method for verifying the effectiveness of special threaded joints considering roughness according to claim 5, characterized in that, Step 1 specifically involves: defining the contact between the special threaded joint coupling and the tubing body, establishing four contact pairs: the torque shoulder surface, the conical sealing surface, the threaded bearing surface, and the guide surface, and setting the interference fit of the contact pairs; setting the material properties as follows: elastic modulus of 2.06×10⁵ MPa, Poisson's ratio of 0.3, yield strength of 758 MPa, tensile strength of 862 MPa, and selecting a bilinear elastoplastic strengthening model; setting the mesh size of the tubing body to 0.5; refining the mesh size of the torque shoulder and tubing end sealing surface to 0.1; and refining the mesh size of the rough micro-protrusions on the coupling end sealing surface to 0.

001.

7. A method of verifying the effectiveness of a premium thread joint taking roughness into account according to claim 6, characterized in that, The Coulomb friction model was chosen to simulate the friction between the main sealing surface of the special threaded joint and the surface at the contact point of the oil pipe thread teeth.

8. The method for verifying the effectiveness of special threaded joints considering roughness according to claim 6, characterized in that, Using the Newton-Raphson principle, nonlinear static analysis was performed on the four contact pairs to obtain the equivalent stress cloud diagram and contact pressure distribution curve of the four contact pairs of the special threaded joint. The effectiveness of the model was verified based on the equivalent stress and contact pressure of the four contact pairs.

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