Characteristics and Experimental Research on Performance of the Seal Structure of Deepwater Collet Connector

Abstract

The sealing reliability of collet connectors is essential within underwater production systems. This paper is based on the lens gasket sealing mechanism and Hertzian contact theory, establishing mechanical models for the core sealing components in preloaded and working states and analyzing the minimum required axial preload force for sealing. According to the sealing principles of the connector, the force characteristics of each sealing element are analyzed in both preloaded and working states. The interplay of forces between these elements is subsequently determined. Furthermore, the amplification of axial preload force within the sealing structure is confirmed through simulations of contact characteristics. Finally, the accuracy of theoretical and simulated results is confirmed through experimental validation.

1. Introduction

As shallow-water oil and gas resources continue to deplete annually, the extraction of resources from greater depths has posed escalating challenges in underwater operations. Solely relying on human intervention is no longer adequate for aiding in the installation of deep-sea oil and gas pipeline connections. Consequently, innovative pipeline connection technologies have arisen. The domain of subsea equipment interconnection and sealing technology, crucial for deep-sea oil and gas field subsea production systems, constitutes a universally recognized technological challenge [1]. The effectiveness of sealing and contacting performance in subsea connectors profoundly determines the success of these connections.

The earliest inquiries into contact issues trace their roots to 1882, with Hertz [2] leading the exploration of contact between two elastic surfaces. Hertz’s contact theory examined interactions between smooth and equally sized elastic bodies, laying the foundational principles of contact mechanics. Deep-sea pipeline connectors commonly utilize spherical or conical metal gaskets, with the lens gasket being the prevailing choice. A lens gasket’s sealing surface is spherical, creating a ring contact when it interfaces with the conical pipeline sealing surface. This transforms into a ring band with increasing preloading force [3]. The localized deformation at the interface between the spherical and conical surfaces results in a limited effective contact area. Consequently, this results in increased contact stresses as well as enhancing sealing performance capable of accommodating varying pressure and temperature conditions. Considering the hysteresis of the stress-displacement of gaskets, Sawa T et al. [4] obtained the relationship between gaskets stress and leakage rate based on the finite element analysis and gasket sealing test and examined the method of estimating leakage amount. Fang et al. [5] established a simulation model of the elastic contact area ratio, the elastic-plastic contact area ratio and the plastic contact area ratio of the end face using fractal parameters to characterize the surface topography. They analyzed the effect of surface morphology on the sealing characteristics of mechanical seal end faces by simulation modeling. Wei et al. [6] employed contact fractal models for the sealing surface and average membrane thickness, using simulation analysis to investigate the influence of sealing surface width on contact characteristics between mechanically sealed end faces. Wang et al. [7] established boundary conditions for the sealing performance and formulated equations for the contact pressure of connector seals, based on the mechanics of metal static sealing. Comparative experiments demonstrated that connectors optimized with this equation exhibited improved sealing performance. Murtagian et al. [8] introduced sealing parameters and their critical values based on experimental findings, establishing novel sealing standards suitable for assessing metal-to-metal seals, particularly in the petroleum sector. Yang et al. [9] streamlined the sealing structure and proposed a theoretical model correlating sealing contact stress. Finite element analysis was applied to validate the model’s accuracy. Li et al. [10] examined the mechanical behavior of metal sealing rings in subsea wellhead connectors under preloading and operational conditions. They employed theoretical calculations and finite element methods to investigate the mathematical relationship between metal sealing contact stress and structural parameters. Li et al. [11] used finite element analysis to explore the thermal-stress coupling issue of metal seals in subsea wellhead joints. They established energy conservation equations and derived finite element equations for stress fields and transient temperature fields. Wei et al. [12] applied the superposition principle of elasticity to formulate a critical average contact pressure formula for mechanical connectors in subsea pipelines, validating the accuracy of this mathematical model through finite element analysis. Zhao et al. [13] utilized a mechanical analysis method based on the double-conical structure of high-pressure vessels, providing a theoretical linkage between metal sealing gasket contact stress, structural parameters, and operational pressure. This relationship facilitates the derivation of the unit sealing load equation for metal sealing gaskets under residual preloading conditions.

The scholars mentioned above conducted analyses on lens-type metal gaskets for diverse connector types, employing Hertz’s theory, consequently enhancing the theoretical understanding of sealing performance in subsea pipeline connectors. As a pivotal component of deep-sea pipeline connections, the collet connector assumes the responsibility of linking pipeline terminal facilities, consequently emphasizing the paramount importance of reliability in subsea operational environments. Zhang et al. [14] developed a fuzzy risk matrix analysis approach grounded in conventional risk matrix methodology, integrating expert assessment and fuzzy theory. They applied this approach to case studies involving subsea collet connector installations, thereby establishing a theoretical basis for the effective deployment of subsea connectors. Peng et al. [15] introduced the black-box optimization method for the tightening mechanism of collet connectors, based on a mathematical force transmission model. They investigated the correlation between friction coefficients and the mechanical efficiency of the tightening mechanism, providing valuable insights for engineering applications. The reliability of collet connectors also encompasses the performance of their sealing structures, with a primary focus on maintaining effective seals during operational conditions. Zhang et al. [16] introduced a method for determining the ultimate torsional resistance of subsea collet connectors through finite element simulation analysis. As a result of these calculations, they proposed a novel criterion for the failure of subsea collet connector seals: an effective sealing width no less than zero. Utilizing Hertzian theory, Yun et al. [17] investigated the sealing contact characteristics of collet connectors equipped with lens-type sealing gaskets. They developed a mathematical model for contact stress and validated it through experimental analysis. Wang et al. [18] assessed the bending performance of collet connectors in sealing conditions, considering the mechanical structure and operational principles of the collet connector. Theoretical calculations of bending stress were substantiated by bending experiments. Investigating the sealing characteristics of subsea joint sealing structures under transient thermal-structural coupling, Liu et al. [19] illustrated how sudden temperature fluctuations and variations in oil and gas pressure can impact the reliability of connector sealing performance. Yun et al. [20] investigated the contact characteristics of subsea collet connectors under steady-state temperature fields with thermal-structural coupling effects. They developed a heat transfer model for seawater layers situated between sealing structures, uncovering the susceptibility of lenticular sealing gaskets to high pressures at elevated temperatures. Zhang et al. [21] established the relationship between sealing contact load and clamping force, constructing a contact model between the lenticular gasket ring and hubs grounded in Hertzian theory. They introduced a compression limit equation and utilized it in the structural optimization of collet connectors.

The researchers above primarily employ the finite element method to assess the sealing performance of the collet connector’s sealing structure. This analysis yields crucial data supporting the reliability of collet connector sealing within a complex submarine environment. Nevertheless, there exists no precise depiction of the mechanical model concerning the core seal of the collet connector, and there is a notable absence of theoretical analysis regarding the minimum force essential to achieve effective sealing within the connector’s structure. Within subsea oil and gas pipeline connection equipment, upper and lower flanges, along with sealing rings, constitute core elements of connector sealing structures. The structural dimensions of these components directly influence the sealing performance of the connector. In this paper, based on the lens pad sealing mechanism and Hertzian contact theory, the mechanical model of the core seal is established based on the collet connector in the preloaded state and the working state, the force characteristics of the sealing structure are analyzed, and finally the accuracy of the mathematical model is verified through the simulation analysis and test, so as to provide relevant theoretical support for the design of the sealing structure of the collet connector and the installation of the connector.

2. Mathematical Model of Forces on Sealing Structure

Figure 1 depicts a schematic of the sealing structure. Where $D_k$ represents the contact diameter, $\alpha$ stands for the sealing surface cone angle. An analysis of the sealing mechanism of the lens gasket seal reveals that the magnitude of the axial preload force significantly influences the sealing effectiveness of the connector [22]. Therefore, it is imperative to conduct a comprehensive investigation into this parameter. To facilitate an analysis of the influence of axial preload force on connector sealing across the entire sealing process, this paper divides the process into two distinct states: the preloaded state and the operational state. These divisions are based on the force distribution experienced by the sealing ring during the connector sealing process.

2.1. Mathematical Model of Forces on Sealing Ring

2.1.1. Analysis of Axial Forces on Sealing Ring in Preloaded State

During the preloaded state, the sealing ring experiences compressive forces applied by the upper and lower flanges. The application of this compressive force transforms the initially circular contact between the sealing ring and the upper and lower flange into a circular band, leading to localized deformation within this band. This deformation is essential for ensuring the reliability of the connector’s seal [23].

Figure 2 illustrates the force distribution on the sealing ring in the preloaded state, taking into account the forces acting on the upper and lower spherical surfaces of the sealing ring due to the normal compressive forces $G_0$ from the conical surfaces of the upper and lower flanges, along with the associated frictional forces $f_0$. The sum of the axial components of these forces corresponds to the axial preload force applied to the sealing ring, denoted as $Q_0$, and the radial combined force is $W_0$.

$$Q_0=\pi D_{k}aq\frac{\sin (\alpha +\rho )}{\cos \rho },$$

(1)

$$a=\frac{\pi q_{\max }r}{E^{*}},$$

(2)

where $a$ denotes the sealing width, $q$ signifies the normal contact stress on the sealing contact area, the friction angle $\rho =8^{°}30^{\prime }$, and $q_{\max }$ represents the maximum contact stress.

$$\frac{1}{E^{*}}=\frac{1-{\mu }_1^2}{E_1}+\frac{1-{\mu }_2^2}{E_2},$$

(3)

where $E_1$ and $E_2$, respectively, represent the elastic moduli of the sealing ring and flange material, and ${\mu }_1$ and ${\mu }_2$ denote the Poisson’s ratios of the sealing ring and flange material.

2.1.2. Analysis of Axial Forces on Sealing Ring in Working State

During the working state, the sealing ring experiences not only compressive forces from the upper and lower flanges but also the pressure exerted by the internal medium. This pressure operates within the gap created when the sealing ring contacts the upper and lower flanges. This induces a tendency for the upper and lower flanges to separate, leading to a reversal of the frictional force between the conical surfaces of the flanges and the spherical surface of the sealing ring. As a result, the contact stress between the flange and the sealing ring decreases.

Figure 3 illustrates the force distribution on the sealing ring in the working state. $G_0{}^{\prime }$ indicates the positive pressure of the seal acting on the flange. $Q_0{}^{\prime }$ represents the combined axial force. $W_0{}^{\prime }$ indicates radial partial force. The tangential frictional force $f_0{}^{\prime }$ on the conical surface of the flange is directed toward the sealing ring along the contact diameter. The formula for computing the axial sealing force $Q_0{}^{\prime }$ in the operational state is provided below.

$${Q_0}^{\prime }=\frac{\pi }{4}{D}_k{}^{2}p+\pi D_{k}aq\frac{\sin (\alpha -\rho )}{\cos \rho },$$

(4)

The internal medium pressure $p=34.5\mathrm{MPa}$.

2.1.3. Analysis of Minimum Required Axial Preload Force for Sealing

In the design methodology of sealing structures, contact stress between sealing surfaces serves as a common criterion for assessing sealing performance. Inadequate contact stress fails to cause local deformation of asperities on the sealing surface, thus inhibiting the filling of microscopic surface gaps and hindering effective sealing. Conversely, excessive contact stress results in the generation of excessively high surface stresses at the point of contact between the spherical and conical surfaces. If this surpasses the material’s ultimate strength, the spherical surface of the sealing ring may experience crushing, fracture, or distortion, ultimately resulting in seal failure. Therefore, the contact stress value should fall within a specified range, avoiding extremes of both too high and too low values [24]. Within a certain range, higher contact stress leads to a tighter and more effective seal connection, enhancing sealing performance.

In the context of the collet connector’s sealing structure addressed in this paper, under operational conditions, the contact stress between the sealing ring and the upper and lower flanges must meet the following criteria:

$$q\ge mp,$$

(5)

In conclusion, it can be inferred that the sealing structure must adhere to the following equation to fulfill the minimum axial preload force requirement in both operational states:

$$Q_0=2\pi D_{k}ay\frac{\sin (\alpha +\rho )}{\cos \rho },$$

(6)

$$Q_0{}^{\prime }=\frac{\pi }{4}{D}_k{}^{2}p+2\pi amp\frac{\sin (\alpha -\rho )}{\cos \rho },$$

(7)

In the context of metal ring seals employing lens-type gaskets, for instance, when 316 stainless steel or other mild steel materials are chosen as the sealing ring material, the minimum preload-to-pressure ratio is denoted as $y=126.6\mathrm{MPa}$, accompanied by a sealing gasket coefficient denoted as $m=6.5$ [25].

2.2. Mathematical Model of Forces on Sealing Ring

During the sealing process of the connector, the axial preload force needed for the sealing ring is indirectly determined by applying loads to the driving ring. The acquisition of preload force involves the transmission of forces among the driving ring, collet, flange, and sealing ring [26]. To ensure that the connector meets the sealing requirements, it is essential to understand not only the axial preload force acting on the sealing ring but also the analysis of force distribution within the sealing structure. This analysis results in the establishment of the relationship between the axial preload force and the externally applied load. Consequently, the design of the installation tool is based on the magnitude of the loading force applied to the driving ring.

2.2.1. Analysis of Axial Forces on Sealing Ring in Preloaded State

As depicted in Figure 4, in the preloaded state, the upper and lower flange sealing conical surfaces encounter vertical reaction forces $Q_0$ and friction forces $f_0$ from the sealing ring. These forces act in the opposite direction to the force applied to the sealing ring. The upper and lower flange conical necks experience clamping forces $Q_1$ and $Q_2$, as well as friction forces $f_1$ and $f_2$, respectively, from the collet. These friction forces are oriented along the slopes of the flange conical necks, moving away from the sealing ring. Furthermore, the lower flange experiences a vertical supporting force $F_N$ from the base, which is directed upward.

By conducting a force analysis along the axial directions of the upper and lower flanges, the magnitudes of axial forces experienced by the upper and lower flange conical necks are obtained as follows:

$$Q_1=Q_0,$$

(8)

$$Q_2=Q_0-F_N,$$

(9)

In the preloaded state, the collet experiences both reactive forces and friction forces from the upper and lower flanges, as well as compressive forces and friction forces from the driving ring. These friction forces act downward along the rear surface of the collet. The driving ring is subjected to both the reactive force from the collet and the loading force applied by the installation tool. The force distributions for these two components are depicted in Figure 5.

The force balance equation in the axial direction of the collet is as follows:

$$Q_1=Q_2+Q_3,$$

(10)

where $Q_3$ presents the axial force exerted by the driving ring onto the collet in the preloaded state.

The force balance equation in the radial direction of the collet is as follows:

$$W_1=W_3-W_2,$$

(11)

where $W_1=Q_1\tan (\beta +\rho )$; $W_2=Q_2\tan (\beta +\rho )$; $W_3=\frac{Q_3}{\tan (\gamma +\rho )}$.

Where flange conical neck angle $\beta ={30}^{\circ }$; collet backside inclination angle $\gamma =3^{\circ }$; and frictional angle $\rho =8^{\circ }30^{\prime }$.

The force balance equation in the axial direction of the drive ring is as follows:

$$F_q=Q_3,$$

(12)

where $F_q$ represents the axial loading force applied by the installation tool.

The relationship between the axial force exerted by the installation tool and the axial force required for sealing can be obtained by substituting Equation (8) through (11) into Equation (12).

$$F_q=\frac{2Q_0\tan (\beta +\rho )}{\tan (\beta +\rho )+\frac{1}{\tan (\gamma +\rho )}},$$

(13)

The deformation of Equation (13) yields the mechanical gain coefficient of the seal structure K:

$$K=\frac{Q_0}{F_q}=\frac{\tan (\beta +\rho )+\frac{1}{\tan (\gamma +\rho )}}{2\tan (\beta +\rho )},$$

(14)

After substituting the specific parameters of the connector’s sealing structure into the calculation, K is determined to be 2.46. This demonstrates that the designed sealing structure can transform relatively modest external loads into substantially higher axial preload forces applied to the sealing ring.

2.2.2. Analysis of Axial Forces on Sealing Ring in Preloaded State

As shown in Figure 6, during working conditions, the upper and lower flange’s conical sealing surfaces endure vertical reaction force $Q_0{}^{\prime }$ and friction forces $f_0{}^{\prime }$ imposed by the sealing ring, opposing the force applied to the sealing ring. The upper and lower flange conical necks each experience clamping forces and friction forces applied by the collet. The upper and lower flange conical necks are, respectively, subjected to clamping forces $Q_1{}^{\prime }$ and $Q_2{}^{\prime }$, as well as friction forces $f_1{}^{\prime }$, $f_2{}^{\prime }$, from the collet. These friction forces are directed along the slopes of the flange conical necks, moving away from the sealing ring. Additionally, the lower flange experiences a vertical supporting force $F_N{}^{\prime }$ from the base, which is directed upward.

By conducting a force analysis along the axial directions of the upper and lower flanges, the magnitudes of axial forces experienced by the upper and lower flange conical necks are obtained as follows:

$$Q_1{}^{\prime }=Q_0{}^{\prime },$$

(15)

$$Q_2{}^{\prime }=Q_0-F_N{}^{\prime },$$

(16)

In the working state, the collet undergoes reactive forces and friction forces from both the upper and lower flanges, in addition to compressive forces and friction forces from the driving ring. These friction forces exert a downward effect along the rear surface of the collet. The driving ring is solely subjected to the reactive force originating from the collet. The force distributions for these two components are shown in Figure 7.

The force balance equation in the axial direction of the collet is as follows:

$$Q_1{}^{\prime }=Q_2{}^{\prime }-Q_3{}^{\prime },$$

(17)

where $Q_3{}^{\prime }$ represents the axial force exerted by the driving ring onto the collet in the working state.

The force balance equation in the radial direction of the collet is as follows:

$$W_1{}^{\prime }=W_3{}^{\prime }-W_2{}^{\prime },$$

(18)

where $W_1{}^{\prime }=Q_1{}^{\prime }\tan (\beta -\rho )$; $W_2{}^{\prime }=Q_2{}^{\prime }\tan (\beta -\rho )$; and $W_3{}^{\prime }=\frac{Q_3{}^{\prime }}{\tan (\rho -\gamma )}$.

The value of $Q_3{}^{\prime }$ can be solved from the above equation as:

$$Q_3{}^{\prime }=\frac{2\tan (\beta -\rho )\tan (\rho -\gamma )}{1-\tan (\beta -\rho )\tan (\rho -\gamma )}{Q}_0{}^{\prime },$$

(19)

Upon incorporating the precise parameters of the connector’s sealing structure into the calculation, it is derived that $Q_3{}^{\prime }=0.079Q_0{}^{\prime }$ and $f_3{}^{\prime }=0.12Q_0{}^{\prime }$. This indicates that when the external loading force is withdrawn from the sealing structure, the driving ring only needs to provide a minimal amount of frictional force to preserve the sealed condition. This guarantees the reliability of the sealing structure.

2.2.3. Analysis of Axial Forces on Sealing Ring in Preloaded State

Figure 8 shows the variation curve of the maximum contact stress between the upper and lower flanges and the sealing ring during axial preloading. The curve illustrates a rising trend in the maximum contact stress as the axial preloading pressure increases. Nevertheless, the slope of the curve gradually decreases, signifying a gradual slowdown in the rate of maximum contact stress increase. This phenomenon arises from the initial state in which the sealing ring initially contacts the upper and lower flanges in a circular manner. However, with increasing axial preloading pressure, localized deformation occurs on the spherical surface of the sealing ring, leading to an increase in the contact area. This transformation results in a gradual transition to a band-like contact configuration, slowing down the rate of contact stress increase. As exemplified by point A on the curve, when the preloading pressure reaches 3.1 MPa, the maximum contact stress measures approximately 126 MPa. This value slightly exceeds the minimum sealing pressure ratio in the preloaded state, highlighting the appropriateness of this preloading pressure magnitude to meet the sealing requirements. When converted, this value corresponds to an axial preloading force of 14.6 tons experienced by the upper flange.

Figure 9 shows the variation curve of the maximum contact stress between the upper and lower flanges and the sealing ring in working conditions. To meet the sealing requirements under an internal pressure of 34.5 MPa, it is crucial to verify that the maximum contact stress between the sealing ring and the upper and lower flanges meets the following criterion:

$$q\ge mp=6.5\times 34.5=224.25\mathrm{MPa},$$

(20)

Point B on the curve indicates that, when the axial preloading pressure rises to 8.8 MPa, the maximum contact stress reaches 224.5 MPa, satisfying the previously mentioned criterion. This signifies that, at this point, the sealing requirement has been met. Converting the value of 8.8 MPa to the axial preloading force experienced by the upper flange, it equals 41.4 t.

In this paper, the angle and contact diameter of the sealing ring are denoted as $\alpha ={70}^{\circ }$ and $D_k=160\mathrm{mm}$, respectively. Upon determining the maximum contact stress, it can be obtained from Equations (2) and (4) as follows:

The theoretical value of the sealing width is $a=4.82\mathrm{mm}$. The critical axial sealing force value under operational conditions is ${Q_0}^{\prime }=39.7\mathrm{t}$.

3. Simulation Analysis of Sealing Structure Contact Characteristics

In the preceding sections, this paper has solely conducted a theoretical analysis of the force distribution among the critical components of the sealing structure in the two specified states. The force transfer relationship between the components was established. However, the stress and strain conditions of these components during the sealing process remain unknown. Given the complexity of the model, employing finite element simulation represents a viable approach to analyze the sealing structure in its sealed state. This method will produce more realistic stress and strain profiles.

3.1. Model Establishment and Parameter Configuration

While the upper and lower flanges, sealing ring, and driving ring within the sealing structure display axial symmetry, the collets do not form a unified structure in the circumferential direction. Instead, twelve collets are evenly distributed around the flange, resulting in the entire sealing structure lacking strict axial symmetry. Utilizing a 2D axisymmetric approach for analysis would produce less accurate results. Conversely, conducting a comprehensive analysis of the entire sealing structure introduces considerable computational complexity, hindering the achievement of convergent results. To improve analytical efficiency, this paper focus on a single collet and isolates the corresponding segment of the sealing ring, flange, and driving ring. The resulting analytical model is depicted in Figure 10.

The boundary conditions for the individual collet CAE model are shown in Figure 11. A fixed constraint is applied to the bottom surface of the lower flange to ensure its immobilization. No-friction constraints are enforced on the segmented surfaces of the upper and lower flanges, sealing ring, and driving ring to simulate the restraining forces exerted by the circumferential segments on these surfaces. Frictional contact is modeled between the upper and lower flanges and the sealing ring, with a friction coefficient of 0.15. A pressure load is applied to the top surface of the driving ring, simulating the axial force exerted by the installation tool on the driving ring. The material for the upper and lower flanges is selected as 12Cr2Mo1, with ultimate strength ${\sigma }_{b1}=515\mathrm{MPa}$ and yield strength ${\sigma }_{s1}=310\mathrm{MPa}$. The material for the sealing ring is 316 stainless steel, characterized by ultimate strength ${\sigma }_{b2}=510\mathrm{MPa}$ and yield strength ${\sigma }_{s2}=205\mathrm{MPa}$. Both materials possess an elastic modulus denoted as $E=2.1\times {10}^{11}\mathrm{MPa}$ g and a Poisson’s ratio indicated as $\mu =0.3$.

3.2. Simulation Results and Analysis

The primary goal of the contact characteristic simulation analysis is to ascertain the magnitude of the loading force applied by the installation tool required to meet the sealing condition under the working state, characterized by an internal medium pressure of 34.5 MPa. This involves ensuring that the maximum contact stress between the sealing ring and the upper and lower flanges stays within acceptable limits (${\sigma }_{\max }\ge 224.25\mathrm{MPa}$). Additionally, this analysis seeks to identify stress and strain distributions among critical components in this particular state. Contact stress values on the sealing sphere are systematically recorded by progressively adjusting the axial force applied to the driving ring until achieving a satisfactory result. Ultimately, a contour map displaying the resulting contact stress on the sealing ring is shown in Figure 12 at an axial force of $F_q=18.0\mathrm{t}$. The contour map reveals a predominant ring-shaped contact stress distribution on the sealing sphere, with the highest contact stress measuring 226.22 MPa. This value meets the sealing criteria under operational conditions, confirming the sealing structure’s capability to effectively establish a seal against an internal pressure of 34.5 MPa at this specific axial force. By referencing the axial preloading force on the upper flange in the sealed state, as determined in Section 2.2.3, the simulated mechanical gain coefficient is calculated as $K^{\prime }=41.4/18.0=2.3$. The minimal difference between this value and the theoretically calculated mechanical gain coefficient $K=2.46$ obtained in Section 2.2.1 provides evidence of the simulation’s fidelity.

Figure 13 depicts the distribution of contact stress on the surface of the sealing sphere. The graph illustrates that the contact stress reaches its peak at the central region of the sphere’s width, gradually diminishing on both sides until it reaches zero. Based on this data, Figure 14 presents the distribution curve of contact stress across the width of the sealing sphere. This curve aids in determining the critical sealing width in the working state of the sealing ring. The boundaries of this crucial sealing width align with the points on the curve where the contact stress reaches zero. The distance between these two endpoints, approximately 4.2 mm, closely matches the theoretically calculated value of 4.82 mm, indicating a slight discrepancy.

Figure 15 presents the contact stress distribution on the clamping surface of the collet. Upon examining the graph, it becomes apparent that the contact stress is lower in the central region of the contact width. It gradually increases towards both sides. This phenomenon occurs because contact is established between the end portions of the flange cone neck surface and the clamping surface of the collet on both sides. As a result, higher contact stress is experienced at these specific locations.

Figure 16 depicts the extracted distribution curve depicting contact stress across the width of the collet’s clamping surface. The graph reveals that the highest contact stress is located near the lower endpoint of the collet’s clamping surface, measuring 205.9 MPa. Conversely, the lowest contact stress is found in the upper-central region of the contact, measuring approximately 110 MPa.

Figure 17 presents the equivalent stress contour map for both the sealing ring and the collet. The graph indicates that the maximum equivalent stress in the sealing ring is 149.22 MPa, localized within the contact ring region of the sealing sphere. This value remains well below the yield limit of the sealing ring material, set at 205 MPa. This observation indicates that the sealing ring has not experienced plastic deformation in this condition. Conversely, the highest equivalent stress in the collet is located near the lower endpoint of its clamping surface, measuring 124.95 MPa. This value significantly differs from the yield limit of the collet material, which is 310 MPa. Consequently, the collet is resistant to plastic deformation.

4. Study of Sealing Performance Testing

4.1. Sealing Ring Internal Pressure Test

An internal pressure test was conducted on the designed sealing ring to subject the test apparatus to pressurized loading, with the goal of determining the minimum axial preloading force needed for the sealing ring to effectively seal at the design pressure of 34.5 MPa. Additionally, an additional preloading force was applied to validate the sealing ring’s ability to withstand 1.5 times the design pressure (51.75 MPa), thereby confirming the reliability of the designed sealing mechanism. The experimental setup primarily consisted of a 200 t press, a test apparatus, a pressure pump, and hydraulic piping. The experimental schematic is illustrated in Figure 18, and the experimental procedure is presented in Figure 19.

Figure 20 illustrates that after the internal pressure test, the sealing ring displays distinct indentation marks on the sealing sphere, creating a symmetrical ring-shaped pattern. The width of these indentations corresponds to the sealing width. Measuring this width to be approximately 4.4 mm closely aligns with both the theoretical analysis result (4.82 mm) and the finite element analysis result (4.2 mm).

After analyzing the experimental data, the correlation between sealing pressure and the axial preloading force applied to the sealing ring was established, as illustrated in Figure 21. The curve clearly indicates that, at lower axial preloading forces (below 10 t), the sealing ring does not meet the sealing requirements and cannot effectively contain pressure. However, as the preloading force gradually increases to approximately 15 t, the sealing ring begins to demonstrate effective sealing performance. This indicates that, at this preloading force level, the contact stress on the sealing ring’s sphere surface exceeds the minimum required sealing pressure, closely aligning with the simulated analysis value of 14.6 t. The sealing ring attains the sealing design pressure of 34.5 MPa when the preloading force reaches 42 t, whereas achieving sealing at 1.5 times the design pressure (51.7 MPa) requires a preloading force of 60 t.

4.2. Sealing Structure Performance Test

The primary purpose of the sealing structure performance test is to evaluate the sealing capabilities of the comprehensive sealing assembly, which includes the upper and lower flanges, sealing ring, collet, and drive ring. Simultaneously, the test aims to determine the axial force magnitude required to achieve sealing under internal pressures of 34.5 MPa and 51.7 MPa.

Figure 22 shows both the schematic and real-world images of the sealing structure performance test. The test involves introducing pressurized water into the assembled connector’s interior and maintaining pressure to investigate the relationship between its sealing performance and applied loading force. The results of the sealing structure performance test are presented in

Table 1. Data of holding pressure under different hydraulic cylinder loads and pressing pressure (MPa).

	Pressing Pressure (MPa)	10.0	12.0	14.0	16.0	18.0	19.3	20.0	22.0	24.0	25.2
Hydraulic Cylinder Load (t)
15.0		15.0	15.0	15.0	15.0	15.0	15.0	15.0	15.0	15.0	15.0
20.0		15.3	19.0	20.0	20.0	20.0	20.0	20.0	20.0	20.0	20.0
25.0		15.3	19.0	22.8	25.0	25.0	25.0	25.0	25.0	25.0	25.0
30.0		—	—	22.8	26.9	30.0	30.0	30.0	30.0	30.0	30.0
34.5		—	—	—	26.9	30.6	34.5	34.5	34.5	34.5	34.5
40.0		—	—	—	—	30.6	34.5	38.4	40.0	40.0	40.0
45.0		—	—	—	—	—	—	38.4	42.3	45.0	45.0
51.7		—	—	—	—	—	—	—	—	46.8	51.7
55.0		—	—	—	—	—	—	—	—	46.8	51.7

. The experimental findings clearly demonstrate that the connector’s sealing structure can effectively seal at the design pressure of 34.5 MPa when subjected to a loading force of 19.3 t from the hydraulic cylinder. However, achieving sealing at 1.5 times the design pressure (51.7 MPa) requires an increased loading force on the hydraulic cylinder, which needs to be raised to 25.2 t.

A comparison among the critical axial force required for sealing design pressure from theoretical calculations, simulated analysis, and actual experimental results, along with the loading force applied by the installation tool and the calculated mechanical gain coefficient, is presented in

Table 2. Comparison of results.

	Critical Sealing Axial Force (t)	External Applied Load (t)	Mechanical Gain Coefficient K
Theoretical Calculation	39.7	16.14	2.46
Simulation Analysis	41.4	18.0	2.3
Actual Experiment	42.0	19.3	2.21

.

From Table 2, it can be observed that the deviations among the three sets of data are relatively small. The critical sealing axial force derived from simulation analysis demonstrates a 3.5% variation when contrasted with theoretical calculations, while the applied load displays an 11.5% discrepancy. Conversely, experimental outcomes reveal a 5.8% divergence for the critical sealing axial force and a 19.58% disparity in applied load when contrasted with theoretical calculations. These disparities can be attributed to the distinction in criteria: theoretical calculations and simulation analyses are grounded in the principle of leak prevention, while actual experiments hinge on the occurrence of leaks as their decisive factor. Consequently, there is a closer alignment between theoretical and simulation results, although experimental axial and loading forces marginally exceed those derived from theoretical calculations and simulation analyses. Nevertheless, the overall disparities remain minor and are notably smaller than the numerical values themselves, thus confirming the accuracy of both theoretical and simulation outcomes.

5. Conclusions

This paper focused on the analysis of the sealing structure of a 6-inch vertical-guided non-integral collet connector, with a particular focus on force characteristics and experimental investigations into sealing performance. The primary findings and conclusions can be summarized as follows:

(1) A mechanical model of the collet sealing components is developed for both pre-loaded and working conditions. Mathematical models are formulated to determine the minimum preloading force necessary for achieving sealing and its associated sealing width. Contact characteristic analysis of the core sealing components is carried out, elucidating the fluctuation patterns in the maximum contact stress of the sealing ring under axial preloading in both preloaded and working conditions. The minimum axial preloading force required to satisfy the sealing criteria is ascertained based on these findings.

(2) The force characteristics of the sealing structure are investigated. Stress analyses are conducted on every component of the sealing structure in both preloaded and working conditions. Relationships governing force transfer between components are established, leading to the determination of the mechanical gain coefficient of the sealing structure in response to axial loading. Contact characteristic simulations of the sealing structure are conducted to obtain contact stress and sealing width data for both the sealing ring and collet under working conditions. This validates the amplification behavior of the sealing structure in response to axial preloading force.

(3) A performance test on the sealing ring was conducted, revealing that a minimum axial preloading force of 42 t is necessary to meet the sealing requirements. Performance tests on the sealing structure demonstrates that it meets the sealing criteria when the installation tool exerts a loading force of 19.3t. A comparison of the minimum axial preloading force and tool loading force among experimental, calculated, and analyzed results serves to validate the soundness of the sealing structure design and the analytical methods proposed in this paper.

This paper conducted force analysis and developed a mechanical model for the sealing structure components of the collet connector. In the design and installation process of the collet connector, these analyses serve as a theoretical foundation, offering insights into the sealing reliability of the sealing structure components and providing a reference for the design of loading forces applied by installation tools. Moreover, they play a pivotal role in ensuring the operational reliability of the collet connector in underwater pipeline connections.