Integrated Design of Hydraulic Coupling Bolts for Large Shaft Systems

Abstract

Hydraulic coupling bolts are used in a wide range of industrial sectors, where ensuring the structural integrity and reliability of shaft systems is of paramount importance. However, research on systematic design methods for these specialized bolts is still lacking. In this study, an integrated design was used on hydraulic coupling bolts with M72 specification, considering both the tightening and untightening processes. First, the second tightening load was determined based on material strength, stress concentration and safety factors. Subsequently, the upper and lower limits of the first tightening loads were calculated using the thick-walled cylinder theory. An appropriate first tightening load maintaining the tightening force in both the axial and radial directions was obtained using finite element analysis. Design variables for the adapter configuration and oil passage shape were selected, and their impact on structural integrity was assessed using finite element analysis. The optimal combination of these design variables was derived. Finally, operational experiments for hydraulic coupling bolts were conducted according to the design results. The test results demonstrated a successful tightening and untightening process, confirming the effectiveness of the proposed design method.

1. Introduction

Coupling is broadly defined as a mechanical device transmitting rotational motion between shafts [1]. It can be categorized into two types: rigid coupling and flexible coupling. The key distinction lies in their ability to address relative displacements between shafts, with rigid coupling lacking this capability and flexible coupling incorporating elastic elements to compensate for such displacements [2]. For this reason, flexible couplings have recently garnered significant attention, evidenced by a multitude of publications [3,4,5,6,7,8,9,10,11,12]. Nevertheless, flange coupling, a representative form of rigid coupling, remains a prevalent method for joining large shaft systems subjected to repeated high shear loads during shaft rotation, owing to its capacity to transmit substantial torque, coupled with a straightforward structure and cost-effectiveness [2].

In practice, hydraulic coupling bolts are extensively employed for such a rigid coupling system. When a general-type bolt is used to secure a flange, the presence of a gap between the bolt and flange hole can potentially lead to the bolt loosening over time. To mitigate this issue, hydraulic coupling bolts use sleeves to fill the gap between the bolt and the flange hole, as shown in Figure 1. The inner surface of the sleeve and the contact surface of the bolt have a certain slope. While the structure of the coupling bolt may be somewhat complicated, it offers numerous benefits. The use of hydraulic pressure makes the tightening and loosening process fast. Furthermore, the disappearance of the gap between the bolt and the coupling hole ensures both secure fastening and efficient torque transmission. Accordingly, hydraulic coupling bolts play a crucial role in various industrial fields, including ships, power plants, and aircraft, where maintaining the structural integrity and reliability of shaft systems under continuous high-stress conditions holds the utmost significance. Figure 2 shows the tightening of the hydraulic coupling bolts [13]. First, bolts and sleeves are inserted into the flange hole (Figure 2a). Subsequently, a primary tightening load (i.e., the first tightening load) is applied to the bolt using a hydraulic tensioner as the maximum thickness part of the sleeve is restrained in the axial direction. During this process, the sleeve with an inclination on the inner surface is expanded by the bolt, resulting in radial contact pressure against the flange hole in an interference fit state, as illustrated in Figure 2b. Following this, the second tightening is performed by applying a tensile force to the bolt while fixing one end of the bolt thread with a nut (Figure 2c). Finally, a compressive force is generated between the nuts and the coupling after the oil pressure is relieved, as shown in Figure 2d.

Despite its significance, there have been relatively few studies conducted on coupling bolts for shaft systems. Jeong et al. [13] established selection criteria to determine the clamping load of shaft coupling bolts in power plants through finite element (FE) analysis. They also explored the impact of various shape variables, such as the gap between the coupling and sleeve, sleeve thickness, and sleeve angle, on the contact pressure generated during the tightening process. Shepstone [14] introduced design methods for bolted shaft coupling and theoretically calculated the stress distribution acting on bolts fastened to couplings. Lee et al. [15] investigated the tightening force and bolt stress for two different types of con-rod bolts of a medium-speed diesel engine: one fastened by hydraulic devices and the other tightened by torque wrenches. In addition, the effect of lubricating conditions on the tightening force and structural integrity of the torque tightening bolts was experimentally examined. Cho et al. [16] proposed a method to evaluate the fatigue durability of the connecting rod bolts in a high-speed engine using FE analysis. The reliability of the method was validated by comparing the results with those obtained from a fatigue endurance limit test. Ryu et al. [17] performed FE analysis on the hydraulic coupling bolt fastening and examined stress variation at the interface between the bolt and the sleeve as a function of the insertion displacement of the bolt. Jang [18] designed the oil passage shape of hydraulic coupling bolts using FE analysis to facilitate the disassembly of the bolt and sleeve, ultimately enhancing the convenience of maintenance work. Nils et al. [19] conducted an FE analysis on the structural integrity of a two-stroke ship engine system coupling bolt under maximum torque. Wu et al. [20] proposed a novel flat-face coupling system in hydraulic power transmission equipment. This system significantly reduces the resistance resulting from high hydraulic fluid pressure during coupling by incorporating an instantaneous pressure relief module. Through a series of computational fluid dynamics numerical investigations, they achieved a design with optimal flow characteristics and hydraulic power transmission efficiency.

Existing studies primarily concentrated on assessing the fastening force and structural strength of coupling bolts through FE analysis and often overlooked the complete operation of the bolt, which restricts their applicability to the design process. Furthermore, there is a lack of research to verify the reliability of design and analysis results through actual operational experiments, especially when it comes to coupling bolts for large shaft systems. Therefore, in this study, an integrated design approach that encompasses both the tightening and untightening process was established for hydraulic coupling bolts with an M72 specification, which were designed for use in large shaft systems. In Section 2, the initial step involved determining the second tightening load by considering material strength and conducting a theoretical analysis that involved stress concentration and safety factors. Following this, the upper and lower limits of the first tightening load were calculated based on the thick-walled cylinder theory. FE analysis was then performed under these load conditions for the tightening process to determine the suitable first tightening force, ensuring secure fastening both axially and radially. In addition, design variables related to the shapes of the adapter (Section 3) and oil flow passage (Section 4) were selected, and a series of FE analyses was performed on the tightening and untightening process to identify the optimal variable combination from the viewpoint of structural integrity. Finally, as described in Section 5, prototypes of hydraulic coupling bolts were produced, and operational tests were performed to assess the validity of the design method proposed in this study. The entire design process is schematically illustrated in Figure 3.

2. Calculation of Tightening Load

2.1. Second Tightening Load

The sequence of calculating the tightening load starts with determining the second tightening load with great attention to the axial tensile stress in the bolt, which is a primary concern for operational safety during the overall tightening process. The bolt material was a low-alloy steel known as SNCM439, which contains elements, such as chromium (Cr), molybdenum (Mo), and nickel (Ni). The mechanical properties for analysis were obtained from the tensile test and are shown in

Table 1. Mechanical properties of SNCM439.

Material	Yield Stress [MPa]	Tensile Strength [MPa]	Elongation [%]
SNCM439	700	1100	12

. Figure 4 schematically illustrates the design of the bolt intended for use in a large shaft system, based on the existing hydraulic coupling bolt with the M72 specification, while the detailed dimensions are not disclosed in this paper. The second tightening load (F₂) was determined by considering factors, such as yield stress (σ_y), stress concentration factor (K_t), and safety factor (SF). The stress concentration factor was estimated based on the minimum cross-section shown in Figure 4, using FE analysis (see Section 2.3). The SF, which is dependent on the operating conditions, was set to the value provided by the manufacturer. The formulas for calculating the second tightening load are shown below.

$$F_{2,\mathrm{m}\mathrm{a}\mathrm{x}}=A_{\mathrm{m}\mathrm{i}\mathrm{n}}·{\sigma }_{\mathrm{y}}$$

(1)

$${\sigma }_{\mathrm{n}\mathrm{o}\mathrm{m}}=\frac{F_{2,\mathrm{a}\mathrm{r}}}{A_{\mathrm{m}\mathrm{i}\mathrm{n}}}$$

(2)

$$K_{\mathrm{t}}=\frac{{\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}}{{\sigma }_{\mathrm{n}\mathrm{o}\mathrm{m}}}$$

(3)

$$F_2=\frac{F_{2,\mathrm{m}\mathrm{a}\mathrm{x}}}{K_{\mathrm{t}}·SF}$$

(4)

$$P_2=\frac{F_2}{A_{\mathrm{t}}}·10$$

(5)

where F_2,max is the maximum allowable load during the second tightening process, A_min is the minimum cross-section area, σ_nom is the nominal stress, F_2,ar is the second tightening load that was arbitrarily applied to compute the stress concentration factor, σ_max is the maximum stress obtained through the FE analysis at the minimum cross-section, P₂ is the hydraulic tensioner pressure required for the second tightening load, and A_t is the inner area of the tensioner where the hydraulic pressure acts. Initially, the maximum allowable load was computed using Equation (1). Subsequently, the stress concentration factor was determined by combining Equations (2) and (3) with the FE analysis results from Section 2.3. Following this, Equation (4) was employed to calculate the second tightening load, which was ultimately converted into the corresponding hydraulic pressure through Equation (5).

Table 2. Calculation results for parameters related to the 2nd tightening load.

Parameters	Values
F2,max [kN]	2492
Amin [mm2]	4059
F2,ar [kN]	1000
σnom [MPa]	246
σmax [MPa]	424
Kt	1.72
SF	2.0
F2 [kN]	825
At [mm2]	11,310
P2 [bar]	730

presents the calculated results for the mentioned parameters. Based on these calculations, the second tightening load (F₂) was 825 kN, which is considered suitable for maintaining the structural strength of the hydraulic coupling bolt during its operation.

2.2. First Tightening Load

The thick-walled cylinder theory is applicable for analyzing structures with a cylindrical shape, where the thickness is greater than one-tenth of the diameter [21]. Based on the assumption that the sleeve is equivalent to a thick-walled cylinder, the upper and lower limits for the first tightening load were determined. First, the lower limit of the first tightening load (F_1,l) was calculated, considering the gap (δ) between the coupling and the sleeve that exists before tightening, as depicted in Figure 5. To ensure that the sleeve sufficiently creates contact pressure with the coupling during the first tightening process, it is necessary to apply a load that expands the sleeve at least as much as the existing gap. The internal pressure required to expand the sleeve by the gap can be calculated with respect to the maximum thickness of the sleeve using Equation (6) and then converted into an axial force through Equation (7).

$$p_{\mathrm{i}}=\frac{\delta E(D^2-D_2^2)}{D·D_2^2}$$

(6)

$$F_{1,\mathrm{l}}=\mu ·\pi ·D_3·L·p_{\mathrm{i}}$$

(7)

$$D_3=\frac{D_1+D_2}{2}$$

(8)

where D₁ and D₂ are the maximum and minimum inner diameters of the sleeve inclination part, respectively, D is the inner diameter of the coupling, E is the elastic modulus, p_i is the internal pressure required to expand the sleeve by the gap, F_1,l is the lower limit of the axial force required to form the internal pressure p_i, μ is the friction coefficient, L is the sleeve length, and D₃ is the average inner diameter of the sleeve inclination part, defined by Equation (8).

The upper limit of the first tightening load (F_1,u) was determined based on the structural integrity of the sleeve. When the bolt is press-fitted to expand the sleeve, resulting in an internal pressure (p_i), the maximum shear stress (τ_max) generated on the inner surface of the sleeve can be calculated as follows.

$${\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{p_{\mathrm{i}}{D}^2}{D^2-D_2^2}$$

(9)

Equation (9) can be reformulated in terms of the maximum internal pressure (p_y) at which yielding occurs on the inner surface of the sleeve, leading to Equation (10). Consequently, the upper limit of the axial force (F_1,u) required to form the maximum internal pressure (p_y) can be calculated using Equation (11).

$$p_{\mathrm{y}}=\frac{D^2-D_2^2}{2D^2}{\sigma }_{\mathrm{y}}$$

(10)

$$F_{1,\mathrm{u}}=\mu ·\pi ·D_3·L·p_{\mathrm{y}}$$

(11)

The lower and upper limits of the calculated first tightening load were 348 kN and 880 kN, respectively. When the second tightening force remains constant at 825 kN, as determined in the previous section, the contact pressure and stress distribution at the interface between the sleeve and the coupling are primarily influenced by the first tightening load. In the following section, we report on the FE analysis conducted within the range between the lower and upper limit loads determined above to obtain the first tightening load that does not exceed the allowable stress while maintaining the required contact pressure between the sleeve and coupling.

2.3. FE Analysis for Tightening Process

During the tightening process, the hydraulic pressure applied to the tensioner causes displacement in the adapter, resulting in the tensioning of the bolt. We simplify the shape of the adapter for analysis, excluding the threaded part. The detailed adapter shape will be considered in the following section. The shape of a coupling bolt with a spiral oil groove is not perfectly symmetric. However, the spiral angle is small, and the effect of the oil groove on the tightening process is insignificant. Therefore, a quarter three-dimensional (3D) model was used for FE analysis, as shown in Figure 6a, based on the results of a previous study [18]. The FE analysis was conducted using the ANSYS Mechanical APDL commercial software package. The overall mesh sizes were determined by referencing the preceding study [18], ensuring continuity with established methodologies and maintaining consistency in the modeling approach. To improve the accuracy of the analysis, finer elements were created on the areas where contact occurs, such as between couplings and sleeves and between bolts and sleeves. A mesh independent test was performed on the stress concentration zone of the bolt shown in Figure 4, due to its significance for structural integrity. By refining the element size from 0.0015 to 0.0012 mm, the stress concentration factor converged to a constant value of 1.72 at an element size of 0.0012 mm. Consequently, a mesh consisting of approximately 340,000 elements and 670,000 nodes was generated. The FE model included four distinct types of 3D elements: tetrahedral 4-node elements, hexahedral 8-node elements, wedge 6-node elements, and pyramid 5-node elements. Each of these elements featured three translational degrees of freedom per node [22]. The selection of elements was based on their unique advantages: tetrahedral elements for modeling complex geometries, hexahedral elements for superior computational efficiency and accuracy in regular structures, and pyramid and wedge elements for compatibility with a combination of tetrahedral and hexahedral elements [23,24,25]. A full integration scheme was consistently applied to all elements, demanding approximately one hour of computational time for each simulation.

The tightening load was applied in three distinct steps, as shown in Figure 6b. Step 1 involves the first tightening process in which the bolt is inserted into the coupling hole, causing radial compressive stress. Step 2 is the unloading process of the first tightening load, and Step 3 is the second tightening process of applying axial tensile force by extending the bolt. The boundary conditions of the analysis are depicted in Figure 6c. In Step 1, the axial displacement of the thickest part of the sleeve was constrained, and in Step 2, this constraint was removed. Furthermore, in Step 3, the end of the bolt opposite to the one connected to the adapter was constrained in the axial direction to simulate the effect of being tightened with a nut. Symmetry conditions were consistently applied to the longitudinal cross-section of the bolt throughout the entire process to restrict displacement in the direction perpendicular to the plane. For the coupling, constraints were applied in directions other than the radial direction. The friction coefficient at the contact surfaces was set to 0.18 with reference to [13,19], and nonlinear analysis was conducted to account for the contact nonlinearity between the coupling and the sleeve and between the sleeve and the bolt.

The FE analysis results for the first and second tightening processes are shown in Figure 7. First, Figure 7a represents the von-Mises stress distribution on the bolt when arbitrary first and second tightening loads were applied to a quarter FE model, set at 87 kN and 250 kN, respectively. The analysis revealed a maximum stress of 425 MPa in the fillet part of the minimum cross-section of the bolt after the second tightening process. Subsequently, the stress concentration factor (K_t) was calculated using Equation (3) based on this result. Figure 7b displays the variations in the mean contact pressure and maximum von-Mises stress on the sleeve, as the first tightening load changes while keeping the second tightening load constant. The x-axis in the graph represents the first tightening load for the quarter model. As the first tightening load increased, the mean contact pressure also increased due to an increase in the interference fit. However, after the second tightening, the contact pressure decreased in comparison to the first tightening since the bolt extended axially and reduced in diameter. Within the allowable stress limit defined by the SF, the first tightening load was 452 kN (113 kN in a quarter model), which ensures the contact pressure between the sleeve and the coupling after the second tightening. This value is approximately equivalent to 400 bar as the tensioner hydraulic pressure. Figure 7c illustrates the contact pressure distribution on the sleeve after the entire tightening process under the load conditions, as per the design results, while Figure 7d shows the von-Mises stress distribution on the sleeve. It was observed that the clamping load in the radial direction was secured, as evidenced by the contact pressure generated across the entire contact surface between the sleeve and the coupling after the second tightening process. Meanwhile, the contact pressure decreased as the thickness of the sleeve increased because the expansion of the outer surface of the sleeve was relatively reduced. In addition, the analysis of stress distribution on the inner surface of the sleeve in contact with the bolt confirms that the structural integrity of the sleeve can be maintained after the tightening process.

3. Design of Adapter Shape

3.1. Design Variables

The adapter, which is directly coupled with the bolt, is a critical component that applies a tensile force corresponding to the applied hydraulic pressure to the bolt. Moreover, it is the most frequently damaged part during the tightening process in industrial applications. Therefore, the structural integrity of the adapter was evaluated according to the design variables. First, among the factors influencing the structural strength of the adapter, the thread length and the pitch were selected as design variables, as depicted in Figure 8.

Table 3. Values of design variables for adapter at each level.

Variables	Level 1	Level 2	Level 3
Pitch [mm]	2	3	-
Thread length [mm]	61	76	91

displays the values corresponding to each level of the chosen design variables. In addition, the upper limit of the thread length was determined based on the minimum allowable minor diameter of the adapter tip calculated using Equation (12) below. Finally, as shown in

Table 4. Two-way table for FE analysis of adapter.

Simulation No.	Pitch [mm]	Thread Length [mm]
1	2	61
2	2	76
3	2	91
4	3	61
5	3	76
6	3	91

, a two-way table was created according to the combination of design variables, and FE analysis was performed based on this matrix.

$$d_{1,\mathrm{a}}=\sqrt{\frac{4P}{\pi {\sigma }_{\mathrm{a}}}}$$

(12)

where d_1,a is the minimum allowable minor diameter, P is the axial load, and σ_a is the allowable stress.

3.2. FE Analysis of Structural Integrity of Adapter

The selected design variables above are related to the thread shape of the adapter. Analysis of the integrity of a thread shape generally requires an FE model with a large number of elements, which can be computationally time-consuming. Therefore, unlike the analysis of the previous tightening process, we focused solely on modeling the adapter and bolt, omitting the analysis of nonlinear contact between the bolt and sleeve and between the sleeve and coupling, which are not important for the current analysis. Accordingly, a linear static analysis was performed, applying the second tightening load (F₂) that induces the maximum stress on the bolt and adapter in the axial direction. Figure 9 displays the 3D FE model, which consisted of approximately 200,000 tetrahedral 4-node elements and 300,000 nodes. A full integration scheme was consistently applied to the elements, necessitating approximately three minutes of computational time for each simulation. A finer mesh was employed on the contact surface of the threaded part of the bolt and adapter to enhance the accuracy of the analysis [26]. The friction coefficient was applied as 0.2 for conservative design by referring to the results of previous studies [27,28].

Figure 10 shows the von-Mises stress distribution on the adapter according to the design variables. It can be found that in each case, the stress notably increases near the adapter tip, which is consistent with the results of the study by Xu et al. [26]. They examined the change in stress distribution acting on premium threaded connections with slanted threads like adapters and revealed that the last four to six threads at the end bear most of the load. The FE analysis results in this study also confirmed that as the thread length increased, the adapter maintained its structural integrity. This is attributed to the reduction in the load applied per unit thread as the number of threads increased. On the other hand, when the pitch decreases, it results in a larger contact area, which tends to enhance structural stability. However, this effect is relatively minor compared to the influence of thread length. Therefore, considering the allowable stress of the material, the final shape of the adapter was determined with a thread length of 91 mm and a pitch of 2 mm.

4. Design of Oil Passage Shape

4.1. Design Variables

During untightening, oil flows between the bolt and the sleeve through the passage to generate hydraulic pressure, resulting in both an axial force pushing the bolt against the originally inserting direction and a radial force simultaneously expanding the sleeve. Hence, the shape of the oil passage is a key design parameter that influences the structural strength of the bolt and sleeve during the untightening process [18]. In industrial situations, the hydraulic coupling bolts frequently become stuck within the sleeve during disassembly. This leads to maintenance delays, necessitates extra steps to forcibly separate the coupling bolts, and can result in damage to both the bolts and sleeves due to excessive external loads. Therefore, this study simulated the untightening process of the hydraulic coupling bolt through FE analysis under actual operating pressure, aiming to identify the optimal shape for the oil passage to ensure structural integrity and confirm the sound operation of the process. As depicted in Figure 11, the pitch and oil passage length were selected as design variables.

Table 5. Values of design variables for oil passage at each level.

Variables	Level 1	Level 2	Level 3
Pitch [mm]	9	10	11
Oil passage length [mm]	154	158	162

presents the values of design variables at each level, and

Table 6. Two-way table for FE analysis of oil passage shape.

Simulation No.	Pitch [mm]	Oil Passage Length [mm]
1	9	154
2	9	158
3	9	162
4	10	154
5	10	158
6	10	162
7	11	154
8	11	158
9	11	162

is a two-way table for which FE analysis was performed.

4.2. FE Analysis of Untightening Process

In the FE analysis of the untightening process, we used the results of the tightening process conducted in the previous section. As shown in Figure 12, the untightening hydraulic pressure was applied to the oil passage on both the bolt surface and inner surface of the sleeve after tightening. The analysis of the untightening process consists of two steps. Step 1 involves the release of the originally applied tensile force on the bolt, and in Step 2, hydraulic pressure is applied to the oil passage. The untightening hydraulic pressure in the second step was set to be the same as the operating pressure of the tensioner applied to the second tightening process. Throughout the analysis, a boundary condition was imposed by constraining the displacement in the direction perpendicular to the longitudinal plane using the symmetry condition for the quarter model. In the case of the coupling, directions other than the radial direction were also constrained. As in the tightening process, nonlinear analysis was performed due to contact nonlinearity between the bolt and the sleeve and between the sleeve and the coupling. Because the separation between the bolt and the sleeve leads to the divergence of the solution in static analysis, the sub-step function was used, and simulation results at the beginning of the separation were analyzed.

Figure 13a shows the variation in the maximum von-Mises stress on the sleeve in relation to the design variables during the untightening process. It should be noted that the allowable stress limit of 490 MPa was determined using a lower SF of 1.43 compared to the tightening process because the load is locally applied only to the oil passage during the untightening process. For the identical oil passage length, reducing the pitch leads to a decrease in the stress applied to the sleeve. Similarly, when the pitch remains constant, increasing the oil passage length ensures structural integrity, although the pitch has a relatively greater effect than the oil passage length. Consequently, decreasing the pitch and increasing the length of the oil passage result in a larger total passage area, which allows the untightening process to be performed at a lower hydraulic pressure and more smoothly. Based on the analysis results, a pitch of 10 mm and an oil passage length of 158 mm were chosen as the optimal design conditions for the oil passage, which can enhance workability without exceeding the allowable stress level. Figure 13b,c show the von-Mises stress distribution on the bolt and sleeve, respectively, under the selected design conditions. It is evident that the structural integrity of the designed hydraulic coupling bolt is secured during the untightening process by comparing the von-Mises stress distribution with the allowable stress limit.

5. Operational Experiment of Hydraulic Coupling Bolts

To verify the results of the design and structural analysis of coupling bolts performed in this study, prototypes of coupling bolts were fabricated, and tightening and untightening experiments were conducted. Figure 14 shows all the components of the coupling bolt with the M72 specification and the hydraulic pump manufactured for the experiment. The material of the bolt and sleeve was SNCM439. Before conducting the experiment, a thorough examination of the bolt and sleeve was carried out to identify any potential flaws using liquid penetrant testing by the Korea Testing and Research Institute. The entire test procedure, equipment calibration, and repeatability were meticulously overseen and validated by the Research Institute of Medium and Small Shipbuilding.

The procedures and results for coupling bolt operation are displayed in Figure 15. First, oil was applied to the hydraulic tensioner at a pressure of 400 bar, as shown in Figure 15a, which is the first tightening pressure determined from the FE analysis results. This induced the tensile force to the bolt through the adapter in the direction of the red arrow, as indicated in Figure 15a. While being inserted in the interference fit state, the bolt expanded the sleeve in the radial direction, resulting in the first tightening force by a contact pressure. Following this, a pressure of 730 bar was employed for the second tightening process, as shown in Figure 15b. With one end fixed by the nut, the bolt was tensioned, which was subsequently clamped by the nut in the distance ring, as shown in the inset of Figure 15b. When the hydraulic oil was released, the elastic behavior of the bolt generated a compressive axial force, i.e., second tightening force, on the contact surfaces between nuts and the coupling. The untightening process was performed in the reverse order of the tightening process. The clamping force in the axial direction was unloaded by tensioning the bolt with the same pressure as that of the second tightening process and loosening the nut in the distance ring. To release the radial fastening force, oil was supplied into the passage through an oil injector, as shown in Figure 15c, and the oil pressure was gradually increased within the range of the second tightening pressure. Consequently, the bolt was effectively disengaged from the sleeve in the direction of the blue arrow, as indicated in Figure 15c. The results of the experiment show that the proposed design method and FE analysis model were effective in designing the hydraulic coupling bolt, leading to sound tightening and untightening processes under the operation conditions determined through theoretical and FE analyses. Therefore, we believe that the proposed design method could be widely used to design hydraulic coupling bolts for large shaft systems.

6. Conclusions

In this study, a design method considering the entire operation process of an M72 specification hydraulic coupling bolt for a large shaft system was proposed. First, the tightening load conditions, which guarantee both secure tightening and structural integrity after the first and second tightening steps, were established by combining theoretical formulas with FE analysis. Next, extensive FE analysis was conducted to optimize the configurations of the adapter and the oil passage with a focus on structural strength during tightening and untightening operations. Finally, based on the design and analysis results, a prototype of a hydraulic coupling bolt was manufactured, and actual operational experiments were performed to validate the proposed design method. The main conclusions are summarized as follows:

The second tightening load was calculated considering the yield stress of the material, stress concentration and safety factors, yielding a value of 825 kN, which is equivalent to 730 bar of tensioner hydraulic pressure. While keeping the second tightening load constant, the contact pressure and von-Mises stress distribution on the sleeve evaluated by FE analysis were primarily influenced by the first tightening load. Within an acceptable stress range, the first tightening load suitable for ensuring both secure clamping and structural integrity during the entire tightening operation was determined to be 452 kN, corresponding to 400 bar of tensioner hydraulic pressure.

The pitch and length of the thread of the adapter were selected as design variables. FE analysis demonstrated that increasing the thread length and decreasing the pitch enhanced the structural stability of the adapter. Consequently, the optimal combination of variables was identified as a 2 mm pitch and a 91 mm thread length.

In the design of the oil passage shape, two design variables, oil passage length and pitch, were chosen. FE analysis of the untightening process was conducted to assess the influence of each variable on the maximum von-Mises stress experienced by the sleeve. It was revealed that decreasing the pitch and increasing the passage length led to a larger total area for the passage, resulting in a lower hydraulic pressure for the untightening. The optimal oil passage shape was determined to be a pitch of 10 mm and an oil passage length of 158 mm, considering both structural integrity and workability.

Operational experiments using an actual hydraulic coupling bolt with M72 specification were performed to verify the effectiveness of the suggested design method. It was confirmed that both the structural integrity and sound operation of the bolt with the optimized shape were secured under the load conditions determined through theoretical calculations and computational analysis. Therefore, it is expected that the findings of this study will be valuable for designing various hydraulic coupling bolts of large shaft systems.

The present study holds significant value as it proposes an integrated approach to hydraulic coupling bolt design, considering both tightening and untightening processes through theoretical and numerical analyses, thereby distinguishing it from existing methods. However, it is important to note that the proposed design was developed based on an existing bolt configuration, and the design variables were determined through practical case studies without explicit decision-making criteria. To achieve a genuine “integrated design”, a more systematic approach, involving a reconsideration of each critical aspect of the coupling bolt configuration, must be undertaken without being constrained by the existing bolt structure. This represents a crucial direction for our ongoing research efforts.