# Integrated Design of Hydraulic Coupling Bolts for Large Shaft Systems
## 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. Figure 1: Schematic illustration of a hydraulic coupling bolt assembly. Figure 2: Description of a hydraulic coupling bolt tightening process: (**a**) insertion; (**b**) sleeve fitting (1 st tightening); (**c**) nut clamping (2 nd tightening); (**d**) oil pressure relief [13]. Despite its significance, there have been relatively few studies conducted on coupling bolts for shaft systems. [PERSON] 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. [PERSON] [14] introduced design methods for bolted shaft coupling and theoretically calculated the stress distribution acting on bolts fastened to couplings. [PERSON] 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.