Theoretical analysis on vibration transmission control in a shaft-hull system excited by propeller forces via an active multi-strut assembly
Introduction
Underwater vehicles have attracted extensive attention for their ever-increasing ability in exploration and detection. However, protection of the ocean environment by reducing underwater noise imposes requirements on the acoustic performance of underwater vehicles. Structural vibration induced by the propulsion system is an important factor to consider in the sound radiation of underwater vehicles (Caresta and Kessissoglou, 2010; Chen et al., 2017; Li et al., 2017). Suppressing the vibration transmission from the propulsion system to the hull structure is an effective measure to reduce vibration and sound radiation and accordingly improves the acoustic performance of underwater vehicles (Merz et al., 2009; Su et al., 2018).
Longitudinal vibration of the propulsion shafting system is dominant since its magnitude is about four times that of the lateral vibration. However, with the development of control measures for the propulsion shafting system, the longitudinal vibration has been reduced significantly and hence contributes less to the radiated sound (Dylejko et al., 2007; Liu et al., 2019; Merz et al., 2013; Pan et al., 2008). In this circumstance, the influence of the lateral vibration becomes prominent. As a result, it is necessary to suppress the lateral vibration of the propulsion shafting system in order to reduce the vibration and sound radiation of the hull structure. The transmission paths of the lateral vibration are diverse due to the multiple bearings in the shafting system and the complicated transfer characteristics (Qin et al., 2020; Xie et al., 2019). In addition, the fundamental function and shock resistance of the propulsion shafting system must be guaranteed no matter whether the vibration control is adopted. Therefore, constraints and compromises will be inevitable in the lateral vibration control of the propulsion shafting system.
An accurate dynamic model of the propulsion shafting system is the basis for the investigation of the vibration characteristics of the shaft-hull coupled system, as well as the analysis and simulation of active control methods. At present, common modeling methods include analytical/semi-analytical methods (Chen et al., 2015; Qu et al., 2013, 2019; Sun et al., 2018), numerical methods (Huang et al., 2017; Li et al., 2019; Merz et al., 2007; Wang et al., 2019), experimental methods (Leader et al., 2013) and their combinations (Chen et al., 2018, 2019). Note that analytical/semi-analytical methods are of higher computational efficiency than the numerical methods, but they are usually restricted to simple structures. Meanwhile, experimental methods can be inconvenient and time-consuming. Therefore, the combinations of analytical and numerical methods are often preferred in design stages. The FRF-based synthesis method can divide the whole system into several subsystems, whereby each subsystem can be modeled independently by the most suitable methods, i.e. analytical/semi-analytical methods, numerical methods and/or experimental methods. The FRFs of subsystems can be synthesized to obtain the dynamic model of the whole system. On the basis of ensuring computational efficiency and precision, the FRF-based synthesis method is of higher flexibility and adaptability in dealing with large-scale complicated systems with multiple elastic bodies.
There are many studies on active control strategies to control vibration transmission (Caresta and Kessissoglou, 2012; Sutton et al., 1997; Wrona et al., 2020; Yang et al., 2020). For active control of vibration and sound radiation of complex structures such as the propeller-shafting system and hull of an underwater vehicle, the strategy that directly controls the hull vibration with a large number of actuators and transducers is not applicable in most circumstances due to the cost and energy consumption. Therefore, it is preferred to place actuators in the vibration transmission path from the shaft to the hull. In this indirect control strategy, both the number and the location of error transducers are of great influence on the power flow of vibration. Even so, the consistency between the suppression of the responses of error transducers and the attenuation of the hull vibration should be guaranteed in active vibration control.
In order to suppress the transmission of lateral vibration in the shaft-hull system excited by the propeller forces, an active stern support of smooth spherical joints is proposed in Xie et al. (2020), and accordingly, the friction in the spherical joints is neglected in the modeling. However, in practical applications, smooth spherical joints are too hard to realize and can have a significant influence on the lateral vibration transmission. In the case of smooth spherical joints, lateral vibrations of the shafting system are transmitted to the hull structure mainly along the axis of each strut. However, if the joints are not smooth or the struts are rigidly connected, lateral vibrations will transmit through the translational and rotational motion of the joints of the struts. Therefore, it is necessary to take into account realistic operation conditions in the modeling and analysis of vibration transmission via the active struts.
In this paper, an active multi-strut assembly that is rigidly connected to the hull and the stern bearing is investigated. The following discussion is organized in four sections. In Section 2, the dynamic model of the shaft-hull system is developed using the FRF-based synthesis method. In Section 3, the power flow in the shaft-hull system with the involvement of the active struts is analyzed. The feasibility of active control and two strategies are discussed in Section 4 and conclusions are summarized in Section 5.
Section snippets
Modeling of the shaft-hull system
The shaft-hull system is presented in Fig. 1. In this system, the active multi-strut assembly is proposed to replace the traditional stern bearing support and it is rigidly connected to the stern bearing housing and the annular end plate of the hull structure, respectively. This is different from that in Xie et al. (2020), where both ends of the assembly are connected by spherical joints. In Fig. 1, the shaft is supported by three bearings, i.e. the stern bearing, the intermediate bearing and
Analysis of power flow
Power flow reflects the ability for the interfacial force to do work on the interface and the transmission of vibration energy (Hambric, 1990; Xiong et al., 2003; Zhao et al., 2015), which can be expressed as follows:where F and V denote the interface force and velocity, respectively, and they are both complex numbers. The superscript * denotes conjugate and Re{} denotes the real part. Lateral vibrations of the propulsion shafting system induced by the propeller forces
The feasibility of active control
Two control strategies are considered and the placement of the error transducers is shown in Fig. 6. In the control strategy that uses three error transducers (Fig. 6a), the struts L1 and L6 operate in parallel, so do the struts L2 and L3, L4 and L5. The three groups of struts respond to the three error transducers, respectively. In the control strategy that uses six error transducers (Fig. 6b), the struts L1-L6 respond to the six error transducers, respectively.
The two control strategies of
Conclusions
An active multi-strut assembly is proposed to attenuate vibration transmission from the propulsion shafting system to the hull of an underwater vehicle. The struts of the assembly are assumed to be rigidly connected to the stern bearing housing and the hull. As a result, the power flow at the ends of each strut involves translational and rotational DOFs, and the transmission of vibration cannot be suppressed by merely controlling the axial vibration of each strut. Two control strategies that
CRediT authorship contribution statement
Xiling Xie: Methodology, Validation, Formal analysis, Investigation, Writing - original draft. Dequan Yang: Software, Data curation, Investigation. Di Wu: Software, Validation, Data curation. Zhiyi Zhang: Conceptualization, Resources, Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was partly supported by the National Natural Science Foundation of China (Grant No. 11672180).
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