**1. Introduction**

Thermodynamic underwater vehicle power system includes the main engine and multiple auxiliary engines. As shown in Figure 1, the power plant is integrated and supported to the housing through front and rear vibration isolators. The basic function of the vibration isolators is to support the entire power plant, which are called "supporting devices". In addition to vibration isolators, there are also some pipes connected auxiliary engines to the housing, such as sea-water pipes, fuel pipes and oil pipes. The main function of these pipes is to complete the transportation of seawater, fuel and oil, without support functions, collectively referred to as "un supporting devices". The mechanical vibration of power plant during operation transmit to the housing through these supporting and unsupporting devices, and then generate radiated noise in the ocean. The sea-water pump is one of the major vibration and noise sources in the underwater vehicle power system. There are two basic directions to decrease the impact of the sea-water pump generated vibration for the whole vehicle in practical engineering, the first is reducing the vibration of the pump itself, e.g., reduce rotting speed and the optimized structural form. The second is decreasing the vibration transmission in the transfer path. Compared with reducing the vibration of the pump, which needs to sacrifice pump power and increase development cost, the same effectiveness can be achieved from the transfer path without affecting the performance of the product.

**Figure 1.** The position of the sea-water pipe in the power system.

The sea-water pipe as the exclusive path to transport the seawater from ocean to the vehicle is the primary path to transmit the mechanical and fluid-excited vibration of sea-water pump to housing during operation. Therefore, the vibration reduction design of the sea-water pipe is of great importance for the silence of underwater vehicle. Single layer metal bellows (SLMB) are widespread applied for its easy processing and long life in practical engineering. However, the pipe could not offer significant and stable vibration reduction for its large stiffness and small damping. In order to reduce fluid induced pulsation, a muffler usually be utilized inside a SLMB. However, the presence of the muffler has an effect on the flow of water in the pipe. As a result, under technically feasible conditions, engineers first consider the flexible connection without a muffler between the sea-water pump and the housing. Due to its good vibration isolation and impact resistance, the flexible pipe can effectively isolate the transmission of mechanical vibration energy of the power equipment to the housing. Besides the function of vibration reduction, the advantage of flexible pipes also includes the role of displacement compensation to avoid a great displacement induced by the equipment force. As the primary transfer path from the sea-water pump to the housing, the design of flexible pipe is much more significant for the vibration reduction of the housing. Nevertheless, subject to the compact internal space of the power plant, the length of the pipe is usually very short. Furthermore, the diameter of the pipe will not be small for the underwater vehicles need enough seawater for cooling and squeezing. Therefore, the pipe commonly owns the feature of short in length and large in diameter, this type of flexible pipe is difficult to design.

Dynamics of fluid-conveying pipes have been well-explored in theoretical [1–10] and experiment research [11,12]. Tan [13] investigated the vibration characteristics of pipes conveying fluid in the super-critical range using Timoshenko beam theory for the first time. FEM [14–16] is also the most popular method up to now. However, experiment methods are the most direct means to evaluate the vibration isolation effectiveness of isolators. Enrique [17] took the experimental method to investigate the two-phase flow-induced vibration in pipes, they found that dynamic pipe response increases with increasing mixture velocity and void fraction, what is more, the hydrodynamic mass parameter is proportional to mixture density. Zhou [18] and Pan [19] focused experimental research on a vibration isolation platform for momentum wheel assembly and laminated rubber bearings to isolate metro generated vibration respectively. Kaiming Bi [20] proposed properly selected viscoelastic materials and constraining layers vibrations of above-ground pipelines can be effectively mitigated.

Double layer metal bellows (DLMB), rubber pipes (RP) and bellows coated rubber (BCR) are widely used for isolation in other engineering. However, the vibration effectiveness of the pipes has not been well explored. Especially for the sea-water pipe installed in underwater vehicles, when the sea-water pump rotates at different speeds, the excitation force and seawater pressure generated by the operation are also different. In the engineering, the working environment of the sea-water pipe is extremely complicated, and the excitation forces are varied. At the same time, in order to meet the assembly and use requirements of the product, the structure of the sea-water pipe is usually complicated, and it is difficult to accurately obtain the dynamic characteristics of the flexible pipes through theoretical calculation. To provide more comprehensive experiment evidence that testifies to the effectiveness of pipes mentioned above for the isolation of sea-water pump generated vibration, a test method was designed and carried out in the laboratory. To simulate the practical working condition, the vibration was induced by a sea-water pump and the pipes were installed between the pump and the simulation holder. In the tests, SLMB, DLMB, RP and BCR were tested respectively. In order to evaluate the isolation effectiveness of flexible pipes at different vibration levels of the sea-water pump, tests were carried out under four different rated operation speed of the sea-water pump, i.e., 1700 r/min, 2000 r/min, 2300 r/min and 2600 r/min. By drawing the energy level transfer coefficients under different frequencies and rotate speeds, a universal approach to evaluating the isolation effectiveness of the sea-water pipe was provided, and the isolation effectiveness of SLMB, DLMB, RP and BCR under various levels of rpm were demonstrated.

## **2. Design of the Test Specimens**

The position of the sea-water pipe in the power system is shown in Figure 1 and the sea-water pipe used in the underwater vehicle is shown in Figure 2. The sea-water pump assembly and the housing were connected by the pipe, which usually is composed by a flange, a straight line part and an elbow. In practice engineering, it is difficult to change the structure form of the flange and elbow restricted by the housing and pump structures. As a result, the straight-line part was the only part of the pipe that could be improved for better isolation effectiveness.

**Figure 2.** The structure diagram of the sea-water pipe.

To improve the flexibility of pipes and reduce the vibration transport to the housing from the pump, the following direction could be chosen: (i) reduce the pipe stiffness through adjusting the pipe structure; (ii) add high damping rubber sleeve; (iii) replace metal pipes with viscoelasticity pipes and (iv) increase pipes length.

Following the above design principles, three types of flexible pipe were designed and processing, i.e., DLMB, RP and BCR, their structures were shown in Figures 3–5. In the main view of Figure 3, the straight-line part of DLMB consists of a double metal bellows and an external metal braid. The wavy lines in the main view represent the bellows, which owns a wavelength of 3 mm and a thickness of 0.35 mm. The black and white segments represent a protective steel wire braid layer. The black and red ridges each represents a layer of bellows in the partial zoom diagram. The material of the RP was

hydrogenated nitrile rubber and the thickness was 3 mm. Figure 5 represents the structure diagram of BCR, which consisted of a bellows and a metal braided layer, with a rubber coating represented by a reticulated line on the outermost layer. Whose thickness was 2 mm. The material parameters of the above three pipes were present in Table 1.

**Figure 3.** The structure diagram of double layer metal bellows (DLMB).

**Figure 4.** The structure diagram of rubber pipe (RP).

**Figure 5.** The structure diagram of and bellows coated rubber (BCR).

**Table 1.** Material parameters.


Compared with SLMB, DLMB owns the lower flexural stiffness under the same operation load. The vibration energy was consumed by the friction performed between the two-layer metal bellows and reached the aim of reducing the vibration transmission from the sea-water pump to the housing. Furthermore, there was a layer of metal mesh outside the bellows, which provided adequate axial and radial bearing capacity as well as increases the structural damping.

The material of RP was hydrogenated nitrile rubber, the high damping of the rubber could promote the mechanical impendence of the pipes, the vibration energy could be reduced by the shear deformation of the pipe.

To promote the structural damping of DLMB, a BCR was formed after a layer of rubber was covered on the outer surface of the double-layer.

#### **3. Test Setup**

The test setup and photo were shown in Figures 6 and 7. The sea-water pump as the vibrator of the test was riveted in the output shaft of the test bench and driven by the electrical machinery. The front and the end of the tested pipe were connected with the pump and water supply pipe respectively. Furthermore, water supply pipe was supported by the holder, which was a plate with sufficient thickness. The holder was riveted in the workbench with four bolts. The water return pipe was connected with the output of the pump. In the test, the water was transported from the water supply pipe to the pump through the tested pipes and then back to the cistern through water return pipe. There was no connection between the workbench and the electrical machinery. They were respectively fixed on the ground surface. Theoretically, in the test, there were two vibration transmission paths from the sea-water pump to the holder, one was transmitted through the sea-water pipe and the other was transmitted to the workbench through the ground. Compared with the vibration energy transferred through the sea-water pipe, the energy that the second path transfers was sufficiently low. Therefore, we could reasonably ignore the impact of this path, which would not affect the test results of the vibration isolation effectiveness of sea-water pipes.

The surface area of the sea-water pump housing was small and thick in the test. At the other end, the holder owned sufficient thickness. Therefore, in this test, we considered both the sea-water pump and the holder as a mass. In order to accurately evaluate the vibration isolation effectiveness of these pipes, we paid attention to the average vibration reduction effectiveness in multiple directions. As a result, six monitoring points were set in this model. The acceleration of each point was monitored by an acceleration transducer. Three monitoring points were set in different directions on the pump surface and represented the acceleration of the pump. Other monitoring points were on the surface of the holder in three directions and represented the acceleration after the pipe transported. The average responses value of the three directions at both ends of the pipes was utilized to characterize the vibration energy level before and after vibration isolation. The type of acceleration transducers was PCB353B04, the data acquisition system was LMS SCADAS Mobile SCM05, and the LMS.Test.Lab software was used for the acceleration test.

**Figure 6.** Schematic diagram of the test system.

**Figure 7.** Testing the vibration isolation effectiveness of RP.

In the progress of the test, different vibration energy was induced at different rotate speed of the pump driven by the electrical machinery, which was controlled by the control system of the test bench. In each test condition, the sea-water pump was allowed to run stably for 3 min. After the sea-water pump speed, flow rate and inlet and outlet pressure recorded by the pump platform were stable, time-domain vibration data acquisition was started. The signal acquisition time was 1 min. After the data collection for all working conditions was completed, we performed FFT (Fast Fourier Transform) post-processing, and the selected window function was the Hanning window.

#### **4. Load Scheme**

Four stages of tests were considered, the reasons of the operation condition selection included: (i) there were many rated operating speed of underwater vehicle. (ii) The vibration energy level of the pump nonlinear increased with the increasing rotation speed and the tested pipes all owned the strongly nonlinear feature, which was obviously impacted by the vibration energy level and the frequency of the vibrator. Therefore, to accurately assess the vibration reduction effectiveness of the tested pipes in engineering, the following objectives were pursued:

