**5. Isolation E**ff**ectiveness under Design Rpm**

Figure 8 showed the results of tests carried out on the four kinds of pipes under 1700 r/min to verify isolation effectiveness. The horizontal axis represented the test frequency, which was from 10 to 10,000 Hz, the dates were recorded at 1–3 octave(s), the curves were combined with center frequency of each 1–3 octave(s), the vertical axis represents the vibration energy level transfer coefficients λ, which was defined as

$$
\lambda = \frac{N\_2(f)}{N\_1(f)} \tag{1}
$$

where *N*2(*f*) was the averaged vibration energy level of transducers in all three directions, which represented the response of the holder, and *N*1(*f*) was the averaged vibration energy level of transducers in three directions, which represented the vibration energy of the sea-water pump. If λ was less than unity, it meant that the vibration energy of holder was lower than the sea-water pump, the pipe owned the ability of isolation to mitigate the vibration transport from the pump to the holder, otherwise, the pipe could not be used to alleviate the vibration transport.

The main reasons for choosing to evaluate the vibration isolation effectiveness of flexible pipes in a wide frequency range were as follows:


**Figure 8.** Signal-to-noise ratio of the sea-water pump vibration response at 1710 r/min.

Figure 8 compares the vibration response of the sea-water pump at 1710 r/min with the background noise (the vibration response obtained by the sensors when the sea-water pump is not working). It can be seen from the figure that at the peak of the sea-water pump's response, the signal-to-noise ratio reached 80 dB, and outside of the response peak frequency points, the signal-to-noise ratio at other frequencies had reached more than 40 dB. As the rotation speed increases, the response of the sea-water pump increased. This signal-to-noise ratio was sufficient for evaluating the vibration isolation effectiveness of sea-water pipes.

As shown in Figure 9, for all the pipes, multiple peaks were observed within the test frequency range. However, compared with other pipes, SLMB obviously owned more peaks. What is more, for SLMB, λ remained more than unity in the test frequency range except individual center frequencies, which represented that the pump vibration was magnified to the housing by SLMB in most frequency bands, the pipe offered insignificant vibration reduction.

**Figure 9.** Test results under 1710 r/min: (**a**) single layer metal bellows (SLMB); (**b**) DLMB; (**c**) BCR and (**d**) RP.

The maximum of λ for SLMB, DLMB and BCR within the test frequency range were all observed at the center frequency 63 Hz. It suggested that the natural frequency of the three isolation systems located between 56.2 and 70.8 Hz, which meant their operation stiffness were very similar. The maximum of λ for RP occurred at the center frequency 100 Hz, which represented that the RP owned greater stiffness in operation than other pipes. This was because the structural stiffness of RP was affected by seawater pressure, and the stiffness increased sharply as the inlet pressure of sea-water pump increased. Whereas the maximum of λ for the RP was 4 for its high damping, this was lowest in all pipes.

It can be seen from Figure 9b that the transfer coefficients for DLMB were less than unity below 50 Hz and above 1000 Hz. This suggested that the pump vibration transmitted to the holder was alleviated by the pipe within the above frequency range. Moreover, the transfer coefficients kept oscillation decreasing above the nature frequency, which meant the vibration reduction effectiveness was improved with the increasing frequency.

In Figure 9c, the transfer coefficients for BCR were less than unity above 1250 Hz, and continuously decreased with the rise of frequency. However, the vibration was magnified in other frequency bands. The transfer coefficient for the RP in Figure 9d was less than unity above 2000 Hz and was lower than 0.1 above 6300 Hz, which was the lowest in all pipes.

Figure 10 showed the test results of transfer coefficient curves for the four tested pipes under 2000 r/min. The transfer coefficient for SLMB was greater than unity or close to unity within the test frequency. The transfer coefficient for DLMB was less than unity above 1000 Hz, and continued to reduce. This indicated a stable and positive vibration reduction effectiveness of the DLMB in high frequency. BCR offered good isolation effectiveness above 3150 Hz. The transfer coefficient for RP was less than 1.2 below 63 Hz and lower than 0.1 above 6300 Hz.

It can be seen from the above analysis that the test results of isolation effectiveness of different pipes were basically consistent when the speeds of the sea-water pump were 1710 r/min and 2000 r/min. DLMB owned a stable vibration isolation effectiveness in the frequency band above 1000 Hz, and the

vibration isolation effectiveness became better as the frequency increased. BCR also applied stable vibration isolation effectiveness in the high frequency band, but due to its higher damping, its resonance region was wider, and the frequency of vibration isolation was higher than DLMB. The transmission coefficient of RP in the frequency band below 100 Hz was close to 1, which indicated that the vibration of the sea-water pump was not significantly amplified by the RP, and at the same time, RP owned the lowest transfer coefficient in high frequency bands. Unfortunately, SLBM had almost no vibration isolation effectiveness in the test band.

**Figure 10.** Test results under 2000 r/min: (**a**) SLMB; (**b**) DLMB; (**c**) BCR and (**d**) RP.

In order to find the vibration isolation effectiveness of the pipes at higher sea-water pump speeds, the transfer coefficient for the four pipes at 2300 r/min and 2600 r/min were tested. The results were shown in Figures 11 and 12. Similarly, SLMB offered insignificant isolation effectiveness within the frequency range shown in the figures. DLMB and BCR offered good vibration effectiveness in high frequency. RP always offered the most stable isolation effectiveness below nature frequency, which was the lowest in all pipes, but this phenomenon was more significant at 2600 r/min.

The test results under four different conditions showed some consistency. However, subject to the influences by material nonlinearity and different excitation forces of the sea-water pump at different rotating speeds, there were also some inconsistencies. The frequency at which DLMB began to provide vibration isolation effectiveness had increased at 2300 r/min to 2600 r/min compared with the results under 1710 r/min and 2000 r/min. When the speed of the sea-water pump rose from 2300 to 2600 r/min, the transmission coefficient of BCR was greatly reduced in the frequency band below 200, especially at about 80 Hz, which was also the resonance frequency band of the vibration isolation system, the decrease was most significant. However, at the frequency range of 1000 Hz upwards, the peak of the curve slightly increased. Similar with the test results of the BCR, the transmission coefficient curve of RP was suddenly reduced and owned a transfer coefficient of less than unity in the low frequency band when the speed of the sea-water pump rose from 2300 to 2600 r/min, but the high-frequency vibration isolation effectiveness was not as good as the results at other rotating speeds.

**Figure 11.** Test results under 2300 r/min: (**a**) SLMB; (**b**) DLMB; (**c**) BCR and (**d**) RP.

**Figure 12.** Test results under 2600 r/min: (**a**) SLMB; (**b**) DLMB; (**c**) BCR and (**d**) RP.

It can be seen from the above test results and analysis that none of the flexible pipes had a good vibration damping effectiveness at all sea-water pump speeds and full frequency bands. DLMB owned a stable vibration isolation effectiveness at all speeds in high frequency bands, but had a high transmission coefficient in low frequency bands. The low-frequency vibration reduction effectiveness of BCR and RP were improved, but the high-frequency vibration isolation effectiveness was weakened. This just reflects the complexity of engineering research. In engineering practice, the multi-speed and wide-band vibration responses of sea-water pumps are inevitable, and a vibration isolator cannot take into account the full-band vibration isolation function. In order to effectively reduce the vibration transmission of seawater pumps, it is necessary to use a certain speed and a certain frequency band as input conditions for vibration isolation design under the premise of accurately analyzing the vibration frequency spectrum, so as to design vibration reduction pipes that best satisfies the engineering practice.
