Experimental Investigation of Vibration Characteristics in a Centrifugal Pump with Vaned Diffuser

In order to investigate the vibration characteristics of centrifugal pump, a centrifugal pump with vaned diffuser whose specific speed is 190 was chosen for this research. Both the experiments of energy performance and vibration characteristics of the pump were performed.-e results indicate that when flow rate of the pump is 270m/h, the head is 15.03m and the efficiency is 71.47%. -emaximum efficiency is 71.71%when the flow rate of the pump is 233m/h and the head is 16.92m. And a wide frequency band of vibration appears at 600Hz at outlet flange of the pump. -e vibration intensity at the outlet flange is largest. -e vibration intensities at both sides of bearing casing are slighter than those at outlet flange and larger than those at motor base.-e vibration intensity at the motor base is larger than that at pump base, and the vibration intensity at the pump body is the lowest. -e vibration intensity of monitoring point M4 in the X direction under 0.8Qd is 1.27mm/s, which is the maximum under three flow rates.


Introduction
e vibration characteristics of centrifugal pump affect its safety in engineering application.e good vibration resistance not only ensures the stable operation but also prolongs the service life of pump.Corresponding to this, the severe vibration will lead to decrease of safety, the reliability, and the stability of the pump.So, vibration reduction has become an important part of the performance improvement of centrifugal pump.Many scholars have studied the vibration source of the centrifugal pump.Jeon and Lee [1] who studied the flow field, vibration, and noise in a centrifugal pump with numerical simulation found that the vibration and noise of the centrifugal pump are mainly caused by the internal flow-induced vibration.Huang et al. [2] found that the pulsation of internal flow of centrifugal pump is the main source that causes vibration and noise.And the vibration of a marine centrifugal pump is reduced by the structure of the double-channel volute and guide vane.
After determining the vibration source, vibration of centrifugal pump becomes more convenient to monitor and weaken.e vibration mechanisms of the centrifugal pump were studied by numerical simulation and experiment measurement [3][4][5][6][7][8].Fiebig and Korzyb [9] performed numerical simulation on the structure vibration in a centrifugal pump.Jiang et al. [10] numerically simulated the internal flow-induced vibration and noise of a centrifugal pump based on LES.
e results indicated that it is feasible to predict the flow-induced noise in rotating machinery by the fluid-structure coupling simulation.Dai et al. [11] measured the vibration of pump as turbine under different rotation speeds and flow rates.It was found that the level of vibration rises with the increase of rotation speed and flow rate.Sun et al. [12] and Zhou [13] studied the influence of off-design condition deviation on vibration.Duan et al. [14] and González et al. [15] analyzed the vibration signal and the cause of the vibration of the centrifugal pump.Wang et al. [16] measured and analyzed the pressure pulsation, vibration, and noise characteristic of a multistage centrifugal pump under different flow rates.
However, the experimental research studies on vibration of centrifugal pump with vaned diffuser are relatively less so far.erefore, the vibration characteristics of a centrifugal pump with vaned diffuser, whose specific speed is 190, were measured and analyzed to provide the basis for the subsequent structure optimization and vibration reduction.), where units of flow rate, rotational speed, and head are m 3 /s, r/min, and m, respectively).e structure diagram of the centrifugal pump with vaned diffuser is shown in Figure 1.

Experimental Bench
e pump body, including suction chamber and discharge chamber, was directly casted by stainless steel.In order to improve flow surface accuracy, the impeller and vaned diffuser were firstly formed by 3D printing and then casted by stainless steel.e wax molds of impeller and vaned diffuser are shown in Figure 2(a).
e impeller, vaned diffuser, and pump body after casting are shown in Figure 2(b).

Experimental Bench.
e experiment sketch and bench are shown in the Figures 3(a) and 3(b), respectively.Experiment equipment of energy performance includes a motor, a flow meter, two pressure transmitters, a three-phase PWM digital power meter, etc. e flow rate, head, and power were measured severally by the flow meter, pressure transmitters, and digital power meter in the experiment.All of the experimental data were managed and analyzed by the data acquisition instrument.
Energy performance curves of the centrifugal pump with vaned diffuser are shown in Figure 4.It can be observed from Figure 4 that under the design flow rate (i.e., Q d ), the head of the pump is 15.03 m and the efficiency is 71.47%.Under 0.8Q d , the head of the pump is 17.26 m and the efficiency is 70.25%.Under 1.2Q d , the head of the pump is 12.59 m and the efficiency is 65.88%.e maximum efficiency is 71.71% when the flow rate of the pump is 233 m 3 /h and the head is 16.92 m.

2.3.
e Arrangement of Monitoring Points.Monitoring points M1∼M16 were selected to measure vibration characteristics of the centrifugal pump with vaned diffuser.
ese points were at the outlet flange (M1), the inlet flange (M2), the bearing casings (M3 and M4), the pump base, and motor base (M5∼M8).e front pump cavity, which is shown in Figure 5(b), is between pump body and front cover shroud.Corresponding to this, the rear pump cavity shown in Figure 5(c) is between pump body and rear cover shroud.Monitoring points M9∼M12 and M13∼M16 were located on the surface of front pump cavity and rear pump cavity, respectively.e positions of the sixteen monitoring points are shown in Table 1.

Experimental Results and Analysis of Vibration
e vibration velocity measured by the three-phase transducer concludes the horizontal direction, the axial direction, and the vertical direction, that is, the vibration velocity in the X, Y, and Z direction.

Amplitude of Vibration Velocity.
e vibration intensity is proportional to the vibration velocity when the vibration frequency is within the range of the intermediate frequency.
e centrifugal pump is an intermediate frequency machine, so the vibration velocity can commendably reflect the vibration level of the pump.e vibration velocity was selected as a parameter to analyze the vibration of the pump.Figure 6 shows the vibration velocities at monitoring points M1∼M8 of the centrifugal pump with vaned diffuser under different flow rates.
(1) e amplitude ranges of vibration velocity in the X, Y, and Z direction are expanded gradually, and the trends of amplitude of vibration velocity are similar.e amplitude of the vibration velocity decreases gradually with the increase of flow rate from 0.2Q d to 0.6Q d .e amplitudes of vibration velocity at majority monitoring points increase when the flow rate increases to 0.8Q d .e amplitude of the vibration velocity decreases when flow rate increases to 1.2Q d , and there is a certain increase when the flow rate increases from 1.2Q d to 1.3Q d .
(2) e range of amplitude of the vibration velocity in the Z direction is more extensive than that in the X direction and Y direction, i.e., the difference in the Z direction between maximum and minimum value of the amplitude is the largest.Except for difference of vibration velocity value, the change trends of the vibration velocity at each monitoring point are consistent.(3) In three directions, the minimum vibration velocity amplitudes of M1∼M8 appear in the range of 1.0Q d to 1.2Q d .And the vibration amplitudes at monitoring point M5 (right side of pump base) are the smallest.ese amplitudes are 0.35 mm/s in the X direction, 0.38 mm/s in the Y direction, and 0.3 mm/ s in the Z direction, respectively.(4) e amplitude of vibration velocity at the outlet flange (M1) is higher than that at other monitoring points.ere is a noticeable rise in amplitudes of vibration velocity in the Z and Y direction from 0.8Q d to 1.0Q d and the amplitudes of vibration in the Y direction increase by 75% because the outlet flange is located at the end of the diffuser section of pump body, whose vibration is more affected by pressure pulsation at the outlet and flow vortex in diffuser section.Shock and Vibration 3 M1∼M8.Amplitudes of vibration velocity at M9∼ M16 present a regular tendency, that is, decreasing firstly and then increasing slightly with the increase of flow rate.
(2) Vibration velocities at the monitoring points on the pump body are mainly in the X direction.e vibration at monitoring points M9∼M16 is mainly caused by the shunt phenomenon when the fluid  flows through the impeller and the vaned diffuser and the impact of the fluid on the pump body.(3) In the X direction, the amplitude of vibration velocity at M10 is relatively larger, whose value is 2.1 mm/s.ere are drastic changes in vibration velocity at M10, and the minimum value of vibration velocity is 0.47 mm/s because monitoring point M10 is located near the outlet of the front pump cavity, whose vibration velocity is greatly affected by the internal flow of diffuser section.e amplitude of vibration velocity at M10 is larger than that at other monitoring points.

Frequency Spectrum of Vibration.
e frequency spectrums of vibration in each X, Y, and Z direction are compared and analyzed.
e frequency spectrums of vibration at M1∼M8 and M9∼M16 are shown in Figures 8 and 9.
It can be observed from Figure 8 that there are relatively more excitation frequencies at monitoring points M1∼M8, and the main excitation frequency is rotating frequency (25 Hz), 2nd harmonic, 3rd harmonic, 4th harmonic, 5th harmonic (i.e., blade passing frequency), and 6th harmonic of rotating frequency.e amplitude of vibration velocity at outlet flange (M1) is larger than that at other monitoring points, and a wide frequency band of vibration appears at 600 Hz at M1. e vibration at M1 includes flow-induced vibration and mechanical vibration because outlet flange is rigidly connected with outlet pipes and the vibration of the outlet pipeline passes to M1 through the pipeline.In the X, Y, and Z directions, there is high frequency vibration that is produced by the overlap between the natural frequency of mechanical force and flow force, which is related to mechanical vibration and vibration through pipeline.

Shock and Vibration
Moreover, the mechanical vibration at pump foot (M5 and M6) is relatively smaller, and amplitudes of vibration at M5 and M6 are lower than those at other monitoring points because the pump foots are fixed by foundation bolts.
It can be indicated from Figure 9 that the vibration in the X and Y direction at the outside of the pump body (M9∼M16) is smaller than that in the Z direction.e main direction of vibration is the Z direction, which is mainly caused by the mechanical vibration.
For flow-induced vibration, the main vibration frequency is the rotating frequency (25 Hz), 2nd harmonic (50 Hz), 3rd harmonic (75 Hz), 4th harmonic (100 Hz), and 5th harmonic of rotating frequency (125 Hz). e monitoring points at front pump cavity are more susceptible to flow-induced vibration than those in rear pump cavity.e monitoring points in rear pump cavity are located on the pump cover, which makes the vibration more affected by mechanical vibration.So the high-frequency vibration is easy to appear at those monitoring points.
Figure 10 shows the frequency spectrum of vibration in X, Y, and Z direction at M1∼M8.
As can be observed in Figure 10, the main frequency at outlet flange (M1) and inlet flange (M2) is 5th harmonic of rotating frequency (125 Hz), which is the same with blade passing frequency.e secondary frequencies are 3rd harmonic of rotating frequency (75 Hz) and 4th harmonic of rotating frequency (100 Hz). e vibration at M1 and M2 is mainly horizontal vibration, and the amplitude of the vibration in the X and Y direction is much higher than that in the Z direction.A wide frequency band of vibration caused by the vibration of pipeline appears in the range of 400∼500 Hz at M1, and the amplitude in the Y direction is the maximum.
ere is high frequency vibration at M2 in the range of 800 Hz∼1000 Hz, which is caused by the mechanical vibration.Figures 10(c) and 10(d) show the vibration at M3 and M4. e vibration velocity in the X direction at M3 and M4 is larger than that in the Y and Z direction.e main frequency at M3 is the 3rd harmonic of rotating frequency (75 Hz). e main frequency at M4 is the 5th harmonic of rotating frequency (125 Hz), and the secondary frequency is the 3rd harmonic of rotating frequency (75 Hz). e vibrations at M3 and M4 are mainly radial, which is caused by the excitation force of imbalance of the rotor.
e main frequencies at the pump foot (M5 and M6) and motor base (M7 and M8) are the rotating frequency (25 Hz), 3rd harmonic of rotating frequency (75 Hz), and 5th harmonic of rotating frequency (125 Hz).ere are differences in the distribution of frequency.
For monitoring points M7 and M8, the peaks of vibration velocity at the rotating frequency (25 Hz) are larger than those at other main frequencies.is is because the monitoring points M7 and M8 are arranged on the motor base and mainly affected by the vibration of the motor in which main frequencies are the same with rotating frequency.For monitoring points M5 and M6, the peak of vibration velocity at 5th harmonic of rotating frequency (i.e., blade passing frequency) is larger than that at other main frequencies because monitoring points M5 and M6 are arranged on the pump body base, which is mainly affected by the pressure pulsations of the fluid.

Vibration Intensity.
Vibration intensity is an important parameter that is used to evaluate the vibration state of machine.
e calculated value of the vibration intensity V max is the maximum value of the root mean square of the vibration velocity in the X, Y, and Z direction under 0.8Q d , 1.0Q d , and 1.2Q d and can be obtained by the following equation: where N is the number of discrete points of the measured signal, v is the vibration velocity of the pump, and V ims is the root mean square of the vibration velocity.e vibration intensities of each monitoring point are shown in Figure 11.
e vibration intensity at the outlet flange (M1) is larger than that at other monitoring points, and the vibration intensity at the inlet flange (M2) is 54% of that at M1.According to the above analysis, the main frequencies at M1 and M2 are both 5th harmonic of rotating frequency (125 Hz), which is the same with blade passing frequency, and the vibrations at those monitoring points are mainly affected by the pressure pulsations of the fluid.But M1 is additionally affected by the diffusion impact and flow separation that happen in the diffuser section of the pump, which leads to the increase of the vibration intensity.
Comparing the vibration intensities on both sides at bearing casings (M3 and M4), there is a significant difference in the magnitude of the vibration intensity, and the vibration intensity at M4 is larger than that at M3. e vibration at monitoring points M3 and M4 are mainly affected by the motor.And the monitoring point M4 is placed closer to the motor so that the vibration intensity at M4 is larger than that at M3. e average vibration intensity on the bearing is 0.76 mm/s, which is only lower than the vibration intensity at the outlet flange.
For the base of pump and motor, the average vibration intensity on the pump bases (M5 and M6) is 0.57 mm/s, and the average vibration intensity on the motor bases (M7 and M8) is 0.69 mm/s.And both are lower than the average vibration intensity on the bearing casings.
e vibration intensity distributing in the front pump cavity (M9∼M12) is not uniform.e vibration intensity at M10 is the maximum because monitoring M10 is located at the upper side of front pump cavity, which is affected by the unstable flow in the diffuser section of the pump.e average vibration intensity on pump body is 0.52 mm/s, which is the lowest.
Because the bearing casings could transmit vibration energy between two vibration sources (i.e., motor and pump), M3 and M4 at the bearing casing were selected as the main monitoring points to further analyze the vibration state of the pump.Table 2 shows the vibration intensities at M3 and M4 in the three directions under 0.8Q d , 1.0Q d , and 1.2Q d .
It can be indicated from Table 2 that the vibration intensities in the X and Z direction are larger than those in the Y direction.And the maximum of the vibration intensity at M4 under 0.8Q d is 1.27 mm/s.e vibration mainly happens in radial direction because the vibration of the motor is generated by the excitation force of imbalance of the rotor and the vibration of the pump is caused by the imbalance when the impeller rotates.
e average vibration intensity in the X direction under 0.8Q d , 1.0Q d , and 1.2Q d is 0.95 mm/s, 0.7 mm/s, and 0.63 mm/s, respectively.And the average vibration intensity in the Z direction under 0.8Q d , 1.0Q d , and 1.2Q d is 0.78 mm/ s, 0.76 mm/s, and 0.71 mm/s, respectively.e vibration intensity gradually decreases with the increase of flow rate.It might be because the internal unsteady flow and the flowinduced vibration are serious when the pump is operated under low flow rate, and the flow-induced vibration decreases with the increase of flow rate.e vibration intensity in the X direction under 1.2Q d is smaller than that in the Z direction because of the imbalance caused by the outlet of the pump body.

Conclusions
In this research, an experimental bench of a centrifugal pump with vane diffuser was built and several monitoring points were located at the pump base, motor base, flanges, bearing casings, and pump body.e energy performance and vibration characteristics of the pump under different flow rates were measured.e vibration velocity, vibration frequency domain, and vibration intensity of the pump were analyzed.
e maximum efficiency is 71.71% when the flow rate of the pump is 233 m 3 /h and the head is 16.92 m.Under 1.0Q d , the head of the pump is 15.03 m and the efficiency of the Shock and Vibration pump is 71.47%.Under 0.8Q d , the head of the pump is 17.26 m and the efficiency of the pump is 70.25%.Under 1.2Q d , the head of the pump is 12.59 m and the efficiency of the pump is 65.88%.
Analyzing frequency domain spectrum of vibration, the flow-induced vibration and mechanical vibration are the main vibration source in the centrifugal pump with vane diffuser.
e vibration velocity in the radial direction is larger, and the vibration velocity in axial direction is relatively smaller.
Based on the vibration intensity at monitoring points, the vibration intensity at the outlet flange is largest and the vibration intensities at both sides of bearing casing are smaller than those at the outlet flange and larger than those at the motor base.e vibration intensity at the motor base is larger than that at pump base, and the vibration intensity at the pump body is the lowest.
e vibration intensity of monitoring point M4 in the X direction under 0.8Q d is 1.27 mm/s, which is the maximum under three flow rates.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Figure 7 Figure 1 :Figure 2 :Figure 3 :
Figure7shows the amplitudes of vibration velocity in the X, Y, and Z direction at monitoring points M9∼M16.(1)Comparing Figures6 and 7, amplitudes of vibration velocity at M9∼M16 are generally lower than those at

Figure 4 :Figure 5 :
Figure 4: Energy performance curve of the centrifugal pump with vaned diffuser.

Figure 6 :
Figure 6: Amplitudes of vibration velocity at M1∼M8 in the (a) X direction, (b) Y direction, and (c) Z direction.

Figure 11 :
Figure 11: Vibration intensity at each monitoring point.

Table 1 :
Arrangement of vibration monitoring points.