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

Authors: Kai Wang; Xin Lu; Xianghui He
Journal: Shock and Vibration
 (2018)

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## Abstract

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. The results indicate that when flow rate of the pump is 270 m3/h, the head is 15.03 m and the efficiency is 71.47%. The maximum efficiency is 71.71% when the flow rate of the pump is 233 m3/h and the head is 16.92 m. And a wide frequency band of vibration appears at 600 Hz at outlet flange of the pump. The vibration intensity at the outlet flange is largest. The vibration intensities at both sides of bearing casing are slighter than those at outlet flange and larger than those at motor base. The vibration intensity at the motor base is larger than that at pump base, and the vibration intensity at the pump body is the lowest. The vibration intensity of monitoring point M4 in the X direction under 0.8Qd is 1.27 mm/s, which is the maximum under three flow rates.


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## Body

## 1. Introduction

The vibration characteristics of centrifugal pump affect its safety in engineering application. The 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. The vibration mechanisms of the centrifugal pump were studied by numerical simulation and experiment measurement [3–8]. 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. The 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. Therefore, 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.


## 2. Experimental Bench

### 2.1. A Centrifugal Pump with Vaned Diffuser

Design parameters of a centrifugal pump with vaned diffuser are as follows. The design flow rateQd is 270 m3/h, the design head Hd is 15 m, the rotational speed n is 1450 r/min, and the specific speed ns is 190 (ns=3.65nQ/H3/4, where units of flow rate, rotational speed, and head are m3/s, r/min, and m, respectively). The structure diagram of the centrifugal pump with vaned diffuser is shown in Figure 1. The 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. The wax molds of impeller and vaned diffuser are shown in Figure 2(a). The impeller, vaned diffuser, and pump body after casting are shown in Figure 2(b).Figure 1
Structure of the centrifugal pump with vaned diffuser.Figure 2
Component of centrifugal pump. (a) Wax models of impeller and vaned diffuser. (b) Component after casting.
(a)
(b)


### 2.2. Experimental Bench

The experiment sketch and bench are shown in the Figures3(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. The 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.Figure 3
(a) Sketch of the experiment bench. (b) Experiment bench of the centrifugal pump with vaned diffuser.
(a)
(b)Energy performance curves of the centrifugal pump with vaned diffuser are shown in Figure4. It can be observed from Figure 4 that under the design flow rate (i.e., Qd), the head of the pump is 15.03 m and the efficiency is 71.47%. Under 0.8Qd, the head of the pump is 17.26 m and the efficiency is 70.25%. Under 1.2Qd, the head of the pump is 12.59 m and the efficiency is 65.88%. The maximum efficiency is 71.71% when the flow rate of the pump is 233 m3/h and the head is 16.92 m.Figure 4
Energy performance curve of the centrifugal pump with vaned diffuser.


### 2.3. The Arrangement of Monitoring Points

Monitoring points M1∼M16 were selected to measure vibration characteristics of the centrifugal pump with vaned diffuser.These 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).The front pump cavity, which is shown in Figure5(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.Figure 5
Arrangement of vibration monitoring points: (a) M1∼M8, (b) M9∼M11, and (c) M14∼M16.
(a)
(b)
(c)The positions of the sixteen monitoring points are shown in Table1.Table 1
Arrangement of vibration monitoring points.
Monitoring point
M1
M2
M3
M4
Location
Outlet flange
Inlet flange
Left side of bearing casings
Right side of bearing casings
Monitoring point
M5
M6
M7
M8
Location
Right side of pump base
Left side of pump base
Left side of motor base
Right side of motor base
Monitoring point
M9
M10
M11
M12
Location
Right side of front pump cavity
Upside of front pump cavity
Left side of front pump cavity
Downside of front pump cavity
Monitoring point
M13
M14
M15
M16
Location
Left side of rear pump cavity
Upside of rear pump cavity
Right side of rear pump cavity
Downside of rear pump cavity


## 2.1. A Centrifugal Pump with Vaned Diffuser

Design parameters of a centrifugal pump with vaned diffuser are as follows. The design flow rateQd is 270 m3/h, the design head Hd is 15 m, the rotational speed n is 1450 r/min, and the specific speed ns is 190 (ns=3.65nQ/H3/4, where units of flow rate, rotational speed, and head are m3/s, r/min, and m, respectively). The structure diagram of the centrifugal pump with vaned diffuser is shown in Figure 1. The 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. The wax molds of impeller and vaned diffuser are shown in Figure 2(a). The impeller, vaned diffuser, and pump body after casting are shown in Figure 2(b).Figure 1
Structure of the centrifugal pump with vaned diffuser.Figure 2
Component of centrifugal pump. (a) Wax models of impeller and vaned diffuser. (b) Component after casting.
(a)
(b)


## 2.2. Experimental Bench

The experiment sketch and bench are shown in the Figures3(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. The 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.Figure 3
(a) Sketch of the experiment bench. (b) Experiment bench of the centrifugal pump with vaned diffuser.
(a)
(b)Energy performance curves of the centrifugal pump with vaned diffuser are shown in Figure4. It can be observed from Figure 4 that under the design flow rate (i.e., Qd), the head of the pump is 15.03 m and the efficiency is 71.47%. Under 0.8Qd, the head of the pump is 17.26 m and the efficiency is 70.25%. Under 1.2Qd, the head of the pump is 12.59 m and the efficiency is 65.88%. The maximum efficiency is 71.71% when the flow rate of the pump is 233 m3/h and the head is 16.92 m.Figure 4
Energy performance curve of the centrifugal pump with vaned diffuser.


## 2.3. The Arrangement of Monitoring Points

Monitoring points M1∼M16 were selected to measure vibration characteristics of the centrifugal pump with vaned diffuser.These 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).The front pump cavity, which is shown in Figure5(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.Figure 5
Arrangement of vibration monitoring points: (a) M1∼M8, (b) M9∼M11, and (c) M14∼M16.
(a)
(b)
(c)The positions of the sixteen monitoring points are shown in Table1.Table 1
Arrangement of vibration monitoring points.
Monitoring point
M1
M2
M3
M4
Location
Outlet flange
Inlet flange
Left side of bearing casings
Right side of bearing casings
Monitoring point
M5
M6
M7
M8
Location
Right side of pump base
Left side of pump base
Left side of motor base
Right side of motor base
Monitoring point
M9
M10
M11
M12
Location
Right side of front pump cavity
Upside of front pump cavity
Left side of front pump cavity
Downside of front pump cavity
Monitoring point
M13
M14
M15
M16
Location
Left side of rear pump cavity
Upside of rear pump cavity
Right side of rear pump cavity
Downside of rear pump cavity


## 3. Experimental Results and Analysis of Vibration

The 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 theX, Y, and Z direction.


### 3.1. Amplitude of Vibration Velocity

The vibration intensity is proportional to the vibration velocity when the vibration frequency is within the range of the intermediate frequency. The centrifugal pump is an intermediate frequency machine, so the vibration velocity can commendably reflect the vibration level of the pump. The vibration velocity was selected as a parameter to analyze the vibration of the pump. Figure6 shows the vibration velocities at monitoring points M1∼M8 of the centrifugal pump with vaned diffuser under different flow rates.(1)
The amplitude ranges of vibration velocity in theX, Y, and Z direction are expanded gradually, and the trends of amplitude of vibration velocity are similar. The amplitude of the vibration velocity decreases gradually with the increase of flow rate from 0.2Qd to 0.6Qd. The amplitudes of vibration velocity at majority monitoring points increase when the flow rate increases to 0.8Qd. The amplitude of the vibration velocity decreases when flow rate increases to 1.2Qd, and there is a certain increase when the flow rate increases from 1.2Qd to 1.3Qd.(2)
The range of amplitude of the vibration velocity in theZ 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 1.0Qd to 1.2Qd. And the vibration amplitudes at monitoring point M5 (right side of pump base) are the smallest. These 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)
The amplitude of vibration velocity at the outlet flange (M1) is higher than that at other monitoring points. There is a noticeable rise in amplitudes of vibration velocity in theZ and Y direction from 0.8Qd to 1.0Qd 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.Figure 6
Amplitudes of vibration velocity at M1∼M8 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)Figure7 shows 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 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 theX direction. The 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 theX direction, the amplitude of vibration velocity at M10 is relatively larger, whose value is 2.1 mm/s. There 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. The amplitude of vibration velocity at M10 is larger than that at other monitoring points.Figure 7
Amplitudes of vibration velocity at M9∼M16 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)


### 3.2. Frequency Spectrum of Vibration

The frequency spectrums of vibration in eachX, Y, and Z direction are compared and analyzed. The frequency spectrums of vibration at M1∼M8 and M9∼M16 are shown in Figures 8 and 9.Figure 8
Frequency domain of vibration at M1∼M8 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)Figure 9
Frequency domain of vibration at M9∼M16 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)It can be observed from Figure8 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.The 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. The 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 theX, 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.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 Figure9 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. The 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). The monitoring points at front pump cavity are more susceptible to flow-induced vibration than those in rear pump cavity. The 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.Figure10 shows the frequency spectrum of vibration in X, Y, and Z direction at M1∼M8.Figure 10
Frequency domain of vibration in theX, Y, and Z direction at (a) M1, (b) M2, (c) M3, (d) M4, (e) M5, (f) M6, (g) M7, and (h) M8.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)As can be observed in Figure10, 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. The secondary frequencies are 3rd harmonic of rotating frequency (75 Hz) and 4th harmonic of rotating frequency (100 Hz). The 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. There is high frequency vibration at M2 in the range of 800 Hz∼1000 Hz, which is caused by the mechanical vibration.Figures10(c) and 10(d) show the vibration at M3 and M4. The vibration velocity in the X direction at M3 and M4 is larger than that in the Y and Z direction. The main frequency at M3 is the 3rd harmonic of rotating frequency (75 Hz). The 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). The vibrations at M3 and M4 are mainly radial, which is caused by the excitation force of imbalance of the rotor.The 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). There 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. This 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.


### 3.3. Vibration Intensity

Vibration intensity is an important parameter that is used to evaluate the vibration state of machine. The calculated value of the vibration intensityVmax is the maximum value of the root mean square of the vibration velocity in the X, Y, and Z direction under 0.8Qd, 1.0Qd, and 1.2Qd and can be obtained by the following equation:(1)Vims=1N∫n=0N−1v2n,where N is the number of discrete points of the measured signal, v is the vibration velocity of the pump, and Vims is the root mean square of the vibration velocity.The vibration intensities of each monitoring point are shown in Figure11.Figure 11
Vibration intensity at each monitoring point.The 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. The 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. The 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.The vibration intensity distributing in the front pump cavity (M9∼M12) is not uniform. The 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. The 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. Table2 shows the vibration intensities at M3 and M4 in the three directions under 0.8Qd, 1.0Qd, and 1.2Qd.Table 2
Vibration intensity at monitoring points M3 and M4 (unit: mm/s).
Direction
Flow rate
M3
M4
X
0.8Qd
0.63
1.27
1.0Qd
0.56
0.85
1.2Qd
0.53
0.74
Y
0.8Qd
0.59
0.62
1.0Qd
0.52
0.53
1.2Qd
0.41
0.45
Z
0.8Qd
0.63
0.93
1.0Qd
0.64
0.88
1.2Qd
0.59
0.83It can be indicated from Table2 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 0.8Qd is 1.27 mm/s. The 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.The average vibration intensity in theX direction under 0.8Qd, 1.0Qd, and 1.2Qd 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 0.8Qd, 1.0Qd, and 1.2Qd is 0.78 mm/s, 0.76 mm/s, and 0.71 mm/s, respectively. The vibration intensity gradually decreases with the increase of flow rate. It might be because the internal unsteady flow and the flow-induced vibration are serious when the pump is operated under low flow rate, and the flow-induced vibration decreases with the increase of flow rate. The vibration intensity in the X direction under 1.2Qd is smaller than that in the Z direction because of the imbalance caused by the outlet of the pump body.


## 3.1. Amplitude of Vibration Velocity

The vibration intensity is proportional to the vibration velocity when the vibration frequency is within the range of the intermediate frequency. The centrifugal pump is an intermediate frequency machine, so the vibration velocity can commendably reflect the vibration level of the pump. The vibration velocity was selected as a parameter to analyze the vibration of the pump. Figure6 shows the vibration velocities at monitoring points M1∼M8 of the centrifugal pump with vaned diffuser under different flow rates.(1)
The amplitude ranges of vibration velocity in theX, Y, and Z direction are expanded gradually, and the trends of amplitude of vibration velocity are similar. The amplitude of the vibration velocity decreases gradually with the increase of flow rate from 0.2Qd to 0.6Qd. The amplitudes of vibration velocity at majority monitoring points increase when the flow rate increases to 0.8Qd. The amplitude of the vibration velocity decreases when flow rate increases to 1.2Qd, and there is a certain increase when the flow rate increases from 1.2Qd to 1.3Qd.(2)
The range of amplitude of the vibration velocity in theZ 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 1.0Qd to 1.2Qd. And the vibration amplitudes at monitoring point M5 (right side of pump base) are the smallest. These 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)
The amplitude of vibration velocity at the outlet flange (M1) is higher than that at other monitoring points. There is a noticeable rise in amplitudes of vibration velocity in theZ and Y direction from 0.8Qd to 1.0Qd 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.Figure 6
Amplitudes of vibration velocity at M1∼M8 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)Figure7 shows 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 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 theX direction. The 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 theX direction, the amplitude of vibration velocity at M10 is relatively larger, whose value is 2.1 mm/s. There 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. The amplitude of vibration velocity at M10 is larger than that at other monitoring points.Figure 7
Amplitudes of vibration velocity at M9∼M16 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)


## 3.2. Frequency Spectrum of Vibration

The frequency spectrums of vibration in eachX, Y, and Z direction are compared and analyzed. The frequency spectrums of vibration at M1∼M8 and M9∼M16 are shown in Figures 8 and 9.Figure 8
Frequency domain of vibration at M1∼M8 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)Figure 9
Frequency domain of vibration at M9∼M16 in the (a)X direction, (b) Y direction, and (c) Z direction.
(a)
(b)
(c)It can be observed from Figure8 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.The 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. The 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 theX, 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.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 Figure9 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. The 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). The monitoring points at front pump cavity are more susceptible to flow-induced vibration than those in rear pump cavity. The 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.Figure10 shows the frequency spectrum of vibration in X, Y, and Z direction at M1∼M8.Figure 10
Frequency domain of vibration in theX, Y, and Z direction at (a) M1, (b) M2, (c) M3, (d) M4, (e) M5, (f) M6, (g) M7, and (h) M8.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)As can be observed in Figure10, 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. The secondary frequencies are 3rd harmonic of rotating frequency (75 Hz) and 4th harmonic of rotating frequency (100 Hz). The 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. There is high frequency vibration at M2 in the range of 800 Hz∼1000 Hz, which is caused by the mechanical vibration.Figures10(c) and 10(d) show the vibration at M3 and M4. The vibration velocity in the X direction at M3 and M4 is larger than that in the Y and Z direction. The main frequency at M3 is the 3rd harmonic of rotating frequency (75 Hz). The 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). The vibrations at M3 and M4 are mainly radial, which is caused by the excitation force of imbalance of the rotor.The 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). There 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. This 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.


## 3.3. Vibration Intensity

Vibration intensity is an important parameter that is used to evaluate the vibration state of machine. The calculated value of the vibration intensityVmax is the maximum value of the root mean square of the vibration velocity in the X, Y, and Z direction under 0.8Qd, 1.0Qd, and 1.2Qd and can be obtained by the following equation:(1)Vims=1N∫n=0N−1v2n,where N is the number of discrete points of the measured signal, v is the vibration velocity of the pump, and Vims is the root mean square of the vibration velocity.The vibration intensities of each monitoring point are shown in Figure11.Figure 11
Vibration intensity at each monitoring point.The 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. The 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. The 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.The vibration intensity distributing in the front pump cavity (M9∼M12) is not uniform. The 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. The 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. Table2 shows the vibration intensities at M3 and M4 in the three directions under 0.8Qd, 1.0Qd, and 1.2Qd.Table 2
Vibration intensity at monitoring points M3 and M4 (unit: mm/s).
Direction
Flow rate
M3
M4
X
0.8Qd
0.63
1.27
1.0Qd
0.56
0.85
1.2Qd
0.53
0.74
Y
0.8Qd
0.59
0.62
1.0Qd
0.52
0.53
1.2Qd
0.41
0.45
Z
0.8Qd
0.63
0.93
1.0Qd
0.64
0.88
1.2Qd
0.59
0.83It can be indicated from Table2 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 0.8Qd is 1.27 mm/s. The 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.The average vibration intensity in theX direction under 0.8Qd, 1.0Qd, and 1.2Qd 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 0.8Qd, 1.0Qd, and 1.2Qd is 0.78 mm/s, 0.76 mm/s, and 0.71 mm/s, respectively. The vibration intensity gradually decreases with the increase of flow rate. It might be because the internal unsteady flow and the flow-induced vibration are serious when the pump is operated under low flow rate, and the flow-induced vibration decreases with the increase of flow rate. The vibration intensity in the X direction under 1.2Qd is smaller than that in the Z direction because of the imbalance caused by the outlet of the pump body.


## 4. 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. The energy performance and vibration characteristics of the pump under different flow rates were measured. The vibration velocity, vibration frequency domain, and vibration intensity of the pump were analyzed.The maximum efficiency is 71.71% when the flow rate of the pump is 233 m3/h and the head is 16.92 m. Under 1.0Qd, the head of the pump is 15.03 m and the efficiency of the pump is 71.47%. Under 0.8Qd, the head of the pump is 17.26 m and the efficiency of the pump is 70.25%. Under 1.2Qd, 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. The 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. The vibration intensity at the motor base is larger than that at pump base, and the vibration intensity at the pump body is the lowest.The vibration intensity of monitoring point M4 in theX direction under 0.8Qd is 1.27 mm/s, which is the maximum under three flow rates.



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*Source: 9486536-2018-12-24.xml*