Investigation of effect of pump rotational speed on performance and detection of cavitation within a centrifugal pump using vibration analys

Investigation of effect of pump rotational speed on performance and
detection of cavitation within a centrifugal pump using vibration analysis
Ahmed Ramadhan Al-Obaidi *
Department of Mechanical Engineering, Faculty of Engineering, Mustansiriyah University, Baghdad, Iraq
A R T I C L E I N F O
Keywords:
Energy
Industrial engineering
Mechanical engineering
Applied sciences
Natural sciences
Centrifugal pump
Pump rotational speed
Cavitation
Vibration technique
Frequency domain analysis
Time domain analysis
A B S T R A C T
Cavitation is an essential problem that occurs in any pump. It highly contributes to deteriorating the performance
of the pump. In industrial applications, it is important to detect and decrease the effect of the cavitation in pumps.
In this work, detecting and diagnosing the cavitation phenomenon within centrifugal pumps using vibration
technique was investigated. The results obtained for vibration signal in both time and frequency domains were
analysed in order to gain a better understanding about the detection of cavitation in the pumps in question. The
effect of different operating conditions including various flow rates and pump rotational speeds related to the
cavitation were measured. Different statistical features in time domain analysis (TDA) and also the Fast Fourier
Transform (FFT) technique for frequency domain analysis (FDA) were applied.
1. Introduction
The origin of vibration in centrifugal pumps might occur from various
types of sources, including hydraulic and mechanical excitation forces [1,
2, 3, 4, 5, 6]. This leads to an increase in the levels of vibration that might
decrease the performance of the pump and hence results in causing
damage in the pump parts such as the impeller and volute. It may also
lead to decreasing the pumps bearing life and the seal failures [7, 8, 9,
10]. The measurements of vibration in centrifugal pumps can be utilised
for several applications including quality control and condition moni-
toring (CM) [11, 12, 13]. The hydraulic and mechanical sources of vi-
bration in centrifugal pumps occur as a result from several problems. This
comprises problems of flow distribution including high velocity, and
interaction between the rotating part such as impeller and the stationary
part such as the volute through the rotation of the impeller in the pump
particularly at volute tongue region. Furthermore, hydraulic sources of
vibration in centrifugal pumps includes blades passing forces, hydraulic
imbalance, recirculation flow, cavitation, system instabilities, water
hammer and so on [14]. Generally, as described in the experimental
setup in study four, the pumping system comprises several parts. This
pumping system includes the centrifugal pump, an electrical motor and
its related flow loop piping system such as pipes, elbows, fittings, and
valves. Even through regular operation conditions, various kinds of
physical processes create vibration such as hydraulic interaction with the
piping system, improper installation or maintenance, application for the
pump, and manufacturing designs and different types of faults [15].
Typically, the mechanical vibration sources in the pump includes several
sources such as pressure fluctuations created in the fluid, imbalance,
misalignment between shafts connections, and damaged bearings [16].
In addition, other mechanical sources incorporate mechanical forces,
improper usage of the pump as provided in the installation manual and
the conditions emerging from the pumps’ incorrect assembly and from
wear [17, 18]. When cavitation occurs in the different types of machines
(e.g. propellers, turbines, and various kinds of pumps), it leads to drop-
ping in pressure particularly at the eye of the impeller below the water
vapour pressure. As a result, this leads to increasing the level of noise and
vibration due to unstable flow which, in turn, causes an increase in the
pressure fluctuations within a pump [15]. When cavitation starts to occur
within the pump, the first formations of bubbles are very small leading to
the bubble collapse inside the pump. As cavitation continuous inside the
pump, the bubbles collapse then occurs close to the surface of the
impeller, which eventually erodes the impeller and hence, causes pitting
on the surface of the impeller and volute. Because the formation and
collapse of bubbles happen randomly, the incipience and development of
* Corresponding author.
E-mail address: ahmedram@uomustansiriyah.edu.iq.
Contents lists available at ScienceDirect
Heliyon
journal homepage: www.heliyon.com
https://doi.org/10.1016/j.heliyon.2019.e01910
Received 27 November 2018; Received in revised form 2 April 2019; Accepted 3 June 2019
2405-8440/© 2019 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Heliyon 5 (2019) e01910

cavitation can cause high noise and vibrations within the pump [15].
Over the last decade, there have been increasing interests in using con-
dition monitoring (CM) methods for detecting cavitation. There are
several reasons behind this method as it decreases the costs of machines
maintenance and hence, enhance productivity and safety in the industry.
In this study, the vibration signal is analysed as it is one important
technique in the condition monitoring of centrifugal pump in order to
early predict and diagnose the inception and development of cavitation
occurrence within the pump. Also in this research, the vibration signals
would be collected via the use of an accelerometer (vibration sensor) that
has been positioned close to the volute tongue region of the centrifugal
pump. The reason behind selecting this position is because this is a part in
the pump that has high effect due to the high interaction between the
rotating part (impeller) and stationary part (volute) as clearly shown that
in previous study. For this experimental work, in order to study the wide
range of operation conditions and also to detect the different levels of
cavitation, the centrifugal pump has been subjected to various flow rates
and pump rotational speeds the pump. The flow rate has been changed by
throttling the ball valve at the discharge pump side and then adjusted
step by step. Furthermore, the analysis of vibration signals under
different above operation conditions using time domain analysis (TDA)
and frequency domain analysis (FDA) are performed using MATLAB code
in the next sections. The sources of vibration in the centrifugal pump
during different operational conditions has been evaluated and then the
revealing of how the incipience and development of cavitation influences
the pump vibration level. Furthermore, it presents and discusses the
experimental outcomes of using vibration technique for monitoring
cavitation within the centrifugal pump on the experimental setup. Also,
the study would provide an analysis of the vibration signals in time
domain using time wave form analysis (TWFA). Then, it uses various
statistical features such as peak, RMS, peak-to-peak and variance values
in order to predict and diagnose the cavitation phenomenon under
various operation conditions. For further analysis of the characteristics of
cavitation phenomenon inside centrifugal pump, the vibration signal in
time domain is converted to frequency domain analysis (FDA) through
the use of (FFT) technique which can be suitable in predicting and
diagnosing cavitation in the pump. This study further focuses on ana-
lysing the vibration signal in frequency domain based on different range
of frequencies. Furthermore, it analyses the vibration amplitude in fre-
quency domain by using different features such as mean and RMS on the
vibration amplitude values. This analysis is essential in order to obtain a
better understanding and also more information regarding the detection
of the occurrence of cavitation within a pump for various frequency
ranges, and thus finding the sensitive frequency range for predicting
cavitation. Cavitation flows in centrifugal pumps have been investigated
in the literature using various approaches to predict cavitation conditions
as two-phase flow. These studies are by Zhang et al. [19] which studied
the vibration features in centrifugal pump that has a special slope in the
volute. In their work, they have proposed and analysed vibration char-
acteristics in the pump with a special slope volute to decrease the vi-
bration and offer a new technique to decrease vibration level in the
pump. They gained vibration signals at various flow rates and the
compared between the slope volute and conventional spiral volute pump.
The results have shown that the vibration level of slope volute pump was
lower than the conventional pump as illustrated in figure under different
frequency. Therefore, they have found using slope volute pump it can be
decrease efficiently the vibration level in the centrifugal pump. Suhane
[20] studied the effect of radial clearance on pressure pulsations by using
vibrations and noise signals in the centrifugal pump under different flow
and radial clearances between impeller and diffuser 1.5mm, 3.7mm,
6.8mm respectively. The author used horizontal type pump with diffuser
the impeller designed with eight blades and the diffuser composed of
seven blades. As a result, at low flow rate both vibration and noise levels
were low and they high under high flow rate, as well the vibration and
noise levels were minimum at the maximum radial clearance between
impeller and diffuser. In addition, the author observed that from
experimental outcomes when increasing the radial clearance, the lower
pressure fluctuations occur. Farokhzad et. al [21]. experimentally
investigated the relationship between vibration signal and fault diagnosis
within the centrifugal pump under different operating using conditions
monitoring system. They have been tested two different configurations
the first one was broken impeller and the second one was faulty seal
conditions. They collected vibration signals from the pump using the
accelerometer sensor which was positioned on the in the bearing of the
shaft. The results have shown that an important change in the trend of
vibration signal as a function of fault at various operating conditions. The
value of RMS for healthy pump conditions was on suitable status, but it
was increased due to the broken impeller and seal faulty on critical status.
Luo et al. [22] researched on statistical features of vibration signals in the
centrifugal pump. The parameters of the test pump were flow rate 50
m3
/h, head 32m, rotational speed 2900rpm, the number of blades 6,
impeller inlet and outlet diameters 75mm, and 174mm respectively. The
results have shown that when the pump works under flow instability
conditions, the dynamic characteristics of the pump were changed.
Therefore, the statistical analysis of vibration signal (probability density
factor PDF, Standard deviation, and Kurtosis) could be a useful technique
of predicting unstable flow in the pump. The statistical features of vi-
bration signal in time domain and frequency domain are a good indicator
for predicting intensity changes and the onset of cavitation in the pump.
Tan and Leong [23] experimentally studied detection of cavitation in the
centrifugal pump using vibration signal. They tested the pump under
three operating conditions including BEP, 90% of BEP and 80% of BEP.
The design parameters of the pump were six vanes, and the motor was
coupled to three phases with pump rotational speed of 2500rpm. The
results have shown that the vibration amplitude was a significant in-
crease under cavitation as compared to normal operating condition. The
possible reason for the increase the vibration amplitude during cavitation
was due to the formation and collapses the bubbles particularly in the eye
of an impeller. Zargar [24] detected cavitation within the centrifugal
pump related oil industry for cooling circulation water system. They have
detected cavitation phenomenon within a pump using condition moni-
toring system by analysis the vibration signal in time wave form and
frequency domain using FFT method. They have found that the trend of
vibration signal was suddenly increased under cavitation. Hence,
decrease in the performance of the pump. As seen in the above studies
and after looking at as well as studying the literature presented in this
work the flow field and cavitation phenomenon in the centrifugal pump
need more investigation. Therefore, in this current work, the hydraulic
pump performance and the internal flow of the centrifugal pump are
analysed under different operation conditions. The effect of various flow
rates and pump rotational speeds on the performance, internal flow and
detection of cavitation in the centrifugal pump are experimentally car-
ried out based on vibration analysis technique. Moreover, the vibration
signal within a centrifugal pump in both time and frequency domains are
also investigated in order to obtain more information regarding the
detection of cavitation in the pump using various Statistical Features.
Furthermore, studying different frequency ranges in frequency domain
analysis (FDA) on cavitation detection within the centrifugal pump also
investigated. The Experimental Setup for the Centrifugal Pump.
The main aims of this present study are to determine the pump per-
formance and detect cavitation in the centrifugal pump experimentally.
The detection of cavitation experimentally has been achieved by using
vibration through the use of accelerometer as well as pressure using two
pressure transducers at suction and discharge of the pump under the
different range of operation conditions. To achieve this aim experimen-
tally, it was essential to construct and design an appropriate experimental
setup for the centrifugal pump, where the designing of this experimental
setup would be discussed in more details in the next section.
Fig. 1 depicts the main different experimental setup components of
test rig setup of the centrifugal pump. The centrifugal pump can supply
water to the tank with a maximum pressure about 10bar. The selected
flow loop system was re-circulatory and included a plastic water tank,
A.R. Al-Obaidi Heliyon 5 (2019) e01910
2

PVC clear pipe and PVC connections components. The tank capacity has
been based on the maximum flow rate. The inlet pipe diameter of the
pump is 2 inches. Also, the outlet pipe diameter of the pump used is 1.25
inches. Thus, a reducing coupling of 1.25–1.5 inches has been used to
connect the outlet pipe to the water flow meter line because the diameter
of water flow meter is 1.5 inch. The tank is made of plastic with di-
mensions of 95 90 110cm. The entire section pipes are a transparent
pipe the reason behind that is to permit observation when the cavitation
occurs. There are several reasons behind selecting the latter type of pipe.
Firstly, the clear pipes are easier to install. Secondly, they are easy to
connect them and thirdly they are low cost as compared to the stainless-
steel pipes. Furthermore, the PVC pipes do not necessarily allow for
complicated tools to be used in connecting the different pipes together, as
the entire connections between pipes are made using a solvent welding
type (solvent cement and cleaning fluid) However, the PVC clear pipes
have some disadvantages such as lack of rigidity. The connections of the
flow loop of the centrifugal pump and the water tank are made through
use of various sizes of PVC pipes [25, 26].
2. Experimental
2.1. Effect of various flow rates to predict the performance and cavitation
within a centrifugal pump
For analysis purpose in this study, vibration technique has been used
in order to predict cavitation. The centrifugal pump was operated
experimentally at different flow rates (three stages of flow rates). The
first stage was at low flow rate, and the second stage was at design flow
rate and the last stage was at high flow rate as summarised in Table 1.
Pump rotational speed N ¼ 2755rpm was kept constant corresponding to
0.95Nd, where Nd represents the design pump rotational speed and it is
equal to 2900rpm, due to the maximum pump rotation speed for this
experimental setup which was 0.95 of Nd. The next section presents the
results of the pump performance and predicting cavitation that have been
obtained from experimental calculation based on the different flow rates.
One key aim in this experimental study is to calculate the pump head.
Therefore, several experimental measurements have been conducted to
find the pump performance under various operation conditions.
Furthermore, the suction and discharge pressures signals of the pump can
be obtained through the use of two pressure transducers at suction and
discharge sides of the centrifugal pump. The data includes pressure sig-
nals and calculated head are processed through use of MATLAB code as
shown that in next section.
2.2. Analysis on the instantaneous outlet pressure of the centrifugal pump
under various flow rates
Fig. 2 depicts the raw data of the instantaneous outlet pressure from
the centrifugal pump in time domain, under different flow rates starting
from 103 (l/min) to 378 (l/min) with pump rotatinal speed of 2755rpm.
It can be seen that the instantaneous outlet pressure signals changes as
the flow rate also change. Moreover, the magnitudes of the pressure
fluctuations decrease with increases in flow rate. The possible reasons
behind that are due to the hydraulic and mechanical losses as well as the
effect of the occurrence of cavitation leading to causing more unstable
flow within the pump. However, it can be observed that these changes in
the instantaneous outlet pressure do not provide a clearer picture
regarding the detection of cavitation in the pump. Therefore, further
investagations are then required to detect cavitation using different sta-
tistical features in order to analyse the instantaneous outlet pressure
signals in time domain in the next section.
2.3. Calculate the head and NPSH of the centrifugal pump under various
flow rates
Time domain analysis (TDA) is used to analyse the raw data of the
instantaneous head under various flow rates with different statistical
features. Fig. 3 depicts the trend of peak, minimum and RMS features for
the head under different flow rates from 103 (l/min) to 378 (l/min) with
pump rotatinal speed of 2755rpm. It is evident that the above mentioned
head features in the pump all follow a downward continuous trend with
increasing flow rate due to the same reasons given above. Moreover, the
trend for all the above features rapidly decreases when the pump oper-
ates at flow rate higher than 350 (l/min). The reasons are because of the
high intraction between impeller and volute and due to the occurrence
and development of cavitation within a pump.
Fig. 4 depicts the mean head of the pump under various flow rates
measurements which has also been summarised in Table 1-with a pump
rotational speed of N ¼ 2755rpm. From this figure, it can be clearly be
seen that the changes in the pumps’ flow structure as flow rate increased
from lower to the higher value and the interesting point is here to notice
the change of head in the pump. It can be observed that the trend of head
gradually decreases when flow rate increases. Moreover, from this figure,
it can be seen that the head is changing in a periodic manner as the
pressure changes in the pump. Due to three main possible reasons, the
first one is due to the high interaction between the impeller and tongue
volute region which generated by the impeller rotational speed. The
second reason is related to the non-uniform distribution of pressure
distribution in the volute due to the asymmetrical cross-section area of
the volute, and finally, the important reason is the occurrence of incep-
tion and development of cavitation within the pump. Moreover, it can be
seen also from this figure that when the pump operates under high flow
rate, it leads to decrease in the head within the pump and then also lead
to reduction in the pressure at the inlet eye of the impeller below the
water vapour pressure. Hence, that leads to cause cavitation phenome-
non, and it will develop in the pump when the flow rate is increased.
Further investigation also shows that the head rapidly decreases when
Fig. 1. Centrifugal pump flow loop including: 1- Main flow loop inlet valve, 2-
Centrifugal pump inlet valve, 3- PVC suction pipe, 4- Inlet pressure transducer,
5- Centrifugal pump, 6- outlet pressure transducer, 7- Main suction pipe flow
loop. 8- PVC discharge pipe. 9- Discharge vale. 10- water flow meter. 11- Water
tank. 12- Hopper.
Table 1
Range of flow rate for the pump under pump rotational speed of 2755rpm.
Range of flow rate (l/min)
378 370 365 362 352 342 331 320 310 302 276 252 227 200 177 152 103
3

the pump operates at flow rate higher than 350 (l/min). The reason is
because of the occurrence and development of cavitation. However, this
phenomenon will be analysed and then discussed in detail in this study
using the vibration technique.
The effect of cavitation phenomenon on the output performance of
the centrifugal pump under different operation conditions would be
discussed. Such conditions would include various flow rates and different
pump rotational speeds using vibration analysis technique. It is essential
to first investigate and then calculate the Net Positive Suction Head
NPSHa of the centrifugal pump so that the relationship with the different
flow rates can be described, as well as also establishing a general
knowledge of the pumps' performance. In this experimental study, the
centrifugal pump has been tested under different measurements of flow
rates corresponding to normal operation conditions (without cavitation
conditions) and with cavitation conditions. The cavitation characteristics
of the centrifugal pump that are monitored as important part of this study
are plotted in Fig. 5. This figure depicts the Net Positive Suction Head
available, and Net Positive Suction Head required against different flow
rates based on inception and development of cavitation in the pump [27].
For this purpose, the pumps’ flow rate can be changed through pro-
gressively throttling the discharge valve and then keeping the suction
valve open at100% and keeping the pump rotational speed constant at
2755rpm. The experimental data for the H-NPSHr curve for the centrif-
ugal pump has been provided by the manufacturers (Pedrollo company
pump model F32/200H).
From this figure, the different regions of cavitation are quite
apparent. The first one was when the pump works under low flow rate
making no cavitation to occur in this region. At this point, the NPSHa is
higher than the NPSHr. For the second region, the flow rate is higher than
350 (l/min) and at this region, cavitation begins to occur in the pump
where the intersection between the two curves for NPSHa and NPSHr
already occurred. That means the development of cavitation starts at this
Fig. 2. A) Discharge pressure of the centrifugal pump from 371 to 300 (l/min), B) From 275 to 101 (l/min) at pump rotational speed of 2755rpm.
4

point. The third important region is when cavitation within the centrif-
ugal pump starts to increase as the flow rate increases more than 350 (l/
min) due to decrease in the pressure at the eye of the impeller below the
water vapour pressure and hence, at this point, the NPSHa becomes
smaller than the NPSHr. Also, it is clear that the signs of cavitation
include deteriorating of the performance of the pump. Additionally,
during the experimental measurements for the centrifugal pump, incep-
tion of cavitation rapidly deteriorated at the flow rate higher than design
flow rate. Also, it can be seen from this figure that cavitation has occurred
at flow rate between higher design flow rate range of 300 (l/min) and
350 (l/min). As well as it can be clearly seen that the level of cavitation
was increased with the flow rate increased. Furthermore, based on the
above results regarding the relationship between the NPSHa and NPSHr
with the pumps’ flow rate, it can be seen that the value of NPSHa and
NPSHr have a high effect on the performance of the pump. In this current
study, investigation and discussions regarding the performance of the
centrifugal pump under cavitation conditions have been carried out using
vibration technique. The details of the influences of various experimental
operating conditions including different flow rates and pump rotational
speeds are discussed and analysed in detail in the following sub section.
3. Results and discussion
3.1. Predicting cavitation within a centrifugal pump using vibration
technique under various flow rates
In this research, an attempt has been made to investigate the pumps’
behaviour under the effect of normal operating and cavitation conditions
through the application of vibration technique. This technique necessi-
tates a particular sensor such as accelerometer sensor and an accurate
signal evaluation processing technique. The purpose was to analyse the
vibration signal related to cavitation condition within a pump under
different operating conditions. Moreover, results corresponding to the
vibration signal under various flow rates, through calculations and
analysis of the signal amplitude in time and frequency domain within the
pump, have been presented to predict and diagnose cavitation. Simul-
taneous evaluation of the different experimental measurements based on
normal operation (without cavitation) and detection of cavitation con-
ditions have been performed using MATLAB code. In this study and
through the experimental tests, the vibration signals are collected using
an accelerometer sensor as mentioned earlier. Furthermore, the perfor-
mance of the centrifugal pump parameters such as discharge flow rate,
Fig. 3. A) Peak, B) minimum and C) RMS features of the head under different
flow rates and pump rotational speed of 2755rpm.
Fig. 4. Head of the centrifugal pump under pump rotational speed 2755rpm.
100 150 200 250 300 350 400
0
1
2
3
4
5
6
7
8
9
)
m
(
H
S
P
N
Flow rate (l/min)
Pump NPSHr
NPSHa
Fig. 5. The cavitation characteristics of the centrifugal pump under different
flow rates.
5

inlet, and outlet pressure are measured through the use of various types
of sensors including water flow meter, two pressure transducers at suc-
tion and discharge sides of the centrifugal pump. The various types of
signals from all above sensors are sampled, collected and saved through
the use of data acquisition type dynamic data acquisition and analysis
system model YE7600 from Global Sensor Technology (GST) which made
by SNOCERA PIEZOTRONICS. In this experiment, the pump was in
operation for each test under the different flow rates. The capacity of the
centrifugal pump has been divided depending on the flow rate at the
different regions. Region one was at the low flow rate starting from 100
to 250 (l/min). The second region was at design flow rate 300 (l/min),
and the last region was at high flow rate higher than design flow from
320 to 378 (l/min), and the range of these flow rates depended on pump
rotational speed.
During each experimental test for the vibration signal sampling pro-
cess, the pump rotation speed was kept constant at the different flow
rates. In these experimental measurements, each experimental test has
been repeated at least 3 times. In order to obtain and provide more
reliable consistent data sets, collecting and repeating each operation test
will help to comprehend the characteristics of the vibration signals and
hence, acquire more dependable diagnostic features in predicting cavi-
tation within the pump. This study would collect and then analyse the
vibration signals under various flow rates. These signals were obtained
and collected through the use of the sensor such as an accelerometer type
CA-YD-1182. At the input of the voltage signal obtained from the
accelerometer has been collected then sampled at 96kHz in the data
acquisition system. Furthermore, the numbers of data points in each of
these experimental measurements were equalled to 2880000 points. Of
recently, in order to measure vibration in the system, an accelerometer
has been widely used as the most appropriate vibration sensor. There are
several reasons behind using this type of sensor. Firstly, it can be used for
wider ranges of frequency. Secondly, it is easy to install on the machine.
Thirdly, it is reliable for vibration measurement and finally, it can be used
effectively to predict various conditions such as healthy or faulty
equipment. Currently, there are many applications associated with
pumps in the industry. Therefore, condition monitoring in pumps has
become a significant application as it can allow the extension of the life of
the pump as well also decrease the cost of maintenance. In this research, a
methodology has been proposed in detecting the inception and devel-
opment of cavitation within the centrifugal pump. This firstly method-
ology that would be discussed in this study is based on the vibration
signal analysis methodology in both time and frequency domain under
different operation conditions. Fig. 6 depicts the flow chart analysis of
the vibration data for detecting cavitation within the pump. In this study,
the vibration analysis methodology has been suggested for detecting the
inception and development of cavitation within a centrifugal pump.
Based on signal processing monitoring system through the use of vibra-
tion signal, under a wide range of operation conditions. Such conditions
include different flow rates and pump rotational speeds. The methodol-
ogy has been used in this research which consists of different stages and
the brief details of this experimental stages are as follows:
➢ The first stage includes collecting the experimental test measure-
ments of the raw vibration signals from the centrifugal pump under
the different ranges of operating conditions using accelerometer.
➢ Analysing the vibration signal based on time domain (TD). First
compare the various raw vibration signals under the different oper-
ation conditions using the graph of the time wave form analysis
(TWFA). Second is to then analyse the vibration signal by using
different statistical features such as peak, RMS, peak-to-peak and
variance values.
➢ Detect various levels of cavitation (no cavitation, inception, devel-
opment, and full development of cavitation) within a pump by using
above features.
➢ Compare between above-mentioned features to find the sensitive
feature in order to detect different levels of cavitation.
➢ Analysis the vibration signal based on frequency domain (FD) using
FFT technique firstly, analysis the raw vibration signal based on
various frequency ranges (low and high-frequency ranges).
➢ Find the sensitive frequency range for detecting different levels of
cavitation in the pump using waterfall figures (three-dimension fig-
ures) to compare between vibration signals under different
conditions.
➢ Analysing the amplitude of the vibration signal under different fre-
quency ranges and wide range of operating conditions based on fre-
quency domain (FD) using different statistical features such as mean
and RMS vibration amplitudes.
➢ Detect different levels of cavitation (no cavitation, inception, devel-
opment, and fully development of cavitation) within a pump by using
above features.
➢ Compare between above features in order to find the sensitive fre-
quency range in frequency domain analysis (FDA) in order to detect
different levels of cavitation within a pump. Furthermore, all above
stages have been processed using MATLAB code.
The details of analysing the vibration data in time and frequency
domain under different range of operation conditions and frequency
ranges using above methodology are presented and discussed in the next
sections.
3.2. The vibration signal analysis based on time domain (wave form)
In the time wave form analysis (TWFA) of vibration acceleration
signal have been compared under normal and cavitation operating con-
ditions. The experimental results have been depicted and grouped based
on different flow rates. The cavitation phenomenon within a pump can be
detected using condition monitoring system by time wave form analysis
(TWFA). Different vibration waveforms signals collected by accelerom-
eter sensor that is mounted on the centrifugal pump casing are illustrated
in Fig. 7. This figure depicts the relation between the amplitude and time
for the vibration waveform signals under various flow rates for different
operation conditions were considered which are normal operation con-
ditions without cavitation and abnormal operation conditions with
cavitation are listed in Table, and pump rotational speed of 2755rpm. It
can be seen from this figure there are different levels of vibration am-
plitudes according to the change in the flow rate. For example, when the
pump works under the low range of flow rate such as, between 152 and
302 (l/min) the levels of vibration amplitudes are almost the same. It is
also worth noticing that at a low range of flow rate the levels of vibration
amplitudes are lower than that when the pump operates under high flow
rate. However, at the high range of flow rate for example, from 331 to
352 (l/min) the vibration levels begun to increase. Obviously, at the
range of flow rate from 362 to 378 (l/min) the values of vibration am-
plitudes rapidly increase, the results depict that the vibration amplitude
signal increases with flow rate increases. Two possible reasons can be
considered behind this phenomenon. The first one is due to the high
interaction between the impeller and volute tongue region such inter-
action occurs particularly in this region due to two important reasons.
The first one when the trailing edge blades of the impeller are near and
then they crossed the tongue region during rotation of the impeller, and
the second reason when the tongue area was in between two trailing edge
blades of the impeller. The second main reason to increase the vibration
amplitude is mostly due to the incipient cavitation phenomenon taking
place at the high flow rate, and it will develop when the flow rate is
increased. In this case, the trend for the vibration amplitude was more
random with high peaks when compared with normal operating condi-
tions. The reason behind this is that when cavitation occurs in the pump,
it generates very small bubbles and these small bubbles collapse and
hence, leads to changes in the shape and amplitude of the vibration
signals. Furthermore, it can be seen that the occurrence of cavitation is
one key reason that causes instability in the flow within a pump. By
6

comparing between figures (a) and (p), it can be concluded that vibration
signals are sensitive to predicting cavitation within a pump.
As it is evident in above figure, the change in the level of vibration
amplitude varies according to flow rate changes. However, such vari-
ances have revealed that the useful evidence concerning information
regarding for detecting cavitation phenomenon within a pump using time
wave form analysis (TWFA). For extraction of useful raw data features,
statistical analysis is used in condition monitoring (CM) method, which
depends strongly on the kind of signal under investigation. In order to
obtain further information with regards to analysing the vibration sig-
nals, this section has analysed the vibration signal in time domain
through the use of various types of statistical features such as peak, RMS,
peak-to-peak and variance values. In order to obtain clear idea regarding
how the vibration amplitude is changed under different flow rates, and
hence to predict and diagnose the cavitation phenomenon within a
centrifugal pump under various operation conditions. Furthermore, the
analyses above features are performed using MATLAB code. The level of
vibration stability of a pump is associated with the pump flow rate. For
this study, the design of experimental setup for the centrifugal pump loop
system can operate under different operation conditions.
3.3. Analysing the vibration signal using peak and RMS values in time
domain
As mentioned earlier, to analyse the sample of vibration signals under
various operation conditions, different statistical features of vibration
signals have been used in time domain analysis (TDA) including peak and
RMS values. The peak and Root Mean Square (RMS) value function in the
vibration signal has been a useful function for monitoring condition
systems. These statistical features are widely used in condition moni-
toring in referring to the signal energy content. The calculation of RMS
value is obtained through the use of an equation as given in study four.
The raw vibration data are obtained from experimental setup and then
processed in time domain. Fig. 8 depicts the analysis of vibration signal
for a centrifugal pump using above statistical values. In order to detect
the inception and development of cavitation conditions, various types of
operation conditions of flow rates such as at low flow rate from 100 to
250 (l/min), design flow rate at 300 (l/min) and high flow rate from 320
to 378 (l/min) has to be conducted with the pump rotational speed kept
constant at 2755rpm. It can be seen that from these figures there is a
small indication of the variance in vibration level at flow rates below 350
(l/min). Though, at a flow rate above 350 (l/min), the vibration level
witnesses a significant increase. However, the results from the experi-
mental measurements have showed that the same trend occur for all the
Fig. 6. Flow chart analysis of vibration data processing.
7

statistical features on the vibration signals under the different flow rates.
All of these statistical parameter trends, rapidly increases, when the
centrifugal pump operates under flow rate of 350 (l/min). One of the
main reasons is because of the occurrence of cavitation at this particular
flow rate. The second reason is due to the interactions between the
impeller and volute tongue region which then results to the pressure
fluctuations reaching the highest peak inside the pump occurring very
close to this tongue region. However, the values and levels of the pressure
fluctuations inside the pump increase or decrease in magnitude as the
trailing edge blades of impeller is near or far away from the volute tongue
region. Moreover, it can be noticed that for flow rate between 100 to 300
(l/min), the RMS value is approximately lower than that of the peak
values as seen in Figure This is due to the flow instabilities within the
pump under high flow rate. Furthermore, it can be noticed that the
rapidly starting value increase was earlier for the peak feature as
compared to the RMS feature. The results depict that using peak and RMS
features in time domain analysis (TDA) have the capability in order to
predict cavitation in the centrifugal pump under high flow rates. Due to
the characteristics of cavitation in centrifugal pumps, as illustrated in
earlier sections in Figure, it was obvious that when the flow rate was
higher than design flow rate, it led to inception of cavitation of the pump.
On this basis and from above findings it can be concluded that cavitation
was the central problem behind the increase in the level of vibration in
the centrifugal pump. Hence, the vibration signal analysis in the time
domain can be considered as an indication to first determine the pump's
condition, in addition to when cavitation has occurred in the pump.
Fig. 7. A) Vibration amplitude from 382 to 307 (l/min) and B) from 302 to 103 (l/min) at 2755rpm.
8

Additionally, the peak feature value was more sensitive as compared to
RMS feature for detecting occurrence of cavitation. The investigation of
vibration signals through the use of peak and RMS values offer useful
information regarding a centrifugal pump condition. Hence, analysis of
the trend of vibration amplitude, together with the flow rates could
provide a good indicator for detecting cavitation. Consequently, different
statistical parameters to monitor the trend of vibration amplitude such as
peak-to-peak and variance values can be used to predict cavitation as we
would see in next section.
3.4. Analysis of the peak-to-peak and variance values based on time
domain (TD)
The relationship between the vibration level and various flow rates
within a centrifugal pump can provide more information regarding the
detection of cavitation through the use of other different types of sta-
tistical features trends such as peak-to-peak and variance values. The
variance value can be calculated through using the equation given in
study four. For further analysis, the vibration signals in time domain for
the centrifugal pump in Fig. 9 depicts the peak-to-peak and variance
values, under various flow rates, under a pump rotational speed of
2755rpm. It can be clearly seen that from these figures that the values of
peak-to-peak and variance have approximately the same trend as
compared to the trends of peak and RMS values. It can be observed that
there is no significant change in peak-to-peak and variance values when
the centrifugal pump operates under low flow rate from 100 to 300 (l/
min). Also, as seen at a flow rate beyond 350 (l/min), the vibration
amplitudes witnessed a fast increase as shown in these figures. For
comparison between different flow rates, the level of vibration amplitude
has been rapidly changed with the increase of the flow rate value
particularly in the flow rate from 350 to 378 (l/min). When the centrif-
ugal pump operates at low flow rate, while the pump rotation speed is
kept constant at 2755rpm, it can be observed that no cavitation occurred.
While at the same rotational speed but under high flow rate, inception of
cavitation then begins to occur at the pump and as the flow rate increases
continuously, cavitation then also increases leading to the pump working
under a fully developed cavitation. In other words, it can be seen that
when the NPSHa is smaller than the NPSHr, that leads to cavitation
occurrence. Furthermore, it can also be observed that the peak-to-peak
value increase rapidly when compared to the variance value. From the
above finding, it can be concluded that the peak-to-peak value was more
sensitive as compared with variance value. Also, the result shows that the
use of statistical features such as peak-to-peak and variance values in
order to analyse the vibration data in time domain acquired from
experimental measurements can be a suitable technique to identify the
inception and development of cavitation in the pump under different
operation conditions. Based on the above results, it can be observed that
the occurrence of cavitation within a pump was the important reason to
increase the level of vibration amplitude.
The analysis of vibration signals using peak, RMS, peak-to-peak, and
variance values in time domain show rapid increase at flow rate 352 (l/
min). Based on above results, vibration amplitude can be used as the
threshold to detect cavitation and hence, this threshold can be used to
identify the different levels of cavitation within a pump. Furthermore, the
analysis of variation in the levels of vibration amplitude, within a cen-
trifugal pump under different experimental measurements of flow rate in
time domain analysis (TDA), agreed with characteristics of cavitation
that has been presented using the NPSH curve.
Based on the above investigation, it can be seen that the analysis of
vibration signals amplitude, using different statistical features in time
domain have approximately the same trend when compared with the
characteristics of cavitation that has been presented using the NPSHr
curve. The NPSHr and vibration signals increase as the flow rate also
increases. In order to further quantify the vibration signals using the
different statistical features, Table 2 summarises the peak, RMS, peak-to-
peak, and variance value under different levels of cavitation conditions at
various flow rates and pump rotational speed of 2755rpm. It can be seen
that the values of all above statistical features of the vibration signal are
increased as the level of cavitation increases, which follow the same
trend as that of the NPSH curve. That due to when cavitation process
occurs in the pump, and it will develop at the high flow rate that leads to
cause unstable flow and hence increase the pressure fluctuations as a
result that lead to the increase the level of noise and vibration.
Furthermore, the results have shown that the severity of cavitation has
different levels increase. No cavitation at the low flow rate 103 (l/min),
inception at 331 (l/min), development of cavitation at 352 (l/min), and
obviously the highest-level of cavitation (fully development) occurs at
378 (l/min). It can be concluded that from above results the level of
Fig. 8. A) Peak and B) RMS values of the vibration amplitude in the centrifugal pump at 2755rpm.
9

vibration stability and severity of cavitation within a pump is directly
associated with the pump flow rate.
During the experimental tests of the centrifugal pump, it can be
clearly noticed that the vibration signal changed in time domain at flow
rate higher than 350 (l/min) that mean at this point the pump was
operated under cavitation conditions the main reason behind that is due
to the NPSHr was higher than NPSHa. Furthermore, based on the char-
acteristics of cavitation within a centrifugal pump, and the analysis of
vibration signal in the time domain that depicted in the above figures. It
can be observed that the cavitation was the significant reason to increase
the vibration of the pump, and hence based on vibration signal investi-
gation, it can be concluded that the analysis of vibration signal in time
domain analysis (TDA) provides the initial indication to predict the
cavitation in the pump. Therefore, for more investigations and under-
standing in order to predict and diagnose the inception and development
of cavitation in the centrifugal pump more specific features are required.
These features can be found through transforming and analysing vibra-
tion signals in the frequency domain (FD) by using of Fast Fourier
Transform (FFT) technique. The details of analysis vibration data in
frequency domain under different range of flow rates and frequency
ranges are presented and discussed in the next section.
3.5. The analysis of vibration signals based on frequency domain (FD)
As mentioned in the previous section, the level of vibration signal
amplitude highly depends on the operating conditions of flow rate inside
the pump. The results from time domain analysis have revealed that
when the pump is being operated under low flow rate that is less than the
design flow rate, a minimum level of vibration will occur. But when the
pump is working under condition that is higher than the design flow rate,
more vibration and noise occurs. This is attributed to several reasons but
one reason is mostly because of the interactions between the impeller
blades and part of the volute tongue, close to the tongue region. Another
reason can be due to increase in turbulent flow within the pump. The
most important reason is due to the cavitation phenomenon that has
occurred at high flow rate. The vibration signals have been collected
through the use of an accelerometer sensor. The cavitation phenomenon
in the pump can be identified by finding the variation in vibration signal
amplitudes as would be discussed in detail in the next section.
3.6. The analysis of baseline frequency in the centrifugal pump
Fig. 10 depicts the frequency of the vibration signal for the centrifugal
pump under design flow rate 300 (l/min), and based on the range of
frequency 0Hz to 1kHz and pump rotational speed of 2755rpm. It can be
seen that from this figure, the frequency ranges between 0Hz and 1kHz
and the characteristics of the frequencies that have occurred in the pump
are due mostly to the periodicity in the flow within the centrifugal pump.
Due to the interaction between impeller blades and flow being pumped
and high interaction between the impeller blades with stationary part
(e.g the volute tongue region) as mentioned earlier, it can be observed
that two main dominated frequencies that have been generated at the
range of frequency the dominated frequency in this range are associated
with the shaft rotating frequency (Rf), the blade passing frequency (BPF)
and their harmonics. Also, it can be seen that from this figure the first
rotational frequency under design flow rate has occurred at 45.91Hz and
its second, third, and fourth harmonics have occurred at 91.8, 137.7, and
Fig. 9. A) Peak-to-peak and B) variance values of the vibration amplitude within the centrifugal pump at 2755rpm.
Table 2
Peak, RMS, peak-to- peak, and variance value under different levels of cavitation
conditions at different flow rates and pump rotational speed of 2755rpm.
Severity of
cavitation
Flow
rate
Peak
value
RMS
value
Peak-to-
peak value
Variance
value
(l/
min)
(m/s2
) (m/s2
) (m/s2
) (m/s2
)
No Cavitation 103 30.78 6.71 63.43 45
Inception of
cavitation
331 79.88 13.25 165.87 43.3
Development of
cavitation
352 117.40 20.61 242.86 175.6
Fully Development
of cavitation
378 457.66 73.82 921.14 5099.6
10

183.6Hz respectively. Also, the first blades passing frequency is taking
place at 229.58Hz, and its second harmonic has occurred at 459.16Hz.
Furthermore, it can be noticed that there are some additional frequencies
are generated due different sources such as the driving motor and the
cooling fan that has been used in order to cool the pump motor.
Many researchers into pumps applications have used high vibration
frequency range higher than 20kHz to predict and diagnose any faults
and failures. In this current study, an attempt has been made to use and
analyse low frequency ranges, less than 20kHz, for detecting cavitation
within a centrifugal pump. The important reason behind using latter
technique is to decrease the cost of the accelerometer sensor. The details
of using this method in frequency domain analysis (FDA) under different
range of flow rates are presented and discussed in the next section.
3.7. The analysis of vibration signals based on frequency domain under
various flow rates
Several experimental measurements have been carried out to measure
the vibration signal. To analyse further, frequency domain analysis has
been carried out in studying the effect of the different measurements of
the flow rates on the vibration amplitude. For this purpose, the three-
dimensional figure has been used in this section. This figure allows
comparing more than one vibration amplitude signal in frequency
domain and hence it can be illustrated that from this figure how the vi-
bration amplitude it changes within the centrifugal pump under various
operation conditions. For this purpose, in order to study the effect and
sensitivity of using different frequency ranges and also to analyse, detect
and then diagnose the inception and development of cavitation within
the centrifugal pump by using vibration signal in frequency domain, the
range of broadband frequency is divided into four main parts to obtain an
apparent conception concerning the dominant frequencies in the pump:
the first part deals with a low range of broadband frequency starting from
0Hz to 1kHz. While, the second part deals with range of broadband
frequency is starting from 1kHz to 2kHz, the third part is starting from
2kHz to 10kHz and final part from 10kHz to 15kHz as illustrated in the
next section.
3.8. Predict the cavitation within a pump at frequency range from 0Hz to
2kHz
Fig. 11 depicts the three-dimensional figure of vibration signals in the
frequency domain based on the different range of frequencies. The first
one is at low range frequency from (a) 0Hz to 1kHz and the second one is
at range of frequency between (b) 1kHz and 2kHz under various
measurements of flow rates and the rotational impeller speed of
2755rpm. It can be seen that from both figures, there are small variances
in the level of vibration amplitude within the centrifugal pump when the
pump is operating less than 300 (l/min). However, it can be clearly
observed that there is a significant increase in the level of vibration
amplitude that occurred, when the pump is operated under flow rate
higher than 350 (l/min). It can be noticed that this increase in the level of
vibration amplitude occurs for both range frequencies from (0Hz to
1kHz) and (1kHz–2kHz) respectively. The reason behind that is due to
the high interaction between water and the blades of the impeller, as well
as the interaction between the impeller and volute. Moreover, one
important reason is due to the occurrence of cavitation within the pump.
Also from this figure, it is worth observing that under flow rate higher
than 350 (l/min), the development of cavitation has already occurred.
This is due to the smaller vapour bubbles generated in and around the
impeller passages and hence, the bubbles impeding the flow rate being
pumped. As a result, these bubbles cause increase in the level of vibration
and noise inside the pump which then results in a decrease in perfor-
mance of the pump. Therefore, a decrease in the pump performance is a
reliable indication of cavitation has occurred in the pump. Also, the
dominated frequencies for both frequency ranges are associated with the
shaft rotating frequency (Rf), blade passing frequency (BPF) and their
harmonics. Furthermore, as mentioned in this section, it can be observed
that the level of the vibrations was closely related to the occurrence of
cavitation in the pump.
3.9. Predict the cavitation within a pump at frequency range from 2Hz to
15kHz
Fig. 12 depict the three-dimension vibration signal in frequency
domain analysis (FDA) and the frequency range is from (a) 2Hz to10 kHz
and (b) 10 Hz to 15kHz respectively, under various flow rates and the
pump rotational speed of 2755rpm. It can be seen that these range of
frequencies have the same trends as compared to previous figures for
level of vibration amplitude in frequency domain under flow rate less
than 350 (l/min). However, the trend of vibration amplitude increases
with flow rate increases; it is also worth observing that the vibration
amplitudes under high flow rates have much higher intensities as com-
pares to the low flow rate due to the occurrence of the inception of
cavitation at the flow rate lower than 350 (l/min). After the inception of
cavitation has occurred, variations in the level of vibration amplitude
increases as flow rate increases. When the cavitation increases continu-
ously, it means the pump is operating under the conditions that cavita-
tion has developed fully, leading to the level of increased amplitudes in
the vibration signal, particularly under higher flow rate. Because of the
occurrence of cavitation in the pump, bubbles begin to form and collapse
within the pump which directly affect the level of the vibration ampli-
tude. Furthermore, it can be observed that high-frequency range was
more sensitive for detecting cavitation particularly at high flow rate as
compared to low-frequency range.
It can be found that from above findings, the vibration amplitude
when the pump works under inception and fully developed cavitation
was higher than without cavitation condition (at the low flow rate) under
the different range of frequencies as shown that in previous figures. The
explanation for an increase in the level of vibration amplitude can be
clearly noticed in the high flow rate, is due to the inception and devel-
opment of cavitation process within a centrifugal pump at that time.
Whereas, the occurrence of cavitation is due to decrease the inlet pres-
sure at the eye of impeller under the water vapour pressure, causing the
formation of bubbles in this region. During the decrease in the inlet
pressure, these bubbles begins to grow in size due to the increasing flow
rate that then leads to increase in the velocity of flow, which causes
further decrease in the inlet pressure in this area. When cavitation start
occurs, it increases the vapour bubbles thereby causing the level of vi-
bration to increase due to the flow at inlet eye of an impeller becoming
more turbulent. This is mostly due to the implosions of the bubbles
Fig. 10. Baseline frequency of vibration signal range from 0Hz to 1kHz at
design flow rate at 2755rpm.
11

surrounding the surface of the impeller. Furthermore, this process of
collapsing and formation of bubbles could cause damage to the parts of
pump particularly on the blades of impeller and hence, causes significant
decrease in the performance of the pump. It can be seen that from above
analysis the vibration amplitudes vary with the flow rates and different
range of frequencies. Also, the above figures depict that the vibration
amplitude for the range of frequency lies between (0–1.5 m/s2
), the
range frequency 1–2kHz was (0–1 m/s2
), at high range frequency
2–10kHz was (0–2 m/s2
), and at range frequency 10–15kHz was (0–3 m/
s2
). Hence, it can also be noticed that the vibration amplitude increases as
the range of frequency also increases and these ranges of frequency vary
according to the different flow rates. As a result, from the above finding,
it can be concluded that when the flow rate increases, the vibration
amplitude is increased. That has led in providing a good indication as to
when cavitation occurs within the pump. The inception of cavitation
occurred before flow rate of 350 (l/min) and it was fully developed when
flow rate was higher than 350 (l/min). It was further noticed from the
above figures that there are two dominant frequencies which are the
rotation frequency (Rf) and blade passing frequency (BPF). From the
peak of these frequencies and their harmonics, they can provide an
alternative indication as to the occurrence of cavitation.
It can be seen that from above figures the range of frequency 10kHz-
15Hz was more sensitive to detect the cavitation within a centrifugal
pump as compared to the other range of frequencies. However, it can be
observed that the range of frequency 1kHz-2Hz was as sensitive to detect
the cavitation. The results have shown that the vibration, within a cen-
trifugal pump are due to the occurrence of cavitation phenomenon that
characteristically causes increase in the level of vibration amplitude,
which can be noticed under the different range of frequencies between
0 to 15kHz. Also, the results have shown that the use of FFT technique for
signal processing in frequency domain to detect cavitation within a
centrifugal pump was effective technique.
3.10. Analysis of vibration amplitude in frequency domain using different
statistical features
As shown in the previous section, 3-D figures are used in order to
analyse the level of vibration amplitude based on different range of fre-
quencies. It can provide more knowledge regarding the inception and
development of cavitation in the pump. However, during this experi-
mental work, analysis of the vibration signal based on the frequency
domain also helps to detect cavitation within a pump. Moreover,
comparing the vibration amplitude under various operation conditions
helps to match the variations in the level of vibration amplitude with the
different characteristics of cavitation of the pump. This section has
analysed the vibration amplitude signal in frequency domain, by using
different statistical features such as mean and RMS vibration amplitude
values. Furthermore, the analyses of these features are performed using
MATLAB code. In this section, in order to obtain more details regarding
the analysis of vibration signal, different range of broadband frequencies
have been used due to the accelerometer sensor having also, a wide range
of frequency band and hence, can be used to measure the different range
of frequencies in the centrifugal pump. For comparison purpose in this
study, the vibration under different range of frequencies will be analysed
and discussed during the investigation in order to find the sensitive range
of frequency to detect the occurrence of cavitation within a pump.
Fig. 11. A) Vibration amplitude under various flow rates and the vibration frequency range from 0 Hz to 1kHz, and B) 1kHz–2 kHz at 2755rpm.
Fig. 12. A) Vibration amplitude under various flow rates and the vibration frequency range from 2Hz to 10kHz, and B) 10Hz to 15 kHz at 2755rpm.
12

3.11. Analysis of vibration frequency using mean vibration amplitude
value
Fig. 13 depicts the analysis of vibration signal using mean vibration
amplitude value for various range of frequencies namely (0Hz–1kHz),
(1kHz–2kHz), (2kHz–10kHz), and (10kHz–15kHz) respectively under
operation conditions including flow rate as summarised in Table, and
pump rotation speed of 2755rpm. The same trend can be seen in the
vibration amplitude under both low and high range of frequencies. The
minimum vibration amplitude for the low flow rate is less than the design
flow rate of 300 (l/min), and no significant change in the level of vi-
bration amplitude at this operation conditions. However, the results have
showed that a rapid increase in the level of vibration amplitude for the
high flow rate which is higher than design flow rate in excess of 350 (l/
min). It then means that this increase signifies that cavitation has
occurred and has starts to increase within the pump which was due to the
fact that NPSHr was higher when compared to the NPSHa. These results
show a strong agreement with the result obtained from the previous
section. It can therefore be concluded that the level of vibration ampli-
tude provides a good indication to predict and diagnose cavitation in the
pump. Moreover, it was further noticed from above analysis of the level
of vibration amplitude that the result is not limited to any particular
range of broadband frequencies. However, it can be achieved through the
use of various ranges of broadband frequency.
3.12. Analysis of vibration frequency using RMS vibration amplitude value
For further analysis of the vibration signal in frequency domain,
Fig. 14 depicts the analysis of vibration signal using RMS vibration
amplitude value for different range of broadband frequencies namely
(0Hz–1kHz), (1kHz–2kHz), (2kHz–10kHz), and (10kHz–15kHz) respec-
tively, under operation conditions including different flow rates as shown
in Table and pump rotation speed of 2755rpm. It can be clearly seen that
the RMS value has the same trend of the vibration amplitude in the mean
value, but different values of the vibration amplitudes. During the
experimental measurements, it can be seen that there is no significant
change in the vibration amplitude between 100 and 300 (l/min). But the
vibration amplitudes are rapidly increased at the high flow rate higher
than 350 (l/min). That means at this point, the pump operated under
cavitation conditions due to NPSHr being higher than NPSHa.
It can be observed that from above results the use of statistical fea-
tures such as mean and RMS values to analyse the vibration signal in
frequency domain can provide more information regarding the predic-
tion of cavitation within a centrifugal pump. Furthermore, during the
experimental investigation in this study, it has been observed that the
low range frequency between 0Hz to 2kHz is sensitive to predict the
cavitation. Therefore, from above result it can be concluded that the
analysis of vibration signal based on different ranges of broadband fre-
quencies from 0Hz to 15kHz are efficient in order to predict cavitation
particularly at the range of broadband frequency between 1 and 2kHz. At
frequency range of 1–2kHz, there is no significant change when the pump
is operating below 350 (l/min) as shown in the figure, and the maximum
RMS value was 0.088 m/s2
at around 152 (l/min). However, after 350 (l/
min), the RMS value increases to 0.113 m/s2
at 365 (l/min) meaning that
the percentage increase for the RMS was 21.45%. Moreover, this in-
creases in the level of vibration signal was due to interaction between the
impeller and volute and also due to the occurrence of cavitation in the
pump as mentioned earlier. As a result, an accelerometer sensor with low
range of frequency can provide a good indication to predict and diagnose
cavitation in the pump and hence, leads to decrease in the cost of sensor,
as compared to using an accelerometer with high range of frequency.
Furthermore, the analysis of variation in the levels of vibration amplitude
within a centrifugal pump under different experimental measurements of
flow rate in frequency domain analysis (FDA) under different range of
frequencies were agreed with characteristics of cavitation that has been
presented using NPSH curve. Based on the above findings, it can be seen
100 150 200 250 300 350 400
0
0.1
0.2
Frquency range (0Hz-1kHz)
100 150 200 250 300 350 400
0
0.2
0.4
Frquency range (1kHz-2kHz)
100 150 200 250 300 350 400
0
0.5
1
s
/
m
(
e
d
u
t
i
l
p
m
a
n
o
i
t
a
r
b
i
V
2
)
100 150 200 250 300 350 400
0
0.5
1
1.5
Flow rate (l/min)
Fig. 13. Mean vibration amplitude value of the frequency range from 0Hz to 15 kHz at 2755rpm.
13

that when cavitation occurs in the pump, the level of vibration increases.
This happens because of the formation and growth of the vapour bubbles
within the impeller channels. Moreover, when these bubbles move and
reach the higher-pressure region in the pump, they start to rapidly
collapse, causing more unstable flow and then also cause increase in
pressure fluctuations within the pump which then leads to increase in the
level of vibration. Also, the above investigations have shown that the
analysis of the vibration amplitude signals using different statistical
features in frequency domain, have approximately the same trend as
compared to the characteristics of cavitation that has been presented
using the NPSHr. Therefore, for further quantifying of the vibration
signal in frequency domain analysis (FDA), Tables 3 and 4 summarise the
mean and RMS vibration amplitudes values under different levels of
cavitation conditions at different flow rates, pump rotational speed of
2755rpm and for different frequency ranges. It is evident that the values
of all above statistical features of the vibration signal are increased as the
level of cavitation increases. That is due to when cavitation occurs in the
pump, and it will increase particularly at a high flow rate, causing more
unstable flow which then increases the level of vibration. Furthermore, it
can be concluded that the level of vibration and severity of cavitation
within a pump is directly related to the pump flow rate.
Generally, after the investigation and discussion conducted
100 150 200 250 300 350 400
0
0.2
0.4
100 150 200 250 300 350 400
0
0.5
1
s
/
m
(
e
d
u
t
i
l
p
m
a
n
o
i
t
a
r
b
i
V
2
)
100 150 200 250 300 350 400
0
0.5
1
1.5
Flow rate (l/min)
100 150 200 250 300 350 400
0
0.1
0.2
Fig. 14. RMS vibration amplitude value at frequency range from 0Hz to15 kHz at 2755rpm.
Table 3
Mean vibration amplitude value under different levels of cavitation conditions at different flow rates and pump rotational speed of 2755rpm.
Severity of cavitation Flow rate Mean value Mean value Mean value Mean value
(l/min) 0Hz-1kHz 1kHz–2kHz 2kHz–10kHz 10kHz–15kHz
(m/s2
) (m/s2
) (m/s2
) (m/s2
)
No Cavitation 103 0.0471 0.0609 0.0343 0.0904
Inception of cavitation 331 0.0719 0.0635 0.0652 0.2097
Development of cavitation 352 0.0619 0.0725 0.1065 0.3235
Fully Development of cavitation 378 0.1284 0.288 0.4742 1.0666
Table 4
RMS vibration amplitude value under different levels of cavitation conditions at different flow rates and pump rotational speed of 2755rpm.
Severity of cavitation Flow rate RMS value RMS value RMS value RMS value
(l/min) 0Hz-1kHz 1kHz–2kHz 2kHz–10kHz 10kHz–15kHz
(m/s2
) (m/s2
) (m/s2
) (m/s2
)
No Cavitation 103 0.0578 0.0819 0.043 0.0944
Inception of cavitation 331 0.0866 0.0764 0.0783 0.2223
Development of cavitation 352 0.0766 0.0847 0.1309 0.3434
Fully Development of cavitation 378 0.1595 0.3318 0.5543 1.153
14

concerning the performance and predict cavitation within a centrifugal
pump under various flow rates. The details of the influences of different
pump rotational speeds on the performance and predict cavitation con-
ditions through the use of vibration technique in time and frequency
domain are discussed and analysed in the following sections.
3.13. Effect of various pump rotational speeds to predict the cavitation
within a centrifugal pump using vibration technique
As mentioned and clearly observed in the previous sections, the pump
performance depended directly on the different operating conditions.
Therefore, the flow pattern behaviour distribution such as pressure and
velocity, occurrence of cavitation as well as instabilities in the flow field
within a centrifugal pump can all be predicted differently at various
operational conditions. Hence, all of these parameters can affect the flow
field, performance of the pump, and the detection of cavitation under
various pump rotational speeds. Further analysis on the vibration signal
for this research would be presented in order to predict the cavitation
phenomenon within the centrifugal pump experimentally. The effect of
various pump rotational speeds 2610, 2320, and 2030rpm respectively,
Fig. 15. Comparison between head of the centrifugal pump under different pump rotational speeds.
Fig. 16. Comparison between (A) peak, (B) RMS, (C) peak-to-peak, and (D) variance vibration amplitude values of the centrifugal pump under different pump
rotational speeds.
15

corresponding to 0.9Nd, 0.8Nd, and 0.7Nd where Nd denotes the design
rotational speed, and it is equal 2900rpm have been selected for the
analysis purpose. The pump rotational speed has been precisely
controlled by using the electronic inverter in the control panel. The range
of pump capacity (flow rate) has been changed depend on the pump
rotational speed. The next sections represent the results obtained from
the experimental calculation of the pump under different pump rota-
tional speeds.
For comparison purposes between the above cases, Fig. 15 depicts the
head of the aforementioned cases under different pump rotational
speeds. It can be observed that the head in the centrifugal pump follows a
continuous downward trend with increasing flow rate at various rota-
tional speeds under investigations. Also, it can be clearly seen that the
head under N ¼ 2755rpm is considerably higher than for the other three
cases N ¼ 2610 rpm, N ¼ 2320rpm, and N ¼ 2030rpm. The results have
shown that the pump starts to operate under cavitation conditions at a
flow rate higher than the design flow rate and then increases at a flow
rate high than 350 (l/min). That means that when a pump operates at the
high flow rate, it leads to decrease in the inlet suction pressure faster than
at low flow rate and hence, cavitation will occur quicker. Furthermore,
from the above findings, it can be concluded that the head of the cen-
trifugal pump increases as the pump rotational speed also increases.
Moreover, the pump rotational speeds are proportional to cavitation
occurrence within the pump. That means when pump rotational speeds
increases, occurrence of cavitation also increases due to the decreased
pressure at the inlet eye of impeller which goes lower than the vapour
pressure.
For comparison purposes between the above cases based on time
domain analysis (TDA), Fig. 16 depicts the statistical features such as
peak, RMS, peak-to- peak and variance values of the aforementioned
cases under different pump rotational speeds. It can be seen that the
maximum peak feature for N ¼ 2755rpm is considerably higher than for
the other three cases. For instance, for N ¼ 2610 rpm, it is higher by
13.38%, for N ¼ 2320rpm by 15.48%, and N ¼ 2030rpm by 36.60%.
Moreover, the maximum RMS value for N ¼ 2755rpm is higher that the
remaining three cases already listed by 11.72%, 29.98%, and 52.53%
respectively. Furthermore, the highest peak-to- peak for N ¼ 2610 rpm is
higher than for the other cases by 13.025%, 13.45%, and 33.24%
respectively and also the maximum variance value by 16.66%, 42.19%,
and 75.93% respectively as given in Table 5. From the above findings, it
can be concluded that the pump rotational speeds are proportional to the
increase in the vibration amplitude. This means that when the pump
rotational speed increases, the vibration amplitude also increases due to
Table 5
Summary of the statistical features results of the maximum peak, RMS, peak-to-
peak and variance values of the vibration amplitude under different pump
rotational speeds.
Rotational speed Peak RMS peak-to-peak variance
(rpm) (m/s2
) (m/s2
) (m/s2
) (m/s2
)
2755 457.66 73.82 921.14 5099.6
2610 396.38 65.17 801.16 4249.5
2320 386.80 54.28 797.22 2947.6
2030 294.71 35.04 614.86 1227.0
Fig. 17. Comparison between mean vibration amplitude values of the pump in frequency domain for different rotational speeds at range frequency (A) 0Hz-1kHz, (B)
1kHz–2kHz, (C) 2kHz–10kHz, and (D) 10kHz–1kHz under different pump rotational speeds.
Table 6
Comparison between mean vibration amplitude values of the pump in frequency
domain, under different rotational speeds at 0kHz–15kHz frequency range.
Rotational speed Mean value
0Hz-1kHz
Mean value
1kHz–1kHz
Mean value
2kHz–10kHz
Mean value
10kHz–15kHz
(rpm) (m/s2
) (m/s2
) (m/s2
) (m/s2
)
2755 0.128 0.288 0.474 1.066
2610 0.075 0.243 0.444 0.995
2320 0.071 0.174 0.345 0.864
2030 0.041 0.113 0.176 0.558
16

the cavitation occurrence within a centrifugal pump. When vapour
bubbles form due to cavitation for a long period of time, these bubbles
collapse which causes drop in the performance of the pump and also
damages some parts of the pump due to erosion on the surfaces of the
pump. Furthermore, detection of the inception of cavitation at an earlier
stage will help in prolonging the life of the pump and protecting the
system from emergency shutdown.
Also, for comparison purposes between the above cases based on
frequency domain analysis (FDA), Fig. 17 depicts the mean vibration
amplitude values of the aforementioned cases under different pump
rotational speeds and for the different range of frequencies which include
0Hz-1kHz, 1kHz–1kHz, 2kHz–10kHz, and 10kHz–15kHz. It can be
clearly seen that the maximum mean feature under N ¼ 2755rpm is
considerably higher than for the other three cases as shown in Figure.
Furthermore, the results from the frequency domain analysis have
demonstrated that the mean vibration amplitude value for various
ranged of frequencies can be used to predict different levels of cavitation
within a centrifugal pump, especially at low range frequencies from 0Hz
to 2kHz. However, it can be clearly seen that high ranges of frequency are
more sensitive to predict cavitation as compared to the low range of
frequency as shown in these ﬁgures.
Regarding the changes in vibration amplitude of the mean value for
the centrifugal pump under different pump rotational speeds and various
range of frequencies including 0Hz-1kHz, 1kHz–1kHz, 2kHz–10kHz, and
10kHz–15kHz, Table 6 provides more detailed comparison between all of
the above cases under investigation. The values for the mean feature for
N ¼ 2755rpm, for different range of frequencies are considerably higher
than for all three cases (N ¼ 2610, N ¼ 2320, and N ¼ 2030rpm) as
summarised in this table. It can be seen that the analysis on the vibration
signals in frequency domain, using mean amplitude features, under
different pump rotational speed shows that when the pump rotational
speed increases, vibration amplitude also increases due to increases in
the occurrence of cavitation within a pump under the different frequency
ranges.
Furthermore, for comparison purposes between the above cases based
on frequency domain analysis, Fig. 18 depicts the RMS statistical feature
value for the aforementioned cases under different pump rotational
speeds and for the different range of frequencies which include 0Hz-
1kHz, 1kHz–1kHz, 2kHz–10kHz, and 10kHz–15kHz. It can be clearly
seen that the maximum RMS feature for N ¼ 2755rpm is considerably
higher than for the other three cases. Also, the results from frequency
domain analysis have demonstrated that RMS vibration amplitude value
for various range of frequencies can be used to predict the cavitation
within a centrifugal pump, especially at the low range frequency between
0Hz to 2kHz.
Furthermore, regarding the changes in vibration amplitude and
trends of the RMS value for the centrifugal pump under different pump
rotational speeds and for various range of frequencies which are 0Hz-
1kHz, 1kHz–1kHz, 2kHz–10kHz, and 10kHz–15kHz, Table 7 provides
these comparison between all the above cases under investigation. The
values of RMS features for N ¼ 2755rpm for different range of fre-
quencies are considerably higher than for all three cases (N ¼ 2610, N ¼
2320, and N ¼ 2030rpm) as summarised in this table.
Fig. 18. Comparison between RMS vibration amplitude values of the pump in frequency domain for different rotational speeds at range frequency (A) 0Hz-1kHz, (B)
1kHz–2kHz, (C) 2kHz–10kHz, and (D) 10kHz–1kHz under different pump rotational speeds.
Table 7
Comparison between RMS vibration amplitude values of the pump in frequency
domain under different rotational speeds at 0kHz–15kHz frequency range.
Rotational speed RMS value
0Hz-1kHz
RMS value
1kHz–1kHz
RMS value
2kHz–10kHz
RMS value
10kHz–15kHz
(rpm) (m/s2
) (m/s2
) (m/s2
) (m/s2
)
2755 0.1595 0.3318 0.5543 1.153
2610 0.1095 0.2855 0.5221 1.0789
2320 0.0926 0.1944 0.4111 0.9276
2030 0.0540 0.1762 0.2189 0.6055
17

4. Conclusions
Based on above results in this section, several flowing conclusions
have been drawn regarding the effect of different flow rates and pump
rotational speeds on the vibration signal and performance of the cen-
trifugal pump.
1. The trend for the head of the centrifugal pump gradually decreases
when flow rate is increased due to the hydraulic and mechanical
losses as well as different levels of cavitation occurrence within a
pump
2. When the pump operates under low flow rate, no cavitation occurs
due to NPSHa being higher than the NPSHr. But at flow rate
greater than 350 (l/min), cavitation occurs in the pump
3. The results have shown that when the pump works under unstable
flow rate, it leads to change in the dynamic characteristics within
a centrifugal pump.
4. The level of cavitation within a centrifugal pump has been directly
linked with the pump flow rate and pump rotational speed.
5. Under cavitation process, the vapour bubbles increase due to
decrease of the fluid pressure, lower than the vapour pressure.
Moreover, they have high effects on the flow within a pump.
6. The inception of cavitation process mostly occurred at the eye of
the impeller around or closed to the impeller blades leading edges.
7. The vibration signal analysis in time domain, using different sta-
tistical features can be considered as a first indication to deter-
mine when cavitation has occurred in the pump.
8. The peak and peak-to-peak feature values were the most sensitive
to detect cavitation within a pump when compared to RMS and
variance features.
9. Frequency domain analysis technique to investigate the vibration
amplitude has been a satisfactory technique to predict the incep-
tion and development of cavitation within a pump
10. The use of features such as mean and RMS vibration amplitude
values to analyse the vibration signal in frequency domain pro-
vides more information regarding the prediction of cavitation
within a centrifugal pump
11. The analysis of the variation in the level of vibration amplitude
within a centrifugal pump, under different experimental flow rate
measurements in time domain by using different statistical fea-
tures and also in frequency domain under different ranges of
frequencies was in agreement with the characteristics of cavita-
tion that has been presented using the NPSH curve
12 During the course of further investigation in this study, it was
found that from the analysis the vibration signal using mean and
RMS amplitudes features, for the different broadband range of
frequencies. The results have revealed that using low-frequency
range between 1kHz and 2kHz was sensitive to predict cavita-
tion in the pump. Therefore, it is possible to use an accelerometer
that has low range of frequency which would decrease the cost of
the sensor when compared high range of frequency sensor
13. Based on the above findings, the severity of cavitation can be
gauged by increasing the level of vibration amplitude value. It
provides a good indication regarding the occurrence of the
severity of cavitation within a centrifugal pump
Declarations
Author contribution statement
Ahmed Ramadhan Al-Obaidi: Conceived and designed the experi-
ments; Performed the experiments; Analyzed and interpreted the data;
Contributed reagents, materials, analysis tools or data; Wrote the paper.
Funding statement
This work was supported by the Ministry of Higher Education and
Scientific Research (Iraq).
Competing interest statement
The authors declare no conflict of interest.
Additional information
No additional information is available for this paper.
Acknowledgements
The author would like to thank Mustansiriyah University (www.uom
ustansiriyah.edu.iq) Baghdad – Iraq for its support in the present work.
The measurement data was a part of author PhD degree at University of
Huddersfield (UK). Also, the author would like to thank their support and
collaboration.
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19

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