Vibration Monitoring in a Turbomachine- Pipeline System

Transcription

1 Budapest University of Technology and Economics (BME) Faculty of Mechanical Engineering (GPK) Department of Hydrodynamic Systems Ali Parhikzar B.Sc. Thesis Vibration Monitoring in a Turbomachine- Pipeline System Supervision: Dr. Hegedűs Ferenc Budapest, 2015

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3 Assignment page Page 3

4 DECLARATION BY CANDIDATE I hereby declare that the thesis submitted for the B.Sc. degree at Budapest University of Technology and Economics (BME), is my own original work and has not previously been submitted to any other institution of higher education. I may have discussed the Thesis with others and used advice and suggestions from others in writing it, but the paper is my own original work and is neither copied from another source without proper acknowledgement, nor written for me by another person, in whole or in part. Budapest, December 11 th, (Signature) Copyright Budapest University of Technology and Economics (BME) 2015 Page 4

5 DEDICATION I take pleasure in dedicating this thesis to my uncle, Mr. Alireza Parhizkar, who has been a constant source of support and encouragement during the challenges of graduate school and life and who gave me this chance to peruse my education by his financial support. Thank you. Education is what remains after one has forgotten What one has learned in school. (Albert Einstein) Page 5

6 TABLE OF CONTENTS 1.0 INTRUDUCTION VIBRATION VIBRATION IN CENTRIFUGAL PUPMS SOURCE OF VIBRATION IN CENTRIFUGAL PUPMS Mechanical Causes of vibration Hydraulic Causes of Vibrations Peripheral Causes of Vibrations NOISES IN CENTRIFUGAL PUPMS Mechanical source of noise Hydraulic source of noise Transients In-stationary of flow Pressure pulsations Turbulence in pump Cavitation DIAGONOSIS OF NOISE AND VIBRATION IN CENTRIFUGAL PUMP MEASUREMENT Noise measurement Vibration measurement ANALAYSIS OF MEASUREMENTS DATA Unbalance Eccentricity Bent Shaft Pump and motor misalignment Blade and vane pass vibrations 25 Page 6

7 4.2.6 Flow turbulence Cavitation VIBRATION MONITORING EXPERIMENTAL INVESTIGATION CENTRIFUGAL PUMP MEASUREMENT Formulae for the calculation Calculation of Quantities INVESTIGATION OF VIBRATION MONITORING Analysis of the results Rotational Speed at 1100 [RPM] Rotational Speed at 1400 [RPM] Rotational Speed at 1500 [RPM] SUMMARY AND CUNCLUSION 49 REFRENCES 50 Page 7

8 1.0 INTRODUCTION The contact feeling of vibrating machines is very important because we can understand whether the machine is working properly or not. We can take drivers as an example, usually a routine driver can detect if the car has mechanical issue by the vibration of the steering wheel or by engine knock. Therefore the amplitude of the vibration is important to detect the engine s (or machine s) statues of operation which of course it s natural to have some level of vibration due to small, minor defects. However, when those vibrations exceed the limit, we can assume that there is a mechanical issue. The reason for that is usually because it is unbalanced, misaligned, or worn gears and since not everyone has the experience needed to state a machine's condition based on how it feels. Various measuring equipment have been developed over the years to measure the actual level of vibration. Of course, human detection of faults through touch and feel is somewhat limited, and there are many common problems such as the early stages of bearing and gear failure that are generally out of the range of human perception. Thus, modern instrumentation for measuring vibration on rotating and reciprocating machinery makes it possible to detect developing problems that are outside the range of human senses of touch and hearing. Further, human perception differs from individual to individual. What one person may consider as bad, another may consider as normal. The attempt to follow the changes in machinery condition using human contact is nearly impossible, since engineers can t document on how a machine feels, hence it s incorrect and unprofessional. To overcome this problem, instruments have been developed to actually measure a machine's vibration level and assign it a numerical value. These instruments help engineers to overcome the limitations of human perception. In order to investigate the vibrations, it is necessary to identify the machine and describe the vibration monitoring of a turbomachine (condition monitoring). Page 8

9 Condition monitoring is an important part of condition-based maintenance (CBM) [1, 2], which is known to be the most efficient strategy for carrying out maintenance in a wide variety of industries. Machines were originally run to break, which ensured maximum operating time between shutdowns, but meant that breakdowns were occasionally catastrophic, with serious consequences for safety, repair cost and production loss. When it comes to a Centrifugal pump in the system, the investigation needs to be first defined as: Centrifugal pumps are utilized widely in the oil and chemical industry [3, 4]. Huge amount of energy has been paid to the condition monitoring and fault diagnosis of the centrifugal pump by the field engineers and technicians. Therefore, monitoring of pumps is necessary to prevent a decrease in their efficiency. Condition monitoring of rotating machinery is important in terms of system maintenance and process automation. The main advances in vibration analysis in recent years are the development in signal processing techniques, for vibration diagnostics of gearing systems [5]. The development of the fast Fourier transform (FFT) in 1965 allowed the development of commercial real-time spectral analyzers [6]. Vibration analysis has been used to diagnose machines with rotating internals for some time [7, 8, and 9]. By measuring and analyzing the vibration of a machine, it is possible to determine both the nature and severity of the defect, and hence predict the machine s useful life or failure point. In most common cases, vibration signals can be read from accelerometers mounted on the outer surface of a bearing housing. The signals consist of vibrations from the meshing gears, shafts, bearings, and other components. External vibrations on a pump is measured and used to monitor the operating condition of the pump and diagnose the fault without interfering with the normal operation. Spectral analysis is the most common method is used to examine mechanical vibration. Condition monitoring and fault diagnostics is needed to ensure that the machines run safely. Vibrations signals are important hence in mechanical systems they often carry dynamic information from mechanical elements. These mechanical signals normally consist of a combination of the fundamental frequency with a narrowband frequency component and the harmonics. When a mechanical element is damaged or worn the energy of vibration increases therefore they are related to the revolutions of the rotating system. Page 9

10 Some of the conventional techniques used for fault signals diagnosis include power spectra in time domain or frequency domain, and they can provide an effective technique for machinery diagnosis provided that there is the assumption that the signals are stationary. The main advances in vibration analysis in recent years are the development in signal processing techniques, for vibration diagnostics of gearing systems. Page 10

11 2.0 VIBRATION Vibrations basically are the displacement of a mass back and forth from its static position. A force will cause a vibration, and that vibration can be described in terms of acceleration, velocity or displacement. The force that will cause the vibration, must overcome the structure s mass, stiffness and damping properties. These properties are inherent to the structure and will depend on the materials and design of the machine. Whereas noise is one of the derivatives of vibrations. Both phenomenon affect the centrifugal pump performance and its service life adversely. Sources of vibrations and noise are well known but the methods to trace the exact source are still in development stage [1, 2]. The major challenge in diagnosis of vibrations and noise in centrifugal pumps is service of the centrifugal pump itself. When we compare the machine tools or other utility equipment with centrifugal pumps, diagnosis of the sources of noise and vibrations in machine tools is simpler than pumps as all the components are mechanical and are visible. Whereas in centrifugal pumps, the root of vibrations and noise may lie in mechanical or hydraulic aspects. It is very easy to trace the mechanical causes but it becomes very difficult to trace hydraulic causes. This makes pumps vibration and noise diagnostic very complex. 2.1 VIBRATION IN CENTRIFUGAL PUMPS It is necessary to be interested in vibration in centrifugal pumps because it has a major effect on the performance. Generally, increasing vibration levels indicate a premature failure, which always means that the equipment has started to destroy itself. It is because excessive vibration are the outcome of some system malfunction. It is expected that all pumps will vibrate due to response from excitation forces, such as residual rotor unbalance, turbulent liquid flow pressure pulsation, and cavitation or pump wear. The magnitude of the vibration will be amplified if the vibration frequency approaches the resonant frequency of a major pump, function or piping component. Generally higher vibration levels (amplitudes) are indicative of fault developing in mechanical equipment. Page 11

12 The sources of vibration in centrifugal pumps can be categorized into three types: Mechanical causes, Hydraulic causes and Peripheral causes Mechanical Causes of vibration: Unbalanced rotating components Damage impellers and non-concentric shaft sleeves Bent or warped shaft Pipe strain (either by design or as a result of thermal growth) Inadequacy of foundations or poorly designed foundations Thermal growth of various component, especially shafts Rubbing parts Worm or loose bearing, Loose parts Loosely held holding down bolts Damaged parts Hydraulic Causes of Vibrations: Operating pump at other than best efficiency point (BEP) Vaporization of the product Impeller vane running too close to the pump cutwater Internal recirculation Air entrapment into the system through vortexting etc. Turbulence in the system (non-laminar flow) Water hammer Peripheral Causes of Vibrations: Harmonic vibration from nearby equipment or drivers Operating the pump at a critical speed Page 12

13 3.0 NOISES IN CENTRIFUGAL PUPMS Noise is an important quality and comfort feature of any centrifugal pump. Abrupt noise in pumping system for most of the times is an outcome of vibrations set in pumping system. Although a certain amount of noise is expected from centrifugal pumps and their drives, usually high noise levels (in excess of 100db) is an indication of potential mechanical failure or vibration problems. The occurrence of significant noise levels indicates that sufficient energy exists to be a potential cause of mechanical failure of the pump and piping. Noise in centrifugal pumps and systems can be generated by mechanical motion of pump components and by liquid motion of the pumps and system. 3.1 Mechanical sources of noise Common mechanical sources of noise include vibrating pump components or surfaces because of pressure variations that are generated in the liquid or air. Impeller or seal rubs, defective or worn bearings, vibrating pipe walls and unbalanced rotors are the examples of mechanical sources of noise in pumping systems. Improper installation of couplings in centrifugal pumps often causes noise at twice the pumping speed (Misalignment). If the pump speed is near or passes through lateral critical speed, noise can be generated by high vibrations resulting from imbalance or by rubbing of bearings, seals or impellers. If rubbing occurs, it is characterized by a high-pitched squeal. 3.2 Hydraulic sources of noise Hydraulic sources of noises includes following: Transients: Starting and stopping of pumps with the attendant opening and closing of valves is a major cause of severe transition in pumping systems. The resulting pressure surges, known as water hammer can apply a sudden impact force on pump. The discrete energy produced during the course is then dissipated as noise and is way above the audible noise intensities. Rapid closure of conventional valves used in feed water lines can cause severe water hammer. Page 13

14 Analytical methods are available to evaluate severity of water hammer in a particular piping configuration for different closure rates In-stationarity of flow The in-stationarity of the flow is caused by secondary flows in the impeller due to rotation, the finite number of blades and finite blade thickness, but also by effects of turbulence. The finite number of blades leads to a secondary flow, caused by the asymmetric outgoing flow of the impeller. The finite blade thickness causes a notch in the wake flow. Both effects result in a timedependent incident flow on the resting parts (guide vanes of the diffuser, volute tongue of the guide casing) and consequently excite vibration of these parts. In-stationarity of flow is combined effect of pressure pulsations and turbulence Pressure pulsations due to the finite number of blades Pressure pulsations are detected at discrete frequencies that are multiples of the rotating frequency and the number of blades; these frequencies are also called blade passing frequencies. (BPF): Blade Pass Frequency, (BPF) = number of blades (or vanes) rpm The amplitude of these pressure pulsations depends on a number of design parameters of impeller and diffuser and operating parameters. One of the most important parameters is the distance between impeller and the volute tongue. Smaller distances typically result in much higher amplitude of the BPF. However, this distance also affects the efficiency of the pump. Therefore, in industrial practice often a compromise has to be found between hydraulic efficiency and noise specification Turbulence in pumps Flow turbulence induces vortices and wakes in the clearance space between the impeller vane tips and the diffuser or volute lips. Dynamic pressure fluctuations or pulsations produced in this way can result in shaft vibrations because the pressure pulses impinge on the impeller. Flow past a restriction in pipe can produce turbulence or flow induced vibrations. Fig 1. Page 14

15 Fig 1 -Turbulence and vortices formation in flow through impeller (Reference [5]) The pulsation could produce noise and vibration over a wide frequency range. The frequencies are related to the flow velocity and geometry of the obstruction. These in turn excite resonant frequencies in other pipe components. The shearing action produces vortices that are converted to pressure disturbances at the pipe wall, which may cause localized vibration excitation of the pipe or its components. It has been observed that vortex flow is even higher when a system s acoustic resonance coincides with the generated frequency from the source. The vortices produce Broadband turbulent energy centered on the frequency determined by the following formula: f = S n V D Where: f = vortex frequency (Hz), Sn = Strouhl number (dimensionless, between 0.2 and0.5), D = characteristic dimension of the obstruction. (Reference [10]) Page 15

16 Cavitation Cavitation is the formation of vapor cavities or bubbles in a liquid due to rapid change in pressures. When a fluid suffers a pressure drop below its vapor pressure it evaporates and then collapse when the pressure is raised back to a value higher than its vapor pressure. This implosion generates a shockwave that can damage the pipelines in which the fluid is been transported and is a major cause of wear in the fluid engineering field. Fig 2. Fig 2 - Cavitation bubble imploding creating a jet next to a surface (Reference [11]) Cavitation normally generates random, high frequency broadband energy, which is sometimes superimposed with the blade pass frequency harmonics. Gases under pressure can dissolve in a liquid. When the pressure is reduced, they bubble out of the liquid. In a similar way, when liquid is sucked into a pump, the liquid s pressure drops. Under conditions when the reduced pressure approaches the vapor pressure of the liquid (even at low temperatures), it causes the liquid to vaporize. As these vapor bubbles travel further into the impeller, the pressure rises again causing the bubbles to collapse or implode. This implosion has the potential to disturb the pump performance and cause damage to the pump s internal components. This phenomenon is called cavitation. Each implosion of a bubble generates a kind of impact, which tends to generate highfrequency random vibrations, as depicted in Fig 3. Page 16

17 Cavitation can be quite destructive to internal pump components if left uncorrected. It is often responsible for the erosion of impeller vanes. Fig 4. Fig 3 Effect of Cavitation in Centrifugal Pump (Reference [12]) May cavitation occurs Fig 4 Might be indirect effect of cavitation (Taken from MATLAB solution) Page 17

18 4.0 DIAGNOSIS OF NOISE AND VIBRATION IN CENTRIFUGAL PUMP The diagnosis of noise and vibrations in centrifugal pumps is divided into two steps Noise / Vibration measurement. Analysis of measured vibration values. 4.1 MEASUREMENT Noise measurement Noise heard every day is not a pure sound of only one frequency, but it is often a combined sound that includes various frequency components. Suppose two types of sources were measured and it was found that their sound pressure levels were the same. If the noise is composed of differing frequencies, the countermeasure of soundproofing to be taken would naturally be different. To know the characteristics of a noise and propose preventative measures, it is important to identify the frequency components of that noise. The sound pressure level per Hz is called the "spectrum pressure level". A sound in which all of the spectrum pressure levels are equal (whatever the pitch, the loudness is the same) is called "white noise". The preferred series of octave bands for acoustic measurements divides the audible range into ten bands. The center frequencies of these bands are 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000 and Hz. The actual nominal frequency range of any one of these bands is 2:1. This means that the effective band for the 1000-Hz octave extends from 707 to 1414 Hz. In a frequency analysis, a graph is made of the results of octaveband sound pressure level measurements Fig 5. The frequency scale is commonly divided into equal intervals, between the position designated for each band and the position for the band adjacent to it in frequency. The pressure level in each band is normally presented as horizontal lines centered on the band at the measured level. Page 18

19 Below is an example of octave band frequency analysis. Fig 5 Octave band frequency analysis (Reference [4]) Vibration measurement Mechanical vibrations are most often measured using accelerometers, but displacement probes and velocity sensors are also used. Generally, a portable vibration analyzer is preferred. The analyzer provides the amplification of the sensor signal, it does the analogue to digital conversion, filtering, and conditioning of the signal. Many analyzers also offer advanced processing of the collected signals, as well as storage and display of the data. It is also important to know the location to mount the vibration mounts. We know that a force cause vibration. If we know what types of forces are generating the vibration, we will have a good idea how they will be transmitted through the physical structure of the machine and where they will cause vibrations. With rotating machines, this point is almost always directly on the machine s bearings. Page 19

20 The reason for this is that the various dynamic forces from a rotating machine must be transmitted to the foundation through the bearings. As a rule of thumb, vibration readings on rotating machines must be taken in the horizontal, vertical and axial direction on each bearing as shown in Fig 6 and Fig 7. (Reference [2]) Fig 6 Radial locations of vibration mounts Fig 7 Axial locations of vibration mounts 4.2 ANALAYSIS OF VIBRATION MEASUREMENTS DATA There are many different methods available for analyzing vibration data. The most basic method involves displaying the vibration data in the frequency domain, also called the vibration spectrum. The frequency of the vibration is the number of vibration cycles per time unit. The vibration spectrum is fundamental to vibration monitoring, because it yields the information that is effectively "hidden" in the vibration waveform. Vibration spectra can be represented in various different ways, of which the Fast Fourier Transform (FFT) and the Power Spectral Density (PSD) are the most popular. The concept of the vibration spectrum can be simply explained by means of an example. Page 20

21 Consider the time waveform in Fig 8, which has a frequency of 10 Hz (we can count ten complete cycles during one second) and amplitude of 5 mm (the units of the amplitude could be any unit related to vibration, e.g. displacement, velocity or acceleration). The time waveform is a plot of time vs. amplitude, and is referred to as the time domain. The time domain signal can be converted into a frequency domain representation, which is in fact the spectrum. The spectrum is a plot of frequency vs. amplitude. The FFT for the time waveform from Fig 8 is plotted in Fig 9. We can clearly read from this plot that the frequency content of the signal is 10 Hz, and that its amplitude at 10 Hz is 5 mm. Fig 8. Vibration spectrum (Reference [2]) Fig 9. FFT time waveform (Reference [2]) What now, if our time waveform has more than one frequency present? Let s take a look at another example. Consider the waveforms in Fig 10 (Reference [2]). In the top graph we have our 10 Hz waveform, called S1. The second waveform is a 25 Hz waveform with amplitude 2 mm, which we can call S2. The third waveform, plotted at the bottom, is S1+S2, which yields a much more complex waveform. Let us examine the FFT for S1+S2, depicted in Fig 9 (Reference [2]). We can clearly observe two peaks in spectrum, namely a 5 mm peak at 10 Hz, and a 2 mm peak at 25 Hz. Thus, by only looking at the spectrum, we can characterize our S1+S2 waveform much better than by examining the waveform from Fig 10 (Reference [2]). Page 21

22 The frequency spectrum is hence much easier to interpret and gives us information that is often impossible to observe by just looking at the time waveform Fig 11 (Reference [2]). FFT is explain more in Appendix 1. Fig 10. Vibration spectrum of S1+S2 Fig 11. FFT time waveform of S1+S2 From the trends in FFT time waveform, we can diagnose the cause behind vibrations. Some of the common vibration causes and its diagnosis are given below: Unbalance For all types of unbalance, the FFT spectrum will show a predominant peak at the 1 rpm frequency of vibration, and the vibration amplitude at the 1 rpm frequency will vary proportional to the square of the rotational speed. If the problem is unbalance, this peak usually dominates the vibration spectrum Fig 12 and 13. (Reference [2]) Fig 12. Vibration measurement locations Fig 13. FFT readings showing vibration Peak due to unbalance. Page 22

23 Eccentricity Eccentricity occurs when the center of rotation is at an offset from the geometric centerline, and this may happen if the pump impeller is eccentric due to a manufacturing or assembly error. In the vibration spectrum, the maximum amplitude occurs at 1 rpm of the eccentric component, and will vary with the load even at constant speeds. In the horizontal direction, a phase shift of 90 will be observed Bent Shaft When a bent shaft is encountered with a pump, the vibrations in the radial as well as in the axial direction will be high. Axial vibrations may be higher than the radial vibrations. The spectrum will normally have 1 and 2 components, as shown in Fig 14. If the: Amplitude of 1 rpm is dominant, then the bend is near the shaft center Amplitude of 2 rpm is dominant, then the bend is near the shaft end. This means that when the probe is moved from vertical plane to horizontal plane, there will be no change in the phase reading. Fig14. Bent Shaft (Reference [2]) Page 23

24 Pump and motor misalignment There are basically two types of misalignment that can occur between the motor and the pump: Angular misalignment the shaft centerlines of the two shafts meet at angle Parallel misalignment the shaft centerlines of the two machines are parallel As shown in Fig 15, angular misalignment primarily subjects the motor and pump shafts to axial vibrations at the 1 rpm frequency. A pure angular misalignment is rare, and thus, misalignment is rarely seen just as 1 rpm peak. Typically, there will be high axial vibrations with both 1 and 2 rpm. However, it is not unusual for 2 or 3 to dominate. These symptoms may also indicate coupling problems (e.g. looseness) as well. A 180 phase difference will be observed when measuring the axial phase on the bearings across the coupling. Parallel misalignment Fig 16 results in two hits per rotation; and, therefore a 2 rpm vibration in the radial direction. Parallel misalignment has similar vibration symptoms compared to angular misalignment. As before, a pure parallel misalignment is rare and is commonly observed to be in conjunction with angular misalignment. Thus, both the 1 and 2 peaks will typically be observed. When the parallel misalignment is predominant, 2 is often larger than 1, but its amplitude relative to 1 may often be dictated by the coupling type. When either angular or parallel misalignment becomes severe, it can generate high amplitude peaks at much higher harmonics - (3 to 8 ) or even a whole series of high frequency harmonics. Fig 15. Angular Misalignment (Reference [2]) Page 24

25 Fig 16. Parallel Misalignment (Reference [2]) Blade pass and vane pass vibrations Blade pass or vane pass frequencies are vibrations inherent to pumps and fans. In itself, it usually not problematic or destructive, but can generate a lot of noise and vibration that can be the source of bearing failure and wear of machine components. Blade Pass Frequency (BPF) = number of blades (or vanes) rpm This frequency is generated mainly due to the gap problems between the rotor and the stator. Large amplitude BPF (and its harmonics) can be generated in a pump, if the gap between the rotating vanes and the stationary diffusers is not kept equal all the way around. In centrifugal pumps, the gap between the impeller tip and the volute tongue or the diffuser inlet is in the region of 4-6% of the impeller diameter, depending on the speed of the pump. If the gap is less than the recommended value, it can generate a noise that resembles cavitation. However, a vibration reading will immediately reveal the vane pass frequency of the impeller Fig 17. Also, the BPF (or its harmonics) sometimes coincides with a system natural frequency, causing high vibrations. Fig 17. Page 25

26 Fig 17. FFT waveform pattern for Vane pass pulsations A high BPF can be generated if the wear ring seizes on the shaft or if the welds that fasten the diffusers fail. In addition, a high BPF can be caused by abrupt bends in line work (or duct), obstructions which disturb the flow path, or if the pump impeller is positioned eccentrically within the housing Flow turbulence In pumps, flow turbulence induces vortices and wakes in the clearance space between the impeller vane tips and the diffuser or volute lips. Dynamic pressure fluctuations or pulsations produced in this way can result in shaft vibrations because the pressure pulses impinge on the impeller. Flow past a restriction in pipe can produce turbulence or flow induced vibrations. The pulsation could produce noise and vibration over a wide frequency range. The frequencies are related to the flow velocity and geometry of the obstruction. These in turn excite resonant frequencies in other pipe components. The shearing action produces vortices that are converted to pressure disturbances at the pipe wall, which may cause localized vibration excitation of the pipe or its components. It has been observed that vortex flow is even higher when a system s acoustic resonance coincides with the generated frequency from the source. The vortices produce broadband turbulent energy centered on the frequency determined by the following formula: f = S n V D Page 26

27 Where f = vortex frequency (Hz), Sn = Strouhl number (dimensionless, between 0.2 and 0.5), D = characteristic dimension of the obstruction. An example of a vibration spectrum due to turbulence is shown in Fig 18. Fig 18 - FFT waveform pattern for Flow turbulence (Reference [2]) Cavitation Cavitation normally generates random, high frequency broadband energy, which is sometimes superimposed with the blade pass frequency harmonics. Gases under pressure can dissolve in a liquid. When the pressure is reduced. Under conditions when the reduced pressure approaches the vapor pressure of the liquid (even at low temperatures), it causes the liquid to vaporize. As these vapor bubbles travel further into the impeller, the pressure rises again causing the bubbles to collapse or implode. This implosion has the potential to disturb the pump performance and cause damage to the pump s internal components. This phenomenon is called cavitation. Each implosion of a bubble generates a kind of impact, which tends to generate high-frequency random vibrations, as depicted in Fig 19. Cavitation can be quite destructive to internal pump components if left uncorrected. It is often responsible for the erosion of impeller vanes. Page 27

28 Measurements to detect cavitation are usually not taken on bearing housings, but rather on the suction piping or pump casing. Fig 19 - FFT waveform pattern for Cavitation (Reference [2]) 5.0 VIBRATION MONITORING Vibration Monitoring or Condition monitoring (CM) is the process of monitoring a parameter of conditions in machinery (vibration, temperature, etc.), in order to identify a significant change which is indicative of a developing fault. It is a major component of predictive maintenance. The use of conditional monitoring allows maintenance to be scheduled, or other actions to be taken to prevent failure and avoid its consequences. Condition monitoring techniques are normally used on rotating equipment and other machinery such as pumps, electric motors, internal combustion engines and presses. Since corrosion can lead to unexpected failures that can be costly in terms of repair costs, environmental damage and potential harm to humans, condition monitoring is indispensable to avoid these consequences. By considering all information, which are explained before, it helps us to predict the failures. Page 28

29 6.0 EXPERIMENTAL INVESTIGATION In order to investigate the system, there are two measurements, which are operated at the same time, and these are defined in following ways. At the first step, the measurement is to determine the following characteristic of single-stage centrifugal pump at 11 deferent revolution number (from 480 to 1500 RPM). In the second step, the aim is to investigate the effect of vibration on turbomachine and by using the vibration monitoring techniques. Here it is possible to investigate the changes of amplitudes and frequencies, in order to explain the behavior of turbomachine under vibration effects. As it was mentioned, both steps are doing at the same time, which means by setting a constant revolution number and changing the flow rate by a throttle valve, first of all we measure characteristics of the pump and second of all investigate the spectrum (which is recording by a program called Lab View on the computer in the laboratory of HDS department). 6.1 CENTTRIFUGAL PUMP MEASUREMENT To determine following characteristics of the single-stage centrifugal pump, it is needed to define the functions: H = f 1 (Q) Head as a function of flow rate. P i = f 2 (Q) Input power as a function of flow rare. η = f 3 (Q) Efficiency as a function of flow rate. Low of affinity can be employ. The sketch of the experimental test rig is shown in Fig 21. The water arrives from the reservoir to a centrifugal pump (single-stage) (P) which is driven by the electric motor (M). Then the fluid enters into the pump at the suction side (I) and it leaves at the pressure side (II) through the pipeline towards the metering orifice (MO) and at the final stage, it goes back at the reservoir through the throttle valve (TV). The configuration of the test rig is shown on next page. (Reference [13]) Page 29

30 Fig 21 Test rig (Reference [13]) Manometer 2 Manometer 1 Throttle valve Fig 22 Manometers and Throttle Valve Page 30

31 Rotational speed (revolution number) was controlled by an electric setting board Fig 23. Speed controller Fig 23 Rotational speed controller The rotational speeds were checked by using a Jaquet indicator in the motor Fig 24. Fig 24 Jaquet indicator Page 31

32 Balancing motor Centrifugal Pump Fig 25 Balancing motor and Centrifugal pump Formulae for the calculation Although I tried to give a short explanation of used quantities and equations. During the measurement operating point is set by the help of the throttle valve (TV). (Reference [13]) Inner diameter of the pipe D=53 mm Type of pump BMS 25/48 Type of balancing motor Efk 56 I 4 Arm length of the balancing motor k = 716 mm Diameter of the orifice plate d=30 mm Page 32

33 Measurement of flow rate (Q) Flow rate can be measured by a flange tap orifice according to MSZ ISO Q = α d2 π 4 2 p p ρ water, p p = h 1 g(ρ Hg ρ water ) (1) where: Q is flow rate [m 3 /s], d is orifice throat diameter [m], α is discharge coefficient [-], ρ water is density of water 1000[Kg/m 3 ], p p is pressure drop through the orifice [Pa], ρ Hg is density of mercury 13600[Kg/m 3 ], h 1 Height of Manometer 1 [Hgmm], g is gravity 9.81[m/s 2 ]. Although the value of the discharge coefficient should be determined according to standard in an iterative manner, since its value depends on Reynolds number (Re = v d/ν = Qd/(A ν) ) (we approximate its value to be constant) and the kinematic viscosity is10 6 [m 2 /s]. By subsuming the needed quantities to make a simple equation of this test-rig according to an iterative manner to determine the discharge coefficient by considering an approximation constant Reynolds number. Q[m 3 /s] = [ [m3 /s] Hgmm ] h 1[Hgmm] (2) Head (H) According to definition of the head of the pump and subsuming it to employ the pressure balance equation for manometer 1 and neglecting the geodetic height deference (ρ Hg ρ water ) H = h 1 + Q2 ρ water ( d2 2 π 1 4 ) 2g (3) where: H is head [m], Q is flow rate [m 3 /s], d is orifice throat diameter [m], ρ water is density of water 1000[Kg/m 3 ], ρ Hg is density of mercury 13600[Kg/m 3 ], h 1 Height of Manometer 1 [Hgmm], g is gravity 9.81[m/s 2 ]. Page 33

34 Substituting the known quantities the head is m H[m] = [ ] h 1 [m] [ m 6 /s 2] (Q[m3 /s]) 2 (4) Input Power (Pi) The input power [W] is the mechanical power of the shaft which produces the torque M t [Nm] on the shaft and angular velocity [Rad/s] (5) P i = M t ω The torque acting on the shaft is measured by balancing motor (M) and can be calculated by M t = (m m 0 )g k (6) The mass needed to balance the motor is expressed by: m 0 = ( n n ) ( )2 (7) Where: m is the measured balancing mass[kg], m 0 is the balancing mass needed for idle run[kg], K Arm length of balancing motor [mm], n is revolution number [rpm]. Useful Power (Pu) Efficiency of Pump (η) P u = Q ρ water g H (8) Efficiency of the pump is the fraction of the useful power and input power η = P u /P i (9) where: P u is useful power [w], P i is input power [W]. Page 34

35 6.1.2 Calculation of Quantities In order to make the calculation easier, every units of quantities where converted to the SI units and it has been calculated on Excel. h2 pred Δh 2[Hgmm] Δh 1[Hgmm] m [kg] Q H M P useful P input η η [%] Fig 26 Data calculated in excel for revolution number 1000 [RPM] Page 35

36 Efficiency [-] Head [m] Department of Hydrodynamic Systems The mathematic way to evaluate the number of measurement to predict the different heights on manometer 2 which defines the sets of changes in flow rates is explained in Appendix (3). As all the quantities and needed equations for calculation of the characteristic curve of the pump were expressed, so I am able to plot the curves and identify the polynomial equations of the curves by using Excel. A diagram showing the relationship between 2 variable but interdependent quantities which are heads and flows rate and efficiencies of the pump. In order to contain all the calculations, I added all the diagrams in Appendix (4). H = f 1 (Q) Head as a function of flow rate. Characteristic curve of the pump y = x x Flow Rate [m3/s] at n1000 Poly. (at n1000) Fig 27 Characteristic curve of the pump at revolution number 1000[RPM] η = f 3 (Q) Efficiency as a function of flow rate. Efficiency curve of the pump y = x x Flow Rate [m3/s] at n1000 Poly. (at n1000) Fig 28 Efficiency curve of the pump at revolution number 1000[RPM] Page 36

37 6.2 INVESTIGATION OF VIBRATION MONITORING In order to demonstrate the practical usage of vibration monitoring in a turbomachine, the following experiment was performed. As it was mention before during this measurement, the most important aim is the investigation of the vibration caused by a turbomachine. The configuration of the Test-rig was explained in the previous step, except the part which we can measure the vibration spectrum. Although it is necessary to show the configuration. So the Testrig is exactly the same like what was explained in before but in order to show the sensor and computer, I added the Fig 29. Fig 29 The Test-rig (Reference [14]) The sketch of the system is shown on Fig 29. A BMS 25/48 type centrifugal pump (S) is integrated to the system, the suction side of the pump connects to a water tank. On the vertical pressure side there is a built-in Hottinger Baldwin Messtechnik type pressure transmitter (P) with the measuring range of 0-10 bar. The signal of the pressure transducer goes to Hottinger KWS 3072 type signal processing system (J), from there towards to the computer. Page 37

38 Head [m] Department of Hydrodynamic Systems Analysis of the results Our measurement consisted 11 different amount of revolution number which was controlled by an electronic setting board Fig.(23) with each having various amount of different flow rate where the maximum flow rate was measured when the throttle valve was fully open. Than as we controlled the throttle valve we obtained different flow rates, until the throttle valve was fully closed. Each time the flow rate was set, we calculated the head at each throttle valve position since their relationship is fundemental for the characteristic curve of the centrifugal pump. The characteristic curve contains the different points with respect to the number of flow rates with the number of heads. Fig.(30). Characteristic Curve of the Centrifugal Pump Minimum fully closed Flow Rate [m3/s] Each point has a Spectrum Maximum Fully open n480 n600 n700 n800 n900 n1000 n1100 n1200 n1300 n1400 n1500 Poly. (n480) Poly. (n600) Poly. (n700) Poly. (n800) Poly. (n900) Poly. (n1000) Fig 30 - Characteristic Curve of the Centrifugal Pump (Taken from Excel calculation) Page 38

39 There are many different methods available for analyzing vibration data. The most basic method involves displaying the vibration data in the frequency domain, also called the vibration spectrum. The frequency of the vibration is the number of vibration cycles per time unit. The vibration spectrum is fundamental to vibration monitoring, because it yields the information that is effectively "hidden" in the vibration waveform. We have one vibration spectrum for each measurement of the flow rate which is emphasized by the arrows in the Fig 30. (From maximum to minimum). The figure below will consist an example of the vibration spectrum Fig 31. Rotational speed Harmonics Blade Pass Fig 31 The Vibration Spectrum (Taken from MATLAB solution) Page 39

40 From each revolution number we gather the vibration spectrums hence the different flow rates and plot them in a 3D diagram (X,Y,Z) which consist three axis Frequency[Hz], Amplitude[V] and Flow rate[m 3 /s] respectively. This 3D diagram is called the Waterfall diagram which is a form of data visualization that helps in understanding the cumulative effect of noises and vibrations in the centrifugal pump. With the help of this diagram we can explain the phenomenon such as the Unbalance, Parallel misalignment, Blade pass, Vortex shedding and etc. The waterfall diagram can be seen in Fig 32. Fig 32 Waterfall Diagram of revolution number 1000[RPM] Page 40

41 In case of a high revolution number it is difficult to read and examine the waterfall diagram due to too many vibration spectrums. Therefore to make it clearer, a Contour plot is defined in our MATLAB code which help us to investigate the spectrum pattern easier and more efficient. We build this plot by converting the vector of frequency and flowrate into the matrix form in which we can see the intensity of maximum peaks and minimum peaks easily with the help of different shades of colors. This can be seen in the figure below Fig 33. Fig 33 Contour plot of revolution number 1000[RPM] Page 41

42 Rotational Speed at 1100 [RPM] Unbalance Fig 33 Unusual wave which can be effect of unbalance In this waterfall diagram an unusual wave can be seen and it can be caused by unbalance. Unbalance can make vibration on the turbomachinery and the proof was having vibration during the measurement. The waterfall diagram is given to make it more visible what changes are happening in the waves. For all types of unbalance, the FFT spectrum will show a predominant peak at the 1 rpm frequency of vibration, and the vibration amplitude at the 1 rpm frequency will vary proportional to the square of the rotational speed. If the problem is unbalance, this peak usually dominates the vibration spectrum. The low rotational speed were not discoursed because, during the measurement at low revolution number (rotational speed), motor was mostly balanced. Page 42

43 Rotational speed at 1400 [RPM] One of the interesting measurement which had high vibration at the high flow rate, it was when we set the revolution number to 1400 [RPM], see Fig 34. However, from the waterfall diagram it can be discoursed, what is the reason of the vibration and in which region it was happened. Blade pass Fig 34 Wave form pattern of Blade pass frequency As mentioned in page 41, to be able to analyze the waterfall diagram Fig.34 better, we shall use the contour plot diagram. Thus, the region of the blade pass frequency is shown in the Fig 35 with red color. Page 43

44 Blade Pass frequency Fig 35 Surface plot of blade pass frequency pattern is shown in Red region Blade pass or vane pass frequencies are vibrations inherent to pumps and fans. In itself, it usually not problematic or destructive, but can generate a lot of noise and vibration that can be the source of bearing failure and wear of machine components. Regarding to our centrifugal pump which has 7 blades. Blade Pass Frequency (BPF) = number of blades (or vanes) rpm This frequency is generated mainly due to the gap problems between the rotor and the stator. However, a vibration reading will immediately reveal the vane pass frequency of the impeller. Also, the BPF (or its harmonics) sometimes coincides with a system natural frequency, causing high vibrations. It can be the reason of having a bit high vibration at rotational speed 1400[RMP]. Page 44

45 The last but not least, it is an unusual non uniform alignment of peak which can be seen in brown region in Fig 35 can be indirect effect of cavitation. My educated guess is that at high values of flow rate decrease and increase of amplitude in the peaks in frequencies above 150 Hz can be seen. One of the reasons which this happens, could be the as a result of cavitation. At high flow rates flow velocity rises and pressure drops. If this pressure drop is big enough, there is a chance of cavitation happening between the blades. But the other guess is that indirect effect of cavitation might be everywhere at high frequencies which can be the reason of having noise and it can have effect on all the spectrum but as we are not able to see the phenomenon on the suction side of the pump so it is hard to discussed about it and can be as a question in this project. Page 45

46 Rotational Speed at 1500 [RPM] Due to our experiment, the most noises and vibrations were happing at this rotational speed (n=1500 [RPM]), which makes it more important to investigate on this rotational speed, which is critical in our measurement and it can cause some failure in the centrifugal pump if it works for a long time (be used) at this set rotational speed (n=1500 [RPM]) Vortex shedding Fig 36 Effect of Vortex Shedding (Vortices frequency) in the Red region Vortex shedding can be the effect of having this low peak waves which it is shown in red region in Fig 36, which can be called random waves either. As it was mentioned in Subtitle 4.2.6, in pumps, flow turbulence induces vortices and wakes in the clearance space between the impeller vane tips and the diffuser or volute lips. Dynamic pressure fluctuations or pulsations produced in this way can result in shaft vibrations because the pressure pulses impinge on the impeller. Flow past a restriction in pipe can produce turbulence or flow induced vibrations. The pulsation could produce noise and vibration over a wide frequency range. In this case, it can make excited resonant frequency in pipe-line. Page 46

47 1x Fig 37 Effect of Parallel Misalignment in the Red region As it is show in the Red region, see Fig 37. It is possible to express that mainly at low flow rate (0 to 1[m 3 /s]), we usually have high vibration and loud noise which can be caused by the connection between Pump and Motor, which is called Parallel Misalignment. As a pure parallel misalignment is rare and is commonly observed to be in conjunction with angular misalignment. Thus, both the 1 and 2 peaks will typically be observed. When the parallel misalignment is predominant, 2 is often larger than 1, but its amplitude relative to 1 may often be dictated by the coupling type. It can generate high amplitude peaks at much higher harmonics - (3 to 8 ) or even a whole series of high frequency harmonics. Page 47

48 During the performance of this particular measurement, a loud noise was heard while the equipment was functioning from the beginning until the end that is why the measurement at this rotational speed is more discussable. One of the important factors which cannot be eliminated, is the existence of unbalance motor which can have a negative effect on the Centrifugal Pump. The reason we emphasize it is because during our measurement we observed the unbalance motor vibrating intensively, which was recorded by camera. The other reason of vibration is usually vane pass frequency (Blade pass frequency) in most of the performances. Page 48

49 7.0 SUMMARY AND CONCULSION The main task of this Project was to summarize the reasons of turbomachine failure and a way of monitoring those causes during the operation of the turbomachine. Furthermore, the analysis of the results of Condition Monitoring (Vibration Monitoring) was explained with a practical experiment performed in the laboratory of the Department of Hydrodynamic Systems of the Budapest University of Technology and Economics. The results of our measurement indicate a significant variation in vibration trend as a function of operating conditions. The experimental results demonstrated that the vibration monitoring rig modeled various modes of machine failure. Failure can be caused either by single phenomenon or simultaneous phenomenon. Such phenomenon are as follows: Balancing Motor which can become unbalanced sometimes which will affect the measurement itself. Parallel Misalignment (misalignment of pump and motor) Blade pass and Vane pass Vortex shedding In this measurement an experimental test system was set up and we were able to perform practical tests on the constructed rig to confirm the expected theoretical frequencies that we needed. This experiment was offered complementary strengths in the cause of the analysis of machine failure, and natural allies in diagnosing machine condition. It reinforces indications correlation between vibration condition monitoring and fault diagnosis for centrifugal pump. Both amplitude of the dominating peak and its location along the frequency axis changes in various conditions of pump. Furthermore it can be emphasized that based on my observation during the measurement, when the revolution number was approaching 1500 [RPM], the noise of the turbomachine would dramatically increase when the flow rate was at its maximum. Thus, we can indicate that the noise was as result of high vibration. However, with the same revolution number (rotational speed) but lower flow rate the noise was not that much. Page 49

50 References 1. Jardine, A. K., Lin, D., & Banjevic, D. (2006). A review on machinery diagnostics and prognostics implementing condition-based maintenance.mechanical systems and signal processing, 20(7), Comelius Scheffer Pump Condition Monitoring Through Vibration Analysis Pumps; Maintenance, Design, and Reliability Conference, Centrifugal Pumps 2nd ed Edition, Springer,ISBN Igor J Karassik and Ray Cartor, Centrifugal pumps, Tata McGraw Hill Book Company 2 nd edition, Jauregui, J. C. (2014). Parameter identification and monitoring of mechanical systems under nonlinear vibration. Elsevier. 6. E. Oran Brigham, The Fast Fourier Transform and its applications, Prentice-Hall International Editions 1 st edition Entek IRD International Introduction to vibration technology Edition I, Jul 1984, Tata McGraw hills. 8. Laggan PA Vibration monitoring. IEE Colloquium on Understanding your Condition Monitoring 9. Marcal RFM, Negreiros M, Susin AA, Kovaleski JL Detecting faults in rotating machines. J Instrumentation & Measurement Magazine Wachel, J. C. (1992). Acoustic Pulsation Problems in Compressors and Pumps. Engineering Dynamics Inc ENG/FM_1_CentrifugalPump.pdf Page 50

51 Web Pages: I declare that I used these web pages to understand more about vibration monitoring of centrifugal pumps and their issues ite%20paper%20pumps%20web.pdf Page 51

52 Appendix The first part of my appendix is the numerical expression of FFT (Fast Fourier Transform) which is the method to make the vibration spectrum in Lab view software. Vibration spectrum can be represented in various different ways, of which the Fast Fourier Transform (FFT) is the most popular. Some basic definition was mentioned in the definition part of this thesis, but for more mathematic background, it is necessary to attached more definition which is going to be in appendix (1). Regarding to my supervisor advice, I used the lecture notes of a subject which was lectured by Dr. Hegedus (Measurement technique of Process) at Budapest University of Technology and Economics (BME). I should say thank to Mr. Xabier Manceras Ibarra who documented them on a PDF file which really helped me to use them. Also, I detected a book to complete the first part of this appendix which is located in the references. (Reference [6]) 1. FFT (Fast Fourier Transform) A fundamental application of the FFT is to the multifaceted areas of transform analysis. By developing the relationship between discrete and continues Fourier transforms, we can use the discrete Fourier transform to yields a close approximation to the continues Fourier transform, we expect significant usage of the FFT in computing Fourier transforms. In applying the FFT to the computation of Fourier transforms, keep in mind the most important concept that the discrete Fourier transform implies is periodicity in both the time and frequency domains. If one always remembers that N sample values of the time function represent on period of periodic function, the application of the FFT should result in few surprises. Page 52

53 A. Curve fitting for Continuous functions i) Let g(t) be an approximation function to another f(t) function: Where fi(t) can be either: Periodic function: sin(t), cos(t) Non periodic function: To get the best of approximations we want the distance between both functions to be minimal at all points, it being zero the optimal situation and so: Page 53

54 ii) Let us say we now have vectors. What we would now want to find is the so called orthogonal projection: Best approximation would be that one where the difference between f and g is minimal at all points: As we have N equations for ai, then we will also have N unknowns in our system of equations: B. Continuous periodic Fourier series Function: (t); (t) = (t + T) periodic Basis set:..... Page 54

55 The Fourier approximation of the periodic function would be: Where Inner product is defined as: frequency of the function and T its period. The cosine and sine series are orthogonal to each other, so: Thus, Integral average It is important to note that the Fourier series can be used also in non-periodical functions. C. Discontinuities in when using Fourier approximations: If there is a discontinuity in the function, an error will appear at that point when applying the discrete Fourier approximation. That error will remain regardless of the amount of harmonics used. Here is an example of a discontinuous functions trying to be approximated using the discrete Fourier transform with the use of (i) one, (ii) three, (iii) five, (iv) seven, (v) thirteen, (vi) fifty and (vii) one hundred of harmonics, respectively: Page 55

56 (i) (iv) (ii) (v) (iii) (vi) (vii ) Page 56

57 Spectra: Where: A i = a i 2 + b i 2 Amplitude phase Page 57

58 D. Complex formalism: e iω = cos(ω) + j sin(ω) Function: f(t) Real Basis set: fi = e j ωit ; ; i = N,, N Approximation: Inner product: Properties: If f(t) is real then: ci = c i ai = ci + c i bi = (ci c i) E. Discrete trigonometry: Function: set: fi = (ti) Basis Page 58

59 Inner product: Approximation: F. Discrete Fourier Transform (DFT): This is the special case where the amount of measured point equals the number of basis: n = N There are no stability problems if the sampling rate is high enough, that is, if Δt is small enough. Minor remark: - Fast Fourier Transformation (FFT) can be used instead of the discrete Fourier method. The fast Fourier transform is a simple discrete Fourier transform but very fast. The reason is the amount of basis needed in each of the transforms: FFT~N log (N) DFT~N 2 Page 59

60 G. Shannon sampling theory / Aliasing: When choosing a sampling frequency ( t fs) for a given signal, a problem arises when the chosen frequency is too small: Let us say the original signal is the red one, which has a frequency of 10 Hz. By arbitrarily choosing a sample frequency of 10 Hz we would get 10 different points that can be joined in an infinite amount of ways, being the blue line the most simple of all. By doing so, the original function has been alienated and as a result the new signal looks nothing like the original one. This effect is called aliasing and it needs to be avoided. To avoid aliasing frequencies this is what should be done when using the Fourier Transform: bk = e j 2π fk is periodic in 2π q =,, 1, 0, 1,, ti = r t Equidistant, where r = 0,1, Page 60

61 2. MATLAB CODE function DataLoad close all figure(1); hold on;counter=0; NumberOfMeasurement = 10; ExcelFileName = 'Measure_excel.xlsx'; [Status, Sheets] = xlsfinfo(excelfilename); SerialNumbers = xlsread(excelfilename, Sheets{NumberOfMeasurement}, 'D2:D100'); FlowRate = xlsread(excelfilename, Sheets{NumberOfMeasurement}, 'K2:K100'); Head = xlsread(excelfilename, Sheets{NumberOfMeasurement}, 'L2:L100'); Efficiency = xlsread(excelfilename, Sheets{NumberOfMeasurement}, 'P2:P100'); IntesityMatrix=[]; for k=serialnumbers(1):serialnumbers(end); SpectraFileName{k} = strcat( Sheets{NumberOfMeasurement}, '\', Sheets{NumberOfMeasurement}, '_', num2str(k), '.txt' ); counter=counter+1; FID = fopen(spectrafilename{k}); HeaderLines = textscan(fid, '%s',8); Data = textscan(fid, '%f %f'); X=Data{1}; Y=Data{2}; IntesityMatrix = [IntesityMatrix; Y']; fclose(fid); Z=ones(length(X),1)*FlowRate(k); end RightPlot = plot3(z,x,y); set(gca,'zscale','log','ydir','reverse'); grid on box on xlabel('flow Rate','fontsize',14); zlabel('amplitude','fontsize',14); ylabel('frequency','fontsize',14); [Amax(counter) Index]=max(Y); Fmax(counter)=X(Index); Qmax(counter)=Z(Index); Page 61

62 RightPlot = plot3(qmax,fmax,amax); set(rightplot,'displayname',spectrafilename{k},'linestyle','none','mar ker','.','markersize',15); set(gca,'zscale','log','ydir','reverse'); hold off; figure(2); hold on; [xx,yy]=meshgrid(x,flowrate); size(intesitymatrix) surf(xx,yy,log(intesitymatrix),'linestyle','none'); ylabel('flow Rate [m3/s]','fontsize',14); xlabel('frequency [Hz]','fontsize',14); % It is optional to run the Figure 5, 4 and 3 figure(5); hold on; plot(x,y); grid on box on xlabel('frequency','fontsize',14); ylabel('amplitude','fontsize',14); grid on box on figure(3); hold on; plot(flowrate,efficiency); xlabel('flow Rate [m^3/s]','fontsize',14); ylabel('efficiency [-]','fontsize',14); grid on box on figure(4); hold on; plot(flowrate,head); xlabel('flow Rate [m^3/s]','fontsize',14); ylabel('head [m]','fontsize',14); grid on box on Page 62

63 3. Evaluating the predicted height of Manometer 2 To be able to understand, how we made more mathematical the evaluation of the measurement numbers and applying it to our measurement to make this processes easier, so it is necessary to define this process in this thesis. However, to make the measurement easier, a method was applied to predict the height of Manometer 2 which is used to measure the flow rate. So by considering the fully open Throttle valve which is the maximum flow rate and it s readable as a maximum height on Manometer- 2. Thus, we can evaluate our predicted height of Manometer 2 and by using this height, we can get the flow rate in unit of [ m 3 /s]. Where: i = 1,2,3,.., n h 2,predicted = ( h 2,max N N = 1,2,3,.., n: The number of measurement. (i 1)) h 2,max : The maximum height of Manometer 2. (Fully open Throttle valve). 2 Page 63

64 Head [m] Department of Hydrodynamic Systems 4. Characteristic Curves Characteristic Curves n480 n600 n700 n800 n900 n1000 n1100 n1200 n1300 n1400 n1500 Poly. (n480) Poly. (n600) Poly. (n700) Poly. (n800) Poly. (n900) Poly. (n1000) Poly. (n1100) Poly. (n1200) Poly. (n1300) Poly. (n1400) Poly. (n1500) Flow Rate [m3/s] Page 64

65 Efficiency Department of Hydrodynamic Systems 0.4 Efficiency of pump 0.35 n480 n n700 n800 n900 n1000 n1100 n1200 n1300 n1400 n1500 Poly. (n480) Poly. (n600) Poly. (n700) Poly. (n800) Poly. (n900) Poly. (n1000) Poly. (n1100) Poly. (n1200) Poly. (n1300) Poly. (n1400) Poly. (n1500) Flow Rate [m3/s] Page 65

66 5. Some of Remaining Waterfall diagrams and Surface Plots These are some more waterfall diagrams that can be used for further analysis. The revolution speed of each of the diagram has been noted. n = 480 rmp Page 66

67 n = 600 rmp Page 67

68 n = 1000 rmp Page 68