Fault Detection and Condition Assessment using Vibration

Fault Detection and Condition Assessment using

Vibration Analysis and Failure Mode and Effect Analysis

Daníel Jónsson

Faculty of Industrial Engineering, Mechanical Engineering and Computer Science

University of Iceland 2020

Fault Detection and Condition Assessment using

Vibration Analysis and Failure Mode and Effect Analysis

Daníel Jónsson

60 ECTS thesis submitted in partial fulfillment of a

Magister Scientiarum degree in Mechanical Engineering

MS Committee

Magnús Þór Jónsson

Rafn Magnús Jónsson

Thomas Philip Rúnarsson

Faculty of Industrial Engineering, Mechanical Engineering and Computer science.

School of Engineering and Natural Sciences

University of Iceland

Reykjavik, May 2020

Fault Detection and Condition Assessment using Vibration Analysis and Failure Mode and

Effect Analysis.

Fault Detection & Condition Assessment.

60 ECTS thesis submitted in partial fulfillment of a Magister Scientiarum degree in

Mechanical Engineering

Copyright © 2020 Daníel Jónsson

All rights reserved

Faculty of Industrial Engineering,

Mechanical Engineering and Computer Science

School of Engineering and Natural Sciences

University of Iceland

VR II, Hjarðarhagi 6

107, Reykjavik

Iceland

Telephone: 525 4000

Bibliographic information:

Daníel Jónsson, 2020, Fault Detection and Condition Assessments using Vibration

Analysis and Failure Mode and Effect Analysis, Master’s thesis, Faculty of Industrial

Engineering, Mechanical Engineering and Computer Science, University of Iceland.

Printing: Háskólaprent, Fálkagata 2, 107 Reykjavik

Reykjavik, Iceland, May 2020

Abstract

Modern day industry often depends on rotating machinery operating constantly all year

around. A well-organized and planned maintenance strategy is one of the key features to

obtain a constant and safe operation. To conduct a successful maintenance strategy its

crucial to be able to monitor machines condition when in operation. Numerous ways are

used to monitor machines conditions where one of the main methods is vibration

monitoring and analysis. The reason that initiated this thesis was problematic operation in

one of the main centrifugal fan’s bearings, in one the fume treatment plants at Norðurál

aluminum factory. The main objective of this study is to design and develop a vibration

measurement and analysis system. The system is used to collect vibration data, from the

centrifugal fan’s plummer block bearings, and utilizes known vibration analysis methods to

assess the bearings current condition and to estimate its remaining useful life. Failure

Mode and Effect Analysis (FMEA) is performed on the centrifugal fan components and

setup to establish some indication to pinpoint the bearing problem causes.

The results from the vibration analysis conducted in this study, using the measurements

gathered from the centrifugal fan’s plummer block bearings, showed various fault

indications. The remaining useful life estimation indicated to short bearing life, although

there are some parts of the methodology used that need adjustments and/or modifications

to fit better for this thesis.

Útdráttur

Í nútíma iðnaði er mikið treyst á vélar og tæki sem þurfa að ganga stanslaust allt árið um

kring. Eitt af lykilatriðum til að viðhalda stöðugum og öruggum rekstri er vel skipulögð

viðhaldsáætlun. Til að geta starfrækt vel heppnaða viðhaldsáætlun er nauðsynlegt að geta

fylgst með ástandi vélbúnaðar meðan hann er í rekstri. Margskonar leiðir eru notaðar til að

fylgjast með ástandi vélbúnaðar, þar sem ein af aðal aðferðunum er að fylgjast með titring

og framkvæma titringsgreiningar. Kveikjan að þessu verkefni var vandræða ástand á einni

af búkkalegum í einum aðalblásara reykhreinsivirkis eitt í álveri Norðuráls. Eitt aðal

markmið þessa verkefnis er að hanna og þróa titrings mælingar og greiningar kerfi. Kerfið

er notað til að safna titringsmælingum, frá búkkalegum aðalblásarana, og nýta þekktar

aðferðir til þess að greina mælingarnar til að leggja mat á núverandi ástand og áætla líftíma

legana. Framkvæmd er FMEA greining á íhlutum og skipulagi blásarans til þess að draga

fram vísbendingar um ástæður bilana.

Niðurstöður titringsgreiningar sem framkvæmd var í þessu verkefni, með mælingum

safnað frá búkkalegum aðalblásaranna, sýndi vísbendingar mismunandi bilanir.

Líftímagreining gaf til kynna of stuttan líftíma lega, þó svo að ákveðna hluti

aðferðarfræðinnar þurfi að stilla og/eða breyta til að passa betur að verkefninu.

v

Dedication

I would like to dedicate this thesis foremost to my family, my wife Heiða and my sons

Sigmar and Daníel. With their emotional and moral support, I got the strength to keep

pushing forward and finish this thesis.

vi

Table of Contents

List of Figures ............................................................................................................... viii

List of Tables ................................................................................................................ xiv

Nomenclature................................................................................................................. xv

Acknowledgements ...................................................................................................... xvii

1 Introduction .............................................................................................................. 19

2 Background ............................................................................................................... 21

2.1 Maintenance Strategies ...................................................................................... 21 2.1.1 Breakdown Maintenance ........................................................................... 21

2.1.2 Preventive Maintenance ............................................................................ 21 2.1.3 Predictive Maintenance ............................................................................. 22

2.1.4 Proactive Maintenance .............................................................................. 22 2.2 Failure and Risk Assessment .............................................................................. 23

2.2.1 Failure Mode and Effect Analysis ............................................................. 23 2.2.2 Root Cause Analysis ................................................................................. 28

2.2.3 Fault Tree Analysis ................................................................................... 30 2.3 Condition Monitoring ........................................................................................ 34

2.3.1 Vibration Measurements and Transducers ................................................. 36 2.3.2 Oil/Lubricant Analysis .............................................................................. 43

2.3.3 Thermography .......................................................................................... 44 2.3.4 Performance Analysis ............................................................................... 45

3 Vibration Signals....................................................................................................... 47 3.1 Theory and Classification................................................................................... 47

3.1.1 Vibration Theory ...................................................................................... 47 3.1.2 Vibration Signal Classification.................................................................. 51

3.2 Vibration Signals from Rotating Machinery ....................................................... 53 3.2.1 Shaft Frequency and its Harmonics ........................................................... 54

3.2.2 Rolling Element Bearings ......................................................................... 57 3.2.3 Bladed Machines ...................................................................................... 61

4 Signal Processing and Analysis................................................................................. 63 4.1 Signal Processing Techniques ............................................................................ 63

4.1.1 Signal Conditioning .................................................................................. 63 4.1.2 Fourier Analysis ....................................................................................... 70

4.1.3 Envelope Analysis .................................................................................... 75 4.2 Detection, Diagnostics, and Prognostics ............................................................. 76

4.2.1 Fault Detection ......................................................................................... 77 4.2.2 Diagnostic Techniques .............................................................................. 78

4.2.3 Prognosis .................................................................................................. 81

vii

5 Case Study at Norðurál Aluminum Plant ................................................................ 87

5.1 Fan Setup and History ........................................................................................ 88 5.1.1 Components and Operational Conditions ................................................... 88

5.1.2 Plummer Block Bearings Maintenance History ......................................... 90 5.2 Vibration Measurement and Analysis System ..................................................... 92

5.2.1 Localized Equipment................................................................................. 93 5.2.2 Portable Equipment ................................................................................. 100

5.2.3 Vibration Analysis Software.................................................................... 102 5.3 Assessments and Condition Measurements ....................................................... 104

5.3.1 Assessing Causes for Short Bearing Life ................................................. 104 5.3.2 Assessing Condition and Fault Development using Vibration Analysis ... 109

5.3.3 Remaining Useful Life Estimation .......................................................... 124

6 Conclusions .............................................................................................................. 127

Bibliography ................................................................................................................. 129

Appendices ................................................................................................................... 133

viii

List of Figures

Figure 1: Example of generic FMEA worksheet. ............................................................. 25

Figure 2: Example of severity and occurrence scales. ...................................................... 25

Figure 3: Example of Process FMEA detection scale [5]. ................................................. 26

Figure 4: The logical relationship between FMEA elements [4]. ...................................... 27

Figure 5: Example of a RCA procedure. .......................................................................... 28

Figure 6: Example of a "Five-Whys" problem and solution.............................................. 29

Figure 7: Example of the Cause and Effect Diagram. ....................................................... 30

Figure 8: Example of fault tree event and gate symbols. .................................................. 32

Figure 9: Example of hydrolic system and corresponding fault tree. ................................ 34

Figure 10: Scheme of a vibration measurement and analysis system. ............................... 36

Figure 11: Comparison between Absolute- and Relative Measurements. .......................... 37

Figure 12: Comparison between mounting setups for proximity probes. .......................... 38

Figure 13: Scheme of a Eddy current based proximity probe system. ............................... 39

Figure 14: Two basic types of velocity transducers, Magnet-In-Coil and Coil-In-

Magnet. ......................................................................................................... 40

Figure 15: Three main types of accelerometers, Compression, Bending, and Shear. ......... 40

Figure 16:Typical compression type piezoelectric accelerometer with top connection. ..... 41

Figure 17: Methods for mounting accelerometers. ........................................................... 42

Figure 18: Thermal images of faulty components. ........................................................... 44

Figure 19: Example of a Mass-Spring-Damper System. ................................................... 47

Figure 20: Harmonic cycle, locus of mass-spring motion with respect to time.................. 48

Figure 21: Relations between displacement, velocity, and acceleration. ........................... 49

Figure 22: Vibration spectrum displayed in time domain and frequency domain. ............. 50

Figure 23: Amplitudes comparison for a single harmonic wave. ...................................... 50

ix

Figure 24: Examples of different signal types and their spectral content. .......................... 52

Figure 25: Simplified schematic picture of centrifugal fan setup. ..................................... 53

Figure 26: Comparison between static and dynamic unbalance. ....................................... 54

Figure 27: Comparison between possible misalignments in coupled connections. ............ 55

Figure 28: Typical frequency spectrums for parallel and/or angular misalignments. ......... 56

Figure 29: Examples of mechanical looseness and typical vibration response. .................. 56

Figure 30: Nomenclature of a ball bearing and common types of roller and ball

bearings. ........................................................................................................ 57

Figure 31: Bearing life model, showing common frequency spectrums for each stage. ..... 59

Figure 32: Frequency spectrums of common cases on bladed machines. .......................... 61

Figure 33: Basic non-inverting operational amplifier circuit. ............................................ 64

Figure 34: Schematic diagram of a Delta-Sigma type analog-to-digital converter [14]. ..... 64

Figure 35: Frequency aliasing due to an inadequate sampling rate. ................................... 67

Figure 36: Coparison between response curves for the four main filter types. ................... 68

Figure 37: Leakage error appearing in frequency spectrum, for the non-periodic

signal. ............................................................................................................ 69

Figure 38: Comparison between Rectangular, Hanning, and Flat Top weighting

functions. ....................................................................................................... 70

Figure 39: Matrix representation of the DFT. ................................................................... 73

Figure 40: Matrix B, a modified version of matrix Wkn, with rows shifted. ....................... 74

Figure 41: Factorization of matrix B into three factor matrices X, Y, and Z. .................... 75

Figure 42: Envelope analysis procedure using the Hilbert transform method. ................... 76

Figure 43: Comparison of two spectra, with direct digital comparison, with no

change in operational condition...................................................................... 78

Figure 44: The process of calculating the Spectral Kurtosis of a simulated bearing

vibration signal with localized fault on inner raceway. ................................... 79

Figure 45: Fast Kurtogram for measurement number 2150 of bearing number 3 from

the IMS-Dataset 1. ......................................................................................... 80

Figure 46: Comparison on calculated SK with optimal bandpass filter and with no

filter. .............................................................................................................. 81

x

Figure 47: Trend of kurtosis for bearing 3 from IMS dataset no.1, inner raceway fault

develops at end of lifetime. ............................................................................ 83

Figure 48: Prognostic method as proposed by J.W.Hines & A. Usynin in [29] ................. 85

Figure 49: Norðurál aluminum plant and the location of the pot rooms and FTP’s. .......... 87

Figure 50: Sideview of one of the centrefugal fans and a list of it’s major components .... 88

Figure 51: Current bearing setup and impeller for fans in FTP-1 and FTP-2..................... 89

Figure 52: Rough estimation on force distribution along the driveshaft and the

bearings. ........................................................................................................ 90

Figure 53: Sooted grease in main fan 2 plummer block bearings, in FTP-1. ..................... 91

Figure 54: Damages found in main fan 2 Fan DE bearing, during grease change.............. 92

Figure 55: Electrical circuit for a fifth-order Butterworth filter without any

amplification, where R and C denotes the resistors and the capacitors............ 93

Figure 56: The electrical circuit for fifth-order Butterworth low-pass filter with 1000

Hz cut-off frequency and 22 dB amplification. .............................................. 95

Figure 57: Power circuit for a single accelerometer and a low-pass filter. ........................ 96

Figure 58: Filters theoretical respone displayed on Bode diagram. ................................... 96

Figure 59: The real frequency response of the filters, measured with the oscilloscope. ..... 97

Figure 60: The compact filter unit, with six 1000 Hz low-pass Butterworth filters. .......... 97

Figure 61: NI USB-6000 ADC dimensions and key specifications. .................................. 98

Figure 62: CMCP1100 accelerometer dimensions and key specification. ......................... 98

Figure 63: Localized equipment fitted inside an electric cabinet....................................... 99

Figure 64: Locacalized equipment at site, with electric cabinet connected to 230 V

power grid and accelerometers mounted on bearing housings with

magnetic bases. ........................................................................................... 100

Figure 65: DT9837B dynamic signal analyzer and its key specifications........................ 100

Figure 66: High frequency accelerometer and mounting parts dimensions and setup. ..... 101

Figure 67: Accelerometers mounted on bearing housings, fitted in the eyebolts

threaded holes. ............................................................................................ 101

Figure 68: Graphical user interface for the vibration measurement and analysis

software. ..................................................................................................... 102

xi

Figure 69: Flowchart of measurement and saving process. ............................................. 102

Figure 70: Flowchart for the single measurement analysis process, (continued

flowchart from Figure 69). ........................................................................... 103

Figure 71: Flowchart for the multiple measurement analysis process, (continued

flowchart from Figure 70). ........................................................................... 104

Figure 72: Development of the pot rooms amperage since the year 2010, and time of

bearing change on main fans 1 and 2 in FTP-1. ............................................ 108

Figure 73: Fan DE bearing frequency spectrum, on main fan 1 in FTP-1, from July

2019. ........................................................................................................... 112

Figure 74:Fan DE bearing frequency spectrum, on main fan 1 in FTP-1, from May

2020 ............................................................................................................ 112

Figure 75: Vibration signals envelope comparison between first and last

measurements on Fan DE bearing on main fan 1, in FTP-1. ......................... 113

Figure 76: FTP-1 main fan 1 Fan DE bearing, waterfall graph of the 1.5 kHz to 25

kHz frequency spectrums, from July 2019 to May 2020. .............................. 114

Figure 77: Spectrogram of the first and last vibration measurements, on Fan DE

bearing. ........................................................................................................ 114

Figure 78:Fan DE bearing frequency spectrum, from July 2019 (Bearing New). ............ 115

Figure 79: Envelope spectrum of Fan DE bearing, taken in July 2019 (Bearing New). ... 116

Figure 80: Fan DE bearing frequency spectrum for main fan 2 in FTP-1, from May

2020. ........................................................................................................... 116

Figure 81: Envelope spectrum of Fan DE bearing, taken in May 2020. .......................... 117

Figure 82:Vibration signals envelope comparison between first and last

measurements performed on Fan DE bearing on main fan 2, in FTP-1. ........ 117

Figure 83: Fan DE bearing, waterfall graph of the 1 kHz to 30 kHz frequency

spectrums, from July 2019 to May 2020, for main fan 2 on FTP-1. .............. 118

Figure 84: Frequency spectrums comparison between first and last measurements

performed on Fan DE bearing on main fan 4, in FTP-1. ............................... 119

Figure 85: Envelope spectrums comparison between first and last measurements





performed on Fan DE bearing on main fan 3, in FTP-2 ................................ 121

xii







Figure 91: Overall RMS vibration level for all measurements performed on the Fan

DE bearing, on main fan 2 in FTP-1. ........................................................... 124

Figure 92: Overall RMS vibration level for all measurements after bearing change,

with linear and exponetial trending curves. .................................................. 125

Figure 93: Mean frequency, Skewness, Kurtosis, and Crest factor for all

measurements performed on the Fan DE bearing, on main fan 2 in FTP-

1. ................................................................................................................. 126

Figure 94: ISO 10816-3 vibration severity classification. ............................................... 133

Figure 95: General vibration severity chart, for rotating machinery. ............................... 134

Figure 96: DT9837B Dynamic Signal Analyzer's block diagram. .................................. 141

Figure 97: Visualization on GUI operation, Select data type, load data, and select

amplitude representation. ............................................................................. 143

Figure 98: Visualization on GUI operation, Selecting sensor and weighting window. .... 144

Figure 99: Visualization on GUI operation. Bearing fault frequencies loaded from

database and manually calculated, scale settings, and display of bearing

fault frequencies and geometric parameters. ................................................ 145

Figure 100: Visualization on GUI operation. Measurement settings, CI selection,

Spectrogram setting, and Envelope settings. ................................................ 146

Figure 101: Frequency spectrum comparison between July 2019 and May 2020 for

the Fan ND bearing on main fan 1, in FTP-1. .............................................. 150

Figure 102: Vibration signals envelope comparison between July 2019 and May

2020 for the Fan ND bearing on main fan 1, in FTP-1. ................................ 150


the Fan ND bearing on main fan 2, in FTP-1. .............................................. 151

Figure 104: Vibration signals envelope comparison between July 2019 and May

2020 for the Fan ND bearing on main fan 2, in FTP-1. ................................ 151

Figure 105: Fan DE bearing, waterfall graph of the 1 kHz to 30 kHz frequency

spectrums, from July 2019 to May 2020, for main fan 4 in FTP-1................ 152

xiii


the Fan ND bearing on main fan 4, in FTP-1 ................................................ 152

xiv

List of Tables

Table 1: Accelerometer advantages and disadvantages, comparison between types. ......... 42

Table 2: Span, Dynamic Range, and Signal-to-Noise comparison between common

bit size Analog-to-Digital Converters. ........................................................... 66

Table 3: Date of bearing changes for the plummer block bearings on main fans in

fume treatment plants 1 and 2, with bearings running hours at each time. ...... 90

Table 4: Calculated and used sizes of capacitors. ............................................................. 95

Table 5: Accelerometers amplitude factors. ..................................................................... 99

Table 6: Failure modes, effects, and causes with highest RPN for main fan 2 in FTP-

1, summ-up from the full FMEA-worksheet listed in Table 17, in

appendix F................................................................................................... 106

Table 7: Initial condition assessments on plummer block bearings on main fans in

FTP-1. ......................................................................................................... 110

Table 8: Initial condition assessments on plummer block bearings on main fans in

FTP-2. ......................................................................................................... 110

Table 9: BPFO and BPFI amplitudes comparison between measurements ..................... 118

Table 10: Information on main fan plummer block bearings data, operational data,

and bearing fault frequencies. ...................................................................... 135

Table 11: Fan DE and ND Bearings Lubricant Technical Data (optained from SKF

website). ...................................................................................................... 136

Table 12: Maintenance history for fume treatment plants 1 and 2, for bearings and

grease change interval, for the years 2008 to the summer of 2019. ............... 137

Table 13: Components list for the localized equipment low-pass filter unit (6 filters

in one box). ................................................................................................. 138

Table 14: NI-USB-6000 Analog-to-Digital converter specifications .............................. 139

Table 15: Vibration transducers specifications for the localized equipment. ................... 140

Table 16: Wilcoxon model 736T high frequency accelerometer specifications. .............. 142

Table 17: FMEA-worksheet for main fan 2 in FTP-1 (spreads over three pages). ........... 147

xv

Nomenclature

ADC Analog to Digital Converter

BPF Blade Pass Frequency

BPFI Ball Pass Frequency Inner

BPFO Ball Pass Frequency Outer

BSF Ball Spin Frequency

CED Cause and Effect Diagram

CF Crest Factor

CoM Center of Mass

CPB

DE

Constant Percentage Bandwidth

Drive End

DFT

FD-CI

Discrete Fourier Transform

Frequency-Domain Condition Indicator

FFT Fast Fourier Transform

FMEA Failure Mode and Effect Analysis

FP Failure Probability

FTA

FTP

Fault Tree Analysis

Fume Treatment Plant

FTF

GUI

Fundamental Train Frequency

Graphical User Interface

MTTF

ND

Mean Time to Failure

Non-Drive end

R Reliability

RCA Root Cause Analysis

xvi

REB Rolling Element Bearing

RMS Root Mean Square

RPN Risk Priority Number

RUL

SE

Remaining Useful Life

Spectral Entropy

SK Spectral Kurtosis

SNR Signal to Noise Ratio

STFT

TD-CI

TF-CI

Short Time Fourier Transform

Time-Domain Condition Indicator

Time-Frequency-domain Condition Indicator

xvii

Acknowledgements

I would first like to thank my thesis instructor professor Magnús Þór Jónsson of the

Mechanical engineering department at University of Iceland. Every time I ran into trouble

or had questions regarding the thesis Prof. Jónsson was always willing to help me and

guide me in the right direction.

I would also like to thank Norðurál ehf. for their financial support and financing on the

measurement equipment used during the case study. Without their support this thesis

would surely never been possible.

I would also like to thank Mr. Vilhjálmur Ívar Sigurjónsson for his help during the

preparation of the measurement equipment and all the obstacles we had to overcome to get

everything working.

Finally, I would like to thank the experts, MSc. Rafn Magnús Jónsson, MSc. Einar Friðgeir

Björnsson, and Mr. Bjarni Tryggvason for their contribution on collecting information

during the case study within this thesis.

19

1 Introduction

In today’s world there are countless variations of industries with different process plants

with all types of machinery. Running a good maintenance strategy is one of the most

important part to ensure a good, safe, and reliable operation. The methodology for

assessing the condition of a machinery has evolved greatly over the last decades regarding

techniques, equipment, digital instrument, and computers. Despite decades of experience

and effort we are still trying to achieve the technique of complete prognostics. Monitoring

the condition of machinery vibration analysis is a major part of trying to achieve that goal.

Originally machines were run till they stopped because some component of the machine

broke down, this type of maintenance is called Breakdown maintenance. Next maintenance

strategy was so-called Preventive maintenance, which is based on performing maintenance

work in predetermined intervals so that there is a little chance on failure between repairs.

Predictive maintenance came thereafter, where the philosophy is based on scheduling

maintenance activities from the current condition of the machine. To utilize this

philosophy, it is crucial to be able to determine the internal condition while the machine is

still in operation. There are two main ways to determine the condition of an operating

machine and they are vibration analysis and oil analysis [1], although other methods are

also known.

In modern industry there is a high demand for companies to obtain a reliable operation and

most of all safe for personnel and its surroundings. With constantly increasing complexity

of machinery and their components multiple methods have been developed in last decades

to support and help companies to achieve this goal. Most of these methods are constructed

to identify and locate possible failure modes and to understand the interconnections

between them to try to eliminate them or reduce their affects. To be able to utilize these

techniques, companies must be willing to modify and adjust their operation accordingly to

improve the operation reliability and safety.

Industrial processes usually contain multiple rotating machines working individually or

together, forming complex systems with multiple functions. To be able to assess the

operational condition of each machine or its components it is essential to extract

information that give some indication on the current condition. One of the corner stones in

condition-based maintenance is measuring machines vibration level and is one of the most

widely used method to monitor machines condition. Vibration analysis utilizes the fact that

rotating machines in operation always generate some sort of vibration and to exploit the

features of vibration analysis it is crucial to be able to identify normal operation from

faulty operation.

The vibration generated by a machine can often be linked to periodic events happening

inside the machine, like the rotating driveshaft, meshing gearteeth, rolling element

bearings, and so on. To be able to identify and isolate the vibration source many frequency

analysis techniques have been developed. These methods were designed to detect and

diagnose faulty states and provide information that is utilized for prognosis. To be able to

extract the condition information from a vibration data, and since vast majority of the

20

vibration analysis techniques used today are performed with the help of computers, signal

processing is needed. Signal processing is used to classify all the steps performed on the

vibration data e.g. analog filtering, Analog-to-Digital conversion, windowing, analyzing,

displaying, etc. With computer power constantly increasing the ability to exploit these

methods has increased greatly.

The main objectives in this study is divided into two parts, were the first part is to utilize a

known failure and risk assessment method to identify causes for unusual short operation on

a machine. The second part is to design and develop a vibration measurement and analysis

system. The system is used to perform and collect vibration measurements and to perform

vibration analysis with methods to evaluate machine current condition and also to estimate

its remaining useful life.

To explore these objectives, a case study at Norðuál aluminum plant was performed, where

a large centrifugal fan in one of the companies fume treatment plants has been having

unusual short bearing life. A failure mode and effect analysis is performed on the fan and

its components to establish the cause for the short bearing life. The vibration measurement

and analysis system was put to use to collect vibration measurements and analyze them, to

perform condition assessment on the bearings and to see if there are any factors in the

vibration data to identify and locate the causes for this problem that the company is having.

The thesis is constructed as follows. Chapter 2 is a background review on known

maintenance strategies, failure and risk assessment methods, and general discussion on

condition monitoring and its techniques and equipment. In Chapter 3 the theory on

vibration signals and their classification is presented along with discussion on vibration

signals generated by rotating machinery. In Chapter 4 the signal processing methods used

in this thesis are presented. In Chapter 5 the case study is presented along with the process

of designing and developing the vibration measurement and analysis system. Then finally

Chapter 6 contains general discussion and conclusions.

21

2 Background

In this chapter the most common maintenance strategies used in today’s industry will be

discussed. There are many failure and risk assessments methods known to be practiced for

all sorts of industries and they all have similar objectives. That is to support companies, no

matter what industry they are in, to obtain a reliable operation. The methods, Failure mode

and effect analysis, Root cause analysis, and Fault tree analysis will be introduced.

Common condition monitoring methods and their advantages will be introduced, where

vibration measurements and transducers used when conducting vibration measurements

will be discussed, along with oil analysis, thermography, and performance analysis.

2.1 Maintenance Strategies

There are many maintenance strategies being used in today’s industry and it depends

greatly on the industry or nature of the operation which strategy is used. Most widely

known maintenance strategies today are Breakdown-, Preventive-, Predictive-, and

Proactive-Maintenance.

2.1.1 Breakdown Maintenance

Breakdown maintenance is the most traditional method, where machines are simply run

until they stop or break down because some part of that machine gets damaged. With this

type of maintenance, there is a high possibility of getting the longest time between failures.

The problem with this is when failure occurs it can be catastrophic which lead to multiple

failures and possibly total breakdown of the machine. Breakdown maintenance is

especially inconvenient where multiple machines work together e.g. in a process line

where the whole line stops if one component breaks down. There is also a possibility that

when one component breaks down it damages other parts of the process line. Resulting in a

great increase in repair- and downtime which lead to higher repair cost. In many industries

the downtime is the most expensive factor because it leads to a production loss which

sometimes is much higher than a single machine in the process line. For complex

industries this type of maintenance is hardly ever used, unless there is a backup system.

For less complex industries there is still room for breakdown maintenance e.g. factories

that uses many small machines to produce the same product, and where production rate is

not affected much if one machine breaks down and the failure is unlikely to be catastrophic

[1].

2.1.2 Preventive Maintenance

This type of maintenance is carried out by repairing or changing individual parts of a

machine at regular intervals, usually based on running hours of a machine or calendar days,

so that it is unlikely that the machine breaks down in the meantime. Intervals are often

decided so that the chance of a breakdown of failure between repairs is close to 1-2% [1].

This results that most of the machines could have run two or three times longer between

22

repairs [2]. This philosophy is good for machines that do not run continuously, and the

main advantage is the ability to plan maintenance well ahead and performed at a

convenient time considering production. The risk of catastrophic failure is also greatly

reduced and therefore personal safety of the production is increased. The disadvantages are

that there is still a possibility of unforeseen failures to occur and usually there is too much

maintenance work performed on machines. Using this method means that sometimes a

perfectly good component of a machine is changed for a new one, resulting in a higher

spare part cost. With unnecessary maintenance work the risk of diminished performance

increases and introduces failures that otherwise would not have happened [3].

2.1.3 Predictive Maintenance

Predictive maintenance, also called ‘Condition-Based Maintenance’, is as the name

indicates a method that uses condition measurements to predict for potential failure in a

machine. The condition of machines components is periodically monitored and when

faulty trends start to appear, a maintenance work is scheduled. The method requires that

the maintenance department has access to reliable condition monitoring technique with the

ability to give a good assessment on the current condition and also reasonable estimation

on the remaining lifetime [1]. An obvious advantage is the ability to plan a work directly

from the condition of the machine, meaning that the maintenance work is performed at the

most convenient time. Usually machines components, like bearings, have some indication

that a failure is imminent sometimes weeks or months. Meaning that all spare parts and

materials needed are ordered in time and the work planned and the machine stopped at the

optimum time. Resulting in reduction in the need for large inventory of spare parts. For

over 40 years this method has been used with some success, but initially available

monitoring techniques were limited and surely not always used correctly. In the last 20 or

so years this method is recognized to be most suitable for most cases [1]. A small

disadvantage is that maintenance work is often performed unnecessary because of a wrong

failure analysis. If a company is going to use this type of maintenance, it is essential that

they use specialized equipment suiting their production and properly train their

maintenance crew. For this strategy to work the management must support their

maintenance department and also provide all the necessary equipment and regular training

courses to maintain knowledge within the company [3].

2.1.4 Proactive Maintenance

Proactive maintenance utilizes all the aspects of predictive maintenance and its techniques

but adds the analyzing the root cause of the failure. The fundamental objective of this type

of maintenance is to analyze and perform proactive measures to prevent these failures to

happen again. The strategy uses root cause analysis (RCA) to detect and pinpoint the

problems that cause failure, also it ensures that right techniques are used for installation

and repair. One advantage is it can pinpoint the need for modification or redesign on a

machine to ensure some failure does not happen again [3].

23

2.2 Failure and Risk Assessment

The demand for a reliable and safe operation is increasing each year at the same time

machineries and their components are getting more complex. This causes problems for

companies to keep up with safe and reliability of their operation. Operational reliability

and safety are conventionally accomplished with testing and modification on the operation,

but also with well trained workers both in production and in maintenance. Murphy’s Law

states “If anything can go wrong, it will” assuming that’s true, companies must try to do

everything in their power to prevent that. There are many methods available to help

companies establish safe and reliable operation, and to list just few we have,

• Failure Modes and Effect Analysis (FMEA)

• Root Cause Analysis (RCA)

• Fault Tree Analysis (FTA)

These methods are used in all sorts of industries at all stages of production from the

development or design to manufacturing.

2.2.1 Failure Mode and Effect Analysis

FMEA was first introduced in 1949 by the U.S. Armed Forces with introduction of

Military Procedures document (MIL-P)-1629, “Procedures for Performing a Failure Mode

Effect and Criticality Analysis”. In the 1960s it was used in the Apollo space program to

minimize risk because of the small sample size. Ford Motor Company introduced FMEA

to the automotive industry in the 1970s for safety and regulatory purposes. Automotive

industry started implementing FMEA in the 1980s with standardizing the structure and

methods. FMEA is now used in vast variety of industries throughout the world [4]

FMEA Main Objective

FMEA primary objective is in general to improve the design of the system, subsystems,

components, manufacturing process, and operation. Many other objectives are for

conducting FMEA like,

• Identify and prevent all safety hazards that can occur

• Try to minimize production loss

• Increase production performance

• Implement changes to production- and/or manufacturing processes

• Identify process characteristics

• Develop plans for preventive maintenance strategies [4]

It is important to understand that FMEA is a powerful tool to achieve these objectives, but

there are limitations too FMEA because it does not model the interactions between failures.

If it’s necessary to understand or model the relationships between failures and their causes

and effect a FTA is most likely the proper tool, it is often used with FMEA [4].

24

FMEA Types

There are three types of FMEA that are most common, they are:

• System FMEA

• Design FMEA

• Process FMEA

System FMEA is the highest level of analysis where entire system with all its subsystems

and components is analyzed. It focuses on all system related deficiencies e.g. safety,

integration, interactions between system and other systems, interaction between

subsystems, interaction between subsystems components, interaction with surrounding,

and human interference. Basically, all issues that can affect the overall system not to

function properly. Unique functions and relationships for the system is the focus in system

FMEA [4].

Design FMEA focuses on the design aspect of a product, usually at the subsystems or their

component. Where design-related deficiencies and improvement on the design is the focus

especially considering safety and reliability during operation [4].

Process FMEA focuses on the manufacturing process and how to improve it to ensure that

a product is manufactured according to design requirements. The aim is also to achieve

that goal in a safe way with as little downtime as possible and best possible efficiency.

Process FMEA includes operations in manufacturing and assembly, shipping of products

and incoming materials and parts, storage, labeling, and tool maintenance [4].

FMEA is a systemized group of actions designed to recognize potential failure modes

within a system and evaluate them by severity and probability. Understand the effects

failures can cause on the system and assess the potential risk they could cause, then

prioritize so right actions are carried out [4]. Too utilize FMEA to its fullest it is ideal that

it is carried out by a team of experts with different specialty. Whether it is in design-,

manufacturing-, and/or operation process the objective is to find and correct failures before

they cause larger problems [4].

Figure 1 illustrates an example of generic worksheet with typical FMEA columns. The

Item column lists up each item which the FMEA is going to focus on. Examples on items

are e.g. hydraulic pump, thrust bearing, gearbox, and furnish burner etc. Function column

lists up what each item is intended to do, sometimes items have many functions and it is

important to describe the function(s) as good as possible. Potential Failure Modes lists up

potential failures that can occur for each item, or every way the item is not functioning

properly decided by the analysis team. There may be more than one and sometimes many

failure modes for each function of an item. Potential Effect(s) of Failure lists up every

possible way a failure can impact the system or end user. It depends on the nature of the

analysis if the team decides to use single description of the effect on the system or three

levels of effect, like: [4]

• Local Effect. The impact the failure has on the item or adjacent items

• Next Higher-Level Effect. The impact the failure has on next higher-level

assembly

• End Effect. The impact a failure has on the top-level system and/or end user

25

Often there are many effects for each failure, but for most applications the analysis team

uses only the ones with most serious effects [4].

Figure 1: Example of generic FMEA worksheet.

Severity column lists up how serious the effects are from a failure. Severity scale can vary

from one analysis to another all depends on the size and complexity of the analysis. Often

there are used five or ten ranking levels for severity, for ten ranking levels the one is least

serious and ten being the most serious and is decided regardless of the likelihood of it

happening or being detected Potential Cause(s) of Failure column lists up the reason for

the failure to occur, which is usually found by the team members constantly asking each

other “why did this happen” until they determine the root cause, often there are more than

one cause for each failure. Occurrence column lists the likelihood that a failure and causes

occur in the item being analyzed, like the severity-scale this is a ranking scale usually from

one to ten [4]. Figure 2 shows typical construction of severity and occurrence scales.

Figure 2: Example of severity and occurrence scales.

Current Design Controls columns list up the methods that are planned or are already in

use to prevent or at least reduce the risk that potential failures cause and prevent

catastrophic brake down. As before often there are more than one control for each cause.

Based on pacific criteria the Detection column lists the ranking number associated with the

Responsible

Person

Actions

Taken

Target

Completion

Date

Effective

Completion

Date

1 2 3 4 5 6 7 8 8 9 10 11

Occ

urr

en

ce Current

Design

Controls

(Prevention)

Current

Design

Controls

(Detection) De

tect

ion

R P

N Recommended

Action(s)Ite

m

Function

Potential

Failure

Mode

Potential

Effect(s)

of Failure Seve

rity Potential

Cause(s)

of Failure

Likelihood

of FailureIncidents per Item Rank Effect Severity of Effect Rank

Very High ≥1 in 10 10Failure mode affects safe operation and/or

does not complies with regulations without warning.10

1 in 20 9Failure mode affects safe operation and/or

does not complies with regulations with warning.9

1 in 50 8Loss of main function

(machine inoperable, does not affect safe operation)8

1 in 100 7Degradation of primary function

(machine operable, at reduced performance)7

1 in 500 6Loss of secondary function

(machine operable but lower level components inoperable).6

1 in 2000 5Degradation of secondary function

(machine operable but lower level components at reduced 5

1 in 10,000 4Appearance and/or audible noise(s)

Noticed by most of the users/operators (>75%).4

1 in 100,000 3Appearance and/or audible noise(s)

Noticed by many of the users/operators (50%).3

1 in 1,000,000 2Appearance and/or audible noise(s)

Noticed by some of the users/operators (<25%).2

Very Low Failure is eliminated 1 No Effect No effects 1

High

Moderate

Low

Failure to Meet

Safety and/or

Regulations

Loss of Main

Functionality

Loss of

Secondary

Functionality

Frustrating

and/or

Annoying

26

most suitable controls from the detection-type controls. The detection ranking considers

the likelihood a failure/cause is detected based on the criteria used for the FMEA. The

criteria can vary based on what type of operation, manufacturing or process is being

analyzed. It is a relative ranking based on the scope of the FMEA and does not considers

the levels of severity and occurrence [4]. Figure 3 shows an example of process FMEA

detection scale and should be tailored depending on the task at hand.

Figure 3: Example of Process FMEA detection scale [5].

Risk Priority Number (RPN) column lists the numeric ranking of the risk the possible

failures can have. It is made up from following three elements:

• Severity of the effect

• Likelihood of occurrence of the cause

• Likelihood of detection of the cause

definition of RPN is descriped as,

𝑅𝑃𝑁 = 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 ∗ 𝑂𝑐𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 ∗ 𝐷𝑒𝑡𝑒𝑐𝑡𝑖𝑜𝑛 (1)

RPN is not a crucial part of deciding what actions to take against failure modes, they

usually act as threshold values in the evaluation process of these actions. After calculating

the RPN for each failure mode, the ones with the highest RPN should get the highest

priority when deciding appropriate actions. RPN has some limitations and does not

necessary give the right view on the risk involved with a failure mode associated cause.

Recommended Action(s) column lists the appropriate actions the FMEA team suggests

could reduce or prevent the risk associated with each possible cause of failure. These

Opportunity

for Detection

Criteria

Likelihood of Detection by Process ControlRank

Likelihood

of Detection

No Detection

OpportunityNo current process control; cannot detect or is not analyzed. 10

Almost

Impossible

Not Likely to Detect

at any Stage Failure Mode and/or Error (Cause) is not easily detected (e.g., random audits). 9

Very

Remote

Problem Detection

PostprocessingFailure Mode detection postprocessing by operator through visual/tactile/audible means. 8 Remode

Problem Detection

at Source

Failure Mode detection in-station by operator through visual/tactile/audible means or postprocessing

through use of attribute gauging (go/no-go, manual torque check/clicker wrench, etc.).7

Very

Low

Problem Detection

Postprocessing

Failure Mode detection postprocessing by operator through use of variable gauging or in-station by

operator through use of attribute gauging (go/no-go, manual torque check/clicker wrench, etc.).6 Low

Problem Detection

at Source

Failure Mode or Error (Cause) detection in-station by operator through variable gauging or

by automated controls in-station will detect discrepent part and notify operator (light, buzzer, etc.).

Gauging performend on setup and first-piece check (for setup causes only).

5 Moderate

Problem Detection

Postprocessing

Failure Mode detection postprocessing by automated controls that will

detect discrepant part and lock part to prevent further processing.4

Moderately

High

Problem Detection

at Source

Failure Mode detection in-station by automated controls that will detect discrepant part

and automatically lock part in station to prevent further processing.3 High

Error Detection and/or

Problem Preventation

Error (Cause) detection in-station by automated controls that will detect,

error and prevent discrepant part from being made.2

Very

High

Detection Not

Applicable

Error Prevention

Error (Cause) prevention as a result of fixture design, machine design, or part design.

Discrepant part cannot be made because item has been error-proofed by process/product design1

Almost

Certain

27

actions usually consider existing controls, how important the task is, and what is the cost

and effectiveness of the action to the system [4].

Performing FMEA

Procedure to execute a good and inductive FMEA it is crucial that the FMEA team takes

time to evaluate every possible scenario a problem or failure can occur. There is no

standard method for the sequence a FMEA team performs the analysis, however the

following method is widely used [4]:

1. Review the process and list up all the items included in that process.

2. List up all the primary functions each item has.

3. Enter every potential failure mode for each function and corresponding effects.

4. Rank the most serious effects for each failure mode.

5. Enter all the causes for each failure mode and rank them for occurrence.

6. Enter prevention-type controls and detection-type controls for each cause, and

detection-rank the best detection-type control.

7. Analyze each function through RPN.

8. High severity and high RPN functions are reviewed and appropriate actions are

taken to reduce the risk.

9. Review every high risk FMEA issue and every action taken, with management and

next steps decided.

Figure 4 shows the logical relationship between the elements in a FMEA.

Figure 4: The logical relationship between FMEA elements [4].

To sum up, FMEA is a very structured and reliable method for evaluating systems and its

components. The applications and concepts are convenient, and the approach makes

evaluating complex systems more comprehensible. The downside on FMEA is it is often

tedious, time-consuming, and expensive. The approach is not suitable for multiple failure

analysis and human errors can easily be forgotten [6].

28

2.2.2 Root Cause Analysis

Problems or symptoms of problems are often fixed without regards to the actual causes,

which usually leads to recurrence of the same or similar problems.

Root cause analysis (RCA) is a reactive analysis that is carried out after the problem has

occurred. It is a systematic method for identifying root causes of unwanted events or

failures and approach to solve them. Including the identification of the root and

contributory factors, determination, and development of preventive actions along with

measurement strategies to evaluate the effectiveness of these actions. RCA is in theory a

method that uses common sense techniques to produce a systematic, quantified, and

documented approach to identify, understand, and resolve underlying problems [7]. Figure

5 illustrates an example of an RCA 5 step procedure where the steps are:

1. Identify and delimit the problem.

2. Define, describe, and understand the problem.

3. Identify the root cause(s).

4. Suggest and implement required corrective actions.

5. Monitor the system.

Figure 5: Example of a RCA procedure.

There are many methods available for analysis teams to conduct a RCA, depending on

project type, size, and complexity teams decide what method suits them. To name few

common ones:

• Brainstorming

• The “Five Whys”

• Cause & Effect Diagrams

• Fault Tree

A brief introduction on these methods will be in the following sections, in section 2.2.3

Fault Tree Analysis will be discussed.

29

Brainstorming

Brainstorming is a well-known strategy for problem solving certain types of problems that

occur time and a time within companies. It is a strategy based on a group of people

meeting and exchanging ideas to try to solve the problem. There are some pointers for a

good brainstorming session, which are: [7]

• Collect as many ideas as possible from all team members, without criticism or

judgement when ideas are being born.

• Welcome every idea, no matter how silly they may seem.

• Secondary discussions should not take place during the brainstorming.

• Build on every possible idea born.

• Document all ideas.

• After brainstorming, discuss ideas and possibility for solving the problem.

Typically brainstorming is an early stage procedure to try to understand and solve the

problems at hand. When problems become more complex there is need for more powerful

methods.

The “Five-Whys”

The Five-Whys strategy typically refers to the practice of asking why the failure occurred

five time in order to get to the root cause(s) of the problem. It is a method and does not

require any special technique to perform [7]. Figure 6 illustrates an example of a problem

and solution using the Five-Why method.

Figure 6: Example of a "Five-Whys" problem and solution.

Cause & Effect Diagrams

Cause & effect diagrams (CED), also known as Fishbone diagrams or Ishikawa diagrams,

is a useful technique to perform a more complex RCA. This type of diagram is powerful to

identify all potential contributing processes and factors to the problem. It is performed by

successively asking what effects have occurred and why, and then proceed backwards from

last failure to find the cause. It starts with the most significant event and determining the

cause(s) of it, then the cause(s) for this event’s cause(s) are determined. This chain of

events and causes is continued until no other causes are determined, these causes are

30

verified by determining if the criteria for the root cause have been met [8]. Figure 7

illustrates how the Cause and Effects diagram is constructed, also how its structure looks

like a skeleton of a fish, hence the name Fishbone diagram.

Figure 7: Example of the Cause and Effect Diagram.

2.2.3 Fault Tree Analysis

Fault tree analysis (FTA) is an analytical technique widely used in vast varieties of

industry all over the world. Where the goal is to specify undesired states of a system,

normally a state where safety is compromised, then analyze the system in context with its

environment and operation. This is performed to locate or find every way were these

unusual events can occur. The method uses graphical modeling with vast varieties of

parallel and sequential combinations of faults that can occur. Events associated with

components failing, human errors or any other sort of event represent a fault in the system.

The fault tree depicts all basic events and their relations which ends up with undesired

condition on the system [9].

FTA uses Boolean logic to analyze a fault with combining effects of lower level events,

usually to determine the probability of a complex safety hazard. This is performed to

develop actions to reduce or possibly remove any safety concerns existing in the system.

Usually FTA is applied when the consequences from a failure are great and safety

hazardous and the failure is complex with many smaller events contributing to the event

[4].

FTA & FMEA Differences

There is some fundamental difference between FTA and FMEA, the main difference is that

an FTA is a deductive analysis but FMEA is inductive analysis. In short term, deductive

methods are top-down methods that aim to analyze the effects an initializing fault or event

31

has on a system and analyze it to its root cause. Inductive methods are bottom-up analysis

which aim to analyze the effects a single component or part failing has on the system or

sub-systems [9]. Amongst other differences include:

• FTA represents a graphical solution of complex relationships in the system that

lead to failure, when FMEA uses worksheet to represent its solution.

• FTA recognizes any interactions between failures and every sub-level event that

contribute to the failures, also it considers if two or more sub-level events must be

present for the failure to occur. When FMEA normally just considers each

contributor separately.

• FTA is capable to incorporate the probabilities of each of the sub-level events and

their complex relations to the failure. FMEA does not normally support these

probability calculations of the failure. [4]

FTA is a powerful method when it is crucial to understand all interconnected relationships

between top event, usually some type of fault, and their causes and effects. It is common

that a FMEA team uses FTA when the failure mode gets complex with many causes and if

two or more causes are not unique and occur side by side. By doing that the team gets a

better visual image on the problem’s complex nature.

FTA Events and Gates

In FTA the symbols events and gates are used to represent the logic of the analysis, they do

not necessary correlate to the systems components or part. Fault or another unwanted

occurrence is represented both graphicly and mathematically as an event. Each event is

associated with a probability of occurrence or a distribution function. There are multiple

types of events used in FTA and it depends on the complexity of the system how many

types needed for the analysis, but the most common events are: [4]

• Top-Level Event is the event that the FTA focuses mostly on, every gate or sub-

level events lead up to this event.

• Intermediate Event is a resulting fault because of one or more antecedent causes.

• Basic Event is initiating fault that needs no further development.

• Undeveloped Event is event that is not developed further.

• Conditioning Event is some special condition that applies to one or more gates.

• External Event is an event that usually is expected to occur or not.

Gate is a logical symbol used to display interconnecting events and conditions in the fault

tree. There are two basic types of fault tree gates which are AND-gate and OR-gate, these

gates are most common ones used for the FTA, all other types of gates are simply special

cases of those two. The number of inputs to the logical gates are not limited and sometimes

the inputs are multiple for various reasons. The logical gates used in FTA are: [4]

• AND-Gate, where the output event occurs only if all input events occur.

• OR-Gate, where the output event occurs if at least one input event occurs.

• Voting OR-Gate, where the output event occurs if at least certain number of input

events occur.

• Priority AND-Gate, where the output event occurs only if all the input events

occur in a specific order.

32

• Exclusive OR-Gate, where the output event only occurs if exactly one of the input

events occurs.

• Inhibit-Gate, where input event occurs if all input events occur and other

conditional event occurs.

Figure 8 shows example of FTA symbols used for events and gates, even though there is

no universally standardized way to represent them, this is a widely used method.

Figure 8: Example of fault tree event and gate symbols.

FTA Construction

When constructing a fault tree analysis, the method requires input information from the

system being analyzed. Often this information is gained using known failure mode

methods like FMEA or any other recognized strategy that gives deeper understanding on

the system and its complexity. Commonly the inputs to the fault tree are entered as a

probability value, current or expected, of the respective root node. These probability values

are often calculated reliability (R) values or failure-probability (FP) values, where,

𝐹𝑃 = 1 − 𝑅 (2)

Common method for estimating the statistical probability of a failure is based on the

exponential and Weibull distributions, but other methods are also known to be used.

Equation (3) shows the method that uses exponential distribution and assumes the failure

time to be constant. Where (λ) is the inverse of statistically relevant mean time to failure

(MTTF) of the root node, and (t) can represent e.g. running hours of the component

connected to the node event. The time value can easily be replaced by any relevant

parameter that effects the reliability of the system or any of its components [10].

𝐹𝑃𝑒𝑥𝑝 = 1 − 𝑒−𝜆𝑡 (3)

Primary Event Block Classic FTA Symbol Name of Gate Classic FTA Symbol

Basic Event AND

Intermediate Event OR

External Event Voting OR

Undeveloped Event Priority AND

Conditioning Event Exlusive OR

Transfer Inhibit

Fault Tree Symbols

Event Symbols Gate Symbols

33

Weibull distribution is the most widely used distribution type, it has been applied

successfully for years for modeling lifetime calculations for various equipment e.g.

bearings, jet engines, and composite materials. The Weibull distribution consists of two or

three parameters, shape-, nominal life-, and minimum life parameter, which makes it

versatile. Often the minimum lifetime parameter is not used when calculating failure

probability, Equation (4) gives the two parameter version, where (η) is the nominal lifetime

parameter and (β) is the shape factor [10].

𝐹𝑃𝑤𝑒𝑖𝑏 = 1 − 𝑒

−(𝑡𝜂

)𝛽

(4)

Commonly the first guess for η is a value close to the MTTF value of representing

component. Failure occurrence type and the status of the system decides the shape factor β

where the general rule is, [10]

• If β < 1, The system is at its infant mortality stage, where the failure rate decreases

as a function of time

• If β = 1, The system is at its useful service life, where the failure rate is a constant.

• If β > 1, The system is at its wear out period, where the failure rate starts to

increase as a function of time.

Utilizing data from maintenance database and real time monitoring methods, e.g. vibration-

and lubrication measurements, is very effective strategy to get a good indication on the

failure probability. This is very important since statistical modeling on the failure process

and the wear out period is often inaccurate. As described earlier, the failure probability at

each node of the fault tree is calculated with a method based on Boolean algebra, equations

(5) and (6) show the calculation rules for AND & OR gates when the inputs are failure

possibility values [10].

𝐹𝑃𝑂𝑈𝑇𝐴𝑁𝐷= 𝐹𝑃1 ∗ 𝐹𝑃2 … ∗ 𝐹𝑃𝑛 (5)

𝐹𝑃𝑂𝑈𝑇𝑂𝑅= 1 − (1 − 𝐹𝑃1) ∗ (1 − 𝐹𝑃2) ∗ … ∗ (1 − 𝐹𝑃𝑛) (6)

Example on a hydraulic system is illustrated in Figure 9 and its corresponding fault tree.

The system is made up with two hydraulic pumps driven by two electric motors and a

generator supplying electricity. The pumps supply a flow of hydraulic fluid through the

valve for further use. Here the focus is the failure in which is if there is no flow of

hydraulic fluid from the valve, defined as the top event. Next step is to recognize what

could cause this, first the valve could be closed or blocked for some reason, secondly there

could be no flow from either of the pumps and finally there could be a power loss to the

system, since there is one generator supplying both electric motors. These events are

defined as intermediate events and are connected to the top event with OR-gate, since each

one of these events could cause the top event to happen. Next step is to look at each of

these intermediate events and consider, what could cause them to happen. The valve is not

a complex component and requires no further analysis. The generator is a complicated

mechanism and would need much deeper analysis to find the basic events that cause him to

not work, but to keep the complexity level down the generator will not be analyzed further

in this example. The event when there is no flow from the pumps must be considered

further and since there are two pumps, they must both fail so that this event can occur. Two

new intermediate events are created, and they are if there was No hydraulic fluid from

34

pump 1 and No hydraulic fluid from pump 2. These events are connected to the event No

hydraulic fluid from the pumps with AND-gate because they must both occur at the same

time for that event to happen. The intermediate events No hydraulic fluid from pump 1 and

pump2 are each broken down into two basic events, Failure of pump and Failure of motor

which are connected with OR-gate, since either one of these basic events can cause there

was no hydraulic fluid from pump 1 or pump 2.

Figure 9: Example of hydrolic system and corresponding fault tree.

This is an example version of a fault tree but in practice, the FTA team would need to

analyze the system much deeper to get acceptable results.

To sum up, FTA is a powerful tool to identify all possible causes of a specified undesired

event, known as Top Event. FTA is structured as a Top-to-Bottom method, or deductive

analysis. Utilizing FTA leads to deeper knowledge of system characteristics and design

flaws and insufficient operational and maintenance procedures may be reveled and

corrected during the construction of the fault tree. The downside is that FTA is not fully

suitable for modeling dynamic scenarios. FTA is a binary method and therefore it is

possible it fails to address some problems [6].

2.3 Condition Monitoring

Condition monitoring of machinery is when various parameters related to the mechanical

condition of the machinery are measured. These parameters (like vibration, temperature,

lubricant condition, and performance), help make it possible to determine if the machinery

is in good or bad condition. When these parameters indicate that the mechanical condition

is bad, condition monitoring makes it possible to determine the problems cause [11].

There are countless companies and factories in the world that operate constantly all year

around. To prevent unforeseen stop or breakdown on machinery, it is important to monitor

machinery condition. Condition monitoring is a crucial aspect of running a constant

operation, were it is possible to monitor current condition and predict the future condition

35

while machines are in operation. To obtain information regarding the condition, internal

information must be extracted externally while machines are in operation. There are two

main techniques, Vibration- and Lubricant analysis, used to extract this information,

there are other methods also used e.g. Performance- and Thermography analysis [1].

Condition monitoring systems are categorized into two types, Periodic- and Permanent

Monitoring [1].

Periodic Monitoring, where machines condition parameter(s) are measured, then

analyzed, at some certain time interval. The intervals must be sufficiently shorter than the

minimum required lead times for maintenance and production planning purposes. For fault

detection and diagnosis, advanced digital processing techniques are usually needed (see

chapter 4 for further discussion). Periodic monitoring often provides early stage

information about incipient failure and is usually used where, early warning is required,

advanced diagnostics are required, machine has many measurement points, and machines

are complex. Periodic monitoring has some advantages and disadvantages, they are:

• Advantages, Insignificant cost of monitoring equipment and potentially provides

much more advance warning on impending failures.

• Disadvantages, Unforeseen rapid failures could be missed, which lead to a

catastrophic breakdown.

Permanent Monitoring, where machines condition parameter(s) are measured constantly,

at some fixed point or place, and the measurements are compared to acceptable levels

(often some type of standard like ISO). Permanent monitoring is usually used when

machines must be monitored constantly, and to provide a warning if operational condition

worsens or to shut down the machine when preset limit is exceeded. This is used where

failure on a machine can cause a catastrophic failure to production or surrounding

equipment. In a permanent monitoring system, all transducers are fixed to certain

measuring points, often decided by the manufacturer of the machine or appropriating

standard. Permanent monitoring has some advantages and disadvantages, they are:

• Advantages, it has a quick response to sudden change in operational conditions

and therefore protects the equipment best way possible for unforeseen failures.

• Disadvantages, the cost is very high and usually it is only applied to the most

crucial machines and the most expensive ones. Since the response must be fast it

usually monitors noncomplex parameters, like RMS- or Peak-Values (see further in

section 3.1.1). This results in poorer capability to perform advance vibration

analysis on impending failures, meaning that the warning goes from weeks or

months to days or even hours.

But it must be kept in mind that even if transducers are permanently mounted to a machine,

it is still possible to perform advanced analysis on the vibration signals, just not

continuously. This gives the advantage that periodic monitoring is carried out alongside the

permanent monitoring, giving the possibility to perform measurement at much more

frequent intervals [1].

36

In the following sections the subjects listed below will be discussed, they are:

• Vibration Measurements and Transducers

• Lubricant Analysis

• Performance Analysis

• Thermography

Where the focus will be on the vibration section, although the other subjects will get some

brief introduction.

2.3.1 Vibration Measurements and Transducers

Every rotating machinery has one or more rotating machine elements that turn with the

drive shaft. These elements are e.g. rolling element bearings, impellers, and any other type

of rotors. If, in theory, a machine was perfectly balanced all rotors would rotate perfectly

around their centerline and all acting forces would be equal, hence no vibration. In

practice, every rotating machine generates vibration when in operation, even though it’s in

perfect condition. Often this vibration is directly linked to periodic events like rotating

shaft or impeller. These periodic events generate vibration at some certain frequencies,

thus multiple diagnostic techniques have been developed that are based on frequency

analysis. Not every vibration generated in machinery is based on its shaft rotation e.g.

internal combustion engines have fixed number of combustions every engine cycle. Some

vibration can also be linked to fluid flow in e.g. blowers, turbines, fans, compressors, and

pumps, this kind of vibration often has unique characteristics linked to the housing and

impeller geometry.

Vibration Measurements

For machines vibration measurement, some technical equipment is needed. Various

equipment is used in practice, all from instruments that measure overall vibration to

complex multichannel analyzers with numerous features for analyzing the measurement

data. A scheme of a vibration measurement and analysis system is illustrated in Figure 10.

Figure 10: Scheme of a vibration measurement and analysis system.

Vibration measurements are divided into two main categories, Absolute Vibration and

Relative Vibration. Where absolute vibration is the absolute motion of the bearing housing

or any other component being measured. When relative vibration is defined as the relative

motion between a shaft and its casing or bearing house.

37

Absolute vibration measurements are the most common ones in condition monitoring, and

usually performed with accelerometers. This type of measurement gives more possibilities

to perform more deeper analysis on the machines condition

Relative vibration measurements are often used on large machines that use journal-

bearings, since the relative motion of the shaft is closely related to the oil film thickness in

the bearing. Information about the oil thickness are very useful for rotor dynamics

calculations [1]. Comparison between absolute measurement and relative measurement is

illustrated in Figure 11.

Figure 11: Comparison between Absolute- and Relative Measurements.

Vibration Transducers

To measure vibration in machinery or other structure, a vibration transducer is used. A

transducer is a device that converts the mechanical motion (vibration) into equivalent

electrical signal. There are three parameters in which lateral vibration is expressed, they

are displacement, velocity, and acceleration. Commonly these transducers are called,

proximity probes, velocity transducer, and accelerometers. Each type of transducer has

distinct advantages for certain applications, they also have some limitations, so no single

type of transducer satisfies all measurement needs. So, it is important to consider what type

of transducer is best suited for each job [3].

Proximity Probes

Proximity probes, also known as Eddy current transducers, are the favored transducers for

shaft vibration monitoring on large machinery equipped with journal bearings, e.g. steam

generators in a powerplant. Proximity probes are the only transducers that offer

measurement on shafts relative motion against bearing housing or casing. Most bearing

houses have a horizontal split, especially large bearings, thus the proximity probes are

mounted at 45° angle on both sides of the vertical plane. It is extremely important that the

probes are mounted perpendicular to the shaft centerline, deviation by more than 1-2° will

affect the output sensitivity.

38

There are few methods commonly used for installation of proximity probes, which include

internal, internal/external, and external mounting. During internal mounting the proximity

probes are mounted inside the bearing housing with brackets. The transducers are installed

and gapped properly before the bearing cover is installed again, holes are drilled in housing

for transducers cables. During external/internal mounting a mounting adaptor is used,

giving external access to the proximity probe, but the tip of the probe is inside the bearing.

During external mounting, a bracket is fastened on the outside of the bearing housing and

the proximity probe is mounted on that bracket. This is usually last resort installation,

because this method commonly gives less accuracy due to interference [3]. The difference

between these methods is illustrated in Figure 12.

Figure 12: Comparison between mounting setups for proximity probes.

Proximity probe measurement system consist of the probe, extension cable, and a

‘proximitor’ (oscillator/demodulator). The medium in the gap must have a high dielectric

value, often the medium consists of air or another gas and oil in e.g. journal bearings. It is

essential that the surface whose distance from the tip of the probe is being measured is

electrically conducting, to allow eddy currents to be generated by induction. The

‘proximitor’ generates a high frequency signal where its amplitude is directly dependent on

the distance between the surface and the tip of the probe. The cable is manufactured under

strict tolerances, regarding electrical values, and its length cannot be altered with. If a cable

gets damaged, or its shield, it threatens the measurement quality.

A typical proximity probe can measure linearly a gap range from 0.25 to 2.3 mm with

highest deviation from linearity of 0.025 mm, about 1.1% of full scale with a sensitivity of

7.87 V/mm. The ratio of maximum to minimum value gives a dynamic range less than 20

dB, but the ratio of the maximum to minimum component in a spectrum is limited by the

nonlinearity, at best 40 dB [1].

Linearity is not the biggest limiting factor for the dynamic range of the measurement. The

biggest limitation factor is because of so called runout. Runout is defined as the signal

measured in the absence of actual vibration and is composed of mechanical- and electrical

runout. Mechanical runout is caused because of mechanical deviations of the shaft surface

from a true circle, concentric with the rotation axis. These include low-frequency

39

components as eccentricity, shaft bow and out-of-roundness, and short components like

scratches, burrs, and other local surface damage. Electrical runout is caused by variations

in the local surface electrical and magnetic properties, often caused by residual magnetism,

residual- or local stresses in the material as well as imperfection in the subsurface of the

material [1].

The valid frequency range for proximity probes is usually about 10 kHz, but this can often

be misleading, as the true limit is usually given by certain number of shaft speed

harmonics, this is caused by the dynamic range limitation. Rarely the range goes over the

10th harmonic, due to runout restrictions. Because of these restrictions, proximity probes

diagnostics capability is limited, especially for diagnosing imminent failures with long-

term advance [1]. A scheme of proximity probe system, based on Eddy currents, is

illustrated in Figure 13.

Figure 13: Scheme of a Eddy current based proximity probe system.

Velocity Transducers

The velocity transducer, like the name indicates, is a measuring device that measures the

velocity of a vibrating body. It is widely used for vibration monitoring of rotating

machinery. This type easily installs on most common analyzers and is rather inexpensive,

compared to other types of transducers. It is ideal for general purpose machine monitoring

applications and is available in many different physical configurations and output

sensitivities. These transducers are electromechanical sensors and typically have a

seismically suspended coil in the magnetic field of a permanent magnet. Usually the

permanent magnet is mounted fixed to the housing of the transducer, but it is also known

where the coil is mounted fixed to the housing and the magnet is seismically suspended. It

is said that a mass is seismically suspended when it is attached to a body with a spring.

When the body vibrates the mass moves with it at low frequencies, but when the vibration

exceeds the natural frequency of the mass on its spring, the mass will remain fixed in

space, and the body moves around it [1]. In Figure 14 the two basic types of velocity

transducers are illustrated, often referred to as magnet-in-coil and coil-in-magnet.

Theory of operation is when a coil moves in magnetic field, or the magnetic field moves

near a coil, a voltage is induced in the end wires of the coil. As the coil, or magnet, is

forced to move by the vibrating motion of the housing, a voltage signal correlating with the

vibration is produced. The velocity transducer does not require any external devices to

produce voltage signal, it is a self-generating sensor, and the voltage generated by the

transducer is in direct proportion to the velocity of the motion [3].

40

Figure 14: Two basic types of velocity transducers, Magnet-In-Coil and Coil-In-Magnet.

Velocity transducers are sensitive to gravity and therefore their manufactured differently

for vertical or horizontal axis mounting. Because of this sensitivity a caution must be taken

when mounting them to a rotating machinery. Velocity transducers are also susceptible to

cross-axis vibration, that can damage their functionality and give wrong measurements.

Usable frequency range of the velocity transducer is determent by mechanical parameters

of the components. These parameters are, spring stiffness, material damping, and the

weight of the coil/magnet, which determine the low frequency respond of the transducer.

The resonant frequency of the transducer is usually below 10 Hz and the range are often

between 10 Hz and 1000 Hz [8].

Accelerometers

Accelerometers are the most common transducers used for vibration measurements on

rotating machinery. They have many advantages like, lightweight structure, compact and

ruggedly build, and they have a wide frequency response range. Disadvantages are also

very few, like they cannot measure at 0 Hz. These transducers are very commonly used in

condition monitoring on all kinds of machinery [3].

Piezoelectric accelerometers are the most common used in machine condition monitoring.

These sensors use the piezoelectric properties of some solid materials, often some certain

type of crystals or ceramics. When piezoelectric materials undergo deformation, they

generate electric charge that is proportional to strain. The three main design types of

piezoelectric accelerometers are illustrated in Figure 15, they are, compression-, shear-,

and bending-type.

Figure 15: Three main types of accelerometers, Compression, Bending, and Shear.

41

Figure 16 shows the design of a typical compression type accelerometer where a

piezoelectric element is compressed between a seismic mass and the base, forming a

sensing element. The seismic mass is flexibly supported, where the pre-stressed screw with

piezoelectric element act like a very stiff spring. Resulting in a large stiffness to mass ratio

and therefore very high resonant frequency of the sensor and guaranty of a linear behavior.

Figure 16:Typical compression type piezoelectric accelerometer with top connection.

When an accelerometer is mounted on a vibrating body, the seismic mass and the

piezoelectric materials are forced to move with the vibrating body. The vibrating body

causes the seismic mass to apply force on the piezoelectric elements resulting in slight

deformation, giving a strain proportional to the variation in acceleration. This strain on the

piezoelectric elements causes them to produce electrical charge proportional to the

acceleration of the vibrating body. The electric charge produced by the piezoelectric

elements is quoted in picocoulombs per meter per second squared, pC/(m/s2), often

referred to as the sensitivity of the accelerometer. Electric charge is a quantity that cannot

be transmitted over long distances, that’s why modern types of accelerometers have a build

in pre-amplifier. The pre-amplifier converts the electric charge into voltage signal,

common design converts 1 pC to 1 mV, then the sensitivity of the sensor is expressed in

mV/g [1].

The design of the accelerometer allows it to be attached in any orientation to a machine.

The stiffness of the mass/spring system is high enough so that the orientation does not

affect the measurements (unlike the velocity transducer). However, it is crucial that the

piezoelectric element inside the sensor is not exposed to other load than from vibration.

Therefore, it is essential that the surface that the sensor is to be mounted on is smooth and

flat to prevent any deformation of the sensor’s base. Other factors that can cause a

deformation of the base and cause a faulty measurement are, temperature changes and

excessive torque applied to mounting screws. The compression type accelerometer is the

most prone to these factors, but the other two types are much more resistive to them. Each

types advantages and disadvantages are listed in Table 1 [12].

42

Table 1: Accelerometer advantages and disadvantages, comparison between types.

Modern shear type accelerometers are produced as, Delta-Shear accelerometers, it draws it

name from that there are three piezoelectric elements arranged in a triangle and oriented so

that the effects from base deformation are minimized. This type of accelerometer is quite

sensitive and durable and does not have the disadvantages of the compression type. It has

become the most common type of accelerometer used for machines absolute vibration

measurements [12].

Since accelerometers do not contain any moving parts, they are very durable and reliable,

and they do not need to be calibrated frequently, like the velocity transducer. They are

mounted easily onto machines and they can be used where wide frequency range is

required (0.1 Hz to 30 kHz) and they have large dynamic range, they are also available

with high temperature shield [12].

There are several ways to mount accelerometer to a machine, e.g. using a screw or stud,

glue or other adhesive, magnet, and probe, just to name few. It is important to realize that

the sensor only measures what is happening to itself. Keeping that in mind, attachment

method should be chosen that ensures that the sensor measures the same that is happening

to the machine. Inappropriate attachment degrades the measured data and reduce usable

frequency range of the sensor; therefore, attachment must be chosen accordingly to the

frequency range of interest [12]. This is described in detail in ISO-5348 standard. Figure

17 illustrates very common mounting methods and how the frequency range is affected by

the chosen method.

Figure 17: Methods for mounting accelerometers.

Accelerometer Type Advantages Disadvantages

Low sensitivity

Sensitive for temperature effects

Sensitive for base deformation

Fragile and shock sensitive

Shear Type

Compression Type

Bending Type

Wide frequency range

Quite Durable

Low temperature influence

Wide frequency range

Durable to shocks

Very low frequency measurements

Very high sensitivity

43

Accelerometer cabling is an important part of the measurement chain, through the cabling

the signal from the sensor is transmitted to the analyzing equipment. The electric circuit in

the accelerometer, including the piezoelectric elements, has very high impedance and is

subject to some problems, like pickup of signals from electromagnetic radiation. This is

minimized by using coaxial cables with outer braided wire shield, but it is important that

the wire shield is grounded at only one end of the cable. The best cable connection for best

measuring results is the microdot connector, often used for laboratory measurements.

There are many configurations available on the market that are more convenient to use out

in the field, but it is crucial that the person performing the measurements is aware of the

environment conditions that can affect the measurement results [1].

2.3.2 Oil/Lubricant Analysis

Lubricant- or oil analysis has become increasingly more popular through the years when

companies are conducting a predictive maintenance strategy. The method has evolved

greatly through the years and has become a reliable source for condition monitoring. Oil

analysis has become the second most used method in condition monitoring, after vibration

analysis. It is not merely a tool to analyze the state of the lubricant itself, with the latest

diagnostic tools, it is used as a reliable tool to evaluate the condition of machinery. When

maintenance teams utilize these advanced techniques the reliability of the equipment

increases, and unforeseen failures and downtime are minimized [3].

There are various wear mechanisms that deteriorate machines components, even though

there are many different types of wear, there are just few primary sources resulting in wear.

The mechanisms that contribute to the wear of a component include e.g. misalignment,

unbalance, overload, or excessive heating conditions. Often the lubricant itself is the

source for the wear, e.g. when the lubricant has degraded or become contaminated. Types

of wear that can occur in a machine are: [3]

• Abrasive wear

• Adhesive wear

• Cavitation

• Corrosive wear

• Cutting wear

• Fatigue wear

• Sliding wear

When machines are in operation the lubricant normally carry the debris away. Analysis and

identification of this wear debris can recognize its type and identify the source. Lubricant

analysis can underline the necessity to perform a corrective action to prevent imminent

stops or breakdowns. There are known cases where oil analysis identified defects in a

rotating machinery even before a vibration analysis could detect it. This applies especially

to large slow speed machines with high load level, e.g. diesel engines. For those reasons,

oil analysis has become an important predictive maintenance technique [3].

To implement a condition monitoring program, based on oil analysis, it is important to use

proper tests that will identify unusual wear particles in the oil. Each program must be

customized to the type of equipment being used and monitored, and what types of failures

to be expected. The sampling locations, types of tests, and interpretation of oil analysis

44

depend greatly on what type of machinery is being monitored, e.g. compressor, steam

turbine, diesel engine, gearbox or a hydraulic system [3].

The prime indicators of the machine’s condition or its health are the wear particles in the

oil. There are many known techniques to evaluate the type and concentration of these

particles, these techniques include, spectrometric analysis, particle counting, direct reading

ferrography, and analytical ferrography. It is necessary to trend the condition of the oil

itself, in addition to the wear particle analysis. The condition of the oil has great impact on

how much wear is generated in a machine, good condition reduces generation of wear and

bad condition increases generation of wear. Thus, the analysis of oil condition is a crucial

part of the program, one can argue it is a proactive maintenance program.

Oil analysis is primarily a combination of two types of analyses, where one is of the

lubricant itself and the other one is analyzing the contaminants in the lubricant. Well

known types of oil analysis are: [3]

• Viscosity measurement

• Solids content

• Water content

• Total acid number & Total base number

• Flash point measurement

A detail literature about oil analysis is reviewed in chapter 7 in [3].

2.3.3 Thermography

Infrared thermography is a method based on using a thermal imager to detect heat that is

emitted by an machines component(s). This technique allows the maintenance team to

validate normal operational conditions, and more importantly, locate thermal anomalies

which possibly indicate abnormal condition or faults. Thermo diagnostics is widely known

method used in various industrial situations, including:

• Electrical systems, to locate faulty connections or overloaded circuits.

• Mechanical equipment, to locate hotspots on motors or faulty bearings.

• Fluid systems, to locate line blockage, verify tank level or pipe temperature.

Faulty state of machines components often results in an increase in temperature. Figure 18

illustrates three images of faulty components, first one shows a faulty motor bearing, the

second shows a motor coupling overheating because of misalignment or similar problem,

and the third one shows a faulty journal bearing [13].

Figure 18: Thermal images of faulty components.

45

2.3.4 Performance Analysis

Performance analysis is based on monitoring crucial operational parameters to evaluate

operational condition of a machine. For certain types of machines, a performance analysis

is an effective way to determine if machine is functioning properly. One example where

this method is widely used is in the powerplant industry. Where gas- and steam turbine

engines are permanently mounted with numerus transducers, for e.g. temperature-,

pressure-, and flowrate measurements. Using the information from these transducers it is

possible to calculate various efficiencies and compare them to the normal condition [1].

47

3 Vibration Signals

A basic understanding on how a vibrating system work and respond to external forces is

very helpful when conducting a vibration analysis. In this chapter, definition of vibration

and its classification will be introduced. Vibrating signals from rotating machinery will be

discussed, where the focus will be on machinery made up with rotating shaft, impeller, and

rolling element bearings.

3.1 Theory and Classification

Any motion of a mass, body, or structure that repeats itself after some interval of time is

called vibration or oscillation. Well known examples of vibration are e.g. a swinging

pendulum or the motion of a plucked guitar string.

3.1.1 Vibration Theory

Vibration theory covers the study of oscillatory motions of bodies and the forces associated

with them. In general, a vibrating system includes a means for storing kinetic- and

potential energy, and a means by which energy is gradually lost. A vibrating system

involves the alternately transfer between potential and kinetic energy, and if the system is

damped, the energy is gradually dissipated in each cycle of vibration. If a damped vibrating

system is to maintain its vibration, an external force must be applied to the system to

maintain the vibration. In practice every vibrating system is a damped one.

Mass-Spring-Damper System

A solid understanding of how a mass-spring-damper system responds to an external force

can contribute in understanding, recognizing, and solving problems encountered in

vibration analysis. Figure 19 shows an example of a mass-spring-damper system, where a

mass M is attached to a spring with a stiffness k and on the other side the mass is attached

to a damper with a damping coefficient c.

When an external force F acts on the mass M and moves it forward the spring gets

stretched and the dampers piston moves forward inside the dampers cylinder. The acting

force F must overcome three things, the mass inertia, the spring stiffness, and the

resistance of moving the dampers piston.

Figure 19: Example of a Mass-Spring-Damper System.

48

In practice every machine has three fundamental properties, that together determine how

the machine responds to external forces that cause vibration, just like the mass-spring-

damper system. These properties represent the inherent characteristics of a machine with

which it will resist vibration. These fundamental properties are: [3]

• Mass, M: Represents the inertia of a body to remain in its neutral state of rest or

motion. External forces try to change the state of rest, which is resisted by the mass

of the body. Mass is measured in kilograms [kg].

• Stiffness, k: To bend or deflect a structure certain distance, a certain force is

required. Structures stiffness is a measure of the force required to obtain a certain

deflection. Stiffness is measured in newtons per meter [N/m].

• Damping, c: When an external force sets a structure into motion, the structure has

inherent mechanisms to slow down the motion’s velocity. The ability to reduce the

motion’s velocity is called damping. Damping is measured in newton seconds per

meter [N s/m or N/(m/s)].

The combined effects of a systems mass, stiffness, and damping determine how that

system responds to the effect of external forces. A defect in a machine often results in

increased vibration. The mass, stiffness, and damping of the system try to oppose the

vibration caused by the defect. If the vibration caused by the defect is larger than the net

sum of the three restraining characteristics, the resulting vibration will be higher and the

defect is detected [3].

Vibration Characteristics

By noting the vibration characteristics of a machine, many useful information about its

condition and possible mechanical problems are obtained. By plotting the movement of a

mass with respect to time, in a mass-spring system, it is possible to study the vibration

characteristics. Example of such system is illustrated in Figure 20, where one cycle of

motion takes 4 seconds, hence the frequency f is 0.25 Hz (where f = 1/(cycle or period)).

The motion of the mass from its neutral position, to the top position, back to neutral

position, to the bottom position, and finally returning to the neutral position, represents one

cycle of motion. From this single cycle of motion, all the information needed to measure

the system vibration are obtained. If the motion continues the cycle simply repeats itself.

Figure 20: Harmonic cycle, locus of mass-spring motion with respect to time.

49

This type of motion is called periodic and harmonic, where the relationship between the

displacement of the mass and time are expressed with the following sinusoidal equation,

𝑥(𝑡) = 𝑋0 ∗ sin(𝜔𝑡) (7)

Where x is the displacement, usually stated in micrometers [µm], at any given instant, X0 is

the maximum displacement of the mass, ω is the angular velocity (where ω = 2π*f), and t

represents the time.

When the mass moves up and down, its velocity changes from zero to maximum. The

velocity, usually stated in millimeters per second [mm/s], is the first derivative of the

displacement with respect to time, hence the velocity of the mass is expressed with:

𝑣(𝑡) =

𝑑𝑋

𝑑𝑡= 𝑋0 ∗ 𝜔 ∗ cos(𝜔𝑡) (8)

Since the mass’s velocity is varying, its acceleration, usually stated in meters per second

squared [m/s2] or in g’s, also varies and is obtained by differentiating the equation for

velocity, therefore the acceleration is expressed as:

𝑎(𝑡) =

𝑑2𝑋

𝑑𝑡2= −𝑋0 ∗ 𝜔2 ∗ sin(𝜔𝑡) (9)

Equations (7), (8), and (9) show the mathematical relationships between displacement,

velocity, and acceleration. These relationships show that if the displacement is harmonic,

the velocity and the acceleration are also harmonic, but the phase shifts. From this

perspective, it does not matter which variable is chosen to describe the vibrational

behavior, it is just a matter of scale and the phase shift. Figure 21 illustrates how the scale

and phase relationships are between displacement, velocity, and acceleration when the

maximum displacement X0 equals to 1 mm and angular velocity ω is equal to 2 rad/s.

Figure 21: Relations between displacement, velocity, and acceleration.

Even though there is a clear relation between acceleration, velocity, and displacement it

should also be considered adverse factors that affect the accuracy of the measurement. Its

therefore advisable to choose appropriate way that suits the given task, to give sufficient

signal to noise ratio. In practice, signal noise is always present and when dealing with

50

weak signals it is important to use the right way, since measurement errors increase with

higher noise.

It is important to look at what frequency range machine operates on when choosing

between displacement, velocity, or acceleration. Commonly velocity is used in the

frequency range 10 Hz to 1000 Hz, acceleration is preferred for higher frequencies, and

displacement is usually used for low frequencies [12].

Vibration signal representation

Vibration signals, often referred to as vibration spectrum, are displayed in two main ways,

that is in time domain or in frequency domain. Time domain plot presents the amplitude on

the vertical axis and corresponding time on the horizontal axis. Time domain spectrum is

the sum of all contributing vibration components that are present in the signal. Frequency

domain plot presents the amplitude on the vertical axis and corresponding frequencies on

the horizontal axis. With mathematical techniques it is possible to convert vibration

spectrum from time domain into frequency domain, such methods are discussed further in

chapter 4. Example of a vibration spectrum, measured from a centrifugal blower, is

illustrated in Figure 22, where the spectrum is displayed both in time domain and

frequency domain.

Figure 22: Vibration spectrum displayed in time domain and frequency domain.

To describe vibrations signals, various characteristics are often used, rather than amplitude,

namely, peak value, RMS value, average value, or peak-to-peak value. Where peak value

represents maximum displacement X0 (equals the amplitude for harmonic signals), hence

the peak-to-peak equals two times the maximum displacement. Single harmonic wave is

illustrated in Figure 23 displaying the comparison between these representations.

Figure 23: Amplitudes comparison for a single harmonic wave.

51

The average value, which is not used often in practice, is determent by following equation,

where T is the time period,

𝑥𝐴𝑣𝑒𝑟𝑎𝑔𝑒 =

1

𝑇∫ |𝑥(𝑡)|

𝑇

0

𝑑𝑡 (10)

One of the most common way to describe vibration signals is using the RMS (Root Mean

Square) value, since it is in direct relation with the signal’s energy, it is determent by

following equation,

𝑥𝑅𝑀𝑆 = √1

𝑇∫ 𝑥(𝑡)2

𝑇

0

𝑑𝑡 (11)

Similar characteristics are used for vibration signals that are non-harmonic. When signal is

non-harmonic the practical use for peak- and peak-to-peak-values are hardly any. Since

usually the vibration signals measured in practice are non-harmonic, the RMS-value is

commonly used to describe the signal.

Often the ratio between the peak-value and the RMS-value is used to presume the

prevailing shape of the vibration signal waveform, this ratio is called Crest-Factor (CF) and

is determent with,

𝐶𝐹 =𝑥𝑃𝑒𝑎𝑘

𝑥𝑅𝑀𝑆 (12)

3.1.2 Vibration Signal Classification

Most machine component generate vibration when in operation, these vibrating signals

characterize these components and allows them to be separated from others. Distinguishing

faulty condition from healthy condition becomes possible when the characteristics are

known. The distinguishing features often results from different repetition frequencies, e.g.

gear-mesh frequencies, fault frequencies in rolling element bearings, and fluid flow

frequencies, such as turbulence or cavitation. The gear-mesh frequencies are usually at

harmonics of the rotational shaft speed, when fault frequencies of rolling element bearings

are generally not at harmonic with the shaft speed, and usually frequencies associated to

fluid flow are at random nature [1].

As mentioned, vibration signals are commonly distinguished by the repetition frequencies

of their periodic events, therefore one of the most common method of evaluating signals is

in terms of their frequency spectrum. The frequency spectrum shows how their constitutive

components are distributed by their frequency, and it is created with various forms of

Fourier analysis, which is described further in Chapter 4.

Vibration signals are categorized by their type, Figure 24 shows how the basic breakdown

looks like, with examples how the signals may look like in the time-domain and the

frequency-domain. The most fundamental division is separating into stationary and

nonstationary signals, where stationary signal means its statistical properties are invariant

52

with time, and nonstationary signal are all other signals that do not satisfy the stationary

condition [1].

Figure 24: Examples of different signal types and their spectral content.

Stationary Signals

Stationary signals are divided into two main categories, deterministic and random. Where

deterministic signals are composed entirely of discrete frequency sinusoids, therefore their

frequency spectrum consists of discrete lines at the corresponding frequencies of those

sinusoids. When the frequency, amplitude, and initial phase of these components are

known, their value is predictive at any time in the future or past, hence the term

‘deterministic’. Furthermore, deterministic signals are divided into two parts, periodic and

quasi-periodic. The frequency components of the periodic signal are at integer multiples or

harmonics of the fundamental periodic frequency, often the rotational speed of the

driveshaft. Vibration signal from a gearbox where the input frequency is constant is a

textbook example of a periodic signal. For the quasi-periodic signals, the frequency

components are not entirely all members of a harmonic series. Theoretically, this means

that the ratio between at least two frequency components must be irrational number,

otherwise the signal would be periodic. In practice it means that there is no direct link

between at least two of the frequency components. Commonly known example is a

vibration signal from a multiple driveshaft gas turbine, where each driveshaft generate

families of harmonics, but the total vibration signal is quasi-periodic [1].

Random signals are more complex since their value at any time cannot be predictive. But

for stationary random signals the statistical properties of the signal do not vary with time.

Only from those statistical properties, such as mean value, mean square value, and so on,

can the random signal properties be described [1].

Nonstationary Signals

Vibration signals that are generated when sudden changes occur in a system are called

nonstationary signals. This type of signal are divided into two categories, continuous and

transient. There is no concrete rule for separating these two, but usually it said that

transient signals only exist for a finite length of time and are commonly analyzed as an

entity. Typical example of a transient signal would be the impulsive force generated by a

hammer blow to a structure, and the impulse response of the structure.

53

Nonstationary vibration signal is said to be continuous if it consists of, sine components

with changing amplitudes and/or frequencies, or random signals with statistical properties

that change with time, or with transient appearing with varying intervals and with varying

characteristics in time and frequency [14]. Typical example of a nonstationary continuous

signal is the vibration generated from construction worker operating a jack hammer.

3.2 Vibration Signals from Rotating Machinery

Rotating machinery can include every possible type and variation of equipment and

components that operate on circular motion, it consists of a driver or prime mover, a drive

or power train, and a driven equipment. Electrical motors are a great example on prime

movers, other prime movers include internal combustion engines and turbines. General

definition on power train is the equipment or components that transfer the rotating energy

from the driver to the driven equipment, e.g. drive shafts, gears, belt drives, and couplings.

Driven equipment includes pumps, compressors, mixers, fans, blowers, generators, etc.

In the sense of condition monitoring, changes in vibration indicate change in operational

condition. It is important for maintenance personnel to know how common faults appear in

the vibration spectrum and be aware of any factors that cause these changes to occur and

try to eliminate them or at least reduce them significantly.

Vibration tends to change with operational speed and load, and to simplify, the focus will

be on constant speed and load machinery, where vibration signals from a fan setup, like the

one illustrated in Figure 25, will be discussed. Setups like this generally produce stationary

vibrating signals when in normal operation, occasionally the signals are nonstationary, but

those are usually generated when machine is undergoing run-up or run-down conditions

[1]. This type of setup is similar to the setup studied in the case study of this thesis.

Figure 25: Simplified schematic picture of centrifugal fan setup.

54

3.2.1 Shaft Frequency and its Harmonics

A number of faults occurring in rotating machinery manifest themselves at frequencies

corresponding to the rotating speed of the drive shaft and/or its low harmonics and

subharmonics. The most common faults that manifest themselves at the rotating shaft

frequency and possibly the first few harmonics are, unbalance, misalignment, bent shaft,

and cracked shaft. Faults manifesting itself at subharmonic shaft frequencies are more

common in machinery that includes journal bearings, usually caused by some type of

whirling or wiping, will not be discussed further in this study.

Unbalance

Unbalance occurs when the local center of mass (CoM) isn’t at the center of rotation,

resulting in exciting forces that generate increase in vibration. How the vibrating response

appear depends whether the unbalancing mass on the drive shaft is distributed axially or

localized at some point. Another factor contributing to the response is whether the shaft is

rotating below or over its first critical speed.

When the unbalancing mass is localized on the drive shaft the exciting force will be radial,

generating vibration response mainly in radial directions and very little axially, and the

phase difference between measurement points is 0°, this type of unbalance is commonly

known as static unbalance. If the unbalance is caused by more than one localized mass, the

resulting vibration response is generally in radial and axial directions and the phase

difference between measurement points is 180°, often referred to as dynamic unbalance.

Figure 26 illustrates a comparison between static and dynamic unbalance and how the

frequency response generally looks like, where the phase difference is between measuring

points one and two.

Figure 26: Comparison between static and dynamic unbalance.

Most often drive shafts are axisymmetric, and the bearing supports generally have different

stiffnesses in vertical and horizontal directions, resulting in a different vibration response

in the two directions. Bearings usually have nonlinear stiffness, meaning that even if the

unbalancing force is only acting at the rotating speed, the vibration response will be

distorted to some extend from sinusoidal and the spectrum will include some harmonics of

the shaft speed [1].

55

When the inertia of the rotor is distributed axially, the CoM can vary a lot between each

section, resulting in a radial unbalance force that changes in amplitude and direction

between sections. For a rigid rotor, these unbalance forces are combined into an equivalent

unbalance force that acts at the rotors global CoM and a moment about some CoM axis.

This simplification is done because the overall vibration response is a combination of

purely radial and rocking motions, where the rocking motions can generate axial responses.

Studying rotor motion becomes more complicated when the shaft is long and considered

flexible and operating above the first critical speed. This is often the case for large turbo

machinery like steam turbines in powerplants. This topic is covered in detail in the book

Turbomachinery Rotordynamics, by Dara Childs.

Misalignment

When two or more components are connected together, like electric motor to a drive shaft,

a coupling is used. Couplings are of various kind e.g. muff or sleeve, flanged, flexible,

gear, and etc. and what kind is used depends on machinery and desired functionality. When

components are connected together there’s possibility-for misalignment. There is

possibility for parallel misalignment or angular misalignment or combination of both, this

is illustrated in Figure 27. Often flexible couplings are used to mitigate the effects of

misalignment.

Figure 27: Comparison between possible misalignments in coupled connections.

Misaligned couplings contribute into the shafts bending deflections, where the shafts are

fixed spatially, but rotating with respect to the shafts. The induced bending moments thus

depend on the shafts bending stiffness and must be counteracted by forces at the bearings,

resulting in an increased vibration [1].

Parallel misalignment usually generates vibration response in the first two orders of the

shaft frequency, although sometimes vibration appears in the third order. Rarely vibration

appears on higher orders, but if the misalignment is great, vibration can appear on higher

orders possibly all the way to the eight. The direction of the vibration is in both axial and

radial direction and the vibration phase difference over the coupling is 180°.

Angular misalignment usually generates vibration response in the first two orders of the

shaft frequency, where the second order is dominant in axial direction. Often the third

order appears, but not always, and sometimes the fourth order appears. Like the parallel

misalignment, the angular generates vibration in both axial and radial direction with a

phase difference of 180° over the coupling. In Figure 28 a typical frequency spectrum for

both parallel and angular misalignments are illustrated.

56

Figure 28: Typical frequency spectrums for parallel and/or angular misalignments.

Mechanical Looseness

Mechanical looseness can occur at three locations, internal assembly, looseness at machine

to baseplate interface, and structure looseness. Figure 29 illustrates these three types of

mechanical looseness and their typical vibration response. Structure looseness, type A,

occurs when the machines structure is loose or there are weaknesses in the machine’s feet,

baseplate, or base. This results with an increase in vibration response in the first order of

the shaft frequency, with 180° phase difference between base and baseplate. Mechanical

looseness, type B, is associated with loose bolts, cracks in the frame structure or the

bearing pedestal. This results in an increase in vibration in the second order and often

shows response also in the half and third orders, sometimes even higher orders. Internal

assembly looseness, type C, is e.g. between a bearing liner in its cap, a bearing on a shaft,

or an impeller on a shaft. This kind of looseness is often caused by an improper fit between

component parts. This often results in vibration in the bearings natural frequency region

and multiple orders of the shaft frequency. Noting that looseness of this kind often

generates sub-harmonic multiples at exactly half order and one third order [3].

Figure 29: Examples of mechanical looseness and typical vibration response.

57

Bent Shaft

If a drive shaft gets damaged that results in a permanent bow, the results will be excessive

vibration response that is a combination of misalignment and unbalance responses [1].

Shaft can acquire permanent bow from numerus events e.g. excessive loading, faulty

installation, or rubbing.

Cracked Shaft

Development of a crack in a drive shaft is one of the most serious faults to be detected in

condition monitoring, especially in large machinery, like steam turbines. Where a crack

that is permanently open increases vibration primarily in the first two orders of the shaft

frequency. Crack that opens and closes in each revolution, often referred to as a breathing

crack, also give a rise in vibration at the third order [1]. This topic is covered in detail in

the book Cracked Rotors: a survey on static and dynamic behavior including modelling

and diagnosis, by N.Bachschmid, P. Pennacchi, and E. Tanzi.

3.2.2 Rolling Element Bearings

There are two main types of bearings used in modern industry, rolling contact, and sliding

contact. The main difference is that in rolling contact bearings the main load is transferred

through rolling elements, sliding contact bearing does not have any rolling elements and

operates in a way that the shaft slides in a lubricated sleeve or bushing. For the remainder

of this thesis only rolling contact bearings will be discussed, referring to chapter 12 in [15]

and section 2.2.1.4 in [1] for more information about sliding contact bearings.

Rolling contact bearings, also known as rolling element bearings (REB), are one of the

most widely used components in machines. They are manufactured to take pure radial

load, pure axial load, or combination of both radial and axial loads. Common types of

roller and ball bearings, and nomenclature of a ball bearing are illustrated in Figure 30,

showing also the four fundamental parts of REB, the inner and outer raceways, rolling

elements, and the separator (usually referred to as the cage).

Figure 30: Nomenclature of a ball bearing and common types of roller and ball bearings.

58

Failure of REB is one of the most common reasons for machine breakdown, hence, the

vibration signals generated by bearing faults have been widely studied. There are powerful

diagnostic techniques available to analyze these signals, see section 4.2 for further

discussions on that topic. These faulty bearing vibration signals, often referred to as

bearing frequencies, are defined from the geometry of the bearing and the shaft speed. The

four fundamental components, as described earlier, all generate a distinguishing vibration

when they wear out or get damaged. The formulae for the defect bearing frequencies,

applies to all types of REB, are as follows:

𝑂𝑢𝑡𝑒𝑟 𝑅𝑎𝑐𝑒 𝐹𝑎𝑢𝑙𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐵𝑃𝐹𝑂 =

𝑛 𝑓𝑟

2(1 −

𝑑

𝐷cos 𝛼) (13)

𝐼𝑛𝑛𝑒𝑟 𝑅𝑎𝑐𝑒 𝐹𝑎𝑢𝑙𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐵𝑃𝐹𝐼 =

𝑛 𝑓𝑟

2(1 +

𝑑

𝐷cos 𝛼) (14)

𝑅𝑜𝑙𝑙𝑖𝑛𝑔 𝐸𝑙𝑒𝑚𝑒𝑛𝑡 𝐹𝑎𝑢𝑙𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐵𝑆𝐹 =

𝐷 𝑓𝑟

2 𝑑[1 − (

𝑑

𝐷cos 𝛼)

2

] (15)

𝐶𝑎𝑔𝑒 𝐹𝑎𝑢𝑙𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹𝑇𝐹 =

𝑓𝑟

2(1 −

𝑑

𝐷cos 𝛼) (16)

Where fr is the shaft frequency, n is the number of rolling elements, d is the diameter of the

rolling elements, D is the pitch diameter, and α is the contact angle. Noting that the BSF is

the frequency with which the fault strikes the same raceway, inner or outer, so usually

there are two impacts per period, hence the even harmonics of BSF are often dominant [1].

Under normal conditions, rolling element bearings operate most of their lifetime defect

free, often around 80%. REB faults are usually divided into four stages, where these four

stages represent approximately the last 20% of the bearing lifetime. For easier distinction

between these stages, the vibration frequency spectrum is divided into four zones of

interest. Figure 31 illustrates bearing life model and possible vibration spectrum of these

four stages, noting that the frequency and amplitude axis are not linearly drawn and the

spectral content is simply a snapshot at some time and isn’t meant to imply constant

features throughout each stage [16]. In zone 1 they are always some frequency components

that correspond to the rotation of the shaft and its harmonics, since perfectly balanced

system is not achievable in practice.

Stage 1

First stage of bearing failure appears with low amplitude vibration in the ultrasonic

frequency range, approximately 20 to 60 kHz. Usually it begins with subsurface cracking,

often 0.1 to 0.125 mm below the surface of the inner or outer raceways and are normally

not revealed during a visual examination. Few techniques have been developed by vendors

like SKF, IRD, CSI, and SPM to evaluate these frequencies e.g. Spectra Emission Energy

(SEE), Spike Energy Spectrum (gSE), High Frequency Detection (HFD), and Shock Pulse

Method (SPM) [16].

59

Stage 2

Second stage of bearing failure is when the fault progresses into microscopic pits on the

failed component surface. These defects are invisible to the naked eye and require

magnification to see, and as the failure develops, the pits evolve into cracks, spalls, flakes,

etc. The impacts generated by the microscopic pits cause the bearing components to

resonance at their natural frequencies, often referred to as bearing ringing. The natural

frequencies are usually in the frequency range between 2 kHz and 20 kHz, depending on

the design and mechanical parameters. As the failure progresses the impacts get greater

and periodicity is seen in the vibration spectrum, and peaks with sidebands start to appear

at the natural frequencies, and the ultrasonic frequency peaks grow. At the end of stage 2,

bearing defect frequencies start to appear, sideband frequencies may also be present below

and above the defect frequencies [16].

Figure 31: Bearing life model, showing common frequency spectrums for each stage.

Stage 3

Further progression of the failure causes the initial cracking, spalling, and/or flaking that is

visually apparent in the raceways and/or on the rolling elements but is still confined to the

bearing itself. The vibration signal generated from the impacts is strong enough to generate

peaks at the bearing defect frequencies. The amplitude of the defect frequencies increases,

60

and harmonics appear as the failure progresses. Eventually, other defect frequencies are

detected in both the bearing defect and natural frequency zones of the vibration spectrum.

In addition to the increasing harmonics of the defect frequencies, there are sidebands

associated with the shaft frequency, and the ultrasonic frequency peaks trend upward. The

damage on the components can now easily be seen through visual inspection of the

bearing. The defects frequencies will show different characteristics, depending on where

the fault originates, summarizes as follows: [16]

• BPFO: For outer raceway fault, there are harmonics at the BPFO, usually lower in

amplitude than the main or fundamental harmonic of the BPFO. As the fault

progresses, the amplitude of the harmonics will increase to be higher than the

fundamental harmonic of the BPFO.

• BPFI: For inner raceway fault, there are harmonics of the BPFI along with

sidebands of the shaft frequency. These sidebands are seen at the fundamental

harmonic of the BPFI and its harmonics. As the shaft rotates, the inner raceway

fault vibration peak will rise and fall as the raceway moves through the loading

zone of the bearing.

• BSF: For rolling element fault, a vibration peak may be noticed at the BSF. Since

the fault on the rolling element will strike the outer and inner raceway once per

revolution of the shaft, a vibration peak may be noticed at two times the BSF. Also,

there will be some sidebands around the harmonics of the BSF, these sidebands are

generated at the FTF.

Stage 4

Fourth and final stage of bearing failure is when multiple faults have progressed, and the

bearing is at its end of the life. Often the rolling elements have begun to deform, and the

cage starts to disintegrate or break, at this stage the defect frequencies often start to

disappear. The shaft has more clearance to move around inside the bearing, because of

degradation, resulting in increased amplitude of the shaft frequency and its harmonics. The

noise floor of the entire vibration spectrum often increases because the generated

frequencies will not necessarily occur at the same time interval as before. Defects are no

longer localized, but are distributed around the raceways, resulting in numerous modulated

frequencies and harmonics. The defect frequencies in both zones 2 and 3 are replaced with

a random broadband high frequency component. The ultrasonic frequency peaks may

decrease, but usually it grows excessively just before total failure. Stage 4 bearing failure

usually progresses as follows: [16]

• Impact points are worn out, leaving no sharp edges, reducing defect frequencies in

the high frequency resonance region.

• Periodicity of the impact response decreases, and the amplitude of the defect

frequencies start to decrease.

• Clearance increases as degradation increases, resulting in increased vibration of the

shaft frequency and its harmonics.

• The R.M.S. value of the time domain data start to increase.

Usually, bearing degradation is linear for some period of time and can possibly be trended,

but often as the bearing approaches its end of lifetime the process becomes nonlinear.

61

3.2.3 Bladed Machines

Machines that have a number of uniformly spaced blades or vanes on the rotor are often

referred to as bladed machines e.g. compressors, turbines, fans, and pumps. These blades

or vanes interact with components on the stator to give a periodic excitation of the casing.

The most basic frequency is called blade pass frequency (BPF), and is calculated as,

𝐵𝑙𝑎𝑑𝑒 𝑃𝑎𝑠𝑠 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐵𝑃𝐹 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑑𝑒𝑠 ∗ 𝑠ℎ𝑎𝑓𝑡 𝑓𝑟𝑒𝑞𝑢𝑎𝑛𝑐𝑦 (17)

If a machine is in good condition, these interactions are generally rather small, meaning

that the flow of medium from the rotor is guided to have the correct angle to correspond to

the angle of any guide blades or vanes on the stator. If the medium flow angles change,

more impulsive interactions will occur, resulting in a change in the vibration spectrum.

Medium flow angles can change for various reasons e.g. a blade gets damaged, fouling

buildup, blade wear, or guide blades change for some reason [1]. Figure 32 illustrates how

three typical frequency spectrums, for bladed machines, may look like, including a

diagram of a centrifugal fan.

The frequency spectrum numbered with the letter A, corresponds to the circumstances

described earlier, where the flow angles change. Another example, marked with the letter

B, shows how random sub-harmonic vibration response is generated when the medium

flow is of turbulence nature The third case, marked with letter C, shows how random high

frequency vibration response is generated when cavitation is present, noting that usually

cavitation is recognizable by human hearing.

Figure 32: Frequency spectrums of common cases on bladed machines.

63

4 Signal Processing and Analysis

In condition monitoring the ability to extract relevant information regarding the condition

of machinery is crucial. The science of extracting this information from measured vibration

data signals is called signal processing. Normally this means determining from

measurements certain characteristics that help identifying the source of the vibration to be

able to take appropriate actions to reduce or control it. In this chapter common signal

processing techniques will be introduced and discussed, also, few methods used in fault

detection and diagnostics will be introduced, especially regarding a machine setup

introduced in Figure 25.

4.1 Signal Processing Techniques

Nowadays virtually every signal processing procedure is accomplished using digital

instrumentation. Most vibration transducers used in practice produce analog voltage

signals, that contains some sort of noise. Hence, the first step in signal processing is

usually signal conditioning, followed up with suitable analysis method e.g. Fourier

Analysis.

4.1.1 Signal Conditioning

The most basic definition of signal conditioning is it is a set of operations applied to raw

measurement data, to improve its quality before its processed further. There are multiple

methods that fall under the hat of signal conditioning e.g. amplification, filtering, analog to

digital conversion. Commonly, vibration measurements are conducted using acceleration

sensor connected to signal analyzer. Commercially produced signal analyzers often include

many features for signal conditioning, like analog and digital filtering, excitation,

amplification, analog to digital conversion, and some have configurations to analyze the

signal with Fourier analysis or other known methods.

Amplification

In general, the signals generated by vibration transducers are very weak and have high

impedance. Hence, they cannot be transmitted to the analyzing equipment. These signals

must be amplified before they are processed further. There is a vast variety of different

types vibration transducers manufactured that have different applications and functions.

Vibration transducers are often manufactured with internal electric circuits that include

amplification. As described in section 2.3.1, the piezoelectric acceleration sensors are often

manufactured with a built-in electric circuit, often referred to as IEPE-acceleration sensors

(Integral Electronics Piezoelectric sensors). This internal circuit converts the high

impedance electric charge, produced by the piezoelectric material, into low impedance

voltage signal, which is possible to transmit over long distances.

64

Figure 33 illustrates an operational amplifier, where the amplification is controlled by the

size of the resistors Rin and Rf. Referring to [17], for more detailed discussion about

operational amplifiers and their applications.

Figure 33: Basic non-inverting operational amplifier circuit.

Analog to Digital Conversion

Analog to digital converter (ADC) is a device that is used to convert a continuous analog

signal, which represent an uncountable dataset, into countable dataset, referred to as digital

signal. There are various designs of ADC available on the market, manufactured for

various tasks. For high sampling frequency requirements, the most common design is the

Delta-Sigma type converter, a schematic diagram of this type is illustrated in Figure 34.

Delta-Sigma converters have the following three key features: [14]

• The analog input signal goes through an integrator to a clock driven comparator,

that acts as a one-bit ADC.

• The feedback from the one-bit comparator output goes through one-bit digital-to-

analog converter, which is subtracted from the analog input signal.

• Averaging operation with low-pass digital filter, resulting in increased number of

bits that form the digital value of the output.

Figure 34: Schematic diagram of a Delta-Sigma type analog-to-digital converter [14].

65

The final digital data frequency range for an ADC varies with one of the following two

procedures, [14]

• Lock the digital filter cutoff frequency, so it corresponds to the sampling rate of the

comparator.

• Fix the sampling rate of the comparator, then control the frequency limit and rate of

the digital output data by varying the cutoff frequency of the digital filter and the

decimation degree.

In both cases, the process of oversampling that is followed by low-pass digital filtering and

decimation, increase the effective resolution of the digital output signal by suppressing the

spectral density of the digital noise in the output [14].

Referring to chapter 27 in [11], for more detail discussion about the design and function for

ADC´s.

Resolution and Sampling Rate

There are many specifications that describe ADC performance capability, but there are two

main features that usually are used when comparing ADC capability. One being the

number of bits the ADC uses to form the digital signal and therefore decides its resolution,

and the other one being the sampling rate, that sets the frequency limit of the measured

analog signal.

When converting continuous analog signal into digital sequence with finite number of

possible values imposes resolution problem in the form of a round-off error. ADC

resolution is a function of the number of bits (β) used to form the digital output value and it

is defined in several ways, like Span, Dynamic Range, Peak Signal-to-Noise Ratio, and

Signal-to-Noise Ratio [14].

Span (S): Span is defined as the total number of possible digital values provided by the

output of ADC. Excluding zero, the span is given by the following equation,

𝑆 = 2𝛽 − 1 (18)

Dynamic Range (DR): The dynamic range of an ADC is defined as the ratio of the largest

output value (either positive or negative) to the smallest output value. Excluding the sign

bit if used (one bit to define sign polarity) and assuming a mean value of zero, the dynamic

range in decibels (dB) is given by,

𝐷𝑅 = 10 ∗ log10(2𝛽 − 1)2

≈ 6 ∗ 𝛽 𝑓𝑜𝑟 𝛽 > 5 (19)

Peak Signal-to-Noise Ratio (PS/N): The ratio of the largest value (positive or negative) to

the standard deviation of the digital noise in the output signal, is the definition of the peak

signal-to-noise ratio. With Δx representing the magnitude interval of the output signal, the

standard deviation of digital noise is defined in [18], with the following equation,

𝜎𝑛 =

∆𝑥

√12 (20)

66

Like before, excluding the sign bit if used and assuming a mean value of zero, the peak

signal-to-noise ratio in decibels (dB) is given by,

𝑃𝑆

𝑁= 10 ∗ log10 [12(2𝛽 − 1)

2] ≈ 6 ∗ 𝛽 + 11 𝑓𝑜𝑟 𝛽 > 5 (21)

Signal-to-Noise Ratio (S/N): The ratio of the maximum standard deviation of the signal,

without clipping to the standard deviation of the digital noise in the output signal, is the

definition of the signal-to-noise ratio. S/N in decibels (dB) is given by the following

equation,

𝑆

𝑁=

𝑃𝑆

𝑁− 10 ∗ log10 (

𝑃

𝜎𝑠)

2

(22)

Where σs represents standard deviation of the signal, P represents the peak value of the

signal, and PS/N is defined earlier as peak signal-to-noise ratio. Noting that if the signal is

a sine wave, the ratio (P/σs)2 is equal to 2 (approx. 3 dB), and for random signals it is equal

to 9 (approx. 10 dB) [14].

Table 2 summarizes the difference in span, dynamic range, and signal-to-noise ratio for

common bit size ADC. Where the values displayed assume the mean value of the signal is

zero, which is usually the case for noise and vibration signals. Noting, the values are the

theoretical maximum values, where in practice there are various factors that can reduce the

effective bit size by one or more bits [18].

Table 2: Span, Dynamic Range, and Signal-to-Noise comparison between common bit size

Analog-to-Digital Converters.

Choosing appropriate sampling rate for the analog to digital conversion is governed by the

Nyquist sampling theorem, it establishes a sufficient condition for a sample rate that

ensures that all the information from the analog signal are captured. The Nyquist-

frequency, fN, defines the upper frequency limit for the digital data, it is given by the

following equation, where SR is the sampling rate in samples per second [14].

𝑓𝑁 =

𝑆𝑅

2 (23)

If the analog signal has any information at a frequency above the Nyquist frequency, it will

be interpreted as information that are at a frequency lower than the Nyquist frequency.

This phenomenon, where information above the Nyquist frequency are folded back to

Number of Bits

(excl. sign bit)Span DR (dB) PS/N (dB)

S/N (dB)

Sine Wave

S/N (dB)

Random

8 255 48 59 56 49

10 1.023 60 71 68 61

12 4.095 72 83 80 73

16 65.535 96 107 104 97

24 16.777.215 144 155 152 145

67

frequencies below the Nyquist frequency, is called aliasing. Figure 35 illustrates how

aliasing works, where an original signal that is at 5 Hz is measured at a sampling rate of 6

samples per second, generates aliasing signal at 1 Hz. According to Nyquist sampling

theorem, the sampling rate should be at least two times higher than the frequency of the

signal of interest.

Aliasing is considered a serious error because once the analog-to-digital conversion is

complete, it is hard to recognize if aliasing occurred, and even though its known that

aliasing occurred, its generally impossible to correct the data for the resulting error [14].

Figure 35: Frequency aliasing due to an inadequate sampling rate.

Signal Filtering

The most common types of filters used in vibration signal processing include, low-pass,

high-pass, band-pass, and band-reject filters. Nowadays filtering is generally performed

digitally after the analog to digital conversion, to isolate a selected frequency range of

interest.

Low-pass filter is the most frequently used filtering method in vibration signal processing,

as the name implies it removes the signal content above the designed cutoff frequency.

Low-pass filtering is performed both analytically and digitally. To prevent aliasing in the

digitalized signal its crucial to filter the initial analog signal from the vibration transducers

with an analog low-pass filter, with cutoff frequency below the Nyquist frequency.

Theoretically the cutoff frequency could be half the Nyquist frequency, but no analog filter

has a perfect frequency cutoff, hence the sampling rate is often selected to be at least 2.5

times the cutoff frequency [19].

High-pass filter, like the name implies is the converse of the low-pass filter, it removes

signal content below the designed cutoff frequency and thus passes through the remaining

part of the signal. Frequencies above ten times the rotating speed of the drive shaft, are

generally not focused on in condition monitoring of rotating machinery, hence the use of

high-pass filtering is not commonly used in this field [19].

Band-pass filter is designed to remove signal content that is outside the designed

frequency range of the filter. Band-pass filter is basically a low-pass filter and a high-pass

filter connected in series, where the cutoff frequency of the low-pass filter is higher than

the cutoff frequency of the high-pass filter.

68

Band-reject filter is designed to be like an opposite of the band-pass filter, it removes all

signal content within specific frequency bandwidth.

To describe how filter behaves a response curve is used. The response curve is basically a

graph showing the frequency versus VOUT / VIN ratio, known as the attenuation ratio.

Usually the attenuation ratio is expressed in units of decibels (dB) and the frequency in

Hertz (Hz). Filter response curves are most commonly plotted with decibels on the y-axis

and logarithmic frequency on the x-axis. The cutoff frequency is generally defined where

the power of output signal has reduced by three decibels, -3dB [20].

Figure 36 illustrates how the response curves generally look like for the four main filter

types. The term, center frequency (f0) is used for band-pass and band-reject filters, and it is

the central frequency that lies between the upper (f2) and lower (f1) cutoff frequencies.

Generally, the center frequency is defined as the arithmetic mean of the upper and lower

cutoff frequencies. The width of the filter passband is generally called bandwidth (B.W.),

where the passband is the band of frequencies that do not experience significant

attenuation, often the -3-dB mark, when passing through the filter. Filters stopband

frequency (fs) is where the attenuation reaches certain value, for low-pass and high-pass

filters the stopband is defined as the frequencies beyond the stopband frequency, and for

bandpass and band-reject filters there are two stopband frequencies, where the frequencies

between these two are referred to as the stopband [20].

Figure 36: Coparison between response curves for the four main filter types.

In chapter 5.2 the process of designing analog low-pass filter with cutoff frequency of

1000 Hz will be introduced. Referring to [21] for more detailed discussion about analog

and digital filtering.

69

Windowing

Vibration signals generated from a rotating machinery usually do not have the period

significantly marked and the course of the signal in different periods is not exactly same.

Since, Fourier transformation assumes a periodic function, the resulting frequency

spectrum is distorted, usually referred to as leakage, unless appropriately handled. To

prevent a leakage error, the vibration signal and a weighting function are multiplied in the

time domain. This procedure is generally known as applying windowing to the vibration

signal. There are numerus different types of weighting windows used in practice which

have different characteristics, but the most commonly used in vibration measurements are

rectangular (no window), Hanning, and Flat Top [12].

Figure 37 illustrates an example on how frequency spectrums may look like for two

identical signals, except that one’s sample period results in a periodic signal but the other

one results in a non-periodic signal, resulting in a leakage error for the non-periodic signal.

Figure 37: Leakage error appearing in frequency spectrum, for the non-periodic signal.

According to [22] the following equations define the weighting functions for Rectangular,

Hanning, and Flat Top weighting windows

Rectangular: 𝑤(𝑡) = 1 , 0 ≤ 𝑡 < 𝑇

𝑤(𝑡) = 0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒 (24)

Hanning: 𝑤(𝑡) = 1 − cos (2𝜋

𝑡

𝑇) , 0 ≤ 𝑡 < 𝑇

𝑤(𝑡) = 0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

(25)

Flat Top: 𝑤(𝑡) = 1 − 1.93 cos (2𝜋

𝑡

𝑇) + 1.29 cos (4𝜋

𝑡

𝑇) − 0.388 cos (6𝜋

𝑡

𝑇)

+ 0.0322 cos (8𝜋𝑡

𝑇) , 0 ≤ 𝑡 < 𝑇

𝑤(𝑡) = 0 𝑒𝑙𝑠𝑒𝑤ℎ𝑒𝑟𝑒

(26)

70

In Figure 38 the difference between these weighting functions is illustrated. When

analyzing continuous vibration signals the Hanning weighting is generally used for most

cases and should be used with 66.6% or 75% overlap when analyzing true real-time data.

The Flat Top weighting function is namely used for calibration or when correct amplitude

measurement is needed, e.g. for balancing measurements. Rectangular weighting should be

avoided for most cases, unless for special cases e.g. transient signal analysis [22].

Figure 38: Comparison between Rectangular, Hanning, and Flat Top weighting functions.

4.1.2 Fourier Analysis

The following section supports highly on chapter 3 in Robert Bond Randall’s book

Vibration-based Condition Monitoring [1].

Fourier Series

The basic function of Fourier analysis is to break down signals and represent them as

summation of sinusoidal components. Almost all signals decompose in this manner, with

very few exceptions. This method is commonly used in practice for machine vibration

analysis on periodic signals, generally produced by machines that run at a constant speed

[1].

Any periodic signal is possible to represent with the following equation, also known as a

Fourier series,

𝑔(𝑡) =

𝑎0

2+ ∑ 𝑎𝑘 cos(𝑘𝜔0𝑡)

∞

𝑘=1

+ ∑ 𝑏𝑘 sin(𝑘𝜔0𝑡)

∞

𝑘=1

(27)

where the fundamental angular frequency is represented with ω0. The coefficients are

obtained as follows,

71

𝑎𝑘 =2

𝑇∫ 𝑔(𝑡) cos(𝑘𝜔0𝑡) 𝑑𝑡

𝑇/2

−𝑇/2

(28)

𝑏𝑘 =2

𝑇∫ 𝑔(𝑡) sin(𝑘𝜔0𝑡)

𝑇/2

−𝑇/2

𝑑𝑡 (29)

where one period of the signal is represented with T.

The division into sine and cosine components, for a given periodic signal, depends on an

arbitrary assignment of zero time [1]. The total component at frequency ωk (=k ω0) is

therefore given by

𝐶𝑘 cos(𝜔𝑘𝑡 + 𝜑𝑘)

𝑤ℎ𝑒𝑟𝑒, 𝐶𝑘 = √𝑎𝑘2 + 𝑏𝑘

2 𝑎𝑛𝑑 𝜑𝑘 = tan−1 (𝑏𝑘

𝑎𝑘)

(30)

Clarifying that the sinusoid has a constant amplitude, with the phase angle being that

existing at the arbitrarily defined zero time, where a different time zero only affect the

initial phase φk [1].

By interpreting expression (30) as a sum of rotating vectors, each of length Ck /2, where

one rotates at angular frequency ωk and the other at -ωk, with initial phase φk and -φk , it is

represented as,

𝐶𝑘

2𝑒𝑗(𝜔𝑘𝑡+𝜑𝑘) + 𝑒−𝑗(𝜔𝑘𝑡+𝜑𝑘) (31)

With this interpretation of the Fourier series, an alternative version of equation (27) can be

presented as,

𝑔(𝑡) = ∑ 𝐴𝑘𝑒𝑗𝜔𝑘𝑡

∞

𝑘=−∞

(32)

now the coefficients Ak are complex, and the phase shift is incorporated in the given form,

𝐴𝑘 =

𝐶𝑘

2𝑒𝜑𝑘𝑡 (33)

which is altered as,

𝐴𝑘 =1

𝑇∫ 𝑔(𝑡)𝑒−𝑗𝜔𝑘𝑡

𝑇/2

−𝑇/2

𝑑𝑡 (34)

72

Fourier Transform

Non-periodic signals can also be expressed as a sum of complex exponentials, known as

the Fourier transform. The Fourier transform is obtained from the Fourier series by letting

the periodic time to tend to infinity and removing the division by T [1]. Equations (32) and

(34) then become

𝐺(𝑓) = ∫ 𝑔(𝑡)𝑒−𝑗2𝜋𝑓𝑡𝑑𝑡

∞

−∞

(35)

𝑔(𝑡) = ∫ 𝐺(𝑓)𝑒𝑗2𝜋𝑓𝑡𝑑𝑓

∞

−∞

(36)

where the continuous frequency function f, expressed in Hz, replaces the angular frequency

ωk (rad/s). Equations (35) and (36) are commonly known as the forward and inverse

Fourier transforms and are almost symmetrical, the only difference is being the sign of the

exponent [1].

Sampled Time Signals

Every type of signal that is to be processed digitally must be digitized or discretely

sampled. This results in the inverse case of the Fourier series, where the spectrum is

sampled discretely. The symmetry of the Fourier transform means that the sampled time

signal spectrum is periodic [1]. The forward and inverse transforms for the corresponding

version are,

𝐺(𝑓) = ∑ 𝑔(𝑡𝑛)𝑒−𝑗 2𝜋 𝑓 𝑡𝑛

∞

𝑛=−∞

(37)

𝑔(𝑡𝑛) =1

𝑓𝑠

∫ 𝐺(𝑓)𝑒𝑗 2𝜋 𝑓 𝑡𝑛 𝑑𝑓

𝑓𝑠2

−𝑓𝑠2

𝑤ℎ𝑒𝑟𝑒 𝑡𝑛 = 𝑛∆𝑡 =𝑛

𝑓𝑠

(38)

Discrete Fourier Transform

In principle all sampled time signals are of infinite length, however the record length is

always finite. This leads to the same situation as with the Fourier series, where the

spectrum is discrete, and the time record implicitly periodic. Resulting in a combination of

Fourier series and sampled time signal so that both the time record and frequency spectrum

are periodic and discretely sampled. The continuous infinite integrals of the Fourier

transform therefore become finite sums [1]. Commonly expressed as,

73

𝐺(𝑘) =1

𝑁∑ 𝑔(𝑛)𝑒−𝑗 2𝜋 𝑘

𝑛𝑁

𝑁−1

𝑛=0

(39)

𝑔(𝑛) = ∑ 𝐺(𝑘)𝑒𝑗 2𝜋 𝑘 𝑛𝑁

𝑁−1

𝑘=0

(40)

This is known as the discrete Fourier transform (DFT), and it corresponds closely to the

Fourier series in that the forward transform is divided by the record length N, which gives

correctly scaled Fourier series components. The scaling must be adjusted accordingly if the

DFT is to be used with other signal types e.g. stationary random or transient signals [1].

DFT’s forward operation is interpreted as the matrix multiplication,

𝑮𝑘 =

1

𝑁𝑾𝑘𝑛𝒈𝑛 (41)

where Gk represents the vector of N frequency components, the G(k) of equations (39) and

(40), gn represents the N time samples g(n), and Wkn represents a square matrix of unit

vectors exp(-j2πkn/N) with angular orientation depending on the time sample index n (the

columns) and frequency index k (the rows), this is illustrated graphically in Figure 39 (note

the rotated real and imaginary axes) [1].

Figure 39: Matrix representation of the DFT.

The zero-frequency value G(0) is simply the mean value of the time samples g(n), for the

case where k = 0, as would be expected. When k = 1 the unit vector rotates -1/N-th of a

revolution for each increment of the time sample, giving one complete revolution after N

samples (note that the revolution is negative). When the value of k gets higher, the rotation

speed gets proportionally higher. For k = Nyquist frequency (half the sampling frequency)

the vector turns through -π for each time sample, but it is impossible to see which direction

it rotated. For k higher than the Nyquist frequency the vector rotates (in negative direction)

more than π but is more easily interpreted as having turned through less than π (in the

positive direction). When the time signal is filtered with low-pass filter at half the sampling

frequency (which should always be the case) the second half of Gk will include the

negative frequency components that range from minus one-half the Nyquist frequency to

just below zero [1].

74

Fast Fourier Transform

Calculating the DFT in practice is very time consuming and for some cases impossible

because of the size of computer memory required to complete calculations. To reduce and

simplify these calculations the fast Fourier transform (FFT) algorithm was developed,

which is a very efficient method to calculate the DFT. Looking at the matrix version of the

DFT (equation (41)) it has a form called the radix 2 algorithm where the FFT is based on N

being a power of 2 and factorizes an altered version of the Wkn matrix into log2N matrices

each holding the property that it only requires N complex operations to multiply with them,

instead of N2 operations if multiplied directly. Resulting in reduction in total complex

operations from N2 to N log2 N, e.g. for the common case where N = 210 = 1024 the

reduction is by over the factor of 100 [1].

In Figure 40 the matrix B, a modified version of the matrix Wkn, is illustrated, where the

rows are shifted in a bit reversed order from Wkn. This results in the most significant bit is

indexed rather than the least significant bit, and with increasing row number the phase

increments go from coarse to fine. When multiplying with B the results are in bit reversed

order as well but rearranging to correct address is an easy operation and takes short time

compared to the multiplication [1].

Figure 40: Matrix B, a modified version of matrix Wkn, with rows shifted.

For N = 8 and therefore log2N = 3, the matrix B is factorized into three matrices e.g. X, Y,

and Z where each row contains only two none-zero elements, one being unity. This

factorization is illustrated in Figure 41, where multiplication by each factor matrix only

requires N complex multiplication and additions. This arrangement of the factor matrices

illustrates how the decomposition can easily be extended to higher powers of 2, where the

factor matrices contain increasingly finer rotation, but the top left sub-matrix is always in

the form,

[ 𝐈 𝐈𝐈 −𝐈

]

In special cases further time saving operations are made e.g. radix 4 and radix 8

transforms, and also by factorizing with other than the power of 2, along as the properties

are those of the DFT [1].

75

Figure 41: Factorization of matrix B into three factor matrices X, Y, and Z.

Zoom FFT

When performing DFT the frequency ranges from zero to half the sampling frequency

(Nyquist frequency) with resolution equal to the sampling frequency fs divided by the

number of samples N. In some cases, it is necessary to analyze some parts of the frequency

spectrum in more detail with method called zoom-analysis. As mentioned before the

resolution is defined as,

∆𝑓 =𝑓𝑠

𝑁

and the two ways to improve it are either to increase the number of samples or reduce the

sampling frequency. In modern computers there are virtually no limits on the transform

size performed, so zoom analysis can easily be performed by an oversized transform and

then simply view small part of the solution. Reducing the sampling frequency is done with

shifting the center of the frequency band of interest to zero frequency, so that the frequency

band of interest can easily be isolated with a low-pass filter. The sampling frequency can

then be reduced accordingly, without aliasing errors, since the highest frequency is the half

of the zoom band [1].

4.1.3 Envelope Analysis

A frequency spectrum of a raw vibration signal often contains little information about

bearing faults regarding diagnostic purposes, and over the years Envelope analysis has

been established as one of the main diagnostics methods for bearing faults. When a rolling

element strikes e.g. local fault on the inner or outer raceways of the bearing it generates an

energy impulse that excites the structural resonance frequencies of the bearing and

increases the overall measured RMS value. The Envelope analysis is based on amplitude

modulation on the resonance frequencies at the characteristic defect frequency, and then

demodulate one of the resonances. The condition of the bearing can then be found with

analyzing the envelope frequency spectrum [23].

To carry out an Envelope analysis, the three following steps are involved:

• Step 1: The vibration signal is filtered with band pass filter around the resonance

frequencies, where the energy impulses are amplified.

• Step 2: The band-passed signal is then amplitude demodulated with Hilbert

transformation.

• Step 3: The envelope signal is then extracted and transformed with FFT to obtain

the envelope spectrum for further analysis and diagnosis on the bearing condition.

76

In practice one wishes to band pass filter just around the amplified resonance frequencies

and then obtain the envelope signal with Hilbert transformation e.g. with taking the

analytic signals amplitude spectrum. The complex analytic signal xa(t), is composed of the

real part of the raw signal x(t) and the Hilbert transform of x(t) which is the imaginary part.

The analytic signal is defined as,

𝑥𝑎(𝑡) = 𝑥(𝑡) + 𝑖𝐻(𝑥(𝑡)) (42)

where the Hilbert transform is defined as,

𝐻(𝑥(𝑡)) =1

𝜋∫

𝑥(𝑡)

𝑡 − 𝜏

∞

−∞

𝑑𝜏 (43)

analytic signals envelope can then by calculated with,

𝑎(𝑡) = √𝑥(𝑡)2 + 𝐻(𝑥(𝑡))2 (44)

the envelope spectrum can then be obtained by taking the FFT of the envelope signal,

making it easier to gather information about the impact frequencies and the condition of

the bearing [23]. In Figure 42 the Envelope analysis procedure using the Hilbert transform

method is illustrated.

Figure 42: Envelope analysis procedure using the Hilbert transform method.

4.2 Detection, Diagnostics, and Prognostics

When a machines operating condition starts to indicate that something is not normal, the

first step in the following process, is detecting the faulty state of the machine, followed by

diagnosing the cause of the fault, and finally establishing a reliable prognosis. The

detection of faults is very different when comparing rotating machines, reciprocating

machines, and internal combustion engines. As mentioned in section 3.2, the machine

setup studied in the case study of this thesis is illustrate in Figure 25, so for the remainder

of this chapter only detection, diagnostics, and prognosis regarding rotating machinery will

be discussed, where the main focus will be on REB.

77

4.2.1 Fault Detection

When determining whether some significant changes has occurred in the operating state of

machinery, the measured vibration signal must be processed. The technicians that carry out

the vibration measurements must usually be much more efficient than the one’s working

on diagnostics and prognosis, since commonly there are significant changes in just around

2% of cases analyzed [1].

There are many ways to detect machines fault, one way is to compare the machines

vibration level with standard vibration severity criteria. There are numerus standard

criteria, all based on the original Rathbone and Yates charts, like the one illustrated in

Appendix B. Where vibration severity is represented with constant velocity over most of

the frequency range, and constant displacement at the lower end of the range and constant

acceleration at the higher end. Using dimensional analysis that for a given geometric

shape, Rathbone argued that an object, regardless of size, vibrating at the same velocity

would have the same stress in a given mode at its resonance frequency [1].

German Engineers’ Association (Verein deutscher Ingenieure (VDI)) produced in 1957, a

set of criteria under VDI-2056, that took into consideration machines sizes and supports

and adjusted the vibration levels accordingly. Generating four different machine classes as

listed below,

• Small, on a rigid foundation

• Medium, on a rigid foundation

• Large, on a rigid foundation and

• Turbomachines, considered large on soft foundation

and in 1974, ISO incorporated these recommendations into their standard under the name

ISO 2372, later replaced by ISO 10816, as illustrated in Appendix A.

Known strategy in real time monitoring is to measure the vibration overall RMS value,

usually measured with velocity sensors since its more likely that any changes at any

frequency will affect the RMS value more than otherwise. However, monitoring the

frequency spectra, rather than the RMS value, is more likely to detect changes on whatever

frequency they occur. Known cases, see chapter 4 in [1], show that significant changes in

individual frequency components affect the overall RMS value very little if something,

except in the very last stages of the failures. Hence, its recommended to monitor changes

in the vibration spectra, instead of the RMS level, however this can cause additional

problems e.g. faults can occur over very wide frequency range, fluid film bearings can

extend as low as 40% of the shaft speed and up to as high as orders of 1000 or more for

rolling element bearings [1].

Direct digital frequency spectrum comparison is not advisable, because of undersampling

of discrete frequency peaks, where small changes in speed can cause the frequency peaks

to vary as much as 10dB or higher, since the change in speed is not enough to shift the

frequency peaks from one line to another. Hence, if a direct comparison is made it can

seem like there has been a change in the spectrum, even though the peak values look the

same [1]. This is illustrated in Figure 43, where a comparison of frequency spectra from a

REB on a centrifugal blower which is in unchanged operational condition and running at

78

constant speed. The spectrums look really similar but when compared directly it is seen

that the difference can vary up to 21.25 dB.

Figure 43: Comparison of two spectra, with direct digital comparison, with no change in

operational condition.

This is avoidable by making the comparison with mask spectrum obtained from the

reference spectrum, by displacing it to each side and taking the envelope. Another way to

obtain the mask spectrum is to take the upper envelope of all the spectra over a long

period, where every minor load and speed variations have been accounted for but not so

that the operational condition has changed. This method is most suitable for permanent

monitoring systems where the possibility to collect large amounts of data is at hand.

Referring to section 4.2 in [1] for more detailed discussion about the use of frequency

spectrum.

In section 3.2, common fault and their corresponding vibration spectrums are discussed,

for the equipment studied in the case study of this thesis.

4.2.2 Diagnostic Techniques

There are numerus techniques used when performing fault diagnostic on rotating

machinery e.g. Harmonic and sideband cursors, spectral kurtosis, kurtogram, spectrogram,

and envelope analysis, just to name few.

Harmonics and Sidebands

When harmonic and sideband cursors are added to the diagnostic process the capability

increases greatly of the frequency analysis. Harmonic cursors indicate all members of

specific harmonic family, usually with fine resolution, and the diagnostic capability

depends on the fact that the harmonics are precise integer multiples of the shaft frequency.

Harmonic spacing accuracy is in proportion to the highest order located and when zooming

in the high frequency range, N-th harmonics of the same spacing can then be selected

simultaneously and accuracy increases in proportion to N. Sideband cursor indicates a

family of sidebands with fixed spacing around specific carrier frequency, and since it is not

bound to pass through zero frequency the accuracy isn’t the same as the harmonic’s cursor.

However, the same rules apply regarding improving the accuracy when simultaneous

selecting the number of sidebands in the same family. Harmonic and sideband cursors are

extremely useful when conducting frequency analysis on gears where it is possible to

blindly determine the number of teeth on a gear pair, as long as the gear has a hunting

tooth design, meaning there are no common factors between the number of tooth in the

gears [1].

79

Spectral Kurtosis

Spectral kurtosis (SK) is a powerful tool to determine and characterizing the frequency

band which contains a transient signal, it was originally based on the Short Time Fourier

Transform (STFT) for measuring the impulsiveness of a vibration signal as a function of

frequency. The use of SK was later developed to distinguish between sinusoidal signals

and very narrowband noise signals, e.g. faults like small spalls on rolling elements generate

weak impulses that get masked by surrounding noise, usually with SK values of -1 and 0

[24]. The use of SK for bearing fault detection was first introduced by Jerome Antoni in

[25], and also in [26] along with Robert B. Randall.

In equation (45) Y(t) represents a vibration response from a rolling element bearing, where

g(t) is a series of impulse responses, excited by impulses X at time τk. [1]

𝑌(𝑡) = ∑ 𝑔(𝑡 − 𝜏𝑘)𝑋(𝜏𝑘)

𝑘

(45)

For each frequency instance, the kurtosis is calculated as,

𝐾(𝑓) =

⟨𝐻4(𝑡, 𝑓)⟩

⟨𝐻2(𝑡, 𝑓)⟩2− 2 (46)

where H(t, f) is the STFT obtained by shifting a time window along the record, or the

amplitude envelope function where its square is the power spectrum values at each position

along the record. The resulting kurtosis is dependent on which window length is selected

for the STFT and it must be shorter than the spacing between the impulses but longer than

each individual pulse to obtain maximum value of kurtosis. The process of calculating the

kurtosis with STFT is shown graphically in Figure 44, where a simulated vibration signal

from a REB with localized fault on inner raceway is displayed.

Figure 44: The process of calculating the Spectral Kurtosis of a simulated bearing

vibration signal with localized fault on inner raceway.

80

For further discussion on SK and the effect the window selection has on the result is

studied in great detail in [26], where to short window gives too much smoothing on the

spectral kurtosis graph and to long window reduces the maximum calculated kurtosis,

because of bridging between pulses.

Kurtogram

Faulty bearings generally produce impulsive vibration signal with high kurtosis in the

frequency band where the impulsiveness is dominant and usually very low kurtosis where

the frequency spectrum is dominant with stationary vibration components. This

information has been commonly used to filter out the part of the vibration signal that has

most impulsiveness [1]. Jerome Antoni and Robert B. Randall showed in [26] that the

optimum Wiener filter is the square root of the SK and that optimum matched filter

operates as a narrowband filter where the SK is highest. Individual cases are often very

different from one another, even if they are almost identical, so the best solution can vary

with the bandwidth and the center frequency chosen for the filter. In [26] the optimal

combination is displayed on a graph called the Kurtogram.

Computing the full kurtogram can require large computer memory so numerus, more

effect, methods have been proposed. The fast kurtogram was proposed by Antoni in [27]

which is based on series of digital filters instead of STFT. Where the most recommended

method is using the so called 1/3-binary tree [1].

Figure 45 shows the fast kurtogram for measurement number 2150 for bearing 3 from the

experimental vibration dataset number 1, provided by the Center for Intelligent

Maintenance Systems (IMS). The kurtogram was calculated using MATLAB®, it shows

how spectral kurtosis varies with window length and the frequency band, as mentioned

earlier. In this case the bearing had developed inner raceway fault and from the kurtogram

it is seen that the maximum SK is when window length is 32 and center frequency is at

8.64 kHz with bandwidth of 0.64 kHz.

Figure 45: Fast Kurtogram for measurement number 2150 of bearing number 3 from the

IMS-Dataset 1.

81

Figure 46 illustrates how the SK changes when calculated using the optimal bandpass

filtering parameters found with the kurtogram, the maximum kurtosis changes from 2.08 to

6.42. The kurtogram is commonly used to find optimal bandpass filter parameters for the

envelope analysis to withdraw the signals impulsive components.

Figure 46: Comparison on calculated SK with optimal bandpass filter and with no filter.

4.2.3 Prognosis

One of the main benefits from condition monitoring, besides of the fault detection and

diagnosis, is the ability to obtain reliable prediction as to how long equipment is able to

operate safely and reliably. The definition on equipment’s end of life is when it is no

longer able to operate as it was designed for, and to determine remaining useful lifetime

(RUL) for systems or individual components is the basis of prognosis [1].

Aiwina Heng stated in [28], that condition-based prediction is categorized into two main

methods, physics-based, and data-driven. Where physics-based method requires model of

the failure modes, either physical or mathematical, and then measurements to obtain

indication on the extend the failure mode has progressed. The data-driven method is based

on deriving failure models from measurement data, using statistical processing, usually

with number of historical cases [1].

Fault Trending

Often machinery or individual components of larger systems behave rather predictively,

and failures do proceed in that manner, hence fault trending has been used successfully for

a long time. As mentioned in section 4.2.1, frequency spectrums are commonly compared

to a reference spectrum, obtained when machine is new, to see if notable difference has

occurred. The spectrums are often expressed as constant percentage bandwidth (CPB)

spectra, where the frequency scale is logarithmic and the vibration amplitude (acceleration

or velocity) is expressed on a logarithmic or decibel scale. This strategy could be

considered as a physics-based model method and over the year’s maintenance specialists

have gained valuable experience that has been incorporated into known standards, like ISO

82

10816. It has been shown that a 6-8 dB change in vibration level is considered significant

and a 20 dB change is serious [1].

There are some situations where the 20 dB change is allowed, e.g. changes at high

frequencies in CPB spectra when fault starts to develop in rolling element bearings (REB).

When REB are new or in perfect condition, they generate very little vibration and it is just

as a fault start to develop it starts to generate measurable vibration. Therefore, the first 10

to 20 dB change in vibration is considered not critical. Change in dB can vary with the

initial noise level and therefore it is considered machine and measurement point dependent,

and it is advisable to use the 20 dB change conservatively and as a guide, where further

adjustments need to be made on tolerances, based on experiment and a given situation [1].

When trending vibration parameters, like overall vibration level, one must decide which

type of curve should be fitted to the data to predict the development of the fault and

determine when actions are needed. If linear trending is used the assumption is made that

the fault development causes uniform rate change in severity. Linear trending may not

always be suitable since some faults have feedback effect, leading to an increase in

deterioration rate as a fault develops e.g. with increasing wear of gearteeth increases the

dynamic load on the teeth, resulting in an increased wear rate. For these cases it should be

considered to use exponential curve to fit the data. Experience has shown that it’s not

recommended to fit polynomials to the data, unless there are physical reasons to assume

that the fault should evolve in that manner or other information indicate that it’s suitable

[1].

In practice it can variate how companies decide how their condition monitoring system

trends machines or system components, all based on their importance, cost, and other

factors that companies decide. Trending single frequency parameters e.g. shaft speed is a

common strategy and used all over the world. Sometimes trending more than one

frequency component can give better results, usually done in the upper frequency ranges,

where there are no longer individual harmonics isolated in a single CPB band [1].

Vibration signals impulsiveness is commonly used as a condition indicator for REB and

gears since localized faults in them is characterized by their generated impulsive

components in the vibration signal. Trending these impulses is therefore a widely used

technique to establish a good measure on faults severity. Measuring the crest factor is one

of technique to measure the impulsiveness in a vibration signal, however it is often

unreliable measure since the peak value varies a lot depending on the signals section

analyzed. Another technique to measure signals impulsiveness is kurtosis, which is more

stable than the crest factor since it is averaged over a number of impulses contained in the

vibration signal [1].

In Figure 47 an example is illustrated on how the kurtosis increases over a bearings

lifetime, where it shows steady measurements when bearings condition is acceptable, but

increases fast once fault starts to evolve. This particular data was obtained from the IMS

dataset number one, bearing number three.

83

Figure 47: Trend of kurtosis for bearing 3 from IMS dataset no.1, inner raceway fault

develops at end of lifetime.

Condition Indicators

The construction of a condition indicator (CI) is important task when performing an

estimation on a bearing remaining useful life (RUL). There are multiple methods used to

establish appropriate CI, all from types like the overall RMS value to complex neural

network-based CI.

Based on their nature common condition indicators are separated into three main

categories, time-domain CI (TD-CI), frequency-domain CI (FD-CI), and time-frequency-

domain CI (TF-CI).

Time-Domain CI are e.g. the overall RMS-value, the mean amplitude, Peak-to-Peak

amplitude, and the Crest factor (see section 3.1.1 for their definition). The standard

deviation (STD) in a signal, or higher-order moments of such as Skewness and Kurtosis

are also common time-domain CI.

Where standard deviation is calculated as,

𝑆𝑇𝐷 = √1

𝑁 − 1∑(𝑥𝑖 − )2

𝑁

𝑖−1

(47)

the signal skewness is calculated as,

𝑆𝑘𝑒𝑤𝑛𝑒𝑠𝑠 =

1𝑁

∑ (𝑥𝑖 − )3𝑁𝑖=1

(√1𝑁

∑ (𝑥𝑖 − )2𝑁𝑖=1 )

3 (48)

84

and the Kurtosis is calculated as,

𝐾𝑢𝑟𝑡𝑜𝑠𝑖𝑠 =

1𝑁

∑ (𝑥𝑖 − )4𝑁𝑖=1

(1𝑁

∑ (𝑥𝑖 − )2𝑁𝑖=1 )

2 (49)

where, xi are the measured values at each time instance and is the mean value of all those

values and N is the number of values.

It has been shown that the Kurtosis of a bandpass filtered signal, with optimal filter (as

described in section 4.2.2), follows similar trend as cumulated oil wear debris and hence

has strong potential for estimation of RUL [1].

Frequency-Domain CI are e.g. the mean frequency and the mean-peak frequency.

Where the mean frequency is calculated as,

𝑓𝑚𝑒𝑎𝑛 =

∑ 𝐼𝑖 ∗ 𝑓𝑖𝑁𝑖=𝑜

∑ 𝐼𝑖𝑁𝑖=0

(50)

where N being the number of frequency bins in the data, fi is the frequency of spectrum at

each bin and Ii is the intensity in dB of spectrum at each bin.

The mean-peak frequency is established by extracting features from signals spectrogram,

where peak frequency at each time instance is defined as,

𝑓𝑝𝑒𝑎𝑘 = 𝑎𝑟𝑔𝑚𝑎𝑥𝜔𝑃(𝑡, 𝜔) (51)

where P(t,ω) denotes the signal spectrogram, and the mean-peak frequency is the averaged

of the peak frequencies, defined as,

𝑓𝑚𝑒𝑎𝑛−𝑝𝑒𝑎𝑘 =

1

𝑁∫ 𝑓𝑝𝑒𝑎𝑘 (𝑡)𝑑𝑡

𝑁

0

(52)

Time-Frequency-Domain CI are e.g. the spectral Kurtosis and spectral entropy. See

section 4.2.2 for spectral Kurtosis definition.

The spectral entropy (SE) is a measure on signals spectral power distribution, it is defined

as,

𝐻(𝑡) = − ∑ 𝑃(𝑡, 𝑖)𝑙𝑜𝑔2𝑃(𝑡, 𝑖)

𝑁

𝑖=1

(53)

where P(t,i) is the probability distribution at time t.

85

Advanced Prognosis

Prognosis is divided into two main categories, as mentioned earlier, physic-based, and

data-based and then there is a combination of the two called Hybrid model-based method.

Where the prognostic process is a mixture of reliability and condition-based estimates,

where the focus shifts, during the lifetime of the equipment, from former to the latter [1].

J. W. Hines and A. Usynin proposed great strategy for general prognosis in [29], where the

method is based heavily on experience from the nuclear industry amongst other things. The

strategy is illustrated in Figure 48, where the type I prognostics uses actual failure history

to obtain statistical information about probability of component failure. It usually applies

to all components of the same type, since it gives average results for all components under

average operating conditions, however it leads to an uncertainty for current component [1].

The second type prognostics factors in things that effect machine or components lifetime

e.g. load, running speed, how many running cycles component has served, operational

temperature, environmental conditions such as cleanliness, etc. It is possible to monitor all

of these things for every component as an individual or as a whole, and by adding these

parameters into prognostics the uncertainty of the RUL prediction is reduced [1].

The third and final type of prognostics also includes measures on how components perform

to improve the estimation results on the RUL, this approach is considered the best,

especially in later stages on components lifetime, when deterioration has started to effect

the measured parameters [1].

Figure 48: Prognostic method as proposed by J.W.Hines & A. Usynin in [29]

87

5 Case Study at Norðurál Aluminum

Plant

In this chapter the case study of this thesis will be discussed and the process of selecting,

designing, and building the vibration measurement- and analysis system used for the case

study.

Norðurál is an aluminum plant located at Grundartangi, where the production takes place

in 520 pots in four pot rooms. Large fume treatment plants (FTP’s) are located between the

pot rooms and their main purpose is to reduce the amount of emission released into the

atmosphere e.g. fluoride gases and carbon dioxide. There are four FTP’s operating at the

plant, but the focus in this thesis was on FTP-1, although FTP-2 was also included during

the vibration measurements to get some comparison between the two, due to their

mechanical similarity.

Figure 49 illustrates an overview of the plant, where the location of the pot rooms and

fume treatment plants have been marked. FTP-1 serves pot rooms A and B and FTP-2

serves lower part of pot rooms C and D.

Figure 49: Norðurál aluminum plant and the location of the pot rooms and FTP’s.

The company has been having unusual problems regarding one of the four main fans in

FTP-1, where bearing lifetime have been well below designed lifetime on main fan number

two. Resulting in unreliable operation since an unexpected shutdown of one of the fans

reduces the systems capability to serve its purpose. Although it is possible to operate the

FTP without one fan running it is not ideal in the long run. It leads to increased load on the

remaining fans if the system is to uphold its capacity to treat the plant’s emission.

The objectives of this study are divided into two parts, first part is to apply Failure Mode

and Effect Analysis (FMEA) on fan 2 in FTP-1, to try to identify the cause of the reduced

bearing lifetime. The second part is assessing the current condition of the main fans rolling

element bearings (REB) in FTP-1 and FTP-2 and estimate the remaining useful life (RUL)

of one of the plummer block bearings on main fan 2 in FTP-1.

88

5.1 Fan Setup and History

FTP-1 and FTP-2 are both installed with four parallelly lined centrifugal fans, with rated

power around 900 kW each, applying ventilation from the pots in the pot rooms. The fans

setup is almost identical in both plants, where all components are similar. The fans are in

constant operation all year around, excluding their downtime cause of maintenance issues,

and it is essential that their operation is reliable and safe. If the fans are not operating

consistently the FTP’s efficiency reduces, resulting in an increase in emission release from

the factory. The company has committed itself to operate under strict environmental

regulation regarding emission release, hence it is crucial that the FTP’s are operating

smoothly and without problems.

5.1.1 Components and Operational Conditions

The fans were manufactured by ABB Fläkt Industri AB, they are of backward curved blade

type HACB-200-251-X4-1-2 which is suitable for handling gas containing small amounts

of non-adhesive dust. The fans have an overhung impeller and are mounted on a rigid

foundation with direct drive connection, via a flexible coupling. The impellers are of

welded design and are both statically and dynamically balanced when new. Figure 50

illustrates a sideview of one of the fans and a list of its major components.

Figure 50: Sideview of one of the centrefugal fans and a list of it’s major components

The fans bearings are fitted to the driveshaft and are supported by plummer block type

bearing housings and designed with grease lubrication. Two types of bearings are used in

this setup, excluding the internal bearings of the electric motor which will not be discussed

further in this thesis. The bearing closer to the electric motor, denoted as Fan DE (Drive

End) bearing, is a spherical roller type and the bearing closer to the impeller, denoted as

Fan ND (Non-Drive end) bearing, is a CARB toroidal roller type. The spherical roller

bearing is designed to take high loads, both radial and axial, and has the ability to

accommodate for misalignment. The CARB bearing is designed to take loads exclusively

in radial direction. Table 10 and Table 11, in appendix C, lists all major parameters, for

both bearings and the lubricant, gathered by using the force estimation illustrated in Figure

51 as design inputs in the SKF® Bearing Select software. Where interestingly it shows that

89

the estimated bearing life is over 200k hours for both bearings, the manufacturer however

notes that for calculated bearing life over 100k hours, other failure modes than the ones

included in the current rating life model will dominate and limit the life of the bearing.

Both bearings are mounted on the driveshaft along with adapter sleeves, with so-called

SKF Drive-Up method [30], where the bearings are pressed onto the adapter sleeves with

HMV hydraulic nut. The bearings are fitted inside the housings along with the locating

rings, which fix the bearings position inside the housing. Both bearings are grease

lubricated with SKF LGHP2 high performance grease. Figure 51 illustrates how the setup

looks like with the driveshaft fitted with the bearings, adapter sleeves, and along with their

housings and the impeller.

Figure 51: Current bearing setup and impeller for fans in FTP-1 and FTP-2.

The bearing housings, both Fan DE and ND, are mounted with thermo probe and vibration

accelerometer which monitor temperature and vibration in the bearing housings. The

measured values are logged into the monitoring system for the plant, called SCADA

(Supervisory Control and Data Acquisition). The SCADA system monitors the measured

values from the thermo probe and the vibration accelerometer including other parameters

e.g. electric motor amperage, and gives indication when values exceed predetermined

limits. The vibration measurements are logged as an averaged RMS-value for a given

bearing, commonly as a one-minute average. The SCADA system has the ability to shut

down any of the fans if operational condition gets dangerous because of exceeding

temperature or vibration, however it has its limitations when it comes to advanced

vibration analysis.

Figure 52 illustrates roughly how the force distribution is along the driveshaft on main fans

1 and 2 in FTP-1, where it shows that the Fan DE bearing takes a small axial load and very

small radial load, and the Fan ND bearing receives exclusively small radial load.

According to SKF® the bearings are designed to receive loads well above these values, as

listed in Table 10 in appendix C.

As mentioned earlier the fans are running constantly all year around at fixed speed, approx.

993 rpm, and at load that varies very little, since the ventilation from the pot rooms is a

constant process where aluminum production is a process that cannot stop at any time.

90

Figure 52: Rough estimation on force distribution along the driveshaft and the bearings.

5.1.2 Plummer Block Bearings Maintenance History

The maintenance strategy practiced at Norðurál is somewhat a combination of all three

main maintenance strategies generally practiced. Where breakdown maintenance is often

used on noncrucial and considerably cheap equipment and preventive maintenance is

practiced on machines and components that have somewhat known lifetime. Predictive

maintenance is used on larger and more complex and expensive machines and components,

where possible breakdown can interrupt or effect the production or threaten the safety of

personnel. The technical department at Norðurál uses a very powerful maintenance

software called SAP® (Systems, Applications & Products in data processing) to register

maintenance history and spare part inventory, and plan future work.

The main fans in the fume treatment plants are one of the crucial components in the

operation of the FTP’s and when one of them breaks down it is considered a major

problem and needs immediate attention. Therefore, the fans are under regular planned

maintenance work e.g. visual inspection, grease change, and grease injection at certain

intervals. As mentioned earlier, are the main fans plummer block bearings installed with

condition monitoring equipment, where temperature, vibration, and motor amperage are

monitored constantly.

Table 12, in appendix C, lists bearing- and grease change intervals for the main fans in

FTP-1 & 2 from the year 2008. Table 3 lists up all the bearing changes that have been

performed in FTP’s 1 & 2, where interestingly it shows that main fan 2 has by far the worst

track record when it comes to plummer block bearing life. However, there have been

bearing change on main fan 1 three times, latest in February 2019, and it has currently been

having some operational problems, according to maintenance personnel, and it is expected

that bearing change will be performed in the upcoming weeks/months.

Table 3: Date of bearing changes for the plummer block bearings on main fans in fume

treatment plants 1 and 2, with bearings running hours at each time.

Main Fan No.

2008-05-10 87,144 2008-03-18 85,872 2012-09-24 125,496 (66,768) 2013-11-25 135,744 (56,520)2010-03-12 16,104 2013-04-02 44,1842019-02-18 78,360 (10,656) 2017-09-25 39,288

2017-12-11 1,8482018-02-17 1,6322019-07-05 12,072 (7,368)

FTP-2 2015-04-27 86,808 (44,088)

FTP-1Bearing Change

Date & Running

Hours (current)

4321

91

Main fans 1-3 in FTP-1 were initially started in 1998 and main fan 4 in the year 2000 and

according to Table 3 were the initial bearings in FTP-1 in operation from 10 to 14 years,

which is considered well acceptable bearing lifetime. Barely two years from the first

bearing change, the bearings were changed again on main fan 1 which is unacceptable

lifetime. However, there has not been any bearing change since then, giving the current

bearings a lifetime of approx. 10 years which is considerably fair, although there is a

bearing change imminent. Since the initial bearings were changed, on main fan 2, in the

year 2008 there have been five bearing changes done which is extremely poor durability

and is one of the main reasons for this thesis.

The fans in FTP-2 were initially started in the year 2005 where all the initial plummer

block bearings are still in operation except the ones on main fan 1, which were replaced in

the year 2015 after approx. 10 years in operation. The lifetime of current bearings in FTP-2

is well acceptable and does not cause any concerns regarding their operation.

The problem that the bearings in main fan 2, in FTP-1, has been causing random vibration

spikes now and then and causing an unusual increase in operating temperature. These

vibration spikes have caused the SCADA system to automatically shut down the main fan.

Figure 53 illustrates how the inside of the plummer block bearings has attended to look

like before the maintenance personnel perform bearing grease change. It shows that the

grease is completely damaged and looks like it has overheated.

Figure 53: Sooted grease in main fan 2 plummer block bearings, in FTP-1.

During bearing grease change the maintenance personnel have been encountering some

metal debris and metal threads in the grease, which look like missing parts from the

locking washer and/or the bearing cage. Figure 54 illustrates some of the metal debris,

including some damages on the adapter sleeve and the locking washer. The metal threads

appear to be parts that have been scraped of the bearings cage or its inner raceway,

although it is not able to be certain from these pictures.

92

Figure 54: Damages found in main fan 2 Fan DE bearing, during grease change.

It displays in these pictures that there is a serious problem when it comes to the durability

on the Fan DE and Fan ND bearings on main fan 2 in FTP-1 and the current operating

condition is unacceptable and it’s causing the company great concerns.

5.2 Vibration Measurement and Analysis System

Selecting appropriate equipment for the vibration measurement part of this thesis was one

of the first steps taken. Some of the equipment was designed and build especially for this

thesis and some parts were bought from known suppliers e.g. accelerometers and analog to

digital converters. Vibration analysis software was designed using MATLAB®, where a

graphical user interface (GUI) was built to help performing the analysis part of this thesis

as well as to make it more user friendly.

It was decided to use two sets of vibration measurement equipment, where the first set

(denoted as localized equipment) was placed beside main fan 2 in FTP-1 to take one

vibration measurement every 24 hours on the plummer block bearing housings with two

accelerometers on each (axial- and radial-direction). The second set (denoted as portable

equipment) was thought of as a portable unit to be able to perform vibration measurements

on all other main fans, also with four accelerometers. Although both sets have the same

purpose, there is a difference between the two where the portable equipment is much more

powerful unit with higher resolution and sampling rate.

It was decided to use accelerometers instead of velocity- or displacement transducers. The

velocity transducer is not suitable for the advanced vibration analysis performed, since the

frequency range of velocity transducers is not as wide as the range on accelerometers. The

use of a proximity probe (displacement transducer) is not suitable either, since the probe

requires customize mounting on the plummer block bearing housing and therefore was

ruled out as an option.

93

5.2.1 Localized Equipment

During the design process of the localized equipment it was decided to keep its structure

basic to keep the cost down, since there were limiting funding for this project. Decision

was made to build the analog low-pass filters, with amplification, from scratch, but other

components like accelerometers and ADC’s were bought from commercial manufactures,

along with parts used to assemble the equipment e.g. casings and other structural parts.

The basic design parameters that the localized equipment needed to fulfill were,

• Low-pass filters cut-off frequency to be 1000 Hz, since this frequency range covers

all the bearing fault frequencies and their first few harmonics.

• Sample frequency to be 2500 Hz, with number of samples per measurement 2500,

to keep sampling frequency 2.5 times the low-pass frequency (to avoid aliasing).

• Measure with four accelerometers simultaneously with 24-hour interval (radial and

axial directions on each plummer block bearing housing).

Low-Pass Filter and Amplifier Design and Construction

For this project it was decided to design and build a fifth-order Butterworth low-pass filter

with 22 dB signal amplification, since its rather easy to build and provides reasonably good

precision. The 22dB amplification was included in the design because of the weak electric

signal from the accelerometer. Analog low-pass filters are electronic circuits with resistors,

capacitors, and amplifiers connected in a certain way, where the selection the components

size controls the function of the filter. A fifth-order Butterworth filter is basically

constructed with three Butterworth filters, with one first-order and two second-order filters

connected in series. Figure 55 illustrates a basic electrical circuit for a fifth-order

Butterworth low-pass filter without any amplification.

Figure 55: Electrical circuit for a fifth-order Butterworth filter without any amplification,

where R and C denotes the resistors and the capacitors.

To determine the suitable size of the electrical components so the filters cut-off frequency

is at approx. 1000 Hz its crucial to set up a transfer function for the filter. For convenience

MATLAB® was used to determine the filters transfer function, giving the following,

𝐻(𝑠) =

1

𝑠5 + 3.2361𝑠4 + 5.2361𝑠3 + 5.2361𝑠2 + 3.2361𝑠 + 1 (54)

94

for simplification, the transfer function is factored so it is constructed of one first-order and

two second-order components, which represent the first- and second-order filters

connected in series, resulting with

𝐻(𝑠) =

1

(𝑎1𝑠 + 1)(𝑠2 + 𝑎2𝑠 + 1)(𝑠2 + 𝑎3𝑠 + 1) →

𝐻(𝑠) =1

(𝑠 + 1)(𝑠2 + 1.618𝑠 + 1)(𝑠2 + 0.618𝑠 + 1)

(55)

Sallen-Key method [31] was used when designing the filter, where the constants a are

utilized from equation (55) to establish the size of the electrical components to obtain

desired cut-off frequency.

For simplification it was decided to use 1 kΩ resistors for all the resistors in the electric

circuit, that way only one variable (capacitors size) controls the filters cut-off frequency.

The capacitor size for the first-order filter was calculated as,

𝐶1 =

𝑎1

2𝜋 ∗ 𝑓𝑐 ∗ 𝑅1=

1

2𝜋 ∗ 1000 ∗ 1000= 159 𝑛𝐹 (56)

where fc is the cut-off frequency and R1 is the size of the resistor.

A different approach is used to determine the capacitors sizes for the second-order filters.

The transfer function for the second-order filters is,

𝐻(𝑠) =

𝑘𝑅2𝑅3𝐶2𝐶3

⁄

(𝑠2 + (1

𝑅2𝐶2+

1𝑅3𝐶2

+1

𝑅3𝐶3−

𝑘𝑅3𝐶3

) 𝑠 + 1) (57)

which has a general form,

𝐻(𝑠) =

𝑘𝜔2

(𝑠2 + (𝜔0

𝑄 ) 𝑠 + 𝜔02)

(58)

if k and ω0 are set as 1, the transfer function is rewritten as,

𝐻(𝑠) =

1𝑅2𝑅3𝐶2𝐶3

⁄

(𝑠2 + (1

𝑅2𝐶2+

1𝑅3𝐶2

) 𝑠 + 1) (59)

for simplification, the resistors values are set as 1,

𝐻(𝑠) =

1

(𝑠2 + (1𝑄) 𝑠 + 1)

=1

(𝑠2 + (2𝐶2

) 𝑠 +1

𝐶2𝐶3)

(60)

95

with this information the capacitors size ratios could be established, for both second-order

filters, with the following calculation,

𝐶2 = 2𝑄 , 𝐶3 =1

2𝑄 , 𝑎2 =

2

𝐶2 𝐶4 = 2𝑄 , 𝐶5 =

1

2𝑄 , 𝑎3 =

2

𝐶4

𝐶2 =2

𝑎2=

2

1.618= 1.236 , 𝐶3 =

1

2𝑄=

1

𝐶2=

1

1.236= 0.809

𝐶4 =2

𝑎3=

2

0.618= 3.236 , 𝐶5 =

1

2𝑄=

1

𝐶4=

1

3.236= 0.309

to establish the real sizes of the capacitors the C values are multiplied with,

1

2𝜋𝑓𝑐𝑅=

1

2𝜋 ∗ 106

Table 4 lists up the calculated sizes of the capacitors and the real sizes used to construct the

filter, along with the sizes of the resistors. The real sizes are little bit different from the

ones calculated, this was done to simplify the design process by picking standard size

capacitors closest to the calculated values.

Table 4: Calculated and used sizes of capacitors.

Figure 56 illustrates how the electrical components are arranged, along with two added

resistors which alter the filters function, giving it 22 dB amplification.

Figure 56: The electrical circuit for fifth-order Butterworth low-pass filter with 1000 Hz

cut-off frequency and 22 dB amplification.

Next step was to design a power circuit that supplies an accelerometer and the low-pass

filter. Figure 57 illustrates a power circuit for a single accelerometer and one filter. The

circuit is constructed with numerous components like, on/off switch, LED-diode, constant-

current diode, input connection for an accelerometer and an output connection from the

filter (to the AD converter), and a power supply.

Capacitor [C] 1 2 3 4 5

Calculated Size [nF] 159 129 196 49 515

Used Size [nF] 150 133 183 47 503

Resistor [R] 1 2 3 4 5

Used Size [ Ω] 1000 1000 1000 1000 1000

96

Figure 57: Power circuit for a single accelerometer and a low-pass filter.

Constant-current diode’s purpose is to regulate the current flow to the accelerometer

(approx. 4.8 mA) when the 22μF capacitor works as a gate that stops the current flow from

the power supply to the filter, but allows the filter to receive the voltage signal from the

accelerometer. The LED-diode function is simply to give indication when the circuit is

switched on.

Next step was to test the functionality of the filters and confirm its cut-off frequencies.

Where the standard procedure for defining the cut-off frequency was used, its where the

signals power has been halved or decreased by 3 dB. The theoretical response of the filters

was calculated using MATLAB® and Bode diagram used to draw up the response to

compare it to the real response. Figure 58 illustrates how the theoretical response is for the

designed filters, it shows that the theoretical cut-off frequency is 924 Hz which is

understandable since the electrical components used are not exactly the same size as the

ones calculated during the design process.

Figure 58: Filters theoretical respone displayed on Bode diagram.

The real filters responses were established by connecting the filters to a power source and

use adjustable wave generator as an input signal. The output signal was then measured

using an oscilloscope and the frequency response plotted using Excel®. The results are

illustrated in Figure 59, where it shows that the frequency responses are very similar for all

the filters and the cut-off frequencies results are all very acceptable.

97

Figure 59: The real frequency response of the filters, measured with the oscilloscope.

It was decided to build a compact filter unit with the option to connect six accelerometers

to it, since the objective was to measure with four accelerometers simultaneously, with the

option to add two more if necessary. Table 13 in appendix D lists up all major components

used to build the compact filter unit. Figure 60 illustrates how the filter unit looks like,

where two connection boards with three low-pass filters each are stacked on top of each

other and connected to two 12-volt batteries that are connected in series. The filters and the

batteries, along with the power circuit are placed inside a plastic box, with six BNC-

connection on each side for connecting the accelerometers and the output to the AD

converter.

Figure 60: The compact filter unit, with six 1000 Hz low-pass Butterworth filters.

98

Analog to Digital Converter

The analog to digital converter that was used for the localized equipment was bought from

National Instruments® and is illustrated on Figure 61 along with its dimensions and key

specification, Table 14, in appendix D, lists up further specifications.

Figure 61: NI USB-6000 ADC dimensions and key specifications.

This ADC fulfills the requirements needed for the localized equipment, just barely though

since it has a maximum sample rate of 10 kS/s aggregated amongst all used inputs. There

were four accelerometers used for this setup, resulting in a maximum sample rate of 2500

kS/s per transducer. It would have been good to have higher input resolution but was

acceptable because of cost concerns.

Accelerometers

The accelerometers used for the localized equipment are from STI-Vibration-Monitoring

Inc. named CMCP-1100 standard. These accelerometers come fitted with 5m long integral

cable and a threaded mounting port. Figure 62 illustrates the accelerometer’s dimensions

and key specifications, Table 15 in appendix D lists up more detailed specifications about

theses accelerometers.

Figure 62: CMCP1100 accelerometer dimensions and key specification.

Next step was to calibrate the accelerometers in function, one at a time, connected to the

low-pass filters and the ADC to establish the amplitude’s factor for each of them. This is

important procedure because the amplitude factor scales the measured value, so it matches

the real value. Vibration calibrator from Gilchrist Technology Inc. model 4000 was used

for the calibration process, it has an oscillator with adjustable amplitude and frequency.

99

The calibration procedure was as follows,

• Accelerometers mounted with magnetic base onto the oscillator

• Accelerometers, filter unit, ADC, and laptop (with control software) all connected

• Oscillator vibration preset with amplitude at 5 mm/s2 and frequency at 50 Hz

• Measurements taken at these frequencies, 50, 75, 100, 200, 500, and 750 Hz (with

amplitude declining with increasing frequency)

• Amplitude factor calculated for each frequency and then averaged

The amplitude factors S are listed in Table 5 below, they were calculated for each

frequency interval i and then averaged as,

𝑆𝑓𝑟𝑒𝑞𝑖

=𝑂𝑠𝑐𝑖𝑙𝑙𝑎𝑡𝑜𝑟 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒𝑓𝑟𝑒𝑞𝑖

𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝐴𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒𝑓𝑟𝑒𝑞𝑖

(61)

𝑆𝑡𝑜𝑡𝑎𝑙 =

𝑆𝑓𝑟𝑒𝑞_1 + 𝑆𝑓𝑟𝑒𝑞_2 + 𝑆𝑓𝑟𝑒𝑞_3 + 𝑆𝑓𝑟𝑒𝑞_4 + 𝑆𝑓𝑟𝑒𝑞_5 + 𝑆𝑓𝑟𝑒𝑞_6

6 (62)

Table 5: Accelerometers amplitude factors.

Assembly and Setup

The low-pass filter unit, the Analog-to-Digital converter, and a laptop were mounted inside

electrical cabinet, as illustrated in Figure 63. The accelerometers cables were fitted through

the bottom of the cabinet with waterproof cable glands. Inside the cabinet a multi plug was

fitted for plugging the laptop and filter unit chargers to 230 V.

Figure 63: Localized equipment fitted inside an electric cabinet.

Accelerometer 1 2 3 4

Amplitude Factor 0.240 0.233 0.240 0.227

100

Figure 64 illustrates the localized equipment placed beside main fan 2 in FTP-1, with the

cabinet connected to the factories 230 V power grid. The accelerometers are mounted on

the bearing housings with magnetic bases and placed in axial and radial directions.

Figure 64: Locacalized equipment at site, with electric cabinet connected to 230 V power

grid and accelerometers mounted on bearing housings with magnetic bases.

5.2.2 Portable Equipment

The portable equipment includes high end commercially bought equipment e.g. powerful

dynamic signal analyzer, high frequency accelerometers, low loss coaxial cables, and

threaded mounting components. It was decided to buy very powerful equipment to be able

to perform analysis on the high frequency range to detect early stage bearing faults.

Dynamic Signal Analyzer

Figure 65 illustrates the dynamic signal analyzer and its key specifications. The analyzer is

manufactured by MC Measurement ComputingTM and is a compact unit with very

powerful features for vibration analysis e.g. ADC with 24-bits resolution, sample rate of

105.4 kS/s per channel, and built in high-pass filter and adjustable low-pass filter.

Figure 65: DT9837B dynamic signal analyzer and its key specifications.

101

Accelerometers, Cables, and Setup

The portable equipment’s accelerometers were bought from Wilcoxon Research Inc. and

are compact, high sensitivity, and high frequency accelerometers. Figure 66 illustrates the

accelerometers and their mounting parts along with the cable. These accelerometers have a

frequency range from 2 Hz to 25000 Hz and they are light weight with compact structural

design. They have a threaded mounting hole and coaxial connection with 10-32 threads.

The mounting parts was built specifically for this project, to be able to utilize the threaded

port on top of the bearing housings. The cables are 5-meter coaxial cables with low signal

loss, with one end fitted with BNC connector ( which connects to the dynamic signal

analyzer) and the other with 10-32 threaded connection (connects to the accelerometers).

Table 16, in appendix D, lists up more detailed specification about the accelerometers.

Figure 66: High frequency accelerometer and mounting parts dimensions and setup.

Figure 67 illustrates the accelerometers mounted on the bearing housings, in axial and

radial direction. The threaded holes on top of the bearing housings were used to mount the

accelerometers, these holes are normally mounted with an eyebolt for lifting.

Figure 67: Accelerometers mounted on bearing housings, fitted in the eyebolts threaded

holes.

102

5.2.3 Vibration Analysis Software

To perform vibration analysis on the measurements gathered from the plummer block

bearings, multiple codes were written using MATLAB®. It is a powerful mathematical

computing software developed by MathWorks® Inc. For convenience and more robust

analysis a graphical user interface (GUI) was designed and developed using the GUIDE

user interface environment in MATLAB®. An option to perform measurements directly

using the GUI was also added. Figure 68 illustrates how the GUI lay out looks like.

Figure 68: Graphical user interface for the vibration measurement and analysis software.

Figure 69 illustrates a flowchart on how to perform and save measurements. First step is to

set the measurement sample frequency and how many samples to take. Next step is to

perform the measurement, where the measurement raw data loads in the GUI’s memory.

Next the user can decide to perform vibration analysis of the measurement, referring to

Figure 70, or decide to skip the analysis and name it and save in the database.

Figure 69: Flowchart of measurement and saving process.

103

Figure 70 illustrates a flowchart for the vibration analysis process on a single

measurement. First step is to load a single measurement in the GUI memory, see flowchart

in Figure 71 if two or more measurements are loaded. Amplitude representation

(Acceleration, Velocity, or Displacement), which sensor to examine, and weighing window

(Rectangular, Hanning, or Flat top) are then selected, the user can then choose to scale the

axis on the plots, if desired. Fourier- and Envelope analysis are the two main features in the

GUI to analyze the vibration data. Before the running FFT or Envelope the user can choose

to plot the bearing fault frequencies onto the frequency and envelope spectrums.

Additional feature is included in the GUI to calculate bearing fault frequencies based on

the geometric parameters of the bearing and shaft speed. Setting the order for the band-

pass filter and the method (Hilbert or Demodulation) are additional settings for the

Envelope process. There are four more features available in the GUI to support the analysis

process, these features plot a Kurtogram, the spectral Kurtosis, power spectrum, and the

Spectrogram (which has some additional settings to it).

Figure 70: Flowchart for the single measurement analysis process, (continued flowchart

from Figure 69).

104

Figure 71 illustrates a flowchart for the vibration analysis process for multiple

measurements. They main difference between the multi measurement analysis and the one

with a single measurement is that the multi analysis is mostly thought of as a comparison

between measurements at different time instances. There are two main features for the

multiple measurement analysis, one being a comparison between measurements with FFT

represented either on a waterfall plot (3-dimesional) or conventional frequency spectrum

plot (2-dimensional), and the other one being a condition indicator plotting. The procedure

is similar to the single measurement analysis, where a sensor is chosen, but for the

condition indicator analysis there is no need to choose amplitude representation or

weighting window, after that the axis scales are chosen, if desired.

Figure 71: Flowchart for the multiple measurement analysis process, (continued flowchart

from Figure 70).

Referring to appendix E for more visualization on how to operate the GUI.

5.3 Assessments and Condition Measurements

Next step in this case study was to utilize the techniques discussed in earlier chapters to try

to identify the causes for the problems that Norðurál is having on main fan 2 in FTP-1.

Additionally, to perform vibration measurements and analyze the results and to evaluate

the current condition and establish the remaining useful life (RUL) of the plummer block

bearings on main fan 2 in FTP-1.

5.3.1 Assessing Causes for Short Bearing Life

At appears that the problem occurring on main fan 2 plummer block bearings, in FTP-1, is

isolated to the unusual short bearing lifetime. However, it was decided to perform failure

assessment on the fan setup to try to isolate the cause and to see if there are any combined

effects causing the short bearing life. It was decided to start by performing Failure Mode

and Effect Analysis (FMEA) on the main fan setup.

105

FMEA

The worksheet used for this analysis is similar to the one illustrated in Figure 1, in section

2.2.1, where similar severity and occurrence criteria, as illustrated in Figure 2, and

detection criteria, as illustrated in Figure 3, were used.

In Table 17, in appendix F, the complete FMEA worksheet for main fan 2 in FTP-1, is

illustrated, where the main fan was divided by its main items. The items and their main

functions are, the electric motor which acts as the prime mover, the flexible coupling and

the drive shaft which form the power train, the plummer block bearings that support and

receive axial and radial forces, the impeller which is the driven part, and the foundation

which supports the system as whole.

On next page Table 6 lists up all the failure modes that scored approx. 150 or higher risk

priority number (RPN) (see equation (1) in section 2.2.1) from the analysis. Were all the

effects and causes that scored 200 or more are highlighted. Only one item scored 200,

excluding the plummer block bearings, it was the coupling, for the potential failure mode

where the coupling shatters because of faulty assembly. The risk of this particular failure is

reduced by following assembly instruction and use appropriate equipment to line up the

coupling during the assembly process.

As mentioned earlier, the plummer block bearings are the components that the company

has been having problems with regarding reduced lifetime. There were four potential

failure modes defined for the bearings and the housings. First is damage on rollers,

inner/outer raceways, and/or roller cage where the potential effects being increased

temperature and vibration. The second is structural damage on the housings where the

potential effects are housing and/or fasteners break/crack and increased vibration. The third

one is damage on the adapter sleeve and/or lock ring where the potential effects are

increased vibration and the sleeve/ring breaks. The fourth one is damage on the axial seals

where potential effects are grease contamination and damaged shaft surface.

Both potential effects, increased temperature, and vibration, on rollers, inner/outer

raceways, and/or roller cage have potential causes that have an RPN over 200. Where

increased temperature caused by faulty assembly or reduced grease life score 210.

Increased vibration caused by spalls on the surface of the rollers and/or raceways score

216. Where the risk for the potential causes, for the increased temperature, is reduced by

following assembly instructions and monitor the grease condition regularly. Where the risk

for the potential cause, because of increased vibration, is reduced by monitoring the

vibration level and perform appropriate actions when levels are increasing e.g. greasing

and bearing change.

Same occurred for both potential effects for both the structural damage and damaged

adapter sleeve and/or lock ring failure modes. Where faulty assembly on the bearing

housing scored 270 and increased vibration cause of looseness scored 210. Increased

vibration cause of faulty assembly on the adapter sleeve scored 210, and the effect where

the adapter sleeve and/or lock ring breaks cause of faulty assembly scored 270. The failure

mode for damaged seals did not have any effects that scored over 200. Same applies to the

impeller and foundation although, increased vibration on the impeller cause of faulty

assembly scored 180.

106

Table 6: Failure modes, effects, and causes with highest RPN for main fan 2 in FTP-1,

summ-up from the full FMEA-worksheet listed in Table 17, in appendix F.

The FMEA indicates that the highest risk factors that leads to faulty operation on the main

fan, are often caused by faulty assembly. According to maintenance personnel at Norðurál,

during bearing change and other maintenance work performed on the main fans, all

manufacturers assembly instructions are followed, and certified methods are used when

electric motor, coupling, and driveshaft are lined up. Same applies to the assembly on the

plummer block bearings, where a certified method is used to fit bearings and adapter

sleeves on the driveshaft, so called SKF drive-up method as mentioned earlier. Based on

this information the cause for the short bearing life cannot be pinpointed from the FMEA.

Ite

m

Function

Potential

Failure

Mode

Potential

Effect(s)

of Failure Seve

rity Potential

Cause(s)

of Failure

Occ

urr

en

ce

Current Design

Controls

(Prevention)

Current Design

Controls

(Detection) De

tect

ion

R P

N Recommended

Action(s)

Electric

Motor

Prime

Mover

Electrical

overload

Over

Heating7

Isolation

degrades3

Prevent over-heating,

minmize corrosion, and

physical wear/damage

Through visual

inspection8 168

Set up regular

inspections schedule

CouplingConnect motor

and drive shaft

Structural and/or

fasteners damage

Coupling

shatters10

Faulty

assembly4

Follow assembly

instructions

By double

checking assembly5 200

Make sure assembly

instructions are followed

Drive

Shaft

Deliver torque

to impeller

Structural

damage

Permanent

Bent7

Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Reduced

grease life5

Monitor grease

condition

With regular

checks6 210

Set up regular


Increased

clearance5 Monitor vibration

With automatic

measurements6 180

Monitor bearings vibrations

regularly

Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Spalls on

surface6 Monitor vibration

With automatic

measurements6 216


regularly

Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Foreign object

impacts4

Use protective

covers

Through visiual

inspection5 180

Make sure foreign objects

cannot impact components,

set up protective covers

Looseness 6Tighten bolts with

appropriate torque

By double

checking torque5 210

Make sure assembly


High bearing

clearance5 Use certified parts By measurements 5 175

Monitor bearings vibration

regularly

Increased

vibration7

Faulty

assembly5

Follow assembly

instructions

By double





Adapter sleeve

and/or lock ring

breaks

9Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly


Damaged

shaft surface6

Visually examine

part

By double

checking surface5 150

Set up regular


Material

wear4 Use durable materials

Through visiual

inspection6 168 Use durable materials

Material

fatigue 3

Examine part

before assembly

Through visual

inspection and/or

perform NDT test

7 147 Buy certified components

Misalignment 6

Align components

during

assembly

By double

checking alignment5 150

Follow standardized methods

when aligning parts

Unbalance 6Balance parts

during assambly

By double

checking balance5 150


when balancing parts


appropriate torque

By double


Make sure assembly


Faulty

assembly6

Follow assembly

instructions

By double


Make sure assembly


Faulty

assembly5

Follow assembly

instructions

By double


Make sure assembly



appropriate torque

By double


Make sure assembly


Foundation

Support all

components

of the fan

Structural

damage

Increased

vibration6

Geometria

changes7

Impeller

Creates

pressure

differance

between

suction and

discharge side

Structural

damage

Increased

vibration5

Grease

contamination5

Damaged

seals

Support drive

shaft and

impellers

weight.

(radial forces)

and receive

impellers

thrust

(axial force)

Plummer

Block

Bearings

Housing

and/or

fasteners

cracks/breaks

Increased

vibration

9

7

Damaged

adapter sleeve

and lock ring

Increased

temperature7

6Increased

vibration

Damaged Rollers,

inner/outer

raceways

and roller cage

Structural

damage

Failure Modes, Effects, and Causes with Highest RPN for Main Fan 2 in FTP-1

107

As stated in Table 3, in section 5.1.2, the initial plummer block bearings were in operation

from 85k to 136k hours, which is a well acceptable lifetime for bearings that are in

constant operation. It also states that, for main fans 3 and 4, there has only been a single

bearing change on each since they were initially started. For main fan 1, the bearings were

changed in March 2010 which occurred only 16k hours from first change, but after that

they were in operation for approx. 80k hours before they were changed in February 2019.

According to maintenance personnel are the bearings showing some operational problems

and are expected to be replaced soon, as mentioned earlier, indicating there is some factor

causing the short lifetime on the plummer block bearings on main fan 1 as well. The

bearings on main fan 2 have been changed five times since the initial change in the year

2008, which implies that the problem seems to be isolated to the plummer block bearings

on main fans 1 and 2, although the problem seems to be more serious on main fan 2.

From this information it is assumed that some other factor is causing the short bearing life.

By exploring the maintenance history, other components (items) of the main fan setup are

be ruled out as being the cause for the short plummer block bearing life. The electric motor

has never shown any signs of mechanical faults, although it was changed some years back

cause of isolation deterioration after being in operation for approx. 20 years. According to

maintenance personnel has the coupling always appeared to be in good condition and not

shown any signs of mechanical failure, although it is standard procedure to change the

rubbers in the coupling during bearing change. The driveshafts have always appeared in

good condition, but the shafts surface where the axial seals are located have sometimes

shown surface roughness, most likely resulted from grease contamination caused by

bearing deterioration, in these cases the shaft has been replaced along with the bearing

change. According to maintenance personnel, there has only been one incident where

impeller broke during operation, most likely caused by faulty design since there has never

been any other incident like that on any of the other main fans in all the FTP’s. The

foundation supporting the main fans have never shown any signs of problematic operation

and are since the FTP’s were initially started, and since the initial bearings were in

operation as long they were it is almost impossible to link any of the short bearing life to it.

Looking at the plummer block bearing operational parameters listed in Table 10 in

appendix C, the calculated bearing lifetime is over 200k hours for both bearings, however

the relubrication interval is just 20.3 hours for the Fan DE bearing and 2390 hours for the

Fan ND bearing, indicating that the lubricating setup is most likely not ideal for this

bearing setup with the current operational parameters. Another factor that is also noticeable

is that the speed factor (ndm) limit, for the Fan DE bearing is 150,000 with this kind of

lubrication method, but according to the bearing calculations it currently is 209,000 well

above recommended value.

Based on this information it is concluded that the current lubrication method is not ideal

and should be reconsidered. But giving that the initial bearings were in operation as long as

they were, it is most likely some other factor is also contributing to the short bearing life.

In the complete FMEA worksheet, listed in Table 17 in appendix F, one possible cause for

increased vibration from the rollers, inner/outer raceways, and/or roller-cage is listed, that

is cause from magnetic field. Although this particular cause only scored 96 in RPN, it is

hard to ignore it since other possibilities have not been able to pinpoint the problem and the

fact that there is a strong magnetic field in the pot rooms and its surroundings.

108

Possible Effects from Magnetic Field

In the beginning of February 2020 an expert named Marius Friedman, from the company

Flebu International AS, visited Norðuál to check up and give advice for the main fans in

FTP-1, due to the short bearing life. Based on Flebu long experience with fans in

aluminum plants, he stated that they have encountered similar problems before regarding

short bearing life. Based on the location of the main fans between the pot rooms, where the

bearings are exposed to strong magnetic field, there is possibility that the rollers and the

roller-cage are forced together cause of combination from the magnetic field and low load

on the bearings, resulting in unusual wear on the roller-cage.

Based on earlier experience, the expert suggested that the Fan DE bearing should be

changed to a similar bearing with non-magnetic roller-cage and that the grease lubrication

setup would be changed for circulating oil lubrication. Although this seems to be a

probable solution to the problem, it is hard to ignore the fact that the initial bearings were

in operation as long as they were, raising the question what has changed?

According to Norðurál technical department, the company started to gradually increase the

pot rooms amperage in the year 2010 to increase the aluminum production. Where the

strength of the magnetic field generated in the pot rooms is in direct relation to the strength

of the current flowing through it, it is a possibility that the increased magnetic field could

be contributing to the short bearing life. Figure 72 illustrates how the pot room amperage

increase process has developed since January 2010, where initially the designed pot room

amperage was approx. 180 kA in pot rooms A and B (referred to as line 1) and approx. 200

kA in pot rooms C and D (referred to as line 2). The amperage was gradually increased on

both lines until it reached it current value of approx. 220 kA in the end of 2014 on line 2

and in the beginning of 2016 on line 1.

Figure 72: Development of the pot rooms amperage since the year 2010, and time of

bearing change on main fans 1 and 2 in FTP-1.

109

In Figure 72 the yellow and blue vertical lines indicate the dates of plummer block bearing

change on main fan 1 and 2. It shows that the interval on the bearing change has greatly

increased since the amperage reach it current value, especially on main fan 2 although the

bearings on main fan 1 have been having some operational problems recently, according to

maintenance personnel.

Based on this information it is safe to say that there is strong correlation that the increased

pot room amperage is contributing to the short bearing life. But it is hard to assert that the

magnetic field is the main cause for the short bearing life since main fans 3 and 4 in FTP-1

have not been showing the same problem and none of the fans in FTP-2. Unless the

strength of the magnetic field surrounding the housings on the plummer block bearings on

all main fans is measured and compared to each other, to see if there is some difference

between them. Unfortunately, it was not possible to perform these measurements during

this case study.

Unfortunately, the thesis time frame did not allow further failure assessments to be done

and since FMEA was unable to pinpoint the cause, next steps would be to perform Root

Cause Analysis (RCA) to see if the root cause for the short bearing life could be determent.

Consequently, if the RCA would not pinpoint the cause, a Fault Tree Analysis (FTA)

would be the next step. Using infrared thermography was also an option that was

considered but unfortunately the equipment needed to perform those measurements was

not available and would have to be bought especially for this project, with funds that were

not available.

5.3.2 Assessing Condition and Fault Development using

Vibration Analysis

The first step in the vibration measurement part of this thesis was placing the localized

equipment beside main fan 2 in FTP-1. As mentioned earlier, the equipment was set up to

perform a single measurement every 24 hours, with two accelerometers mounted on each

plummer block bearing housing, measuring in axial and radial directions. The equipment

was in operation from April 2019 to May 2020, performing total of 362 measurements

with sampling rate of 2500 Hz and sampling period of 1 second.

The portable equipment arrived later, cause of shipping delays, and was not operable until

the beginning of July 2019, unfortunately it did not arrive in time before the bearing

change on main fan 2 in FTP-1. As mentioned earlier, the same basic function was used for

this equipment where two accelerometers were used on each plummer block bearing to

measure in axial and radial directions with sampling rate of 100 kHz and sampling period

of 1 second.

Initial Condition Assessments

It was decided to perform a single measurement on both plummer block bearings on all

main fans in FTP-1 and FTP-2, to assess their condition and select bearings to monitor.

This initial assessment was performed by analyzing the bearings frequency spectrums to

inspect if any bearing fault frequencies were present or any other indication of faulty state.

For convenience, the bearing fault frequencies are listed again on next page, gathered from

Table 10 in appendix C.

110

Bearing fault frequencies:

• Fan DE: FTF = 7.1 Hz BSF = 57.2 Hz BPFO = 128.4 Hz BPFI = 169.5 Hz

• Fan ND: FTF = 7.0 Hz BSF = 51.9 Hz BPFO = 118.8 Hz BPFI = 162.5 Hz

The assessment results for FTP-1 are listed in Table 7 and for FTP-2 are listed in Table 8.

Table 7: Initial condition assessments on plummer block bearings on main fans in FTP-1.

Table 8: Initial condition assessments on plummer block bearings on main fans in FTP-2.

Main

FanBearing Decision

Fan DE

(Spherical Roller)

Fan ND

(CARB Toroidal Roller)

Fan DE

(Spherical Roller)

Fan ND


Fan DE

(Spherical Roller)

Fan ND


Fan DE

(Spherical Roller)

Fan ND


Vibration level at shaft frequency is approx. 3 mm/s

Small indication on impellers blade pass frequency.

Indicating unbalance on impeller.


No indication on faults.

Fume Treatment Plant 1: Initial condition assessments, based on vibration measurements

Continue to

Monitor

Continue to

Monitor

(based on history)

Not

Continued

Continue to

Monitor

Vibration level at shaft frequency is approx. 1.7 mm/s







Indication on both BPFI & BPFO fault frequencies and their harmonics.

Indications on vibration rise in the high frequency range, around 5000 Hz.


First harmonic of BPFI noticeable.

1

2

3

4

Measurement Remarks

Vibration level at shaft frequency and its second harmonic is approx.

1 - 1.5 mm/s, nothing to rise concerns.

Roller element fault frequency noticeable at its 4th harmonic.

Minor indication on BPFO harmonics.

Main

FanBearing Decision

Fan DE

(Spherical Roller)

Fan ND


Fan DE

(Spherical Roller)

Fan ND


Fan DE

(Spherical Roller)

Fan ND


Fan DE

(Spherical Roller)

Fan ND


Fume Treatment Plant 2: Initial condition assessment, based on vibration measurements

Measurement Remarks

2





Continued to

Monitor

1


No indication on faults. Not

ContinuedVibration level at shaft frequency is approx. 0.7 mm/s


Not

Continued

Continued to

Monitor

4

Vibration level at shaft frequency is approx. 2.7 mm/s and increases over

next two harmonics (1st. 2.9 mm/s and 2nd. 3.1 mm/s), indicating possible

looseness and/or misalignmment.



3


First two harmonics of shaft frequency are showing, indicating possible

misalignment between shaft and motor.



111

Based on the initial condition assessment it was decided to continue to monitor main fans 1

and 4 in FTP-1 and main fans 3 and 4 in FTP-2. Although plummer block bearings were

changed on main fan 2 in FTP-1 just few days before the portable equipment arrived it was

also included occasionally to see if some faults would develop during the measurement

period. Fan DE bearings on both main fan 1 and 4 in FTP-1, showed indication on bearing

fault frequencies leading to special interest to see how they would develop. Fan DE

bearings on both main fan 3 and 4 in FTP-2 showed indication on possible misalignment

and/or looseness and therefore were included in the following monitoring period to see if

the problem would escalate. They did not show any indication regarding the bearing fault

frequencies and consequently they did not raise any big concerns moving forward.

Continued Measurements and Vibration Analysis

In the period from July 2019 to May 2020 vibration measurements were performed with

the portable equipment, with variable intervals, on the main fans selected from the initial

condition assessments. It appeared that the axial direction sensors on both Fan DE and Fan

ND bearings give more information regarding the frequency spectrum, so in the following

discussion and figures are only the axial sensors used, and each main fan will be discussed

and analyzed separately. The main focus will be on main fans 1 and 4 in FTP-1 since their

initial condition assessment indicated some bearing fault frequencies. The development of

main fan 2, in FTP-1, condition will also be checked, giving its maintenance history is by

far worst. Main fans 3 and 4 in FTP-2 will get some brief discussion on their operational

condition development.

FTP-1: Main Fan 1

There were performed ten measurements on the plummer block bearing housings on main

fan 1, during the case study measurement period. Figure 73 illustrates the 0 to 1300 Hz

frequency spectrum for the Fan DE bearing from July 2019. The vertical dotted lines

indicate the BPFI, BPFO, and BSF fault frequencies and their harmonics. Where the most

vibration is generated at the shaft frequency and its harmonics, as would be expected,

where the 2nd, 6th, and 12th harmonics are visible. This could indicate small misalignment

or looseness, but nothing that raises any concerns. The 4th harmonic of the BSF fault

frequency is showing, with considerably high amplitude (0.4 mm/s) giving it is a bearing

fault frequency, who usually give rather small impulses. There are also small traces of the

BSFO and BSFI fault frequencies harmonics. It indicates that some fault development is

happening inside the bearing, however, the noise floor is rather low in the upper

frequencies which indicates that the faults are not necessarily crucial but important to keep

monitoring.

In Figure 101, in Appendix G, the Fan ND bearing frequency spectrums, from July 2019

and May 2020, are compared, showing that there are only minor indication on BSF fault

frequency and the condition of the bearing has not degraded noticeably and generally

seems to be in good condition. There is some vibration at the shaft speed and on the blade

pass frequency indicating some imbalance on the impeller but has decreased between

measurements therefore not something that rases any concerns. Figure 102, in appendix G,

illustrates the time domain envelopes comparison, for the same measurements, where the

vibration data was band passed filtered with optimal bandwidth gathered from the

kurtogram. Interestingly it shows extremely high kurtosis for both instances, 225 and 587,

indicating high impulsiveness in the signal. This extreme impulsiveness is most likely

112

caused by the fans casing is vibrating close to the Fan ND bearing housing and striking it

randomly.

Figure 73: Fan DE bearing frequency spectrum, on main fan 1 in FTP-1, from July 2019.

Figure 74 illustrates the 0 to 1300 Hz frequency spectrum for the Fan DE bearing since

May 2020. It shows that the vibration at the shaft speed has decreased little bit, but its level

was not of any concerns earlier and remains that way. The amplitude of the BSF 4th

harmonic has increased 42.5% between measurements and is causing concerns. The BPFI

and BPFO have decreased and are not as visible as before, which is not necessarily good

sign since surface spalls often smoothened out with time, meaning that the condition has

possibly gotten worse than before. The increasing noise floor, in the upper frequencies,

also indicates that the bearing faults have increased since before.

Figure 74:Fan DE bearing frequency spectrum, on main fan 1 in FTP-1, from May 2020

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Given the information gathered from the frequency spectrums it was decided to compare

the time domain envelopes and the envelope spectrums between the two measurements.

The comparison between the envelope spectrums did not show any dominant indication

that the bearing condition has gotten worse and did not reveal any strong bearing fault

frequencies or their harmonics. Figure 75 illustrates the comparison between the time

domain envelopes, where the envelopes are calculated similarly as before using optimal

band pass filter to filter the signal. The kurtosis increased little bit between measurements,

meaning increased impulsiveness in the signal, indicating that there have possibly larger

and/or more spalls formed on the rolling elements or inner and/or outer raceways. The

overall vibration level has increased greatly, giving strong indications that the operational

condition has deteriorated since the initial measurement.

Figure 75: Vibration signals envelope comparison between first and last measurements on

Fan DE bearing on main fan 1, in FTP-1.

Figure 76 illustrates the frequency spectrum development in the high frequency range, 1.5

kHz to 25 kHz, for the all the measurements taken on the Fan DE bearing. As described in

section 3.2.2, are increased vibration in the ultrasonic frequency range (often between 20

kHz and 60 kHz, dependent on the bearings structure) the first indication on bearing fault,

and as a fault develops a vibration in the bearing components resonant frequency range

increases (often in the 2 kHz to 10 kHz range). It appears that there is a little bit vibration

increase in the bearing components resonant frequency range, approx. 4 kHz to 9 kHz,

including some development in the 20 kHz range. This gives indication that there are faults

developing in the bearing and it should be monitored more often.

114

Figure 76: FTP-1 main fan 1 Fan DE bearing, waterfall graph of the 1.5 kHz to 25 kHz

frequency spectrums, from July 2019 to May 2020.

Figure 77 illustrates a spectrogram comparison between measurements, showing vibration

increase in the high frequency range and it has become more compact, the vibration level

at the lower frequencies has also increased. Giving indication that there are bearing faults

developing in the bearing, giving similar results like the waterfall graph.

Figure 77: Spectrogram of the first and last vibration measurements, on Fan DE bearing.

FTP-1: Main Fan 2

There were performed seven measurements on the plummer block bearing housings, on

main fan 2, with the portable equipment, during the case study measurement period. There

were bearing change performed in July 2019, so the following measurements give initial

condition assessments on the bearing condition and how its condition developed. Figure 78

illustrates the frequency spectrum, 0 to 1300 Hz, for the Fan DE bearing day after it was

installed. Vibration level at shaft speed is rather small, only approx. 1 mm/s, indicating that

the assembly and alignment was performed correctly. The bearing is showing some

vibration at BPFI and BSF fault frequencies indicating possible defects in the bearing, but

115

it must be kept in mind that the bearing is new and these impulses are most likely going to

smoothened out in the following days or weeks. The noise floor is also very low, indicating

good condition.

Figure 78:Fan DE bearing frequency spectrum, from July 2019 (Bearing New).

In Figure 103, in Appendix G, the Fan ND bearing frequency spectrums, from July 2019

and May 2020, are compared, showing some indication on BSF fault frequency and its

harmonics in the initial measurement but showing reduction in the latest measurement.

There is a possibility that this is caused by that the bearing is brand new during the first

measurement. There are other indications on faulty state, where the noise floor is low for

both measurements and the condition of the bearing has not degraded noticeably and

generally seems to be in good condition. There is some vibration at the shaft speed

indicating small imbalance on the impeller but has decreased between measurements and

does not raise any concerns. Figure 104, in appendix G, illustrates the time domain

envelopes comparison, for the same measurements, where the vibration data was band

passed filtered before the envelope was calculated, as before. The vibration level is very

low in the first measurement with rather low kurtosis of 13.4, compared to the Fan ND

bearing on main fan 1. In the later measurement the vibration level has increased

considerably, and the kurtosis has increased to 327.5, indicating that the impulsive

components have increase greatly between measurements. As for main fan 1, this extreme

impulsiveness is most likely caused by the fans casing that strikes the bearing housing

randomly.

Because of the fact that the BPFI and BSF fault frequencies were showing in the frequency

spectrum, for the Fan DE bearing, it was decided to analyze the envelope spectrum to see if

anything would reveal itself. Figure 79 illustrates the Fan DE bearing envelope spectrum,

taken in July 2019, where the envelope spectrum is calculated as before. Interestingly the

BPFO fault frequency and its harmonics are showing and the BPFI and BSF fault

frequencies did not appear as they did in the frequency spectrum. However, the amplitude

is rather small and giving it is a new bearing and most likely will reduce in the following

days/weeks and does not rise any major concerns but gives reason to monitor the bearing

regularly in the following weeks/months.

116

Figure 79: Envelope spectrum of Fan DE bearing, taken in July 2019 (Bearing New).

Figure 80 illustrates Fan DE bearing frequency spectrum, measured in May 2020, where

the vibration at shaft speed and its 2nd harmonic have decreased between measurements.

The bearing fault frequencies are still visible but have decreased between measurements

which was to be expected. The noise floor has shown minor increase, but the overall

spectrum indicates that the bearing is in good operating condition.

Figure 80: Fan DE bearing frequency spectrum for main fan 2 in FTP-1, from May 2020.

Figure 81 illustrates the envelope spectrum for the measurement performed in May 2020. It

shows that the overall vibration level has increased between measurements, and noticeably

the BPFO fault frequency is no longer as dominant in the spectrum. This gives some

indication that the bearings condition has gotten slightly worse, but nothing that raises any

major concerns.

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Figure 81: Envelope spectrum of Fan DE bearing, taken in May 2020.

Figure 82 illustrates the time domain envelopes displaying similar results as the envelope

spectrum, where both the overall vibration level and the kurtosis, from 3.4 to 8.7, have

increased between measurements indicating more impulsiveness in the signal. However,

the vibration level is still rather low and nothing that should give any concerns.

Figure 82:Vibration signals envelope comparison between first and last measurements

performed on Fan DE bearing on main fan 2, in FTP-1.

Figure 83 illustrates the high frequency range spectrums for all the measurements

performed, with the portable equipment, on the Fan DE bearing. The vibration level first

starts to show an increase in the 10 kHz to 25 kHz range and as time goes the vibration

level decreases in that range and the bearing component resonant frequencies start to show

increasing vibration level. This gives indication on how an early stage bearing fault

progresses from stage one to stage two fault, as discussed in section 3.2.2.

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Figure 83: Fan DE bearing, waterfall graph of the 1 kHz to 30 kHz frequency spectrums,

from July 2019 to May 2020, for main fan 2 on FTP-1.

FTP-1: Main Fan 4

There were performed ten measurements on the plummer block bearing housings on main

fan 4, during the case study measurement period. Figure 84 illustrates Fan DE bearings

frequency spectrums, for main fan 4, from July 2019 and May 2020. The vertical dotted

lines indicate the BPFI and BPFO fault frequencies and their harmonics. The most

vibration is generated at the shaft frequency, as would be expected, but the vibration level

is rather low approx. 1.2 mm/s which indicates that the system is well balanced and

aligned. The BPFO and BPFI fault frequencies are visible in both measurements, giving

strong indication that there are spalls or other damage on the surfaces on the inner and

outer raceways. The BSF fault frequency is not showing any signs, so it appears that the

damages are isolated to the raceways of the bearing. Table 9 shows a comparison on the

amplitude development for BPFI and BPFO fault frequencies and their harmonics for both

measurements. Where the outer raceway fault frequency is showing high increase between

measurements indicating that the potential spalls on the outer raceways surface are

increasing. The inner raceway fault frequency is however showing decrease between

measurements, except for the 3rd harmonic, which is not necessary a good sign since

impact points often get worn out over time and could indicate that the spall has grown

larger between measurements. This bearing should be monitor more frequently in the

upcoming weeks/months and it should be considered for bearing change.

Table 9: BPFO and BPFI amplitudes comparison between measurements

2019-07-05 2020-05-07 Difference 2019-07-05 2020-05-07 Difference1st 0,20 0,32 60% 0,49 0,46 -6%

2nd 0,08 0,15 88% 0,13 0,05 -62%3rd 0,18 0,34 89% 0,42 0,69 64%4th 0,17 0,25 47% 0,44 0,30 -32%5th 0,21 0,22 5% 0,13 0,13 0%6th 0,06 0,06 0% 0,12 0,10 -17%

Ball Pass Frequency Outer (BPFO) Ball Pass Frequency Inner (BPFI)

Har

mo

nic

s

Date

119



Figure 85: Envelope spectrums comparison between first and last measurements performed

on Fan DE bearing on main fan 4, in FTP-1.Figure 85 illustrates the envelope spectrums

for the first and last measurements performed on Fan DE bearing. The first thing that

strikes the eye is that the shafts frequency in the first measurement is not appearing, which

it usually does. Another thing that is odd, is how the BPFO and BPFI bearing fault

frequencies just appear for their first harmonic, but not for higher harmonics and are not

dominant as they appear in the frequency spectrum. This is confusing and strange, since

envelope spectrum usually enhances the impulsive components in the vibration signal,

which bearing faults certainly are. The noise floor has increased little bit between

measurements but nothing that should raise any concerns since the increase is rather low.

The envelope spectrums unfortunately do not give the information as would be expected,

based on the frequency spectrums clear indication on bearing faults.

Figure 86 illustrates the time domain envelopes for both measurements, where the

vibration signals impulsiveness has increased little bit between measurements when the

kurtosis increased from 3.11 to 3.46. The overall vibration level seems to be similar

between measurements indicating that the bearing condition has not changed that much. A

waterfall graph is illustrated in Figure 105, in Appendix G, where the high frequency

spectrum, 1 kHz to 30 kHz, is plotted for all measurements performed on the Fan DE

bearing during the case study measurement period. Showing no indication on that the

bearing’s operating condition has changed.

120



Figure 86: Vibration signals envelope comparison between first and last measurements


Figure 106, in Appendix G, illustrates Fan ND bearings frequency spectrums, for main fan

4, from July 2019 and May 2020. Where the BPFO and BPFI fault frequencies are

appearing in both measurements, with some increase in amplitude between measurements.

Indicating that there are spalls or other surface damage present in the inner and outer

raceways of the bearing. The overall vibration level has not shown increase, which is a

good sign and indicates that the bearings condition is acceptable.

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The mounting hole used to fasten the accelerometers on the bearing housing on this

particular bearing, as illustrated in Figure 67 in section 5.2.2, has a broken piece from old

eyebolt in it. There were only approx. 1 to 2 threads usable in the hole and not possible to

fasten the sensors properly, just tighten it loosely and support it with hand during the

measurement. Therefore, the envelope analysis and high frequency spectrum analysis are

unfortunately not usable since the high frequency components of the vibration signal are

most certainly missing or not as they should be.

FTP-2: Main Fan 3

Figure 87 illustrates the comparison between the frequency spectrums, 0 Hz to 1300 Hz,

for the Fan DE, from July 2019 and May 2020. Where the bearing shows no indication on

any bearing fault frequencies for either measurement. Some vibration is visual at the shaft

speed and its harmonics in the first measurement, indicating possible misalignment and/or

looseness, but levels are rather low and do not raise any concerns, and actually has

decreased between measurements. Similar results were obtained for the Fan ND bearing

and is therefore not included in the summary. There was no bearing fault indication drawn

from the envelope analysis either, so the overall condition is considered acceptable for both

Fan DE and Fan ND bearings on main fan 3 in FTP-2 and will not be discussed further.


performed on Fan DE bearing on main fan 3, in FTP-2

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FTP-2: Main Fan 4

Figure 88 illustrates the frequency spectrums, 0 Hz to 1000 Hz, for the first and last

measurements performed on Fan DE bearing on main fan 4 in FTP-2. There is clear sign of

vibration at the shaft speed and its harmonics were noticeably it has increased between

measurements and more harmonics are noticeable. This strongly indicates misalignment

and/or looseness in the system. Since there are so many harmonics visible in the spectrums

and they increase between measurements it is more likely that the problem is an assembly

looseness, as illustrated in Figure 29 in section 3.2.1, which is progressing.

There are no signs or indications on bearing fault frequencies in the frequency spectrums

and the noise floor is rather low in both measurements indicating that the overall bearing

condition is acceptable. However, it is advisable to inspect the bearing and check for the

possibility that there is an assembly looseness between the bearing and the adapter sleeve

or the adapter sleeve and the driveshaft.



It was decided to perform envelope analysis for both measurements, to see if any bearing

fault would appear. There was no indication on the bearing fault frequencies in the

envelope spectrums. The first measurement however did appear to have strong vibration in

the low frequency range, so it was decided to focus the envelope analysis on the 0 to 200

Hz range. Figure 89 illustrates the envelope spectrums for both measurements where the

FTF fault frequency is showing in the first measurement and the overall vibration level is

rather high. In the last measurement the vibration level has decreased greatly and the FTF

fault frequency is not showing. The excessive vibration and the presence of the FTF in the

first measurement is most likely caused by poor lubrication. Where in the last measurement

there has possibly been grease change shortly before. Unfortunately, the maintenance

history obtained for this case study did not cover these dates.

123

Figure 90 illustrates the time domain envelopes for these measurements, where the kurtosis

decreased from 16.5 to 4.7 between measurements. Indicating that the impulsive

components in the signal have decreased. The overall vibration level has also decreased

which supports that the most likely cause is the bearing grease condition between the two

measurements.

Similar process was performed on the Fan ND bearing where the bearing did not show any

signs of bearing faults. It showed small indication of misalignment and/or looseness but

nothing that raises any concerns. The overall condition is acceptable and will not be

discussed further.



Figure 90: Vibration signals envelope comparison between first and last measurements


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5.3.3 Remaining Useful Life Estimation

Decision was made to use the vibration measurements gathered from Fan DE bearing on

main fan 2 in FTP-1 using the localized equipment. Based on the fact that this is the only

data that spans over the last few months that the prior bearings were in operation, along

with the new bearings and their operation since July 2019. The measurements collected

with the portable equipment are unfortunately too few to make any sensible estimation.

It is not always clear on what type of fitting curve should be used for the RUL estimation

but, using a linear curve is widely used method which assumes that the bearing faults

severity is a linear process. Exponential fitting curves are also widely used, especially in

cases where it is known that the fault can have feedback effects which increase the

deterioration rate exponentially. It is possible to fit other types, but it not widely used

unless in cases where it is known to fit the data, based on experience or other physical

reasons [1]. It was decided to use both linear and exponential curves to estimate the RUL

on the Fan DE bearing to compare their results.

The overall RMS vibration level is a well-known condition indicator for rotating

machinery, so it was decided to perform the estimation of the RUL using the RMS-values.

Figure 91 illustrates the overall RMS vibration level for every measurement performed on

the Fan DE bearing on main fan 2 in FTP-1, excluding the measurements when the fan was

shut off because of maintenance work. It is visible how the vibration level dropped down

after the bearing change in July 2019, but it is noticeable that the trend is slowly going

upwards as one would expect.

Figure 91: Overall RMS vibration level for all measurements performed on the Fan DE

bearing, on main fan 2 in FTP-1.

First step in performing a bearing remaining useful life estimation is to establish some kind

of threshold which indicates that the bearing is at its end of life. The overall RMS value

does fluctuates quite bit between measurements, as seen in Figure 91, hence the method

125

used to establish the threshold was calculating the mean RMS value over the last 15 days

before the bearing change occurred, resulting with the threshold,

RMS-Threshold = 2.75 m/sec2

Next step was to trend the RMS values for all measurements performed after the bearing

change in July 2019 with both linear and exponential curves. The curves coefficients were

found using the fit-function in MATLAB®, resulting with the following fitting equations,

𝐿𝑖𝑛𝑒𝑎𝑟 𝑇𝑟𝑒𝑛𝑑𝑖𝑛𝑔: 𝐹𝑖𝑡𝐿𝑖𝑛(𝑥) = 0.002243𝑥 + 1.388 (63)

𝐸𝑥𝑝𝑜𝑛𝑒𝑡𝑖𝑎𝑙 𝑇𝑟𝑒𝑛𝑑𝑖𝑛𝑔: 𝐹𝑖𝑡𝐸𝑥𝑝(𝑥) = 1.403 ∗ 𝑒0.001341𝑥 (64)

Figure 92 illustrates the overall RMS vibration level for all measurements performed after

the bearing change, in July 2019, including the linear and exponential trending curves. The

horizontal red line is the RMS-threshold established earlier. The RUL estimation is

established where the trending curves cross the RMS-threshold. For the linear curve, the

estimated RUL is 333 days and for the exponential curve it is 228 days. Based on the

exponential estimation the maintenance personnel should prepare for bearing change in

December this year but based on the linear estimation they should prepare in April 2021.

Figure 92: Overall RMS vibration level for all measurements after bearing change, with

linear and exponetial trending curves.

Other condition indicators were also checked but unfortunately their parameters were not

easy to trend to make some sensible estimation on the RUL of the bearing. Figure 93

illustrates the trends for Mean Frequency, Skewness, Kurtosis, and Crest-Factor for all the

measurements performed on the Fan DE bearing on main fan 2 in FTP-1. These condition

indicators are not showing any easy trend able options to perform RUL estimation. The

reason for this is most likely because the localized measurement equipment has too low

sampling frequency, only 2500 Hz. Meaning it does not pick up the bearing components

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resonant frequencies, approx. 3 kHz to 10 kHz, which is the frequency range that bearing

faults usually start to appear, excluding the supersonic frequency range. Giving that the

localized equipment sample rate was 2500 Hz using a 1000 Hz low pass filter, means that

bearing faults that are measurable with this equipment have usually progressed to stage 3,

where the bearing fault frequencies are starting to appear in the frequency spectrum.

To be able to explore these condition indicators, as illustrated in Figure 93, further and

perform RUL estimation based on them, the sampling frequency most likely should have

been at least 25 kHz using a 10 kHz low pass filter. Unfortunately, that kind of equipment

is much more expensive than the one used and was outside the project budget.

Figure 93: Mean frequency, Skewness, Kurtosis, and Crest factor for all measurements

performed on the Fan DE bearing, on main fan 2 in FTP-1.

127

6 Conclusions

The main focus of this project was to design and develop a vibration measurement and

analysis system that is used to collect vibration data and utilize that data to perform

advanced vibration analysis. The system was utilized in a case study at Norðurál aluminum

plant. The purpose for the case study was because of problems Norðurál had been having

regarding one of the centrifugal main fans in one of the companies fume treatment plants

(FTP). The problem described in a way that one of the main fans plummer block bearings

was experiencing to short lifetime, resulting in unexpected shutdowns and interruptions in

the fan’s operation.

Failure Mode and Effect Analysis (FMEA) was performed on the main fan 2, in FTP-1,

setup to try to narrow down and isolate the cause for the unusual short plummer block

bearing lifetime. The analysis showed that the current lubrication setup for the plummer

block bearings was not suitable based on the systems operating condition. However, the

analysis was not able to pinpoint the problems cause, based on maintenance history and

prior lifetime of the bearings. Although possible effects from magnetic field did come up

in the analysis, it was not able to strongly indicate that was the cause. The fact that an

expert, that was brought in by the company to assess the main fans setup, did point out

based on prior experience that a spherical roller bearings operating in a strong magnetic

field are affected by it, resulting in an unusual short lifetime. Another factor that supports

this theory is the fact that the company did increase the pot rooms amperage in the recent

years. Based on this information it is likely that a combined effect from the magnetic field

and the unsuitable lubrication method are the cause for the unusual short plummer block

bearing life.

Two sets of vibration equipment’s were used within the case study, where one was

commercially bought (portable equipment) and the other was partially constructed from

scratch and partially bought from known vendors (localized equipment). The localized

equipment was placed beside main fan 2 in FTP-1, to gather vibration measurements once

a day for over a year. The portable equipment was used to perform occasional

measurements with irregular intervals, with much higher sampling rate and resolution. The

vibration analysis was divided into condition assessments and remaining useful life (RUL)

estimation. The condition assessments were made on all the main fans plummer block

bearings in both FTP-1 and 2, using the vibration data gathered with the portable

measurement equipment. The RUL estimation was conducted using the vibration data

gathered with the localized measurement equipment. In both cases the vibration analysis

software, developed for this thesis, was used to perform all the vibration analysis needed to

conduct the condition assessments and RUL estimation.

The results from the condition assessments showed that the current condition on the main

fans plummer block bearings, in FTP-1 and 2, varied a lot between bearings and fans.

Where some bearings showed no fault indication, when others showed one or more

indications on faulty states e.g. bearing fault frequencies, unbalance, looseness, and/or

misalignment. The overall condition assessment showed that the Fan DE bearings

(spherical roller bearings) are in worse condition than the Fan ND bearings (CARB

128

toroidal roller bearings). Which harmonics with the results drawn from the FMEA, that the

lubrication method used for the Fan DE bearings is not suitable.

For the RUL estimation fortunately, there was bearing change performed approx. two

months after the localized equipment was put in operation. Meaning that the equipment

had gathered vibration data prior and after the bearing change. Unfortunately, the low

sampling rate of the localized equipment limited the options for constructing a condition

indicator. The solution was to use the overall RMS vibration level as condition indicator,

where the threshold value was decided to be the mean RMS-value for the last 15 days

before the bearing change. Linear and exponential trending curves were used to trend the

data gathered after the bearing change to establish the RUL estimation.

Future work would be to perform further fault assessments based on the Root Cause

Analysis and the Fault Tree Analysis, to get deeper understanding on the problem and to

find the root cause. Measuring the strength of the magnetic field surrounding the plummer

block bearings are also an interesting follow up to compare the results between bearings to

see if there is any difference in the strength of the magnetic field surrounding them, given

the fact that their maintenance history is by far worst for main fans 1 and 2 in FTP-1.

Upgrading the localized equipment is advised if it is to be used for further condition

monitoring.

According to the technical department at Norðurál, the company has ordered new plummer

block bearings to replace the ones on main fans 1 and 2 in FTP-1. The new bearings have

the same features, excluding the roller cage which is made out of nonmagnetic material

(copper). They also decided to change the method used to lubricate the bearings, from

grease to circulating oil lubrication. These changes will be made next fall or winter and it

would be interesting to monitor their performance and see if the operational condition

improves.

129

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133

Appendices

Appendix A: ISO 10816

ISO 10816-1 is the basic document describing the general requirements for evaluating the

vibration of various machine types when the vibration measurements are made on non-

rotating parts. ISO 10816-3 provides specific guidelines for assessing the severity of

vibration measured on bearings, bearing pedestals, or housings of industrial machines

when measurements are made in situ. It suits machine sets with power above 15 kW and

operating speeds between 120 r/min and 15.000 r/min, including generators, electrical

motors, blowers, and fans [32]. Figure 94 illustrates the standards vibration severity

classification.

The standard defines four groups of machines, based on size, base, and purpose and

categorizes the working condition into four zones:

• Zone A (green): Vibration level good, e.g. vibration from new machine.

• Zone B (yellow): Vibration level satisfactory, continuous operation without any

restrictions.

• Zone C (orange): Vibration level unsatisfactory, condition satisfactory for a

limited period of time.

• Zone D (red): Vibration level unacceptable, condition unacceptable and damage

could occur at any time.

Figure 94: ISO 10816-3 vibration severity classification.

Rigid Flexible Rigid Flexible Rigid Flexible Rigid Flexible

Zone A

Zone B

Zone C

Zone D

Vibration Severity per ISO 10816-1

0

0 - 1,4

R.M.S. Vibration

Velocity: mm/s

1,4 -2,3

2,3 - 2,8

2,8 - 3,5

3,5 -4,5

4,5 - 7,1

7,1 - 11,0

Machine Type

> 11,0

Group 1 Group 2 Group 3 Group 4

Medium-size machines

with rated power above

15 kW and up to and

including 300 kW;

electrical machines

with shaft height

160 mm ≤ H < 315 mm

Pumps with multivane

impeller and with

separate driver

(centrifugal, mixed

flow,

or axial flow)

with rated power

above 15 kW

Pumps with multivane

impeller and with

integrated driver

(centrifugal, mixed

flow,

or axial flow)

with rated power

above 15 kW

Large machines with

rated power above

300 kW and not more

than 50 MW;

electrical machines

with shaft height

H ≥ 315 mm

134

Appendix B: Vibration Severity Chart

General vibration severity chart, from John S. Mitchell’s 1981 Introduction to Machinery

Analysis and Monitoring, is illustrated in Figure 95.

Figure 95: General vibration severity chart, for rotating machinery.

135

Appendix C: Case Study’s Bearing-, Lubricant-, and Maintenance Data

Information listed in Table 10 were gathered using SKF® Bearing Select v1.2-36 software,

which can be downloaded from the SKF website www.SKF.com. Where the input data was

based on forces and dimensions illustrated in Figure 52, the grease currently being used,

normal cleanliness, and operating temperature approx. 70°C.

Table 10: Information on main fan plummer block bearings data, operational data, and

bearing fault frequencies.

Type: Spherical Roller CARB Toroidal Roller

Designation: 23230 CCK/W33 C 2230 K

Housing: SNL 530 SNL 530

Adapter Sleeve / Lock Nut / Locking Device H 2330 / KM 30 / MB 30 H 3130 L / KML 30 / MBL 30

Oil Seal: TSN 530 U 2TSN 530 U

Locating Rings 2FRB 5/270 2FRB 16.5/270

Mounting Method: SKF Drive-Up SKF Drive-Up

Bore (d): [mm] 150 150

Outer Diameter (D): [mm] 270 270

Width (B): [mm] 96 73

Pitch Diameter (P): [mm] 211.3 206.5

Contact Angle (O): [deg°] 13.167 0

Number of Rollers (N): 18 17

Dynamic Load Rating (C): [kN] 1129 980

Static Load Rating (Co): [kN] 1460 1220

Fatigue Load Limit (Pu): [kN] 137 114

Limiting Speed [r/min] 2200 3200

Bearing Weight [kg] 23.0 17.5

Lubrication Type (grease): SKF LGHP2 SKF LGHP2

Radial Load (Fr): [kN] 3.9 18.9

Axial Load (Fa): [kN] 17.0 0

Minumum Load Met: Yes Yes

Rotational Speed: [r/min] 993 993

Rotating Ring: Inner Inner

Shaft Orientation: Horizontal Horizontal

Operational Temperature (Approx.): [°C] 60 60

Relubrication Interval: [h] 20.3 2390

Speed Factor (Limit): [mm/min] 209000 (150000) 205000 (350000)

Bearing Rating Life: [h] > 200000 * > 200000 *

Fans Power Consumption (each) [kW]

Shaft: [Hz] 16.55 16.55

Cage (FTF): [Hz] 7.1 7.0

Inner Raceway (BPFI): [Hz] 169.5 162.5

Outer Raceway (BPFO): [Hz] 128.4 118.8

Rolling Element (BSF): [Hz] 57.2 51.9

approx. 750 kW

* For rating life results above 100000 hours, other failure modes will dominate and limit the life of the bearing.

Bearing Data

Operational Data

Bearing Fault Frequencies

http://www.skf.com/

136

Table 11: Fan DE and ND Bearings Lubricant Technical Data (optained from SKF

website).

Designation SKF LGHP 2

DIN 51825 code K2N-40

NLGI consistency class 2–3

Thickener Di–urea

Colour Blue

Base oil type Mineral

Operating temperature range –40 to +150 °C

Dropping point DIN ISO 2176 >240 °C (>465 °F)

cSt at 40 °C 96

cSt at 100 °C 10,5

60 strokes, 1/10 mm 245–275

100 000 strokes, 1/10 mm 365 max.

Mechanical stability Roll stability, 50 hrs at 80 °C, 1/10 mm 365 max.

Corrosion protection Emcor: – standard ISO 11007 0–0

Water resistance DIN 51 807/1, 3 hrs at 90 °C 1 max.

Oil separation DIN 51 817, 7 days at 40 °C, static, % 1–5

Lubrication ability R2F, running test B at 120 °C Pass

Copper corrosion DIN 51 811 1 max. at 150 °C (300 °F)

Rolling bearing grease life R0F test L50 life at 10 000 r/min., hrs 1 000 min. at 150 °C (300 °F)

Fretting corrosion ASTM D4170 (mg) 7*

Shelf life 5 years

Base oil viscosity

Penetration DIN ISO 2137

* Typical value

137

Table 12: Maintenance history for fume treatment plants 1 and 2, for bearings and grease

change interval, for the years 2008 to the summer of 2019.

Note: Since the end of 2018, the documentation on grease change has been registered

differently in the maintenance software, but according to maintenance personnel they are

still performing grease change, along with weekly grease injection on selected bearings.

Main Fan

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

46.497$ 2008-05-10 87.144 53.136$ 2008-03-18 85.872 25.838$ 2012-09-24 125.496 25.391$ 2013-11-25 135.744

19.507$ 2010-03-12 16.104 20.994$ 2013-04-02 44.184 (66.768) (56.520)

20.000$ 2019-02-18 78.360 29.926$ 2017-09-25 39.288

(10.656) 9.121$ 2017-12-11 1.848

21.964$ 2018-02-17 1.632

20.000$ 2019-07-05 12.072

(7.368)

704$ 2010-10-26 679$ 2010-10-29 578$ 2010-11-01 451$ 2010-11-19

239$ 2011-04-14 4.080 346$ 2011-04-20 4.152 633$ 2011-04-27 4.248 380$ 2011-05-03 3.960

272$ 2011-10-25 4.656 349$ 2011-10-18 4.344 516$ 2011-10-26 4.368 447$ 2011-11-03 4.416

308$ 2012-04-12 4.080 465$ 2012-04-17 4.368 238$ 2012-05-29 5.184 466$ 2012-04-27 4.224

545$ 2012-10-02 4.152 558$ 2012-10-11 4.248 1.080$ 2012-10-03 3.048 380$ 2012-10-23 4.296

235$ 2013-01-21 2.664 462$ 2013-10-18 8.928 534$ 2012-10-17 336 546$ 2013-04-26 4.440

362$ 2013-02-06 384 653$ 2013-12-27 1.680 473$ 2013-04-15 4.320 472$ 2013-10-21 4.272

424$ 2013-09-30 5.664 1.586$ 2014-04-23 2.808 636$ 2013-12-09 5.712 340$ 2014-05-05 4.704

415$ 2013-10-29 696 668$ 2014-06-18 1.344 627$ 2014-05-08 3.600 508$ 2014-09-11 3.096

511$ 2014-04-01 3.696 445$ 2014-09-01 1.800 354$ 2014-05-15 168 390$ 2015-03-09 4.296

427$ 2014-09-02 3.696 259$ 2015-03-02 4.368 679$ 2014-09-08 2.784 394$ 2015-09-03 4.272

546$ 2015-02-26 4.248 627$ 2015-09-01 4.392 834$ 2015-03-24 4.728 220$ 2016-02-24 4.176

506$ 2016-02-18 8.568 317$ 2016-02-22 4.176 405$ 2015-09-03 3.912 559$ 2016-10-18 5.688

234$ 2016-08-17 4.344 504$ 2016-10-11 5.568 383$ 2016-02-23 4.152 409$ 2017-02-24 3.096

696$ 2017-02-20 4.488 256$ 2017-02-21 3.192 685$ 2016-10-18 5.712 470$ 2017-08-22 4.296

367$ 2017-08-03 3.936 631$ 2017-06-23 2.928 510$ 2017-02-22 3.048 595$ 2018-04-05 5.424

585$ 2018-04-03 5.832 634$ 2017-11-14 3.456 976$ 2017-11-07 6.192 969$ 2018-10-19 4.728

596$ 2018-04-06 3.432 750$ 2018-04-04 3.552

226$ 2018-09-27 4.176 806$ 2018-10-18 4.728

Total Cost 93.381$ 165.403$ 37.534$ 33.387$

Main Fan

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

Cost Date

Running

hours

(current)

33.953$ 2015-04-27 86.808

(44.088)

624$ 2008-05-07 425$ 2008-05-07 534$ 2008-05-07 684$ 2008-05-07

497$ 2010-11-08 21.960 335$ 2010-11-23 22.320 560$ 2010-11-29 22.464 584$ 2010-12-09 22.704

318$ 2011-05-10 4.392 411$ 2011-05-17 4.200 303$ 2011-06-01 4.416 378$ 2011-05-31 4.152

472$ 2011-11-08 4.368 321$ 2011-11-28 4.680 543$ 2011-12-12 4.656 295$ 2011-11-28 4.344

245$ 2012-05-04 4.272 313$ 2012-05-11 3.960 287$ 2012-05-18 3.792 517$ 2012-06-07 4.608

241$ 2012-10-30 4.296 554$ 2012-11-06 4.296 731$ 2012-11-14 4.320 412$ 2012-11-21 4.008

601$ 2013-01-08 1.680 361$ 2013-05-24 4.776 395$ 2013-05-24 4.584 627$ 2013-05-24 4.416

425$ 2013-04-30 2.688 596$ 2013-12-09 4.776 415$ 2013-12-02 4.608 616$ 2013-12-27 5.208

797$ 2013-11-29 5.112 619$ 2014-04-25 3.288 411$ 2014-04-29 3.552 429$ 2014-05-02 3.024

547$ 2014-04-22 3.456 651$ 2014-09-18 3.504 544$ 2014-09-22 3.504 777$ 2014-09-25 3.504

436$ 2014-09-15 3.504 477$ 2015-03-16 4.296 667$ 2015-03-19 4.272 521$ 2015-03-23 4.296

114$ 2015-03-12 4.272 545$ 2015-09-10 4.272 487$ 2015-09-15 4.320 478$ 2015-09-17 4.272

581$ 2015-09-08 4.320 682$ 2016-03-09 4.344 384$ 2016-03-14 4.344 382$ 2016-03-16 4.344

472$ 2016-03-07 4.344 361$ 2016-11-01 5.688 557$ 2016-11-03 5.616 790$ 2016-11-03 5.568

364$ 2016-10-31 5.712 590$ 2017-03-01 2.880 656$ 2017-03-02 2.856 667$ 2017-03-08 3.000

656$ 2017-02-28 2.880 511$ 2017-10-24 5.688 427$ 2017-10-25 5.688 454$ 2017-10-26 5.568

454$ 2017-10-23 5.688 771$ 2018-03-19 3.504 765$ 2018-03-19 3.480 930$ 2018-03-19 3.456

568$ 2018-03-19 3.528 694$ 2018-10-24 5.256 585$ 2018-10-25 5.280 614$ 2018-10-26 5.304

693$ 2018-10-23 5.232

Total Cost 46.137$ 9.216$ 9.251$ 10.155$

1 2 3 4

Grease

Change

Bearing

Change

Fume Treatment Plant 2

Fume Treatment Plant 11 2 3 4

Bearing

Change

Grease

Change

138

Appendix D: Case Study’s Localized- and Portable Equipment

Table 13: Components list for the localized equipment low-pass filter unit

(6 filters in one box).

Size Qty.

Capacitors 33 nF 18

47 nF 6

100 nF 6

150 nF 12

470 nF 6

22 μF 6

Resistors 1 kΩ 36

22 kΩ 6

43 kΩ 6

470 kΩ 6

LED-diode (Red) 1

Constant-Current diode (approx. 4.8 mA) 1

Operational Amplifiers (TI LM324N) 6

BNC-Connectors 6

Power Supply (12 V Battery) 2

Battery Charger (230V/24V) 1

DC Connections for Battery Charger (Male and Female) 1

Box 1

On/Off Switch 1

Electrical Boards 2

139

Table 14: NI-USB-6000 Analog-to-Digital converter specifications

For more detailed specifications visit: https://www.ni.com/pdf/manuals/374113c.pdf

Analog Inputs

Number of Analog Inputs 8, single-ended

Input Resolution 12 bits

Maximum Sample Rate (aggregate) 10 kS/s

Converter Type Successive approximation

AI FIFO 2047 samples

Timing Resolution 125 ns (8 MHz timebase)

Timing Accuracy 100 ppm of actual sample rate4

Input Range ±10 V

Working Voltage ±10 V

Input Impendance >1 MΩ

Overvoltage Protection ±30 V

Trigger Sources Software, PFI 1

System Noise 10 mVrms

Absolute Accuracy at full scale, single-ended 26 mV (135mV at max over temp.)

Digital I/O

Number of Digital I/O 4

Function

P0.0/PFI 0 Static Digital I/O or counter source

P0.1/PFI 1 Static Digital I/O or AI Start Trigger

P0.2 Static Digital I/O

P0.3 Static Digital I/O

Direction Control Each channel individually programmable as

input or output

Output Driver Type Each channel individually programmable as

open collector or active drive

Absolute Maximum Voltage Range 0 V to 5 V with respect to D GND

Pull-Down Resistor 47.5 kΩ to D GND

Power-On State Input

Counter

Number of Counters 1

Resolution 32 bits

Counter Measurements Edge counting, rising or falling

Counter Direction Count up

Counter Source PFI 0

Maximum Input Frequency 5 MHz

Minimum High Pulse Width 100 ns

Minimum Low Pulse Width 100 ns

NI-USB-6000 Specifications

https://www.ni.com/pdf/manuals/374113c.pdf

140

Table 15: Vibration transducers specifications for the localized equipment.

Sensitivity ( ±10%) 10.2 mV/(m/s^2)

Measurement Range ±500 m/s^2

Frequency Range 0.32 Hz to 10000 Hz

Mounted Resonant Frequency 25 kHz

Amplitude Linearity ≤1%

Transverse Sensitivity ≤5%

Shock Limit 70,000 m/s^2 pk

Temperature Range -54°C to 85°C

Waterproof Design

Settling Time 2.5 sec

Excitation Voltage 18 VDC to 28 VDC

Excitation Constant Current 2 mA to 20 mA

Output Impedance <100 Ω

Output Bias Voltage 8 VDC to 12 VDC

Electrical Case Isolation >10,000,000 Ω

Electrical Protection RFI/ESD

Integral Cable 22 AWG, 105°C

Size 9.14 x 9.55 mm

Weight (with 5m cable) 70.7 g

Mounting Thread 1/4-28 UNF-2B

Mounting Torque 2.7 N-m to 6.8 N-m

Sensing Element Ceramic/Shear

Case Material Stainless Steel

Sealing Potted

Wrench Flats 7/16''

1 Hz 850 (µm/s²)/Hz^0.5

10 Hz 100 (µm/s²)/Hz^0.5

100 Hz 27 (µm/s²)/Hz^0.5

1000 Hz 10 (µm/s²)/Hz^0.5

CMCP1100 Standard SpecificationsDynamic Performance

Enviromental

Electrical

Mechanical

Spectral Noise

141

Figure 96: DT9837B Dynamic Signal Analyzer's block diagram.

Note: For more detail discussion and explanation visit:

https://www.mccdaq.com/PDFs/manuals/UM9837.pdf

https://www.mccdaq.com/PDFs/manuals/UM9837.pdf

142

Table 16: Wilcoxon model 736T high frequency accelerometer specifications.

Sensitivity (±5%, 25°C) 100mV/g

Measurement Range 50 g peak

Amplitude Nonlinearity 1%

Frequency Response:

±5% 5.0 - 15,000 Hz

±3 dB 2.0 - 25,000 Hz

Resonance Frequency 60,000 Hz

Transverse Sensitivity, max 7% of axial

Temperature Response:

-50°C -10%

+120°C 5%

Shock Limit 5,000 g peak

Temperature Range -50°C to 120°C

Vibration Limit 500 g

Electromagneticsensitivity, equiv. g 100 µg/gauss

Base Strain Sensitivity 0.005 g/µstrain

Power Requirement: Voltage / Current 18 - 30 VDC / 2 - 10 mA

Electrical Noise, equiv. g:

Broadband 2.5 Hz to 25,000 Hz 150 µg

Spectral 10 Hz 10 µg/√Hz

100 Hz 2 µg/√Hz

1,000 Hz 1 µg/√Hz

10,000 Hz 0.8 µg/√Hz

Output Impedance, max 150 Ω

Output Bias Voltage 10 VDC

Grounding Case grounded

Sensing Element PZT ceramic / compression

Weight 13 g

Material 316L Stainless Steel

Mounting 10-32 tapped hole

Output Connector 10-32 coaxial

Mating Connector R1

Recommended Cabling J93

Wilcoxon Accelerometer: Model 736T Specifications

Electrical

Dynamic Performance

Enviromental

Mechanical

143

Appendix E: Case Study’s Vibration Measurement and Analysis Software

Figure 97: Visualization on GUI operation, Select data type, load data, and select

amplitude representation.

144

Figure 98: Visualization on GUI operation, Selecting sensor and weighting window.

145

Figure 99: Visualization on GUI operation. Bearing fault frequencies loaded from

database and manually calculated, scale settings, and display of bearing fault frequencies

and geometric parameters.

146

Figure 100: Visualization on GUI operation. Measurement settings, CI selection,

Spectrogram setting, and Envelope settings.

147

Appendix F: Case Study’s, FTP-1 Main Fan 2 FMEA Worksheet

Table 17: FMEA-worksheet for main fan 2 in FTP-1 (spreads over three pages).

Excessive load 4Monitor motor

load

Monitor motor

voltage and current2 56

Continue to monitor

motor load

High ambient

temperature6

Make sure ventilation

is satisfying

Monitor ambient

temperature2 84

Set up automatic temperature

measurements with warning

system

To high or low

voltage/current

supply

4

Equip motor with

current and voltage

pretection

Monitor motor

voltage and current2 56

Set up automatic voltage/current

measurements with warning

system

Lack of ventilation 5Make sure ventilation

is satisfying

Increased ambient

temperature2 70

Make sure motor gets

appropriate ventilation

Broken motor fan 4Inspect motor fan

regularly

Motor temperature

increases3 84

Set up regular


Isolation degrades 3

Prevent over-heating,

minmize corrosion,

and

physical wear/damage

Through visual

inspection8 168

Set up regular


Safety brakers fail 3 Test brakers regularlyThrough regular

inspection4 120

Set up regular


Bearing friction 2Keep bearings greased

and cool

Monitor bearings

temperature4 80

Automatically monitor

bearings temperature

Contamination e.g.

oil or other

flamable leftovers

catch fire

2Clean regularly all

contamination

Through visual

inspection7 140

Establish

regular cleaning

schedule

Neighboring work

e.g. Welding/blowtorch2

Make sure all work is

performed with safety

Through visual

inspection7 140

Perform welding and blowtorch

work in teams were one team

member performs visual

inspection

Increased bearing wear 4 3 48

High operating

temperature4 3 48

Motor components

can get damaged 2 3 24

Set up regular


Material fatigue 2Examine parts

before assembly

Through visual

inspection and/or

Perform NDT test


Excessive load 4 Monitor the loadWith automatic

measurements2 80

Continue to monitor

motor load

Faulty assembly 4Follow assembly

instructions

By double


Make sure assembly


Increased

Vibration4

Unbalance and/or

misalignment5

Align and balance

when assembling

By double



when balancing/aligning parts


instructions

By double


Make sure assembly


Misalignment 5Align parts

during assembly

By double


Use certified equipment to

perform alignment/balancing


during assambly

By double





appropriate torque

By double

checking torque5 80

Use certified equipment

to apply torque


during assembly

By double



to perform alignment


during assembly

By double



to perform alignment

Excessive load 4 Monitor loadWith automatic

measurements2 24

Continue to monitor

motor load


before assembly

Through visual

inspection and/or

Perform NDT test



measurements2 60

Continue to monitor

motor load


measurements2 42

Continue to monitor

motor load


instructions

By double


Make sure assembly


Construction error 3 Use certified partsThrough visual

inspection5 105 Buy certified components

Rubbing 4Monitor

temperature

With automatic

measurements3 84

Set up automatic temperature

monitoring


measurements2 42

Continue to monitor

motor load

Faulty design 3 Use certified partsThrough visual


Drive shaft

breaks10

Permanent

Bent7

Drive shaft

twists7

Drive Shaft

Deliver

torque

to impeller

Structural

damage

FMEA worksheet for Main Fan 2 in FTP-1

Ite

m

Function

Potential

Failure

Mode

Potential

Effect(s)

of Failure Seve

rity Potential

Cause(s)

of Failure

Occ

urr

en

ce

Current Design

Controls

(Prevention)

Current Design

Controls

(Detection)


regularly

De

tect

ion

R P

N Recommended

Action(s)

Electric

Motor

Prime

mover

Electrical

overload

Over-Heating 7

Motor catches

on fire10

Excessive

vibration

Decreased

bearing life4

Monitor bearings

temperature and

vibration

Through automatic

and/or regular

inspections and

measurement

Coupling

Connect

motor

and

drive shaft

Structural

and/or

fasteners

damage

Coupling

shatters10

Damaged

rubber

coupling

Increased

wear4

Increased

Vibration4

Increased

temperature3

148

Continued from Table 17

Material friction 4 Monitor temperatureWith automatic

measurements3 84

Continue to monitor

temperature

Unsufficient

lubrication5

Monitor grease

condition

With regular

checks4 140

Set up regular



measurements3 63 Continue to monitor load


instructions

By double


Make sure assembly


High ambient

temperature5

Make sure ventilation

is satisfying

Monitor ambient

temperature3 105

Insure ventilation and make

arrangements if necessary

Reduced

grease life5

Monitor grease

condition

With regular

checks6 210

Set up regular


Increased

clearance5 Monitor vibration

With automatic

measurements6 180


regularly


instructions

By double


Make sure assembly


Spalls on surface 6 Monitor vibrationWith automatic

measurements6 216


regularly





Reduced grease life 5Monitor grease

condition

With regular

checks6 180

Set up regular


roller cage breaks 3Monitor vibration and

use certified parts

With automatic

measurements5 90


regularly and use certified parts

Unbalance 4Balance system

during assembly

By double




Misalignment 4Align components

during assembly

By double



when aligning parts

Magnetic field 2

Monitor magnetic field

and possibly use some

protection shield

By measurements 8 96Use nonmagnetic parts

when possible


instructions

By double


Make sure assembly



before assembly

Through visual

inspection and/or

perform NDT test




Foreign object

impacts4

Use protective

covers

Through visiual

inspection5 180




Faulty design 2 Use certified partsThrough visiual



appropriate torque

By double


Make sure assembly


High bearing

clearance5 Use certified parts By measurements 5 175

Monitor bearings vibration

regularly

Unbalance 4Balance system

during assembly

By double





during assembly

By double



when aligning parts


instructions

By double





Faulty design 2 Use certified parts By measurements 5 70 Buy certified components

Faulty design 2 Use certified partsBy vibration

measurements5 90 Buy certified components


before assembly

Through visual

inspection and/or

perform NDT test



instructions

By double


Make sure assembly



instructions

By double


Make sure assembly


Damaged shaft

surface6

Visually examine

part

By double

checking surface5 150

Set up regular




Damage shaft

surface4 Loss of grease 6 Use certified parts

Through visiual

inspection5 120

Set up regular


Adapter

sleeve

and/or lock

ring

breaks

9

Grease

contamination5

Increased

vibration7

Structural

damage

Increased

vibration7

Housing

and/or

fasteners

cracks/breaks

9

Increased

vibration6

Increased

temperature7

Damaged

Rollers,

inner/outer

raceways

and roller cage

Damaged

adapter sleeve

and lock ring

Damaged

seals

Support drive

shaft and

impellers

weight.

(radial forces)

and receive

impellers

thrust

(axial force)

Plummer

Block

Bearings

149

Continued from Table 17.

Corrosion 3Use anti corrosive

materials

Through visiual

inspection6 126

Use suitable materials that

handle

operational/enviromental

conditions

Material wear 4 Use durable materialsThrough visiual

inspection6 168 Use durable materials

Material fatigue 3Examine part

before assembly

Through visual

inspection and/or

perform NDT test


Blade(s) or other

parts break off2

Examine part

before assembly

Through visiual




Foreign object 2 Keep air ducts clean With regular checks 8 112Set up regular



during assembly

By double



when aligning parts


during assambly

By double





appropriate torque

By double


Make sure assembly



instructions

By double


Make sure assembly






Increased

temperature4 Metal friction 3

Follow assembly

instructions

Through audible

measurements6 72

Set up regular


Corrosion 3 Protect materials Through visiual

inspection5 120

Use suitable materials that

handle operational and

enviromental conditions.

(paint metal surfaces regularly)


before assembly

Through visual

inspection and/or

perform NDT test


Foreign object 3 Use protective coversThrough visiual

inspection5 120 Build protective guards/fences




instructions

By double


Make sure assembly







appropriate torque

By double


Make sure assembly


8

Increased

vibration6

Foundation

Support all

components

of the fan

Structural

damage

Structural

damage

Geometria

changes

Geometria

changes7

Increased

vibration5

Impeller

Creates

pressure

differance

between

suction and

discharge side

150

Appendix G: Case Study’s, Vibration Analysis Figures

FTP-1: Main Fan 1

Figure 101: Frequency spectrum comparison between July 2019 and May 2020 for the

Fan ND bearing on main fan 1, in FTP-1.

Figure 102: Vibration signals envelope comparison between July 2019 and May 2020 for

the Fan ND bearing on main fan 1, in FTP-1.

151

FTP-1: Main Fan 2


Fan ND bearing on main fan 2, in FTP-1.

Figure 104: Vibration signals envelope comparison between July 2019 and May 2020 for

the Fan ND bearing on main fan 2, in FTP-1.

152

FTP-1: Main Fan 4

Figure 105: Fan DE bearing, waterfall graph of the 1 kHz to 30 kHz frequency spectrums,

from July 2019 to May 2020, for main fan 4 in FTP-1


Fan ND bearing on main fan 4, in FTP-1

Documents

Fault Detection and Condition Assessment using Vibration