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APPLICATION OF PREDICTIVE MAINTENANCE TO 
INDUSTRY INCLUDING CEPSTRUM ANALYSIS OF A 
GEARBOX 
BY 
MATTHEW ALADESAYE 
A THESIS SUBMITTED 
IN 
FULFILMENT OF 
THE REQUIREMENTS FOR THE DEGREE OF 
DOCTOR OF PHILOSOPHY 
IN 
THE FACULTY OF GRADUATE STUDIES 
(Institute of Technology and Engineering) 
MASSEY UNIVERSITY AUCKLAND, NEW ZEALAND 
July 2008 
SUMMARY 
The economic implications of equipment failure are called for effective maintenance 
techniques. The research investigates current maintenance practice in several New 
Zealand industries and the improvements that could be obtained by the use of 
predictive maintenance techniques. 
Initial research was undertaken in a senes of case studies within New Zealand 
industries situated in Auckland. The first two cases studies were of preventative 
maintenance techniques of two conveyor lines in a biscuit manufacturing company. 
The results showed a wel l  defined preventive maintenance schedules that was 
Systems Applications Products (SAP) programme was used to managed for daily, 
weekly, monthly and yearly maintenance activities. 
A third case study investigated current predictive maintenance technique involving 
Fast Fourier Transform analysis of shaft vibration to identify a bearing defect. The 
results diagnosed a machine with a ball bearing defect and recommendation was given 
to change the bearing immediately and insta l l  new one. The machine was opened up, 
a big dent was on one of the bal l s  as predicted by the analysis and the bearing was 
changed. 
Research then l ooked at a novel technique cal led Cepstrum analysis that al lows the 
deconvolution of vibration spectra from separate sources. This allows identification of 
several defects from the monitoring of a single vibration signal . Experiments were 
carried out to generate transfer functions for different gear fau lts at two different 
loadings. Blind deconvolution of the signal using a homomorphic fi lter was used to 
separate the source forcing frequencies from the structure resonance effects of the two 
gear faults, indicating that the technique could be used successful ly to monitor 
equipment for a range of gear faults occurring simultaneously. 
11 
CONTENTS 
Chapter 1 
Chapter 2 
Chapter 3 
Chapter 4 
111 
INTRODUCTION 
1 . 1  The Topic of this Thesis 
1 .2 Why Predictive Maintenance? 
1 .3 Aims 
1 .4 Thesis Overview 
LITERATURE REVIEW 
2. 1 Machine Diagnosis and Reliability 
2.2 Predictive Maintenance - Vibration Monitoring 
2.3 Artificial Neural Network 
2.4 Blind Deconvolution and Cepstrum Analysis 
MAINTENANCE STRATEGIES 
2 
3 
5 
5 
8 
1 2  
1 3  
1 9  
3. 1 Introduction 1 9  
3.2 Evolution of Maintenance 20 
3 .2 . 1 F irst Generation 20 
3 .2 .2  Second Generation 20 
3 .2 . 3  Third Generation 20 
3.3 Maintenance Cost 24 
3.4 Maintenance Strategies 24 
3 .4 . 1 Breakdown Maintenance 25 
3 .4.2 Preventive Maintenance 25 
3.4.2. 1 Preventive Maintenance Costs by Frequency 26 
3.4.2.2 Case Study 1 - Fan Drive End Bearing under 27 
Preventive Maintenance 
3.4.2.3 Plant Experience 29 
3.4.2.4 Manufacturers' Recommendations 29 
3 .4 .3  Predictive Maintenance 30 
3.4.3. 1 Case Study 2 - Identification of Deep Grove 3 1  
Bearing Defects by Spectra Analysis 
3.4.3.2 Equipment Speci fications 34 
3.4.3.3 Measured Frequency 3 6  
3.4.3.4 Predicted Frequency 3 7  
FAST FOURIER TRANSFORM TECHNIQUE & ITS 
PITFALLS 
40 
Chapter 5 
Chapter 6 
IV 
4. 1 Introduction 40 
4.2 Complex Number 40 
4.3 Theory of FFT Analyzer 42 
4.4 Case Study 3 - Bearing Failure Due to Shaft Deflection 44 
& Critical Speed 
4.4. 1 N atural Frequency & Critical Speed 44 
4 .4 .2 Whirl ing of Shaft & Critical Speed 46 
4 .4 .3  Deflection & Stiffness 46 
4.4 .4 Permissible Angular Misalignment 47 
4 .4 .5  Results 47 
4.5 Case Study 4 - Fan Imbalance 52 
4.6 Case Study 5 - Root Cause Analysis Technique to 55 
Identify a Gearbox Failure 
THE THEORY OF CEPSTRUM TECHNIQUE 
5 . 1  I ntroduction 
5.2 Gearbox Vibration 
5.3 Transmission Path 
5.4 Transmission Errors 
5 .4 . 1 Static Transmission Error 
5.4.2 Residual Error signals 
5.5 Signal Processing 
5.6 Homomorphic Theory 
5.7 Cepstrum Technique 
5.8 Poles and Zeros Analysis 
EXPERIMENTAL ANALYSIS 
6.1 I ntroduction 
6.2 Gear Test Rig 
6.3 I nstrumentation 
6.4 I nstrumentation for Data Collection 
6.5 The Structure of the Data Files 
6.6 Blind Deconvolution 
6.7 Results 
6.7 . 1 Homomorphic Deconvolution 
6 .7 .2 Poles and Zeros Analysis 
62 
62 
63 
64 
64 
65 
67 
68 
7 1  
73 
78 
8 1  
8 1  
8 1  
84 
84 
85 
85 
87 
94 
99 
Chapter 7 Conclusion and Recommendation 
7. 1 Introduction 
7.2 Discussion 
7.3 Conclusion 
7.4 Recommendations for Future Work 
References 
APPENDIX A: CEPSTRUM TECHNIQUE  AND HOMOMORPHIC 
FILTERING - 1 26 
APPENDIX B :  PREVENTIVE MAINTENANCE - 1 80 
v 
1 04 
104 
1 04 
1 1 2 
1 1 3 
115 
LIST OF TABLES 
Table 1 . 1  Fatal Accident Causes By Category 2 
Table 3 . 1  Questionnaires 2 1  
Table 3 .2  The Summary of Maintenance Evolution 22 
Table 3 . 3  Preventive Mai ntenance Schedule 29 
Table 4. 1 Entek Spectrum Analyzer Characteristics 43 
Table 4 .2 Shaft Conditions 5 1  
Table 4.3 Design and Manufacturing Considerations 5 7  
Table 5 . 1 Comparison of Terms Used in Spectra and Cepstral Analysis 76 
Table 6. 1 The Poles and Zeros from Curve Fitting Cepstra 1 03 
VI 
LIST OF FIGURES 
F igure 3 . 1  Maintenance Strategies Based on Practices in New Zealand 23 
Companies 
F igure 3 .2 Preventive Costs by Frequency 26 
Figure 3 . 3  Steel Manufacturing Company i n  Auckland New Zealand 27 
Figure 3 .4 Multi Hearth Furnace Fan 28 
Figure 3 .5 Fan End Bearing 28 
Figure 3 .6 Spectrum Showing the Bearing Defect 36 
F igure 3 . 7  Acceleration Amplitude versus Frequency 3 7  
Figure 3 .8 The Bearing Defect 3 8  
F igure 3 .9 New Spectrum with Low Acceleration Amplitude 3 9  
Figure 4.] Real and I maginary Plane of a Complex Number 4 1  
F igure 4.2 Fan Bearing H ousing at Drive End, H orizontal Direction 45 
F igure 4.3 Fan Bearing Housing at Drive End, Axial Direction 46 
Figure 4.4 Concentrated Load on a Simply supported Shaft 48 
Figure 4.5 Effect of Shaft deflection on Bearing 49 
Figure 4.6 Effect of M isalignment Angle on Bearing 49 
Figure 4 .7 I mbalance Spectrum with H igh Amplitude 53 
Figure 4.8 Spectrum after Balancing of Fan 54 
Figure 4 .9 Gear with the Broken Teeth 5 5  
F igure 4 . 10 Gearbox Spectrum 56 
F igure 4 . 1 1 The Envelope 56 
Figure 5 . 1  Gearbox Spectrum from the Case Study 63 
F igure 5 .2 Frequency Domain of Graphical Representation 68 
F igure 5.3 Vibration of a Gearbox 69 
Figure 5 .4a The Negatively Inverted Echo Due to Cracked Tooth 70 
Figure 5 .4b The Negatively Inverted Echo Due to SpaIl 70 
F igure 5 .5  S ignal Processing for a Gearbox Diagnosis 72 
Figure 5 .6 Two Signals Deconvolved to Two Separate Signals 73 
Figure 5 .7a Cepstrum of the Cracked Tooth 74 
Figure S .7b Cepstrum of the Tooth with Spall 74 
Figure 5 .7c Cepstrum of the Undamaged Teeth 74 
Figure 5 . 8  Frequency Response of a System 76 
Vll 
Figure 5 .9 System with I nput-Output Relationship 78 
Figure 5 . 1 0  Poles and Zeros P lot From Transfer Function 80 
Figure 6 . 1  Gear Test Rig 82 
Figure 6.2 Cracked and Spal l Gears 83 
Figure 6.3 Gear Test Rig 84 
Figure 6.4 Undamaged Gear Vibration Signal 8 8  
Figure 6 . 5  Cracked Tooth Vibration Signal 89 
Figure 6.6 Spal l Tooth Vibration Signal 89 
Figure 6 .7 Cepstrum of Undamaged Teeth Under 50Nm Load 90 
Figure 6 .8  Cepstrum of U ndamaged Teeth Under 1 00Nm Load 9 1  
Figure 6.9 Cepstrum of Cracked Tooth Under 50N m  Load 9 1  
Figure 6 . 1 0  Cepstrum of Cracked Tooth Under 1 00Nm Load 92 
Figure 6. 1 1 Cepstrum of Spall Tooth Under 50Nm Load 93 
Figure 6 . 1 2  Cepstrum of Spall Tooth Under 1 00Nm Load 93 
Figure 6 . 1 3  Undamaged Gear Under 1 00Nm After Filtering 95 
Figure 6. 1 4  Cracked Gear Under 1 00Nm After Filtering 96 
Figure 6 . 1 5  Spal l Gear Under 1 00Nm After Fi ltering 97 
Figure 6 . 1 6  Smoothed Spectra for Undamaged, Spall and Cracked Gears 1 0 1  
Figure 6.17 Frequency Response of System with Cracked, Spall  and 102 
Undamaged Teeth 
Figure 7 . 1 Cepstra for Different Measurements 1 06 
Figure 7.2 Cepstra for Different Measurements 1 07 
Figure 7.3 Cepstra for Different Measurements 1 08 
Figure 7.4 Cepstra for Different Measurements 1 09 
Figure 7 .5  Cepstra for Different Measurements 1 1 0 
Figure 7.6 Poles and Zeros Frequency Response 111 
Vlll 
ACKNOWLEDGMENT 
I wil l  l ike to express fi rst and foremost my gratitude to my supervisors Dr.  Huub 
Bakker and Johan Potgieter for their guidance and encouragement in the course of this 
research.  Their patience and support are sincerely appreciated. 
I express my special gratitude to my external supervisor, Professor R .B .  Rand all , 
U niversity of New South Wales (UNSW), Sydney, Austral ia, for his guidance, great 
support, patience and his very useful comments. 
I l ike to also acknowledge David Hanson, PhD student at UNS W for his support, 
encouragement, contribution and valuable advice during the time I was carrying out 
my experiments out in the university. 
My gratitude extends to the technical staff of the UNSW, mechanical engineering 
workshop for allowing me to use their faci l ity for my experiments and testing. 
I wil l  l ike to thank Werner Schneider of SchemNZ who got the funding for this 
research from TechNZ. 
It would be impossible to include everyone who has provided help and inspiration 
throughout my stay in Massey University, Albany Campus, Auckland. Let me humbly 
thank fel low students and others who have contributed. 
My deepest gratitude goes to my family members for their love, encouragement and 
unconditional support during the whole course of my Ph. D  work at Massey 
University, Auckland, and for providing a reason to finish as soon as possible. 
Finally, my utmost thanks go to my Heavenly Father and the Lord Jesus Christ. 
Strong biblical convictions form the core of my personal ity and provide my source of 
strength and optimism. I t  would be very remiss not giving glory to whom glory is 
ultimately due. 
IX 
DECLARATION OF ORIGINALITY 
I ,  Matthew Aladesaye, declare that this thesis is my own work and has not been 
submitted in any form for another degree or diploma at any university or other 
institute of tertiary education. Information derived from the published and 
unpubl ished work of others has been acknowledged in the text and a l ist of references 
is given in this thesis. 
I also acknowledge that I have pursued the PhD course In accordance with the 
requirements of the university 's  regulations: 
, Research practice and ethical policies have been complied with appropriately 
, This thesis does not exceed 100,000 words, excl uding appendices. 
c- --
") 
,. �C'v>� 
Signed ., . .  :-: .... . ..... . . .. . . ... ... . ..... . . .. . 
x 
Chapter 1 
Introduction 
1.1 The Topic of this Thesis 
The funding for th is project was obtained from Technology New Zealand by the 
consu lting firm SchemNZ, which was investigated and presented for my PhD research 
work. The aim of the project was to investigate the maintenance practices of d ifferent 
manufacturing companies in NZ and present the best maintenance practice that wou ld 
improve equipment re l iabi l ity, predict fai l ures, reduce maintenance costs and augment 
profitabi l ity. The fol lowing are the common maintenance pract ices in manufacturing 
companies: 
• Breakdown 
• Preventive 
• Predictive. 
This thesis was carried out to meet the fol lowing objectives: 
I .  Explore maintenance and diagnostic strategies 
2 .  Ident i fy possible techniques to d iagnose machine faults. 
1.2 Why Predictive Maintenance? 
The econom ic impl ications due to equipment fai lure are severe. The losses suffered 
by manufacturing companies due to mach inery fai l ure and downt ime for repairs are 
pronounced. 
Table I .  I shows the causes of the aircraft acc idents between the 1 950s and 1 990s. 
Human errors can be reduced by observing the safety regulations, but the mechanical 
fai l ures can be avoided by i nstal l ing condition mon itoring and fau lt diagnostic 
systems wh ich  would give warning as soon as a fau lt develops. 
Table 1.1: Fatal Accident Causes By Category (by percentage) 121 
CAUSE 1950s 1960s 1970s 1980s 1990s 
Pi lot Error 43 34 26 29 30 
Pi lot Error (Weather Related) 9 1 9  1 6  1 7  20 
Pi lot Error (Mechanical Related) 7 5 4 4 6 
Total Pi lot Error 58  58  46 49 56 
Other H uman Error 2 8 9 7 7 
Weather 15 9 1 2  1 4  8 
Mechanical Fai l ure 1 9  1 9  2 1  1 9  20 
Sabotage 5 4 9 1 1  8 
Other Cause 0 2 3 I I 
For an ocean-going merchant vessel carrying 1 00,000 metric tonnes of l iqu id natural 
gas as cargo, losses amount to between US$80,000.00 and US$ I ,000.000.00 per day 
in the event of any machine fai l ure or repair. In add ition, it is estimated that more than 
2000 l i ves have been lost as a result of marine accidents caused by machinery fai l ure 
[ I  ] .  
A Boeing 737 veered off the runway due to the col lapse of the right land ing gear. A 
private p lane experienced engine trouble and crashed. Another one experienced 
mechan ical  fai l ure, d isintegrated and crashed soon after taking off [ I ] . 
Another example is the gearbox of an emergency coal conveyor of a steel 
manufacturing company where the author carried out investigations on pred ictive 
maintenance. The conveyor was out of service for two weeks due to overheating. The 
cost of replacement, production and maintenance was about $2.5  mi l I ion dol l ars. 
1.3 Aims 
The aims of this thesis are: 
• The first and primary objective is to investigate the maintenance practices in  
d i fferent major manufacturing compan ies in New Zealand outl i ned in  chapter 
2 and review predictive maintenance - the use of vibration a sensor and FFT 
data col lector - to predict machine fai l ures. 
2 
• The second objective pertains to the use of existing Fast Fourier Transform 
(FFT) algorithms for predictive maintenance and its l im i tations (presented in  
chapter 4) . 
• The th ird objective is the use of a mathematical re lationsh ip between the FFT 
data and a faulty machine component to determ ine the root cause of the fai l ure 
(presented in chapter 4). Th is techn ique identi fies the root cause of a fai lure 
instead of treating fai l ure symptoms that FFT data analysis presents in most 
cases. 
• The fourth objective is to formulate and develop an extension of the cepstrum 
technique using homomorphic b l ind deconvol ution fi ltering to separate the 
forc ing and transm ission path effects in the signals measured from a gearbox 
(outl ined in chapters 5 and 6). 
1.4 Thesis Overview 
This thesis is organ ized as fol lows: 
Chapter 1: I ntroduction 
This chapter presents the topic of this thesis, why predictive maintenance, existing 
work on the predictive maintenance and scope of the present work . 
Chapter 2: Literature Review 
I n  th is chapter, d i fferent work that had been done on predictive maintenance are 
reviewed and mach ine diagnosis and re l iabi l ity, vibration mon itoring and bl ind 
deconvolution are discussed. 
Chapter 3: History of Maintenance and its Strategies 
This chapter presents the h istory of maintenance and its strategies, evolut ion of 
maintenance, its costs and strategies. 
Chapter 4: Fast Fourier Transform Techn ique and Pitfal ls 
The theory of the Fast Fourier Transform (FFT) is d iscussed with the use of complex 
numbers and the operation of a piezoelectric accelerometer. Case studies are 
presented using the FFT technique, and the pi tfa l l  of this techn ique is d i scussed. 
3 
Chapter 5: The Theory of the Cepstrum Technique 
Th is chapter presents the theory of the cepstrum technique to d iagnose the v ibration 
of a gearbox. The theory of homomorphic deconvolution is a lso presented, coupled 
with the cepstrum analysis and poles and zeros. 
Chapter 6: Experimental Analysis 
Th is chapter presents the experimental analysis. The gear test rig is  expla ined and the 
instrumentation for the data col lection is described. The appl ication of the cepstrum 
technique, homomorphic deconvolution, the poles and zeros analysis are presented. 
Chapter 7: Conclusion and Recommendations 
A summary of the work is given, fol lowed by a l i st of contributions of this thesis. 
Then we bring in  some discussion about the proposed methodology and conclude the 
thesis with some recommendations for the future work . 
4 
Chapter 2 
Literature Review 
2.1 Machine Diagnosis and Reliability 
Maintenance is an act iv ity to ensure that equ ipment is in a satisfactory condit ion and 
rel iable. The goal of maintenance is to ensure that the performance of the equipment 
is satisfactory. 
A good maintenance system contributes to efficiency, customer service, h igh qual ity, 
safety, on-t ime del ivery, and customers' satisfaction . 
McFadden [3 , 4, 5 ,  1 2, 1 8] presented various papers on the appl ication of Wavelets to 
gearbox v ibration signal and analysis of gear vibration in the Time-Frequency 
domain .  Techniques l ike Adaptive Noise Cancel lation, Computer Order Track ing, 
Non Stationary Mode l l ing of Vibrat ion Signals and Synchronous Averaging were 
used to d iagnose mach ine faults[6, 7, 8, 9, 1 0, 1 1 , 1 2, 1 3 , 1 4, 1 5, 1 6, 1 7, 1 9, 20, 2 1 ,  
22, 23, 24, 25] thcse papers could not provide solut ions to resonance effect in  the 
transmission path. 
Tol iyat et a l  [26], described how maintenance has long been a powerfu l  source of 
know-how and when to best schedule production, which needs to comply with 
customers' schedules. S iyambalapitiya et al [27] also described the maintenance 
support act iv ities of manufacturing companies and Vas [28] presented a paper on the 
use of a maintenance programme to manage maintenance strategies. Abrecht et al [29] 
described the basic elements necessary to implement maintenance programs. 
Despite what Tol iyat, S iyambalapitiya, Vas and Abrecht said on maintenance strategy 
and programs, there is sti l l  a m isrepresentation of the maintenance strategies in  
industry. The m isrepresentation relates to the inabi l ity of the authors to c learly present 
the maintenance strategy assoc iated w ith each company, which would have given a 
true reflection of the strategy most compan ies practice and why. This is one of the 
objecti ves of this research, investigating three key maintenance practices; reacti ve, 
preventive and predictive and the companies associated with each type and why. 
5 
Diagnosis is the process of determ in ing the fault responsible for a set of symptoms. 
B lunt et al [ 30], defined it  as the formulation and investigation of a hypothesis about 
the malfunctioning equipment. 
I f  the real cause of the problem is not corrected, then further breakdown is  l ikely to 
occur. 
Diagnosis is the process of determ ining the fault responsible for a set of symptoms. It 
is a lso the formulation and investigation of hypotheses about the malfunction ing 
equ ipment [ 30]. Zakrajsek et al [3 1 ], defined diagnosis as "knowing the d i fference" 
between normal and abnormal behaviours of a mach ine, then one needs to have more 
functional knowledge about the internal structure of the mach ine and the interaction 
of its constituent parts. Minns and Stewart[32], presented a five step strategy for 
d iagnostic  problem solving which they summarised as "formulation and investigation 
of a hypothesis about the mal function ing equ ipment": (i) formu lation of the problem 
by analyzing the situation, making observations, and developing a plausib le 
hypothesis; ( i i )  developing expectations for each of the hypothesis; ( i i i )  selecting the 
hypothesis with the h ighest expectations for leading to the cause; ( iv )  col lecting and 
analysis of data (v) evaluating the hypothesis (v i )  in the case of indec is iveness of the 
hypothesis, the first five steps are repeated as many times as required unt i l  the cause is 
identified. Esh leman [33 ] ,  described i n  h is work that component l i fe expectancy and 
wear rates can only be assessed on the bas is of recorded information that represents a 
true reflection of operat ing cond itions. 
Heinz P. B lock [34], writes on mach ine re l iabi l ity improvement and maintenance cost 
reduction. He d iv ided mach inery rel iabi l ity management in process industries into 
three phases: equipment se lection and pre-erection re l iabi l ity assurance; preparation 
for effective start-up; and post-start-up rel iabi l ity assurance and maintenance cost 
reduction. The techniques and procedures that covered each phase have led to 
improved equipment re l iabi l ity and maintenance efficiencies. 
E isenmann [35] with over 33 years of experience in solv ing mach inery problems 
coupled with numerous technical notes on how to use the app l ication of engineering 
princip les to diagnose and correct machinery malfunctions. The mach inery under 
d iscussion in  the book operates with in  the heavy process industries such as o i l  
refineries, c hemical plants, power p lants, and paper m i l ls. He asserted that the 
majority of mach inery problems that do occur fal l  i nto what he cal ls the ABC 
6 
category, which  are general ly related to A l ignment, Balancing, and incorrect 
Clearances (typica l ly on bearings). Although machines also exhibit other types of 
fai lures, he devoted more time to each of this ABC problem categories due to the 
cont inual appearance of these mal functions. 52 detai led case h istories are combined 
with numerous sample calcu lations and examples to solve real world problems. 
Doebel i n  [36] deve loped an understand ing of the operat ing princ iples of measurement 
hardware and the problems involved in  the analysis, design, and appl ication of such 
equ ipment. He wrote on the treatment of dynamic responses for all types of inputs: 
periodic, transient, and random, on a un iform basis, uti l i s ing the frequency domain.  
He further gave detai led considerat ion of problems involved in  interconnecting 
components. He also presented a deta i led study of measuring instruments and their 
characteristics, which are used in  the mon itoring of processes and operat ions, control 
of processes and operations, and experimental engineering analysis. 
Kuhne l l  [37] states that managers are breaking out of the vic ious cycle  by improving 
the maintenance processes and increasing the effectiveness or productivity of asset 
and human resources. Improving maintenance processes involves re-engineering the 
process and increasing resource effectiveness by moving to a mostly condit ion-based 
maintenance phi losophy and adding maintenance tasks to manage economical ly 
preventable fai lu re modes that h istorica l ly have caused fai l ures. 
H i l l  [ 38 ] ,  described design methodology for fault diagnosis in l i near systems, wh ich 
can also apply to non-l i near cases [38] .  
I serman [39]  surveyed the detection of process fau lts based on model l ing and 
estimat ion methods, coupled with the estimation of unmeasurable process parameters 
and variables. Frank and Koppen-Sel iger [40] , presented fuzzy logic and neural 
networks as another new approach to system mode l l i ng, a paper out l in ing the most 
up-to-date developments in artific ial inte l l igence for fault diagnosis. 
B lock and Geithner [4 1 ], presented how the protitabi l ity of modern industry and 
process plants is  sign ificant ly in fluenced by the re l iabi l ity and maintainabi l ity of the 
machines. They described the probab i l istic and statistical way of thinking when 
deal ing with matters of process mach inery rel iabi l ity, avai labi l ity and safety. 
Jeffrey [42] described the techniques designed to monitor machine operat ion and 
generate information that can be used to anticipate breakdown. He maintained that 
advances in sensors, algorithms, and architectures should provide the necessary 
technologies for effective incipient fai l ure detection. 
7 
Despite the breadth and clarity of the l iterature on this subject of fault diagnosis, there 
is also a problemat ic narrowness, a concern with the fact that d iagnostic strategy is  
experience-based and rel ies on an experienced diagnostician to have been 
"cond itioned" over time for the task. I f  the d iagnosis is defined as responding to 
symptoms and try ing to determ ine the cause(s) of the symptoms, then the d iagnost ic 
dec ision making re l ies more on rule-of-thumb and less on fundamental ( functional 
and behavioura l )  knowledge about the equipment. The l i terature on this subject of 
fau l t  d iagnosis only identified the symptoms of machine problems and not the root 
cause. 
Examples of machine fai l ures inc l ude bearing, gear fai l ures; shaft m isal ignment, 
looseness and imbalance etc . 
Whether the component was operating with in operating parameters is the question 
requ i ring an explanation. Knowledge of previous inc idents could be even m isleading 
in  th is situation. Relying on the patient,s h istory primari ly as the basis for d iagnosis  
cou ld have severe consequences i f  the true cause is not the usual one. To explain how 
a faul t  took place, one needs to trace the situation back unt i l  a satisfactory cause is 
identified. The fact that a component broke down in a machine is  not necessari ly the 
satisfactory cause of the fault, rather, what led to the breakdown of the component is  
part of the objectives of this research .  
2.2 Predictive Maintenance - Vibration Monitoring 
The few companies that have vibration mon itori ng gears use data col lectors that 
operate on Fast Fourier Transform Technique. Th is has been the most widely adopted 
form of condition mon itoring, record ing and analysis of mach ine v ibration s ignatures. 
The l iterature presented here on this subject - Predictive Maintenance-Vibration 
Monitoring, lacks the improvement needed to make a machine rel iable, reduce the 
number of breakdowns and augment profitabi l ity. None of this l i terature is interested 
in the root cause of a fai lure. Even though a lot of work has been done on fau l t  
detection, none of  the  fau lts detected by these writers have been traced down to  the 
root cause. 
The appl ication of statistical analysis to measured diagnostic signals is as old as the 
science of measuring the signal . A review of time domain analysis using stati stical 
8 
methods forms part of v i rtua l ly every PhD thesis and masters dissertation conducted 
in the field of vibration mon itoring. 
In general ,  t ime domain analysis enta i ls  calculating the root mean square, peak val ue, 
crest factor and kurtos is values of a signal .  The root mean square value gives an 
indication of the continuous or steady state ampl itude in a t ime varying signal .  The 
peak level or value is defined as half of the d ifference between the maximum and 
m in imum values in the signal .  Thi s  is not a statistical value and it is known not to be a 
rel iable i nd icator of damage. The crest factor is defined as the rat io of the peak value 
d iv ided by the root mean square value of the signal .  
The kurtosis is  the normalised fourth statistical moment of a signal .  The parameters 
defined above are a lso referred to as overa l l  v ibration parameters. I n  general ,  they are 
calcu lated for each measurement and trended over time to g ive an indication of 
machine cond ition, rather than the condition of specific components in  the machine .  
Thc parameter does not provide any diagnostic information. However, the parameters 
are easy to implement in low cost onl ine monitoring equipment. 
Komura et a l .  [ 43] developed a hand held vibration mon itoring sensor wh ich ut i l ises 
the root mean square, kurtosis and mutations thereof to c lass ify a machine's condition 
according to three categories namely; normal, warning and alert. This is no longer 
widely used because it only provides overa l l  v ibration leve l on a spot which w i l l  te l l  
you where a fau lt i s  coming from and what sort o f  fau lt i t  is, but there is  no 
d iagnostics advantage in this measuring equipment. 
Martin  et al. [44] I smal l  et al. [45] and Oguamanam et al. [46] appl ied statistical 
d istri butions to experimental data measured on gears and gear pump test rigs. A 
synchronous, or t ime domain average, of the vibrat ion signal was calcu lated before 
applying the stat istical d istribution to segments of the t ime domain-averaged signal . 
The segmentation of the signal enables local fault detection on the gear teeth of the 
gears. A beta distribution was fitted si nce the kurtosis of a normal distribution was too 
sensit ive to noise in the vibration data. It was indicated that the rec iprocal of the beta 
kurtosis value could ind icate the presence of a local defect on a gear. 
Howard [47] developed a composite signal averaging techn ique to overcome the 
mon itoring problems encountered when mon itoring gears in  an epicyc l ic gearbox. 
Typical problems were the varying transm ission path to the transducer and the fact 
that mult iple components mesh at the same frequency. Experimental tests were done 
with a progression in  induced gear damage and vibrat ion measurements were taken 
9 
for the various faul t  conditions in order to val idate the techn ique. The composite 
signal averaging techn ique was appl ied to the experimental data and the modulation 
of the averaged s ignals was calcu lated. Kurtos is val ues for the modulat ion were 
estimated and it was shown that the kurtosis  increased as the extent of gear damage 
increased. The kurtosis value of the modulation therefore proved to be an effect ive 
ind ication of gear condition once composite signal averaging had been done. 
Forrester[ 48] did tests to detect early fatigue cracks in gears. The test was of a t ime 
domain s ignal processi ng technique that compares two signals to i ndicate the 
l i ke l ihood that the two signals have the same probabi l ity density function. In essence, 
the tests determ ined whether two signals were s imi lar or not. Forrester [49] stated that 
a faul t  condition cou ld be ind icated by comparing a signal w ith a number of signal 
templates of known faul t  conditions. The techn ique was applied to experimental data 
and its results indicated that the technique could successfu l ly detect the presence of a 
fatigue crack. 
McFadden[50] uti l ised mult ivariate statistics in  combination with princ ipal 
component analysis to detect loca l ised faults in a two stage hel ical gearbox. ( Princ ipal 
component analysis is uti l ised to reduce the dimension of a data set to fewer samples. 
In essence, it is ut i l i sed for data compress ion). V ibration signals under d ifferent faul t  
conditions where measured. Principal components were calculated for the normal or 
no-fault-present cond ition . These components, where statistically represented were 
calculated for the new measurements to observe any deviations from the normal 
condition. The square predictor error is the sum of the squared d i fference between the 
data ind icat ing the normal condition and the measured data. A deviat ion in  the value 
w i l l  indicate a deviation in the condition of the mach ine. 
Accord ing to Randal l  [5 1 ]  the amplitude modulation of the time domain average 
s ignal can be calculated by taking the absolute value of the signal's analytical signal .  
The analytical signal is a complex time signal of which the imaginary part is the 
Hi lbert transform of the real part. Note that the phase modulation can be calculated by 
calcu lat ing the phase of the analytical signal .  
McFadden and Sm ith[52] band-pass fi ltered the t ime domain averaged signal around 
the prominent gear-mesh ing harmonic and removed the gear mesh harmon ic itse lf  in  
order to obtain what they referred to as a residual signal .  The ampl itude modulat ion of 
the residual signal were analysed and the statistical parameters of the residual signal 
was analysed and statist ical parameters of the residual signal modulations were 
1 0  
calcu lated. The methodology proved to be an effective way to detect local defects on 
gears. 
McFadden (52, 53 & 54]  ut i l ised the amplitude and phase modulation of the time 
domain average they band-pass fi ltered around the prominent gear mesh harmon ic to 
detect fatigue cracks in the gears of a he l icopter' s main rotor gearbox. 
McFadden & Howard [55 ]  extended the technique to incorporate al l of the gear 
mesh ing harmonics and appl ied the technique to torsional v ibration measurements 
measured on an experimental test rig with artific ial seeded defects. They conc luded 
that the technique is more sensitive in detecting gear defects when compared to a 
narrow band-fi ltered approach. 
Brie et al. [56] developed an adaptive ampl itude and phase demodulation approach, 
which has lower numerical complexity when compared to the conventional route of 
calcu lating the modulation us ing the Hi lbert transform . The algorithm is  sequential 
which a l lows it to be implemented in real time. 
Wang [57] appl ied a resonance demodu lation technique common to ro l l ing e lement 
bearing defect detection and monitoring to detect incipient gear tooth cracks. The 
methodology is based on the fact that a root crack w i l l  lower gear tooth sti ffness in the 
gear mesh result ing in  impacts as the gear tooth after the damaged gear tooth enters 
the gear mesh . This impacting wi l l  excite the structural resonance. A residual signal is 
calculated from the time domain average and band-pass fi l tered around the structural 
resonance. The band-pass fi ltered residual signal is then demodulated to detect sudden 
changes in the modulation, wh ich are related to the presence of fatigue cracks in the 
gears. 
Spectrum analysis entai ls  the conversion of a time signal to a frequency domain 
representation through a discrete Fourier transform . The term spectrum is used for the 
ampl itude representation versus the positive frequency range of the t ime signal's 
Fourier transform . 
Frequency domain analysis is widely used due to the s impl ic ity in analysing mach ine 
fau lts. At the beginning of th is  research work, the analysis carried out on various 
machines was made with the FFT techn ique. 
The advantage in using spectrum analysis l ies in the fact that the ampl itude at each 
d iscrete frequency can be monitored in contrast to the overa l l  ampl i tude mon itoring 
approach of time domain analysis .  A log scale for the ampl i tude axes can be c hosen to 
improve the dynamic range of the representation . Defects that w i l l  cause a sma l l  
I I  
change in ampl itude at a certain frequency with low ampl itude w i l l  therefore be 
detected much easier in comparison with time domain analysis. 
Lots of work has been done with this technique and the l i terature on it is vast. 
The frequencies at which a certa in defect on a particular component wi l l cause an 
increase in  the amplitude of the spectrum are referred to as defect frequencies. Hence, 
d iagnost ic capabi l ity can be obtained by re lating ampl itude growth at a certa in 
frequency to a part icu lar component i n  the mach ine based on its physical parameters. 
This type of analysis is conventiona l ly used in practice to mon itor plant equ ipment. 
Forrester [58], Matthew [59] and Mechefske [60] have described spectral analysis in 
detai l .  
The book of Goldman [6 1 ]  on  Vibration Spectrum Ana lysis is  based on  h i s  
experience when he  worked at Nash Engineering in  the early 1 970s. The book is  
about problem solv ing in  general based on h is  many years experience. 
Forrester [62] states that the gear mesh v ibration measured on the casing of a gearbox 
descends from the fluctuat ion in gear mesh ing sti ffness as the gears rotate in and out 
of the gear mesh. I f  a time domain average or synchronous average of the v ibration on 
the gearbox casing is calcu lated and band-pass fi ltered around the fundamental gear 
mesh harmon ic, the result ing signal w i l l  approximate a s inusoid where each peak in  
the  sinusoid represents the structural response due to  a gear tooth entering the  gear 
mesh. 
The author wi l l  improve the current d iagnosis  techniques that rely only on monitoring 
some physical characteristics that reflect the cond ition of the mach ine or ident i fy the 
machine fau lts but not the root cause. The author w i l l  use mathematical relationships 
between the condition monitoring data and the fau lty components to determine the 
root cause of a failure; this is presented in chapter 4 .  
2.3 Artificial Neural Network 
Pred ictive maintenance, or cond ition monitoring, is based on continuous monitoring  
of equ ipment through sensor-based data col lection equ ipment and special ised 
technologies to measure specific system variables. A l l  machinery generates vibrat ion; 
the analysis of t he system variables wil l render valuable information about the 
condition of the machines. 
1 2  
Artificial neural nets (ANN) are increasingly being used i n  fault  d iagnosis systems. 
The popular approach to developing ANN-based d iagnostic systems  is to i nduce 
several artificial fau lts into specific mach inery sub-components, acqu i re data 
representative of each fault and train the nets to c lassify them, cross-val idating and 
test ing the trained system with data not used for train ing [3]. 
There has been research work carried out on neural network to detect gear fau lt 
because of its t ime series prediction capabi l i ties [3] ,  [ 1 5 ] ,  [2 1 ], [46], [50], [60]. 
Data from s imulation models have been used occasional ly with varying degrees of 
success. The major gap in the exist ing work is that there is no proper quantification of 
the faul t  induced. Without the knowledge of how severe or subtle the fault induced is, 
there is no way of evaluating the pred ictive method used . On a s imi lar note, many of 
the fau lts detected are either too trivial or too severe; and do not justify the use of 
soph isticated detection methods. Another major drawback in  the field is  that there are 
no benchmarks. What may appear as a serious fault to the un in itiated may be nothing 
more than a blemish to the experienced mechanical engineer. 
2.4 Blind Deconvolution and Cepstrum Analysis 
The term cepstrum analysis is the inverse Fourier Transform of a spectrum. I t  i s  
uti l i sed to detect a series of harmonics or sidebands and to estimate the ir  strength.  The 
various harmonics in a conventional spectrum are reduced to predominantly one peak 
in  what is referred to as the quefrequency domain. Periodicity in  the conventional 
spectrum is  therefore detected. Only a single peak needs to be detected to d iagnose a 
faul t  condition. Logarithmic values of the spectrum are uti l ised in the calcu lation of 
the cepstrum i n  order to improve the dynamic range of the analysis [63]. 
The v ibration spawning from the meshing of a gear pair i n  a gearbox has to be 
transm itted through the shaft, ro l ler element bearings and casing before being 
measured. I t  is common knowledge that this transm ission path has structural 
impedance characteristics in terms of amplitude and phase. I f  the gears rotate at a 
certain frequency, the force being transmitted from the mesh ing gears w i l l  be subject 
to amplitude and phase changes induced by the structural impedance at the particu lar 
frequencies. However, if  the rotational speed changes the forces be ing transmitted 
1 3  
from the mesh ing gears are subject to d ifferent ampl itude and phase changes induced 
by the transmission path impedance at the alternative frequenc ies. As a resu lt, the 
ampl itude and relat ive phase of the measured structural response wil l  be d ifferent 
depend ing on the structural dynam ic characteristics [64]. 
Schaum [64] covers both cont inuous-time and discrete-time signals and systems, 
develops the fundamenta l  input-output relationsh ip for l i near time-variant systems 
and explains the un it impulse response of the system and convolution operation. He 
explored the transform techniques for the analysis of l i near time-invariant systems 
and dealt with the z-transform and its appl ication to discrete-t ime l inear time­
i nvariant. 
Schaum [65] described the fundamental of digital signal processing, description and 
characterisation of discrete-type signals and systems, convolution, and l i near 
coefficient d i fference equations. 
Randa l l  [ 66] suggests that the ceptsrum exists in  various forms, but a l l  can be 
considered as a spectrum ofalgorithmic (ampl itude) spectra. He used these techniques 
for detection of a periodic structure in  the spectrum, e.g from harmon ics, sidebands or 
the effects of echoes. He demonstrated that the effects wh ich are convolved in  the 
t ime signal (mul tipl ied i n  the spectrum) become add itive in  the cepstrum, and 
subtraction there resulted in a deconvolution. He described the appl ications of 
cepstrum, including the study of signals containing echoes (land-based and marine 
seismology, aero-engine noise, loudspeaker measurements) speech analysis (format 
and pitch tracking, vocoding) and mach ine diagnostics (detection of harmon ics and 
sidebands). 
Haykin [67] stated that the book he edited in  1 994 on b l ind deconvolution conta ined 
various a lgorithms for solving the b l ind channel-equal isation problcm. Haykin [68]  
presents a theory that bl ind deconvolution and bl ind source separation origi nated 
independently, yet they are related to each other and constitute the two pi liars of 
unsupervised adaptive fi lteri ng. 
Randal l  [69] described how Fourier analysis led to d ifferent types of signal 
encountered in  practice and how they appear in spectra and other representat ions. He 
a lso treated the convolution subject in some deta i l  and that the output of a l i near 
physical system is obtained by convolv ing the i nput signal with the impulse response 
of the system. 
1 4  
Dalpiaz [70] compared the results obtained from the time-frequency and cylco­
stat ionarity analysis, and those from cepstrum analysis and time-synchronous average 
analysis on a gear pair affected by a fatigue crack, considering two different depths of 
the crack. He concluded that the time-synchronous average and demodu lation 
techniques are able to local i se the damaged tooth, but the demodulation techn ique is 
affected by the transducer location. However, the wavelet transform seems to be a 
good tool for crack detection, if the residual part of the time-synchronous averaged 
signal is processed. 
Lee [7 1 ]  used h igher-order statistics based on third-, fourth-, fifth- and sixth-order 
statistical b l ind deconvolution on impacting signals. He recovered the impulse impact 
signals and improved the estimat ion time between the impacts by comparing the 
effic iency and robustness of the schemes. 
Randa l l  [72] and Angelo [73] stated that cepstrum analysis is insensitive to the phase 
variations in the transmission path. The power spectrum of a signal measured at an 
external point on the casing of a rotati ng mach ine such as a gearbox can be expressed 
as the product of the power spectrum of the source function with the squared 
ampl itude of the frequency response of the transm ission path. By taking the log of the 
transform, the multip lication turns i nto an addition of the logarithmic source function 
power spectrum and the logarithmic frequency response function, to obtain the 
logarithmic spectrum of the response. Th is impl ies that the source and transmission 
path effects are addit ive in  the cepstrum. The transmission path transfer function has 
low quefrequency components, wh ich wi l l  be wel l  separated from the h igh 
quefrequency components representing the source function. Randa l l  [73] appl ied the 
cepstrum analysis to the vibrat ion measured on a gearbox at two different posit ions on 
the casing. He concluded that the spectra of the two signals were different but the 
cepstra were a lmost identical. 
Forrester [ 74] however stated that cepstral analysis is  not very useful in the analysis of 
synchronously averaged signals, s ince the signals is not periodic in  the so-cal led angle 
domain and periodicity is lost when translated to the quefrequency domain. 
A variety of expressions and forms of the cepstrum have been developed. Ch i lders et 
a l .  [75] described the re lationsh ips between the various forms. Wu and Crocker [76] 
developed a modified cepstrum technique to determ ine the magnitude of a structure's 
frequency response function. The novelty of the techn ique is based on the fact that no 
prior knowledge of the input force is required to calcu late the magn itude of the 
1 5  
structural transfer function. Debao et a ! .  [77] appl ied cepstrum analysis to detect 
m isa l ignment, unbalance and bearing damage in generators. Van Dyke and Watts [78]  
uti l i sed the cepstrum analysis as a data pre-processor for an expert system, which can 
detect rol l ing e lement bearing deterioration and predict fau l t  severity. 
Badaoui et al. [79] proposed a mov ing cepstrum i ntegral to detect and local ise tooth 
spa l l s  in gears. The techn ique appl ies a moving window in order to iso late the gear 
tooth fau lts. This enables the detection and local isat ion of local tooth spa l l  on gear 
teeth. The techn ique was appl ied to numerical and experimental data and the authors 
where able to detect l ight spa l l ing on gear teeth. 
Jeung [80] said that a direct measurement of an excitation pulse is not s imple because 
locating sensors at the exact source location is not practical in many engineering 
appl ications. He presented an indirect method for detecting a transient source 
waveform by using a sensor at a remote pos ition and using cepstral analysis as a 
robust inverse filter to smooth out the transm ission path. 
Zhinong [ 8 1 ]  reviewed the app l ication of b l ind source separation in mach ine fau l t  
d iagnosis, considering noise e l imination and extraction of weak signal s, the separation 
of mu l ti-fault  sources, redundancy reduction, feature extraction and pattern 
c lassification based on independent component analysis. The app l ication of b l ind 
source separation i n  machine fault diagnosis has been developed rapidly for the last 
several years [82] .  B l ind source separation provides a new techn ique for the 
separation of mechanical source signals under h igh-level background noise and 
d iagnosis of the compound fau lt [82] .  
M i rko [83]  carried out an assessement for bl ind source separation [BSS]  a lgorithms 
w ith respect to machine diagnosis and verified the appl icab i l ity of a new BSS 
a lgorithm .  
The sound o f  a rotating machine i s  periodical ly (or at least first order cyc lostationary) 
and therefore stationary. The typical interfering sources are normal ly not stationary, 
l ike human speech, hammer blows or c l ick ing of switches [84]. Machine fau lts 
modify the machine sound characteristical ly, therefore observ ing the mach ine sound 
can be a usefu l  means for fau l t  d iagnosis and c lassification [85 ] .  B l ind source 
separation deals with the problem of recovering several sources from l i near m ixtures 
w ithout knowledge about the mixture [85 ] .  
1 6  
A gearbox is an example of an extremely d ifficult case to measure the force at the 
gear mesh which is rough ly fixed in  space, but moving with respect to the meshing 
gears (86] 
A methodology was out l ined to determ ine poles and zeros corresponding to the 
frequency response function (FRF) of a signal transm ission path from response 
measurements alone, w ithout the need to measure the forc ing function. 
Gao [87] presented a paper on the determ ination of frequency response functions from 
response measurements - extraction of poles and zeros from response cepstra by 
adopting the Levenberg-Marquardt and I brah im time domain methodologies for the 
curve-fitt ing purpose. He used the b l ind source separation techniques to separate the 
v ibrat ion sources in internal combust ion engines. He used the bl ind source separation 
techniques to separate the vibration sources in internal combustion engines. 
Cepstrum analysis and H i l bert transform techniques may be usefu l  in  s ituations where 
frequency analysis alone or time signal analysis a lone does not enhance those features 
of the signal that characterise the fault to be diagnosed [88].  
Traditional frequency analysis techniques are not very usefu l  due to the overlap of the 
d ifferent sources over a wide frequency range [89]. 
Peled [90] used a bl ind deconvolution to separate signals from d ifferent sources which  
are convoluted and mixed by the mechan ical systems before being measured. He 
based h i s  methodology on bl ind deconvolution separation, consideri ng the kurtos is  of 
the separated signals com ing from bearings as the measure to be maximised. He tested 
h i s  methodology on s imulated and experimental cases. The results showed the 
e l im ination of t he effect of structural resonances, which often causes severe problems 
in  c lassical diagnostic methods. 
Jerome [9 1 ]  used industrial cases to demonstrate how the spectral kurtos is can be 
efficiently used in the vibration-based condition monitori ng of rotating mach ines. He 
introduced the concept of kurtogram, from wh ich optimal band-pass fi lters can be 
deduced as a prelude to envelope analysis. 
Jerome [92] establ i shed the extent to which spectral kurtosi s  is capable of detecting 
transients i n  the presence of a h igh noise-to-signal ratio and thereby proposed a short­
t ime Fourier-appl ications. 
Jerome [93 ] proposed two robust separation techniques based on the short-time 
Fourier transform to separate the convolutive m ixtures of sources. He ascertained that 
b l ind source separation is the issue of recovering the various independent sources 
1 7  
exc it ing a system given only the measurements of the outputs of the system, and it has 
become the focus of i ntensive research work due to its h igh potential in many 
appl ications. 
Having reviewed the above extensive l iterature, gear faul ts sti l l  remain a d ifficult 
problem to analyse because of the overlapping of the frequencies, s idebands and 
harmonics, which is the reason for this research work; developing a novel technique 
to solve this problem by using cepstrum technique that uses homomorphic b l ind 
deconvol ution to remove the effect of transm ission path transfer functions from 
external ly measured gearbox signals. 
Homomorph ic fi ltering is unique because it w i l l  extract a smooth envelope, which  
enables the  detection of events that are suspected. I t  w i l l  decompose (deconvolve) the 
additive components i nto cepstra components for better diagnosis. Th is is the missing 
piece in the work j ust outl ined. 
The reason for the homomorphic fi ltering over other work on the cepstrum techn ique 
is of two parts: 
• The first part is the detection of those parts in the cepstrum which ought to be 
suppressed in processing. 
• The second part inc ludes the actual fi ltering process and the problem of 
min im is ing the random noise which is enhanced during the homomorphic 
procedure. 
1 8  
Chapter 3 
Maintenance Strategies 
3.1 I ntroduction 
The function of maintenance is to ensure that plant and equipment are avai lable in a 
satisfactory condition for operation when required. The determ ination of what 
constitutes a satisfactory condition for rotating machinery w i l l  depend largely on the 
operating situation, type of industry, process requirements and business objectives. 
In a l l  cases, however, the performance of the maintenance function can be judged by 
the cond ition of machinery, wh ich the fol lowing factors w i l l  ind icate [42]: 
• Performance, this is the abi l ity of the machine to perform its functions. 
• Downtime, operation of the mach ine must be within an acceptable level of 
downtime. 
• Service life, before replacement of the machine is necessary; i t  must provide a 
good return on investment. 
• Ef iciency, the level of effic iency of the machine must be acceptable. 
• Safety, the mach ine must be safe to the personnel .  
• Environmental impact, the operation of the mach ine must be friendly to the 
environment and other equipment. 
• Cost, it is expected to have a maintenance cost with in an acceptable leve l .  
The goal of maintenance is  to  ensure that machinery performance is sat isfactory, 
considering the above factors. Th is chapter covers the brief h istory of trad itional 
machine maintenance and maintenance strategies. 
Most management now see maintenance effic iency as a factor that can affect busi ness 
effectiveness and risk-safety, environmental integrity, energy effic iency, product 
qual ity and customer serv ice and that it i s  not constrained only to p lant avai labi l ity 
and cost. Thus, as the c l imate of doing business changes, so does the need for better 
maintenance programs. 
1 9  
3.2 Evolution of Maintenance 
I n  general ,  the evolution of maintenance is categorized into 3 d ifferent generations: 
• the period of 1 930 's- 1 940's which is referred to as the F irst Generat ion, 
• between 1 950's  to 1 970' s  as the second generation, and 
• the 1 980's unt i l l  date as the third generation [ 1 39]. 
The growth in  maintenance efficiency has become more complex due to equipment 
automation. 
3.2.1 First Generation 
The first generat ion describes the earlier days of i ndustrial ization where 
mechanizat ion was low. Most equipment in the factory was basic and the repairing 
and restoration process was done in  a very short time. Thus, the term downtime did 
not matter much and there was no need for managers to put maintenance as a h igh 
priority i ssue. 
3.2.2 Second Generation 
The second generat ion emerged as the results of growing complexity i n  equipment 
and p lant design. Th is had led to an increase in mechan ization and industry was 
beginn ing to depend on these complex machines. Repair and restoration had become 
more d ifficult with special ski l ls and more time needed to mend the mach inery. As 
th i s  dependence grew, downt ime became a more apparent problem and rece ived more 
attention from management. People were beginning to think that these fai lures should 
be prevented which led to the concept of preventive maintenance. As maintenance 
cost started to rise sharp ly relative to other operating costs, there was a r is ing interest 
in the field of maintenance planning and control systems. 
3.2.3 Third Generation 
Rel iab i l ity had become vital In the maintenance c irc le from the 80s; fa i lure of 
machines would be detrimental to productiv ity and profitabil ity. At th is t ime a 
machine breakdown could have an adverse effect on a plant and its operation . The 
complex ity of mach inery and automation system had been on the increase. 
The evolution of the maintenance strategy is demonstrated in the tab le 3 . 1 and the 
development between the first and third generations are summarised as fol lows: 
20 
• More focus on equipment re l iabil ity and root cause analysis to enhance better 
performance. 
• The technology that can predict and reduce a mach ine breakdown is avai lable. 
The trend of this development is pointing at ways to attain zero breakdowns. 
• Maintenance tools have improved. 
Many organ izat ions have stated zero breakdownslzero in-serv ice fai l ures as their 
maintenance goals. However, since no amount of maintenance can guarantee the total 
e l im ination of fai lures (there is always a probabi l ity of fai l ing but it may be very c lose 
to zero) it is not a real istic objective. A more real istic approach is to avoid, reduce or 
e l im inate the consequences of fai lures. 
Table 3 . 1 and figure 3 .2 present a summary of the survey that the author carried out. 
The survey was conducted through phone cal ls to twenty manufacturing companies 
that have local branches spread across New Zealand. The survey was also conducted 
among the attendees of Vibrat ion Association of New Zealand Conference in the two 
years I attended the conference. Attendance at each was 200 and the attendees 
represented the managers and maintenance planners of various compan ies across New 
Zealand. The author spoke to either the maintenance manger or the maintenance 
p lanner and asked the fol lowing questions in Table 3 . 1  
Table 3.1: Questionnaires 
Questions Answers 
Company's Name 
Type of Processes 
I s  your maintenance reactive or 
preventive or predictive 
What is your maintenance software? 
What is your predictive maintenance 
gear? 
The answers to the above quest ions were col lected by the author and are demonstrated 
in Table 3 .2 and figure 3 . 1 respectively. 
2 1  
The d ifficu lties the author encountered during the survey were that the maintenance 
manager or planner were not interested in the survey. Th is was the reason the author 
dec ided to use telephone i nstead of sending out questionnaire forms. 
Patience and perseverance helped the author to overcome these d ifficu lties. The 
Patience helped to cal l  as many times as possible to speak to the right person; and the 
perseverance helped keep ringing back to get the information the author needed for 
th is  survey. 
Table 3.2 : The Summary of Maintenance Evolution 
First Generation Second Generation Third Generation 
*Break and fix *Preventive maintenance * Predictive maintenance 
maintenance strategy. strategy strategy 
*65% of companies i n  * Job schedul ing and * Equipment rel iabi l ity 
New Zealand use this plann ing * Hazard stud ies and 
strategy. *Low-tech maintenance safety 
programme * Root cause analysi s 
*30% of companies in New * Various maintenance 
Zealand use this strategy. programmes. 
* About 45% have the * About 5% c laim to have 
preventive maintenance the predictive maintenance 
programmes, only about programmes, only about 
30% fol low the routine and 3% practice th is  strategy 
procedures, the rest 1 5% sti l l  w ith diagnosis and 
fix the machines when it re l iabi l ity, the rest 2% sti l l  
break down. fix the mach ines when it 
breaks down and also use 
preventive maintenance 
programmes. 
22 
Maintenance Strategies 
Predictive 
Maintenance, 
Preventive 5% 
Maintenance, 
30% 
Reactive 
Maintenance, 
65% 
Figure 3 . 1 .  Maintenance Strategies Based on the P ractices in N e\\ Zealand 
Companies 
The increased usage of compu ter model l i ng In mai ntenance strategies. rapi d 
de\'e!o pment o f  computer technol ogy ( espec i al ly  i n  the area o f  arti fic i al i ntel l igence 
and expert systems) and co mputer s imulations hav e  i ncreased the p red icti ve 
maintenance tools. Today computers hel p in data co l l ection, data sto rage. s ignal 
processing and analysis of eq uipment fai l u re. 
The react i \"e maintenance is mostly practised by many companies because of l ack of 
i n formation on predict i \ "e m ai ntenance or the cost o f  it or l ack o f  interest .  
For the purpose o f  c l arity. reacti\ "e main tenance i s  broader than man�' peop le  used to 
see it. M any see i t  as a type of maintenance other than pre\ enti \'e and predicti \'e: there 
is more to i t .  The fol lo\\ ing are the broader defi nit ions of reacti \ "e maintenance. 
considering the results of the survey. therefore react i v e  mai ntenance is where l 42 1 : 
• There is 110 p re\'enl i \'e and pred ict i \ e  mai ntenance. but run the machine unti l  a 
fault de\'el ops. is sopped and is fi xed . 
• There is no p red ictive m ai ntenance. p re\,enti \ e  maintenance is i n  place. but 
the routine \\'ork is  ne\'er done or ignored by the maintenance personnel : t he 
machi ne runs unti l a faul t  d e\"elops. i s  stopped and i s  fi xed , 
• Predictive maintenance i s  i n  p lace ( ei t her onl ine o r  off l i ne) but the 
reco mmendati ons based on this st rategy are ignored by the p lant o\mers or 
technicians. the mach ine is run until fai l ure occurs and then fi xed. 
23 
3.3 Maintenance Cost 
Maintenance costs have been a great concern In past years, which a lso affected 
productiv ity and profitabi l ity. Maintenance is the largest s ingle manageable 
expenditure in  the plant, wh ich surpasses the annual net profit of some companies. I t  
is widely accepted that maintenance strategies l ike preventative and predictive 
maintenance programs produce savings of up to 25%, yet 1 /3 of these maintenance 
costs can be saved [42 ] .  Maintenance costs are c lass ified into two types: 
• Labour, materials, services and overhead are costs that are easi ly measured. 
• The second one is not easy to measure, these are the unexpected stops of 
machi ne, unplanned p lant shutdown and breakdown. 
Therefore, it is very important for companies to maximize the effectiveness of their  
maintenance and equipment uptime. According to a survey carried out by the author 
on manufacturing companies across New Zealand, most of their maintenance 
departments are about 30% productive, due to lack of proper maintenance of their 
machines. 
However, maintenance productivity can be drastica l ly improved by the planning and 
schedul ing of maintenance activ it ies. For the past 20 years, most manufacturers have 
only focused on reducing costs in the manufacturing processes to stay competitive as 
a low cost producer [94]. This effort wou ld yield some measurable productiv ity gain 
but  sti l l  excludes the opportun ity for the maximum gain in  overa l l  productiv ity since 
maintenance was often exc luded from these improvement plans [95]. C learly, it i s  
also important to integrate a maintenance program into the improvement agenda of 
the manufacturing compan ies [96]. 
3.4 Maintenance strategies 
A l l  machines have some physical characteristics that reflect their  conditions. A 
normal runn ing level for that characteristic is establ ished when the machine is in good 
condition, any sign i ficant deviation from that level gives a warning that a faul t  may be 
developing and maintenance wi l l  be required. 
Al though the specific requirements of an ind iv idual mach ine are rarely quantified, it 
is important that the criteria by which performance can be assessed are understood 
and monitored. Despite the fact that definite levels of acceptabi l ity are hard to 
establ ish, trends in machine conditions can be observed and should be used as 
24 
ind icators of maintenance requirements. Three types of maintenance strategies are 
d iscussed i n  th is chapter. 
3 .4 . 1 Breakdown Maintenance (React ive) 
This type of maintenance strategy is referred to by some people as reactive or 
corrective or ' break and fix'  maintenance. In Auckland and Wel l ington about 65% of 
the compan ies surveyed use this strategy to maintain the ir mach ines. The approach is  
reactive when the mach ine breaks down or the machine is in the process of breaking 
down. This process shortens the l i fe of the equipment, which often results in  the 
rep lacement of the machine or components. The costs of labour, production, repair 
and parts make the overa l l  maintenance cost under this strategy the h ighest among the 
maintenance practices. Thi s  maintenance strategy is basical ly "run the machine t i l l  i t  
breaks". Advantages to reactive maintenance can be viewed as a double-edged sword. 
l f we are deal ing with new equipment, we expect m in imal incidences of fai l ure. l f our 
maintenance strategy is  only react ive, we wi l l  not expand manpower, dol lars or incur 
cost unti l  something breaks. 
S ince there is no assoc iated maintenance cost, this cou ld be viewed as saving money. 
On the other hand, by waiting for the equ ipment to fai l ,  its l i fe is be ing shortened 
which would result in more frequent replacement. The labour cost assoc iated with 
repair w i l l  be h igher than normal because the fai l ure w i l l  most l i kely requ i re more 
extensive repairs than wou ld have been requ i red i f  the piece of equ ipment had not 
been run to fai lure. 
3 .4.2 Preventive Maintenance (PM) Strategy 
Th is  is a 'time-scheduled' task to prevent breakdown, which is performed on 
machines periodical ly or by schedu les. During this maintenance period, machines are 
opened up and inspected, and then repairs are made. I tems are replaced or overhau led 
at a specified time, no matter the ir  condition. Th is research work investigated 
maintenance strategies in d i fferent companies in New Zealand (see Table 3 .2  and 
Figure 3 . 1 ); about 30% of them operate PM effective ly. Some of these companies 
i ncorporated the ir  maintenance routine into SAP software and col lected the l i st of 
machines due for inspection each week. Examples of this routine work are in  
Appendix B .  This was the PM strategy that was set up for a company that c laimed to 
have a preventive program but sti l l  practised a reactive maintenance strategy. The 
25 
fol lo\\i ng \\ ere i n vestigated befo re the PM was set up: machine history, hypothet i ca l  
fai l ure h istory. man u facturers manual as \\ e l l  as i n ten'i e\\s \\"ith the o perator o f  the 
machi ne and the maintenance team. PM has t\\ O features. which are. act i  \' ity to be 
perfo rmed and freq uency at which it is perfo rmed Fai l ure to assess the t\\'O features 
",i l l  resul t  i n  e i ther under-maintai n i ng or o \'er maintain i ng the machines, Under­
mai ntain i ng machi nes occurs \\ hen PM i s  not perfo rmed o ften eno ugh. w h i l e  o \'er 
mai nta i n i ng i s  \\ hen PM is performed at more freq uent i ntervals than necessary or 
performing act i v i t ies  that add no value to the machine output The companies v is i ted 
during the invest igation sho\ved their preferences for the fol lowing i ntervals when 
speci fying the PM frequencies: \veekly. month ly. q uarterly. s ix-month ly and annual ly .  
3. -1. 2. J I'reventive Maintenance Costs By Frequency 
Breakdo\\n i s  when a mach i n e  i s  operat ing less than s at i s factori ly. Despi te a l l  
attempts at pre\'ention. machine breakdo\\TIs o f  \'ario us kinds do occur and often need 
to be fi xed on an u rgent or emergency bas is ,  It is i mportant to make sure that the real 
cause of the breakdO\\TI is  found and remedied and not j ust  the effect patched up. Root 
cause analysis should be rigorous i n  finding the i nherent cause of the p roblem. I f  the 
real cause of the problem is not corrected then further breakdO\\I1 is  l i kely to occur. 
Monthly 82% 
Quarterl\' 5% 
S i x  M onthl" 8% 
Annual l y  4% 
O\ er-Annual l \' 
P M  Activity Costs by Frequency 
82% 
5% 
4% 
1 %  
8% 
Figure 3 . 2 :  Pre\'ent i \'e M aintenance Costs by Freq uency 
2G 
Figure 3 . 2  sho\\'s oyer 80% o f  the PM e�pendi ture on act i \ i t i es \rith a freq uency 
of one month or l ess, \\'hereas the si x-monthly and ann ual act i y i t ies are onl� '  8 % 
and 4% o f  maintenance costs respecti \·el y .  The fig ure out l i nes the costs i m'ol yed 
during preyent i ye maintenance. 
3 . 4 . 2 . 2  Case Study 1 .  Fan Drive Hnd HeGl'inf? Under Preventive 
Maintenance 
A steel man u facturing company ShO\\l  i n  F i gure 3 . 3  performs di fferent operat ions i n  
s ix  p l ants, which are: I ron, S teel. Meta Coat i ng Line. Colour Coating L i ne, Rol l i ng 
M i l l s  and M i ne S i t e. The mai ntenance strategies i n  these p l ants  were preyent i \'e and 
predict i Ye. The plant o\mers d esigned pre\ ent i \ e mai ntenance ( P M )  for some 
machi nes and pred i ct i Ye for others. 
Fi gure 3 . 3 :  Steel M an u facturing C ompany in Aucklan d  e\\ Zealand 
2 7  
Fi gure 3 . 4:  Mul t i -Hearth F u rnace Fan 
F igure 3 . 5 '  Fan DE Bearing 
28 
Th is case study w i l l  d iscuss a machine under prevent ive maintenance. The mach ine is  
shown in  figure 3 .4, a multi-hearth furnace fan that had a h istory of premature bearing 
fai l ure at the fan drive end (DE) shown in figure 3 . 5 .  The prevent ive maintenance on 
th is  mach ine schedu led its lubrication frequency and when to change bearings as 
shown in Table 3 .3 ,  more PM schedu les can be found in Appendix B. 
Table 3.3: PM Schedule 
Component Frequency 
Motor Bearings Check Lubrication level weekly 
Fan Bearings Change bearings yearly 
The PM schedu les for the bearings shown in Table 3 . 3  were based on the fol lowing:  
• Plant experience 
• Manufacturer' s recommendation 
3 .4 .2 .3 Plant Experience 
Local knowledge of machine performance in the longer term, proved to be a more 
appropriate method of establ ish ing the frequency of major overhaul and other 
maintenance requirements. Before th is  experience cou ld be used to set up the 
prevent ive maintenance, accurate maintenance records were kept so that performance 
patterns and characteristics could be c learly establ i shed. Component l i fe expectancy 
and wear rates can be assessed on the basis of recorded information that represents a 
true reflection of operating conditions. Th is  information wi l l  not be detai led enough ; 
the use of a predictive maintenance technique provides the kind of detai led 
information on which maintenance records can be based. 
3 .4.2.4 Manufactures ' Recommendation 
Most equ ipment manufacturers provide deta i ls  of recommended maintenance 
requ i rements, from ba ic lubrication schedu les to major overhaul informat ion. Th is  
information was used as an in it ial basis on wh ich to determ ine preventive work, such 
as overhaul and routine replacement of components, to be carried out during annual or 
other planned shutdowns. Unt i l  p lant experience ind icates otherwise, it is good to 
fol low these recommendations in the early stages of operat ion. 
29 
I n  th is  case study, the problem was that the DE fan bearing always fai led with i n  3-4 
months and never lasted the one year predicted by PM and not in  any way near the 
bearing l i fe. The p lant maintenance team resorted to this routine without knowing the 
root cause of the premature fai lure. 
Some i nvestigators [97] state that, by perform ing PM as the equipment designer 
envisioned, the l i fe of the equipment would be extended c lose to the design, but 
would not prevent catastrophic fa i lure. The problem with the idea of using PM to 
extend the equipment l i fe has the fol lowing missing components which this thesis wi l l  
address: 
• The root cause of the fai lure 
• No val id data that quanti fies and val idate when a component be changed or 
replaced. 
One of the aims of this research was to use a vibration sensor and a data col lector 
( Pred ictive Maintenance-PDM)  to col lect va l id measured data to d iagnose faults and 
find the root cause of the fai lure, using a mathematical approach and compare the 
calculated values with the component's standard to substantiate the deviat ions from 
the designed values. This w i l l  be d iscussed in  chapter 4. 
3 .4 .3  Pred ictive Maintenance (PDM) 
The condition of a l l  machinery should be under continual survei l lance by both 
operat ing and maintenance personnel .  The casual and routine mon itoring of 
equipment a l l  yield information regard ing the operat ing condit ion on which  
maintenance requirements can be  planned. I t  i s  vital that maintenance personnel 
rea l i se the importance of being critical ly aware of the operating condition of 
mach inery and ensure that their observations are accurately reported. I nspection 
requires the use of the senses and maintenance personnel should develop an eye, ear 
and a nose, for mach ine condition. Recogn ition of normal running characteristics are 
the bas is from which deviat ions can be observed and trends in mach ine condit ion can 
be predicted. 
I n  recent years a variety of techn iques have been developed by which the operating 
condition of mach inery can be either i ntermittently or continuously mon itored. These 
techn iques w i l l  use mechatronics sensors for inspection and detect when mach inery 
deviates from normal operat ing conditions. The most important aspect of these 
30 
techn iques is the abi l ity to provide information on which maintenance requ irements 
can be based. 
Machines are regu larly monitored to determ ine the condition of the machine 
components whi le  the machine is runn ing. I t  is a more cond ition-based approach to 
maintenance, which uses a vibration technique to determ ine if the mach ine wi l l  fai l  
during some future period, and then takes a correcti ve action to avoid the 
consequences of that fai lure. By contrast preventive maintenance is based on a time 
interval .  Condit ion monitoring i nvolves the acqu isition, processing and analysis of 
sensor data related to machine parameters, such as vibrat ion. Developing problems 
can be detected and ident ified at early stages by comparing the data being col lected 
cont inuously, and appropriate dec isions can be made to fix the problem before the 
fai lure becomes a catastrophic one. 
Improvement in operation costs and safety has made pred ictive maintenance a viable 
and cost effective c hoice for the opt imum operation of modern p lants. The 
development of new sensor and computer technology has provided research 
opportunities for scientists and engineers to investigate problems in the area of 
condition mon itoring and fault d iagnosis. Condition monitoring can be off- l ine or on­
l i ne.  Off- l ine is when the data col lector is being used at scheduled intervals to mon itor 
the mach ines, whi l e  on- l ine is when the sensors are permanently fixed on the mach ine 
for continuous mon itoring. Data from both methods are processed until useful 
quantities that best describe the current health of the mach ine are extracted . The 
processed information is then compared against some known or predeterm ined normal 
quantities, and final ly, fau l t  or fa i lure indicating signals are generated . The system 
behaviour can be predicted under various fault conditions for a given set of signals 
and parameters. 
3.4.3. 1 Case Study 2: Identification of Deep Grove Bearing Defects by 
Spectra Analysis. 
Data col lection is the most important step in the evaluation of mach inery condit ion. 
Data should be col lected by plac ing the transducer in  the load zone, the drive end. I f  
th is is not done, the best signal defin ition may not be obtained. I n  order to know 
where to place the transducer, it is good to know the internal machine geometry and 
wh ich problems generate radial or thrust loads. For example, with a rad ial load, the 
best signal can be obtained in  the radial position. With an angu lar contact bearing or a 
3 1  
radial bearing in  a thrust load, the best signal definition can be obtained in the axial 
direction. Data can also be taken where the transfer function is best, for example, put 
the transducer on a bolt head, not the cover. A machine with a defective bearing can 
generate at least five frequencies that have been associated with defective bearings, 
which can be computed by using the fol lowing formulae. Equations 3 . 1 - 3 .5 are valid 
for a bearing mounted wi th outer race stationary and inner race rotating [98] .  
RPS= RPM 
60 
RPS ( Bd 
J 
FTF =-- l - - cos � 
2 Pd 
BPFI = Nb .RPS.( l + Bd cos �J 
2 Pd 
BPFO= Nb .RPS.( l - Bd COS �J 
2 PeI 
BSF= Pd .RPS. ( l - B< COS 2 qyJ 
2Bd �I 
RPM = Revolution per minute 
RPS = Revol ution per second 
FTF = Fundamental train frequency 
BPFI = Ball pass frequency of inner race 
BPFO = Ball pass frequency of the outer race 
BSF = Ball spin frequency 
Bd = Bal l or rol ler diameter 
Nb = Number of bal l s  or rol lers 
P d = Pitch diameter 
� 
= Contact angle 
The above data and definitions are needed to compute values for the frequencies. 
32 
3 . 1  
3 .2 
3 . 3 
3 .4 
3 . 5  
Rol ling element bearing fault frequencies are guaranteed as a result  of fatigue, wear, 
improper i nstal lation, improper l ubrication, and manufacturing faults i n  the bearing 
components. It is possible to use the manufacturer' s  data to find the bal l diameter, 
pitch diameter, number of rol ling elements and the angle between the surface of each 
rol l ing element and the races (called the contact angle) .  Knowing these three values, 
the four fundamental defect frequencies can be calculated accurately .  
The fol lowing equations are needed to  compute the frequencies of bearings mounted 
with the inner race stationary and outer race rotating. Equations 3 .6- 3 .9 are valid for 
the bearing mounted with i nner race stationary and outer race rotating [98] .  
FTF=-- l +�cos� RPS ( B ) 
2 �, 
BPFI = Nb .RPS.(l - Bd cos �) 
2 �, 
BPFO= Nh .RPS.( l + Bd COS �J 
2 P" 
The formula for B S F  is identical for both cases: 
P ( B  2 1 BSF=_d_ .RPS. 1-� cos 2 � 
2Bd Pd 
3 . 6  
3.7 
3 .8 
3 .9 
When the bearing fault  frequencies that appear in  the vibration spectra do not match 
the calculated frequencies, an unanticipated load in the bearing changes one of the 
parameters used in the calculation. The typical parameter that changes is the contact 
angle � [98 ] .  
3 3  
3 .4 .3 .2  J�'qllipmen I Speciticol IOns 
R I ON VA - t o  
The fo l l o\\ i n g  are the detai l s  on the d ata co l l ector used for this case st udy. 
ame of data co l l ector: Rion V A- I 0 
Analogu e 
( 'hannels. 
hansdllcer: 
R i o n  P V- 5 5  
Pi/.o crystal \\  i t h  b u i l t  i n  charge a mp l i fier. 
Signal conditioning 
Buttem o rth fi lters S l o pe - 1 8d B/oct 
H i gh pass: 3 . 1 0. 1  k H/ .. ( at - 1 0% po i nt ) 
Lo\\ pass: I k. 5 k. 1 5 1.... SOt.. H/.. ( at - 1 0% poi nt ) 
6 i n p u t  ranges: ( hal f decade step s )  
I ntegration a n d  double i n tegration. 
Rms and 0 to P eak detector . 
34  
Ampl itude demodu lation, 
Antial iasing, low pass fi lter, 51h order Chebyshev, (tied to sample rate) . 
Analogue to Digital: 
8 bit 
Dynam ic range 48 dB 
Digita l :  
Sampling: 
Window size; 256, (5 1 2  and 1 024 with zoom) 
I nternal triggering; setable level and slope, post and pretrigger. 
A verager modes; instantaneous, I inear, exponential and peak. 
W indow time weighting; Rectangle (none), Hanning, Flat top. 
FFT: Standard; 256 points to 1 00 l i nes, 
Zoom; 5 1 2  points to 200 l ines and 1 024 points to 400 l i nes. 
Other functions: 
Crest Factor, Probabi l ity density, overa l l  level, enveloped acceleration. 
Memory: 
1 00 l ine spectra; 1 80 
Overa l l  level and crest factor; 500 
Display: 
1 28 x 1 28 pixel led. 
Cursor units: 
X axis: Hz, Kcpm, Order, ms 
Y axis: G, m/s2, mm/s, i n/s, mm, m i l s, %, dB 
Interface: 
RS-232, 1 200 - 9600 baud. 
Ambient operating conditions: 
o to 40° C, 20 to 90% RH 
Dimensions: 
2 1 5  (H )  x 1 24 (W)  x 43 (D) mm 
700g 
35 
3 . 4 . 3 . 3  Measured J;;-equenc:y 
The theory o n  the four  fundamental defect frequencies was used to detect bearing 
fai l ure in  an Arrol crane. (60tons). \\ hich carries steel from a furnace to the casti ng 
machine i n  a steel manufacturing company. The crane \yas noisy before \\ e ,,·ere tol d 
to do a yi brat ion chec k. There \yas p reyious y ibrat ion data. The accelerometer \\"as 
placed on the bear ing housing or the input shaft or the primary gearbox in the rad ial 
d i rection and the read ings ,,·ere taken and anal�·sed to ident i fy the defect bearing. The 
spectra i n  figures 3 . 3  and 3 . 4  " ere generated b�· th e data co l lector. 
o <:> 
I ,  , I . 
. t li , , 1;:\I\"!;I:il'lll N,:! �l,\ l'i'�I "::I!\! ,I ,,:\Y,W; li !" !!,'�; f!. :;1,,;) :, j" r,)V 
l 
, jL  I 
t'.i 'H- t 
F i gu re 3 . 6 :  Spectrum Sho\\ ing the Beari ng Defect 
36 
2. 
0 '=' 1 .S 
1 .6 I 1\ 1 . 4 I I 
I 
I 
1 .2 
I l . I � 1 \  10.S I I I I 0.6 , , 
0.4 l ' i 0.2 
O. I , 
O. 40. SO. 1 20. 1 60. 200. 
B4-MH P-U Freq uency ( Hz) 
F i gure 3 . 7 :  Accelerat ion Amp l i tude yersus Frequency 
The spectra sho\\ n i n  figures 3 . 6  and 3 . 7  i nd icate a serious bearing problem, 
fi gure 3 . 6  has its highest freq uency peak ",i th \el ocity amp l i tude o f  1 2 mrn1s and 
the meas ured freq uenc�' \\as 4 3 . 4Hz. Fi gure 3 . G  is the em'el ope, i t  is  a good 
techn i q ue to detect bearing faul ts, and the fact that it is peaky i s  an ind icati on o f  
bearing fault  The em'elope technique enables precise d iagnosis o f  bal l beari ng 
faults .  
In order to yal i d ate the type o f  bear i ng defect . the p redicted frequency \\'as 
calculated by using the bearing's  p arameters. 
3 . 4 . 3 . 4  Predicted } ,  i-equencies 
• Frequencies associated with the \'arious bearing defects can be obtai n ed by 
us ing eq uatio ns 3 . 1 - 3 . 5 .  
• Shaft runni n g  speed = 1 0Hz 
• B,, = 34.93mm 
• Nh = 8 balls 
• Angle = GO 
3 7  
• Fundamental Train Frequency (FT F )  = 3 .9 \ H/.. usi ng eq uat ion 3 . 2  
• Bal l  pass freq uency i nner race ( B P F I ) = <i8. 73Hz using equation 3 . 3  
• Bal l pass F requenc�' of the outer race ( B PFO) = 3 1 . 2 7 Hz using eq uation 3 . 4  
• Bal l spin freq uency ( B S F )  = 2 1 . 7 H/. using equation 3 . 5 
The measured frequency \\'as 43 . 4Hz and the pred icted frequency o f  the bal l SpIn 
rrequency \\'as 2 1 . 7 Hz. The effect o f  the bal l  h i t t ing both outer and inner race \\' i l l  
result i n  a total frequency o f  ( 2 1 . 7 :-.; 2 )  4 3 . 4 H /  . .  This confi rms that t he pro blem was 
coming from the bal ls .  When the bearing \\'as dismant l ed.  the defect bal l bearing 
causi ng the h igh peak \\ as found as sho\\TI in figure 3 . 8 .  
Fi gure 3 . 8 :  The Defect Bearing 
The correcti \'e action the autho r recommended \\'as that the bearing be changed . 
This was d one and another set o f  readings \\'ere taken to see i f  the accelerat ion 
ampl i tude had d ropped. Figure 3.9 sho\\ s the ne\\ spectrum after the bearing was 
replaced. I t  has a 10\\' acceleration ampl i t ude. the noise \\'as e l iminated and the 
crane \\ orked smoothl�· . 
3 8  
10.45 
g 0.4 I 
0.35 I 0.3 
I 
/-I 
0.25 ' I  
0.2 
, ' 0. 1 5  
1 . 0. 1 
\ , , ,1 \ I \ 
0.05 � 
o. I 
o. 40. 80. 1 20. 1 60. 200. 
b4-MHP-D Frequency (Hz) 
F i gure 3 . 9 :  Ne\\ Spectrum w i t h  Lo\\· Accel erat i o n  A m p l i t u de 
P D M  is a good tech n i q ue \\"i t h  \"al i d  data to pred ict system beha\" i o u r  - its appl i c a t i o n  
a n d  p i t fal l s  o f  i t s Fast Fouri er Transform ( F FT) algori t h m  are d i sc ussed i n  c hapter 4.  
39 
CHAPTER 4 
Fast Fourier Transform Technique and Its Pitfalls 
4.1 I ntroduction 
The Fourier transform converts t ime-domain signals to the frequency domain .  Fourier 
analysis can be used to describe systems and their properties in  the frequency domain, 
by break ing down the complex signal into its components at various frequenc ies. Th is  
makes the input and output of systems easier to analyse by expressing them as a 
function of frequency domain instead of time. 
In this chapter, a system response to i nputs of d ifferent frequenc ies is presented. The 
signals are complex and comprise of real and imaginary components. In the frequency 
domain, the Fourier transform is mathematica l ly represented as complex numbers. 
D ifferent case studies are presented here; using the FFT technique to ident ify various 
mach ine fau lts. A number of case studies are presented to i nvestigate where the FFT 
technique could not be used to ident ify the root cause of fai l ures: A mathematical 
mode l l ing approach was used, together with the FFT data, to find the root cause. 
It w i l l  be seen that the forc ing frequencies and the resonance effect can overlap in  an 
FFT making d iagnosis d ifficu lt. Conversely, the cepstrum techn ique using a 
homomorphic fi l ter w i l l  be shown ( in the next chapter) to separate these two effects 
making d iagnosis  much easier. 
4.2 Complex Numbers 
A complex number consists of both real and imaginary components. The Fourier 
analysis a lgorithm converts the time domain to frequency domain, which is the 
representation of frequency components. In order to have in-depth understanding of 
the functions avai lable in  FFT spectrum analysers, complex numbers are presented. 
The poss ib i l ity to find the square root of minus one is the reason why complex 
n umber is  adopted. Mathematic ians solve this problem by giving a value of i to be the 
square root of m inus one, the electrical engineers use this as a symbol of current, 
hence the use ofj as a symbol for the square root of m inus one. I n  this thesis, the 
40 
notat ionj of the electrical engineers w i l l  be used. F igure 4 . 1 shows a complex number 
plotted on the real and imaginary plane, assuming a complex number b + cj . 
Where 
Imaginary 
b + cj 
c 
Ma!7n i t l lcle: 
phase 
h 
F igure 4. 1 :  Real and Imaginary Plane of a Complex Number 
(Magnilude/ = (real component/ + (imaginary component/ 
Phase = tan-I imaginary component/real component 
Complex number (n) = b + cj 
n = complex number 
b = real number 
cj = imaginary number 
R e:::! 1  
4 . 1 
The multipl ication of c and j w i l l  result to a rotation of it by Ti/2 radian. The number j 
describes the square root of negative real numbers, hence 
. ?  1 I = -
The other way to represent a complex number is in form of its magnitude and phase. 
Fourier analysis can be explai ned by using the Fourier series of a period ic function 
a fter the appl ication of the complex number. 
I f  x (I) i s  a periodic function, therefore. 
x (I) = x (I + nT) 4.2 
4 1  
Where 
T = periodic time 
n = any integer 
The continuous-time Fourier transform is shown in equation 4.3. 
X(i) = [, x(t)e-2J' i l 4.3 
The period ic T ---t 00, while the spac ing I iT between harmonics approaches zero and 
X ( t) becomes a continuous function of f and equation 4.4 becomes the continuous­
t ime Fourier transform. 
X(ik ) =+ t x(t )e- J 2n/kl dl 4.4
 
, 
Where 
fi = kji 
kth = harmonic of ji 
I IT to be kji, k i s  zero and negative integers, however, the kth component is obtai ned 
from the i ntegral .  
Mu lti plying the signa l by e-J2JlfxI w i l l  cause a l l  the components at other frequencies to 
rotate and eventua l ly  integrate to zero over the periodic time. 
S ince complex numbers can be plotted on the real -imaginary plane, it i s  evident that 
the spectrum analyzer w i l l  handle the complex numbers the same way as vector 
mechan ics, ca lcu lating both magnitude and phase. 
4.3 Theory of FFT Analyser 
The FFT analyser is the most commonly used piece signal analysis equipment in the 
v ibrat ion field.  Spectrum Analysis defined as the transformation of a signal from a 
t ime-domain representation to frequency has its roots in the early 1 91h century [99] ,  I t  
took a practical man, an  engineer with a good mathemat ical background to develop 
the rationale upon which almost all our modern spectrum analysis techniques are 
based. That engineer was Jean Bapt iste Fourier, work ing for Napoleon during h i s  
invasion of  Egypt on  a problem of  overheat ing cannons when he  derived the famous 
Fourier series for the so lution of heat conduction. It may seem a far cry from 
42 
overheating cannons to frequency analysis, but it turns out that the same equations 
apply to both cases [ 1 00]. 
Fourier later gencra l ized the Fourier series into the Fourier I ntegral Transform . 
The advent of digital signal analysis natura l ly led to the so-cal led Discrete Fourier 
Transform and the Fast Fourier Transform (FFT). The FFT is simply an algorithm for 
calculating the DFT i n  a fast and effi cient manner. 
Cooley and Tukey d iscovered FFT in 1 967, but it ex isted much earl ier. The FFT 
algorithm places certain l im itations on the signal and the result ing spectrum.  For 
instance, the sampled s ignal to be transformed must consist of a number of samples 
equal to a power of two [ 1 0  I ] . 
Most FFT analyzers al low 5 1 2, 1 024, 2048 or 4096 samples to be transformed. The 
frequency range covered by FFT analysis depends on the number of samples col lected 
and on the sampl ing rate. 
Spectrum analyser is a powerfu l  device that is able to do a proper v ibration d iagnosis 
on mach inery .  The condition of the machine and its mechanical problems are 
determ ined by measuring its v ibration characteristics, which are frequency, 
displacement, velocity, acceleration and phase. 
The v ibrat ion ampl i tude is the measure of the severity of the trouble in the mach ine 
and the frequency components indicate the type of faults. 
Case studies are presented on few of the common v ibration problems in machinery, 
which are: 
• Bearing defects 
• Imbalance of rotating parts 
• Worn or damaged gears 
The characteristics of the Entek FFT spectrum analyser the author used I n  th is  
research, are shown in table 4. I 
Table 4. I : Entek Spectrum Analyzer Characteristics 
Resolution 400 l ines 
Frequency range 1 0kHz 
Dynam ic range 96dB 
Number of channels 2 
43 
4.4 Case Study 3:  Bearing Failure Due to Shaft Deflection 
The data presented in  the figures 4.2 and 4.3 was acquired by the author on the drive 
end of the fan beari ng housing of the multi hearth furnace (MHF) F lakt fan, which 
suppl ies draught to F lakt venturi scrubbers in  the i ron p lant of a steel manufacturing 
company in  New Zealand. 
There are four multi-hearth furnace (MHF) Flakt fans and each one is  powered by an 
in l i ne, d i rect drive 1 .3mW electric drive. They were insta l led on site in  late 1 989 and 
modifications to the bearing pedestals were undertaken in late 1 996/early 1 997, which 
i nc luded tria l l ing of d ifferent bearing types in  an attempt to ach ieve an acceptable 
bearing l i fe. The shaft has a simply supported boundary condition with a d iameter of 
1 50mm. The fan impel ler has not been fitted w ith anti-thrust vanes, however, c ircular 
sti ffening rings have been fitted to prevent flutter of the back p late and front sheet and 
these preclude the fitting of anti-thrust vanes. Both the shaft and fan impel ler are 
made from Sandvik SAF 2205 stain less stee l .  The fan bearing at the drive end suffers 
premature fai lures. The fol lowing investigations had become necessary to evaluate the 
root cause of such fai lures and a corrective action was recommended. I nvestigations 
were carried out to validate whether the premature bearing fai lure was due to 
excessive shaft flexing or whirl ing producing large angular misa l ignment at the 
bearing journal . 
I n  th is investigation, h istorical and new data were used to evaluate the shaft and 
impe l ler deflections, critical speed, loading on the bearing and lubrication system . The 
pred icted values and the manufacturer' s standard values (SKF & NSK) for the bearing 
[ 1 03, 1 04, 1 05 ]  were compared, and recommendations were given, considering the 
system operating cond itions, natural frequency, critical speed and deflect ion . 
4.4. 1 Natural Frequency & Crit ical Speed 
Rotating shafts become dynamically unstable at certain speeds, and large vibrations 
are l i ke ly to develop. The speed at wh ich this phenomenon occurs is the critical speed. 
V ibration difficulties frequently arise at the lowest or fundamental critical speed. 
Equations 4 . 1 3  and 4 . 1 4  for a simply supported shaft boundary cond ition were used to 
calculate the speed [ 1 06] . 
44 
Where: 
f= N atural freq uency ( H i':) 
2�.9�41 
ft" , 
IInkf h 
I'u� luu .. u 
g = Acceleration due to gray ity ( m/s2 ) 
6 =  DeOect ion ( m )  
Ne = Crit ical speed ( rp m )  
1 
. -
"�:i11 fa .. . 
fllI(� 11 1 
LJlfc.·t.-bun:Hoft�I.I'lul 
41 t ]  
.' L)ll 1 -4 1\" 
_ _  Y 1�9tl.81 
4. 1 3  
4. 1 4  
'''g 
1. ! I � 
1 0  
.... " --- - --- - -------j 
Figtn'e 4.2: Fan Bealing Housing at Olive End, HOl'izontal Di r'ection. 
45 
l! 
OJC 
) 
... , 
t 
f 
.0 
- Ig pe  
J " 
cO 1� 
l n 
24 8438 milT -- Y 03493=23'--__ _ ___ _ ___ �-_____ -
,I. k:t te 
I tYsitloll:Ul 
n .... kt fnns 
BRG ]A 
Uircl-hun:Axlal 
Figu l'e 4.3: Fan 8eadng Housing at Ol'ive End, Axial Oi l·ection. 
The shape o f  the spectrum in F igure 4.2 is a system response at I S H /., 3 S H /.  and 7 S H /.  
respecti \·el y: h o \\ e\'er. the 7 S H /.  coincides \\' i t h  3:\ runn i n g  speed harm o n i c .  F i gure 
4. 3 is i n  the a:\ia l  d i rect i o n, \\·h i l e  F i g u re 4.2 is in the hori/.Ontal di rec t i o n .  The 
i n d icat i o n is that the fan is runni n g  bel\\ een the first and second criti cal speeds. 
4.4 .2  W h i r l i n g  of Shaft & C r i t i cal S p eed 
Cri t ical speed of shafts may be fo und by any of the means fo r cal culat i ng the natu ral 
frequenc i es \\ ith eq uati ons 4. 1 3  & 4. 1 4  I I OCi I .  Whi rl i ng. i . e . \ i o l ent \'i b rat i o n  at 
cri t ical speeds occurs i n  \ ert i cal as \\ el l as hori/.Ontal sh afts. I n  non-\' ert i cal shaft l i ke 
the one in this case study. grav ity effects may i nt roduce addi t ional c ri t i cal speeds o f  
second order. 
4 . 4 . 3  Deflec t i o n  & S t i ffness 
A shaft may be designed and sti l l  be unsat i s factory because it l acks rigi dity. 
I ns u ffi c i ent ri g i d i t y. or sti ffness. can res u l t  i n  poor performance o f  \'ari ous shaft­
mounted e l ements s uch as bearing. W hen a shaft is t u rn i ng. eccentr i c i ty causes a 
cen t r i fugal force defl ect i o n  \\·h i c h  is res i s ted by the shaft · s  fle:\ural rig i d i ty (n) .  As 
l ong as defl ecti ons are smal l .  no harm is done. 
I n  th is case study, the deflection due to both impe l ler and shaft was used to evaluate 
the critical ity between the bearing's axial and radial loads ratio, using equations 4. 1 5  
& 4 . 1 6  for a shaft w ith a simply supported boundary condition [ 1 06, 1 07, 1 08 ]  
5W,4 6max .shaft = 384£1 
6max impeller=2���1 (a + 2b)�3a(a + 2b) 
Where: 
8 = Deflection 
W= Load (kN) 
I = Length (m)  
E = Young's modulus of elastic ity (Gpa) 
1 =  Moment of inertia (m-4) 
a = Distance from impel ler to reaction 'A '  
b = Distance from impel ler to react ion ' B '  
4.4.4 Perm issible Angular M isal ignment 
4. 1 5  
when a Lb. 
4 . 1 6  
The deflection of the impel ler was used to evaluate the bearing angular m isal ignment. 
The predicted values were compared w ith the manufacturers' catalogues to obta in  a 
va l id  Fa/Fr ratio. 
4.4.5 Results 
The shaft has a bearing simply supported boundary condition and a concentrated load 
( impe l ler) of 900kg. 
47 
360mm 1 940 mm 
r-
r 
900kg 
Figure 4.4 :  Concentrated Load ( lmpel ler) on a Simply Supported Shaft 
Applying c lockwise moment = antic lockwise moment; RB = 2 .93kN 
Applying upward force = downward force; 
RA = 9kN 
Impel ler Venturi Eye Diameter = 1 . 358m 
Area of Impe l ler = nr2 = 1 .4484m2 
Assume 1 00 m i l l ibar is  the gauge pressure on one side: 
Axial Thrust Force ( F) = P x A = 1 4.47kN 
Deflection 
Shaft diameter = 1 50mm 
Moment of inertia ( I )  
4 / = � 
4 
I = 24.85 x 1 0-6mm 
Maximum deflection due to weight of shaft (olllaj, using equation 4. /5. 
4 8 - 5wl 
max 
- 384£1 
= 0.099mm 
Maximum deflection due to impeller (o,nax) 
48 
1 38kg/m 
= 1 .37kN/m 
(bmax) = 2�a;/ (a+ 2b )�3a ( a+2b)  whena Lb. 
= 0 . 1 8 1 mm 
Total deflection = O.28mm 
Permissible Angular misalignment (PAM) 
Bearing 
Deflection due to impe l ler 
11l()mm 
........... .. . . · 8  
....... ............ .. .... ...... ...... .. .. ...... .. .............. ....... . 
0. 1 8 1 mm 
Figure 4.5 : Effect of Shaft Deflection on Bearing 
From Figure 4, 8 = 0.029° 
PAM from manufacturer's catalogue = 2° (The bearing is  SKF 22228 CCK W33 C3, 
tapered bore spherical ro l ler bearing) [ 1 04] 
Effect of Axial Load on Bearing 
Radial  load from impel ler = 1 4.7kN @ 0.029° 
1 4 . 7cos8 
r
·8 
-..... . . . . . . . j. . . .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  . 1 4 .7kN 1 4 .7sin8 
Figure 4.6 :  Effect of Misa l ignment Angle on Bearing 
Axial  load ( Fa) from figure 4.4 = 1 4.7kN 
Radial load ( Fr) = 9.0 I kN 
Critical Speed 
From equations I & 2, crit ical speed (Ne) = 1 785rpm. 
Assuming 60% increase on shaft rotat ional speed : 
49 
Rotational  speed = 1 480rpm 
Considering 60% increase, Ne = 2368rpm 
Deflection due to the 60% increase, using equations 4. 1 3  & 4. 1 4. 
8 = 0. 1 6mm 
Deflection 
Shaft d iameter = 1 50mm 
Moment of i nertia ( \)  = 
nr4 
4 
\ = 24.85 x 1 0·6mm 
Maximum deflection due to we ight of shaft (8max), using equat ion 4. 1 5  [ 1 09] .  
4 
8 - 5wl max 384£1 
= 0.099mm 
Maximum deflection due to impel ler (8max), using equation 4 . 1 6  [ 1 1 0] .  
(8max) = 2�a:l (a+2b )�3a ( a + 2b) whenaL.b. 
= 0. 1 8 I mm 
Total deflection = 0.28mm 
4. 4. 5. 1 Minimum Shafi Diameter 
Assumption 
60% increase over the shaft rotational speed, using equation 4 to find deflection due 
to impe l ler 
(s:: ) \ 1 1  = wab(a+2b)�3a(a+2b) Umax mpe er 27 E 1 1  
4wab(a+2b)�3a(a+ 2b) 
27 £ J[ r 4 l 
4. 1 7  
50 
wab (a+ 2b) �3a(a+ 2b) 
2 1 .2 £  r 4 , 
wab ( a + 2b)  �3a( a + 2b)  
48.8 £ r4 
4. 1 8  
4. 1 9  
Total deflection = Maximum deflection due to shaft + I m pel ler 
OTotal = 
wl 4 wab (a + 2b) �3a(a + 2b) 
--�--+--------�------
60.3 £ r 4 48.8 E r 4 
0. 00016 = 
w = pv 
7850 7r r 2 1 4 9 . 8 1 wab (a+2b) �3a( a + 2b)  
4 + 4 60.3 E r  48.8 E r  
0.000 1 6r4 = 5 . 6 1 4  x 1 0-\2 + 5 . 73 X 1 0-9 
( 1 3 ) 
r = 0.0894m, hence shaft m in i m um d iameter = 1 78 .8mm. 
Therefore the shaft m i n imum d iameter is 1 80mm 
Table 4.2: Shaft Conditions 
Shaft Parameter Present Condition 
Critical speed 1 20% of ru nning speed 
S haft diameter 1 5 0mm 
M axi mum shaft deflection 0.099mm 
M aximum impe l ler 0. 1 8 1 m m 
deflection 
4.20 
4.2 1 
4.22 
Recommended 
Condition 
1 60% of run n i ng speed 
1 80mm 
0.07mm 
0.09mm 
I n  order to val idate the value of the maximum deflect ion obtained, it was used to 
calculate the bearing perm issible angu lar m i sal ignment and then com pared with the 
angle specified by the manufacturers. The predicted angle was 0 .029°, the perm issible 
angu lar m isal ignment indicated by the man u facturer was 2° (SKF catalogue), hence 
the deflection was not the issue at this stage. 
5 1  
Axial & rad ial load rat io for the bearing in quest ion is governed by the man u facturer's 
standard (SKF & NSK ), FalFr = 0.25 [ 1 03,  1 04] .  
The axia l  load on the bearing was incl ined at  a smal l  angle, which was insignificant to 
its horizontal and vertical components as shown under resu lts. 
The Fa/Fr = e. The ratio obtained was 1 .63 wh ich was h igher than the 0 . 2 5  value 
recommended by the m anufacturers. 
The critical speed was 1 78 5 rpm, wh ich was only h igher by 20% of shaft ru nning 
speed. 50% or more is a recom mended value for a critica l  speed to avoid resonance 
effect. 
The predicted FalFr ratio is 1 .63, whi le  the required value shou ld be 0.25,  this would 
req u i re the bearing to be greased more often, otherwise the cage wear is  l i kely to 
become a great concern as a result of the high ratio of 1 .63.  
The critical speed should be at  least 50% more than the shaft runn ing speed . The 
deflection has a signi ficant infl uence on the critical speed. The critical speed was 
increased to 60% of the shaft runn ing speed, the total deflection of the shaft and 
i m pe l ler was calcu lated as 0.07mm + 0. 09mm = 0. 1 6mm. Therefore the m i n i m u m  
shaft d iameter of 1 80mm is recommended t o  reduce the total deflection from 0 . 2 8 m m  
t o  0. 1 6m m  and increase t h e  l i fe span of the bearing. 
4.5 Case Study 4: Fan Imbalance 
Machi nery I m balance is one of the most common causes of v i bration. M ass 
I mbalance in a rotating mac hine often produces excessi ve synch ronous forces that 
reduce the l i fe span of various mechanical elements. Unbalance is caused by an 
asymmetry in the rotating element that results in an offset between the shaft centre l ine 
and centre of mass. I t  represents the most common type of synchronous excitation on 
rotating mac h i nery. U nbalance results from the fact that the centre of gravity of a 
rotating member does not coincide with the centre of rotation, which causes a 
centrifugal force pointing radial ly out from the centre of rotat ion and rotating at a 
speed equal to the speed of the rotating member itse lf. The equation that governs the 
ampl i tude of the unbalance force is as fol lows: 
4.23 
52 
Wh ere 
F = Force (N )  
M = M ass ( kg) 
w = Angular ve l o c i ty ( rad/sec ) 
r = radi u s  ( m )  
The case study i s  about a dedust fan i n  an i ron plant. I t  runs at a speed o f  1 45 0 rpm 
and the i m p e l l er has ei ght b l ades. The ana l y s i s  of the \ ' i b ration data sho \\'ed a h i gh 
\ el o c i t y  amp l i t u d e  of 1 1 . 8 mmls at I x fan speed. \\h i c h  \-vas an i nd i cat ion o f  
i m balance. 
It � l , · ·· · · · 1 · · ·· . .. . . . . . . ... . , . . . . . . . . .... ..... . . . . . . . . . . ..... . . ..  . • 
' . ,;II\llJt,\,J��\;dt� \v,�.,�'I� Jf{lj · ' 
· . · . · . · . 
Figure -l. 7 :  I m balance S p ectru m wi th H i gh A m p l itude at I xFan S p eed 
The am p l i t ude is propo rt i o nal to the amount o f  i m balance, wh i c h  \\ as larger i n  the 
rad ial d i rect ions o f  measurement of I 1 . 8 m mls \'el ocit y amp l i t ude as sho\\TI in figure 
4. 7 .  The figure \\ as obtained by usi ng an Entak Enpac 2500 data co l l ector. 
A seri o us unb alance l i ke the one i n  t h i s  case st udy could destroy the fan or any o f  i t s  
co mponents l i ke t h e  bearings. Se\ 'ere un balance cou ld tear t h e  machi ne fro m  its 
fo undat i o n ;  therefore correcti ve act ion \\'as taken by b al an c i n g the fan. The fan ,,'as 
balanced by using the tvv o-channel Enpac 2500 spectrum analyser \\ i th a balanc i ng 
program. A reference and trigger point \\ as l o cated on the sh aft by s t i c k i ng on a sm al l 
p i ece of tape. The laser l ight centred on the shaft triggered the analyser each t i me the 
5 3  
reference point on the shaft crossed the laser l ight .  The mach ine \\ as run fo r about one 
minute and \\'as stopped \\"hen the phase angle \\'as seen to be stabl e. The phase angle 
is relat i ye to the arb itrari ly selected trigger posi t i on on the shaft used to trigger the 
anah-ser. 
A trial mass of 22g \\"as p laced on the impel l er at /.ero degree \\" i th reference to the 
trigger po int on the shaft and the fan \Vas run second t ime for one m i nute. The d ata 
collector d isp laced the actual mass that \\ ould reduce the i mbalance ampl itude and the 
phase angle. When a machine \yas out o f  balance. a si nusoi d al t ime \\'a\ eform \\'i th a 
freq uency o f  the running speed and a large peak \\ ould be seen i n  the spectrum at the 
I x running speed . A fter the b al anc i ng. more \ ib rati on data was col l ected : the 
spectrum sho\\ ed the imbalance ampl i tude reduced to 1 . 2 mmls from 1 1 . 8 mm/s as 
sho\\ n in figure 4 . 8 .  
· . · . 
I
! ! : : · . 
· . .  · ·.1 . . . . . I� . . . . � . .  ·j-� . . . .  · . . . . · ,  '.··· · ·F . . l .  . .. · · · · · · ·  . . . . . . . .. . . . . . . .. .. . . . . . . . . .  , . . . .. .. .. . . . . . . .. . . . . . .. .... . . . . . . . . . . . . . . . . . . .  . 01 l - � , : P _ I : ·�,;i, ; ;i . -�1' ;;J I · · · ·� ·ti · · · ·i . . . .  ·� . . ..  l ·"tT ·· . . . . . . . . . . .  · · · ·  . ...  �F :· .. [� · .. · . . . .  · .. ·,· ; l ... . ... . . . . . . . . . . . . . . . . .  - . . .. . . .  . ,r" , I I � .\f.. y.' ''\\�i'\,i,!�,l��'+�I:l �)(jl\t��\.v'�d .. t . . . . . . . . . . . . . .. .. . . 
I j .. . . . . . . . . .. .. . . . . . .  < . . . .. . . . . . . . . . . . . .  • . . . . . .  1 . . . ... . .  ,· . . . .  · · · · · ·, . . . .  · · ·  . . . .  · ·  . . . . ....  ·, . .  · ·  . .  t · · · · ·  . . . . . .  · · · ·l. · · · · . .  · ·  . . . . . .  · · ·  . . . .  · · ·  . . . . ..  · ·  - . . ., ' I ' . . . '"5 : : · . · . · . : : 
Figure 4 . 8 :  S pectrum after Balancing of Fan 
54 
4.6 Case Study 5:  Root Cause Analysis Technique to identify gearbox Failure 
During the M arch shutdown in the iron-sand mine site, the raw sand gearbox was 
removed, sent to the central workshop, overhauled and returned to service on the 9th 
March. On the 1 8th of March, a noise was reported from the gearbox and there was 
oil  leaking from the output shaft. The vibration data col lector was used to collect data 
on the gearbox and later analyzed; the diagnosis indicated a strong possibil ity of 
broken teeth. On the 29th March, during a down day, the l id was l ifted for an 
inspection and broken bevel wheel teeth were discovered as shown in figure 4.9 .  
Investigations were conducted to ascertain the root cause of the bevel gear broken 
teeth. 
Firstly, the gearbox vibration level was investigated, using a Fast Fourier Transform 
(FFT) data collector. Secondly, the predicted values obtained for contact and bending 
stresses were compared with the American Gear M anufacturers Associ ation Standards 
(AGMA) and the manufacturer's data to validate the root cause fai lure of the gearbox 
tooth mesh [ I l l ] . 
The design, manufacturing and tooth mesh parameters were investigated to ascertain 
the root cause of the gearbox broken teeth. 
-
Figure 4.9:  Gear with the broken teeth 
After the vibration data was col lected and analysed the spectrum in figure 4 .9  was 
obtained. Gears generate a mesh frequency equal to the number of teeth on the gear 
multipl ied by the rotational speed of the shaft driving it. A high vibration level at the 
mesh frequency is typically caused by tooth error due to wear of the meshing 
surfaces, improper backlash or any other problem that would cause the profi les of 
meshing teeth to deviate from their ideal geometry. 
Gears generate a large number of possible sidebands about the mesh frequency as 
shown in figure 4. 1 0, which is a pitfall  of fast Fourier transform. 
5 5  
Figure 4. 1 1  i s  the em'elope: this ind i cates that there i s  no bearing problem. due to the 
low acceleration ampl i tud e  leyel i n  the figure. 
rnt"';c r/� .0 
, "  . . . . . . . .  -. . . . . . . .• - . . . . . . . . . . . . .. .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. [ 
I 
'( I 1 ' \ J 1 1  ' U I 1 1  / , i, ' I. I I } I, , ) I ' , t , j l � 1 1 1  Hlt! '\'}rl d l l , 1 \  \ ( �/ 1 1  ,�Ij I '  1 \1 1: 1 \ ,  ( :, � i lf 'I · ,1� 1 . \j Ulf . " " ' l fll' r 1 1 1 j , 1 '  " I ' I "  \ ' 1 " . "  
III - - - - - - - . - ._ - - -. . . .  - - ._.--...  - -- - · · · - - - · · -f --·l."r'., .. · � -- · ·----· .t _ _  . ..  ,- - -- - -- - - - - . . .  _--.  -. -- - - . - - -. .  - . - . _ - - - _ . - - . _ . - - - - . - . . . .  - . . . .  
001 . . . . . . .. . . .. . . . . . . .. . .. . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .. . . . . . . . . . . . .. 
0Cll1 
. .  ,s '  
WNH 
' " 
wnh vih mefer J 
Pn51tfon:tJlI 
Will, vi" IIU:lI:f 
vel !.IJIJ !'l(H"ctrum 
IJlrectlon:None 
" ,  
Speed:n. 
7�/ll]/i'IIII!1 9:!J4 AM 
1 "nr,, ) ' / . J 1  5 "'� 
l' H I '  IJ; 
OJ 
Fi gure 4 .  J 0 :  Gearbox Spectrum 
hill 
" 
ill I 
! I 
\ r, . .  _ _  . . .  _ . .  _. _ _ _  . _ _ _ _  . _ .  _ ___ . _  . _  . . . . .  _ _  . . ' • . . .  _ _ _ . _ _ _ _ _ _ . .  _ _ _  . . .  _ . . ..  _. · . . . . . .  · . .  · . .. . i 
L, 
WNH 
wnh vih meter 3 
Position:OO 
I 
," l �� I '} I 
wnh vlb meter 
envelope 500 
Direction:None 
Sllccd:O. 
29111312005 9:5� AM 
F i gu re 4. I I :  The Em'elope 
56 
1 
I 
I 
I 
j 
Table 4.3 shows the i n formation on the gearbox. 
Table 4.3 :  Design and Manufacturing Considerations 
Parameters 
Gear ratio 
Material 
Mounting 
N u m ber of teeth 
Facew idth 
Su rface hardness 
Heat treatment 
Motor speed = 1 480 rpm 
Motor Power = 250kw 
Pinion Torque 
where: 
p = power ( kw) 
Pinion 
I I  
n, = pinion speed ( rpm) 
T, = 1 6 1 3 Nm 
Contact Stress (aH) 
where: 
ZE = elastic coeffic ient (N/mm2) 
9550p 
nl 
Both 
3 . 5454: I 
Steel grade 2 
Stradd led 
80 
58+4 H RC 
Gas carburised 
T, = operating pin ion torque (N m) = 1 6 1 3N/m 
KA = overload factor = 1 .0 
K\" = dynam ic factor = 1 .0 
57  
Gear 
39 
4.24 
4.25 
where: 
KHfJ = load distribution factor = 1 .0 
Zx = size factor = 1 .0 
Zxc = crown ing factor = 1 . 5 
b = facewidth ( m m )  = 80mm 
de' = pin ion outer pitch diameter ( m m )  = 95mm 
Z, = pitt ing resistance geometry factor = 0. 1 2  
v = Poisson 's  ratio = 0.3 
E = Young' s modulus of e lastic ity = 200,000N/mm2 
Therefore: 
CTH = 1 3 83N/mm2 
= 4 x 1 08 cycles = 3 I years 
Permissible Contact Stress (CTHp) 
where:  
CTHlim = al lowable contact stress number (N/mm2) = I 5 5 0N/m m 2  
ZNT = stress cyc le factor 
Zw = hardness rat io = 1 .0 
SH = contact safety factor = 1 .0 
Ko = tem perature factor = 1 .0 
Zz = re l iabi l ity factor = 1 .0 
5 8  
4.26 
4.27 
ZN7' = 3 .4822nL-0 0602 
= 3.4822 x (4x I 08yO 0602 
= 1 . 1  
Therefore: 
(Jl-lp = 1 706N/mm2 
Bending Stress (ar) 
where: 
TI = 1 6 1 3Nm 
KA = 1 .0 
K., = 1 .0 
Mel = outer module = 1 0  
Yx =size factor 
Kf-Ip = 1 .0 
b = 80mm 
del = 95mm 
Yx = 0.4867 + 0.08399mel 
= 0.57 
where: 
reo = cutter rad ius 
4.28 
4.29 
59 
Rill = mean cone d iameter 
where: 
Pili = mean spiral angle 
Hence: 
Therefore: 
OJ = 1 1 5 .2N/mm2 
Permissible Bending Stress (OFP) 
O'FIiIll = 240N/mm2 
= 0.89 
SF = 1 .0 
Ko = 1 .0 
y� = 1 .0 
Therefore: 
O'FP = 2 1 3 .6N/mm2 
4 .30 
4 .3 1 
60 
Since the main objective was to i nvestigate the transmission error due to broken teeth 
of the beve l gear, the fol lowing could be of great influence; design, manufacturing 
and mcsh ing problems. The design and manufacturing problems were investigatcd by 
analytical ly comparing the manufacturer's data with the American Gear 
Manufacturers Assoc iation (AGMA) standard, and then the gearbox l i fe was 
estimated to be 3 1  years from the pitting resistance of the pin ion shown under equation 
4.26. Since the perm issible contact and bend ing stresses were more than the actual 
contact and bend ing stresses, the design and manufacturing problems could be ru led 
out. The only option left was the transmission problem due to tooth mesh . Good tooth 
mesh wou ld reduce the dynamic factor Kv, whi le  a bad mesh would increase it and 
could lead to tooth breakage. The dynamic factor makes a l lowance for the effects of 
gear tooth q ual i ty as re lated to speed and load, hence h igh tooth mesh accuracy 
requires a lower Kv. Having used the above methodologies to val idate the design, 
manufacturing and tooth mesh parameters, however, the most l i kely cause of the 
broken gear tooth was a mesh problem. 
Trained and experienced fitters shou ld carry out the assembly of gear and pin ion to 
avoid m ishand l ing problems, and all documentation be properly kept for future 
record. On instal lation and run up, condition monitoring checks shou ld be carried out 
to establ ish a vibrat ion signature and qual ity control maintenance work . 
The spectrum could be analysed to detect gear broken teeth, but wou ld not tel l  you the 
root cause of the problem . The mathemat ical approach was used with the vibration 
data to find the root cause of the problem. The theory of the cepstrum techn ique to 
d iagnose gearbox problems is presented in the next chapter. 
6 1  
Chapter 5 
The Theory of Cepstrum Technique to Separate Gear mesh and 
Transmission Path Effects 
5. 1 I ntroduction 
The v ibrat ion produced by mating gears contains physical i nformation pertaining to 
the operating condition of the gear teeth. The major sources of v ibration i n  a gearbox 
are the rotating components related to the input and output shafts, which are gears, 
shafts and bearings. 
There are three major forc ing frequencies involved in a gearbox, which are the input 
spced, gearmesh and output speed. Tooth error is developed when the meshing teeth 
deviates from their  ideal geometry. The fol lowing could cause tooth error; poor 
machin ing, wear and improper back lash. Resonance effect from the gear casings can 
increase the gearmesh frequency and the sidebands energy would become large due to 
gear tooth error. The FFT technique wi l l  not te l l  you if changes are com ing from the 
source (meshing frequency) or the transmission path (structure resonance), instead 
this techn ique wi l l  overlap both frequencies on a particu lar order. Cepstrum techn ique 
and homomorphic deconvolution are discussed in this chapter as a solution to this 
short com ing. Techniques in  the l iterature review for machine d iagnosis l ike art ificial 
neura l  network, adaptive noise cancel lation, order track ing, synchronous averaging 
and cepstrum analysis [63 - 93] did not address this problem. 
This chapter presents a new technique for separating forc ing frequency and 
transm ission path effect which employs two signal processing tools; homomorph ic 
deconvolution and cepstrum to diagnose gearbox t�lUlt and overcome the overlapping 
and sidebands problems in the current FFT technique. 
62 
5.2 Gearbox Vibration 
The mesh frequency generated by gears i s  eq ual to the number of teeth on the gear 
multi p l i ed by the rotational speed o f  the shaft. S i d ebands o f  the mesh freq uency are 
due to a mod ulating rotat ional motion from a fai lure of mating teeth to i mpact one 
another at the proper ti me. 
V i brat ion anal�·sts are concerned to d i fferent iate bet\\ een h igh \·i bration amplit udes at 
mesh freq uencies. h igh energy content in the s ideband and the resonance effect fro m  
the structure. 
Goldman 1 6 1 1 presents i n  h is  book on V i b ration Spectrum Analysis that a high 
amplitude leyel at the mesh freq uency can i n d i cate an i nterference fit bet\\"een mat i ng 
gears. but a l arge number of h igh \ e\ el s idebands can i nd i cate non parallel shaft due to 
excess i \  e shaft defl ection. gear tooth crack o r  spal l .  He claims that it is rare for gear 
tooth y i bration to be high \\"i thout a resonance effect. \\·hich causes the y i brat ion 
intens i l�' 10 become large. 
No work has been done to separate the oyerl ap ping resonance effect from the mesh ing 
frequency� Gold man onl�' presents the effect of resonance on mesh frequency, but not 
ho\\ to separate i t  from the sou rce. 
Resonance Effect 
11111 - - - - _ _  • •  _ �  _ _ _ _ _ _  . __ . _ _ _ _  \ - - - - - - - - . - - . _ . - - 0 - t o .  - . - - - - - - ---- • .  _ • • • • - . . • .  - - - - - - . - - -- -- _ . - - - _ .  - - - - - - - - - - - - - - - - . - - . _ .  - - "  
r;lF, I� 
WNI! 
n 
Hz 
wnh vih mc1eT :i 
Puo;itiun:OO 
wnh vib mtttr 
vel ,le Bflcr:hum 
Oiret:liulI:Noflt:' 
4ffi rm 
Sllcr:d:lI. 
19/03/Z005 9:54 AM 
Fill 
Fi gure 5 . 1 :  Gearbox Spectrum from the Case St udy 
63 
Some mach ines, such as gearboxes, produce very compl icated spectrum signatures 
l i ke the spectrum shown in figure 5 . 1 ,  which was col lected on a gearbox handl i ng raw 
iron sand in the m ine site of a steel manufacturing company. The spacing of the 
sidebands around gearmesh frequencies is usual ly equal to one t imes the running 
speed of the shaft. The diagnosis of the gearbox is presented in  chapter 4 by using the 
FFT technique, but the l im itations are the overlapping of sidebands, mesh ing 
frequency and resonance effect, wh ich is where the cepstrum and homomorphic 
deconvolution fi ltering techniques offer a way to simpl ifY the analysis of  these 
signals. 
5.3 Transmission Path 
The v ibrat ion signal of a gearbox is normal ly measured at a convenient position on 
the outside of the gearbox casing by using an accelerometer, wh ich  converts a 
mechanical vibrat ion signals into an electrical signal .  There is corruption of the 
v ibration signal from the source to the measurement point; this is the transm ission 
path effect. The transmission path consists of the structure providing a mechanical 
path from the vibrat ion source to the measurement point. This incl udes the shafts, 
bearings, gears and the gearbox static structure, which are between the source and the 
transducer and modifies the ampl i tude and phase of the vibration signal .  
The periodic variations due to changes in  the number of the meshing teeth, the motion 
of ro l l i ng e lements in  a bearing, as wel l as non periodic variations l i ke flexure of the 
gearbox casing and operating temperature are factors which can cause changes in the 
transm ission path [ 1 1 7] .  In addition, structural damage l i ke cracks in the gearbox 
casi ng w i l l  also change the transm ission path effects. 
5.4 Transmission Error (TE) 
Transmission error is defined as the non conjugacy of a gear pair, that is, the motion 
error defined by the d i fference between the output gear's actual position and its 
position if the gear teeth were perfect in  shape and infinitely sti ff. TE is  defined by 
equation 5 . 1 [ 1  1 8] .  
TE - R re _ (N. \1) ] bp � I' Np PK 
64 
5 . 1 
Where 
Bp = Rotation of the pinion 
Bg = Rotation of the gear shaft 
Np = Number of teeth on the pinion 
Ng = Number of teeth on the gear 
Rbp = Radius base of the pinion 
5.4 . 1  Static Transmission Error (STE) 
The static transm ission error i s  the composite effect of any dev iat ion of the gear teeth 
from perfectly formed involute surfaces. The assumption is that the gears are 
un i form ly spaced, perfect ly formed and complete ly rigid. I n  pract ice, gears deviate 
s l ightly from perfect involute surfaces and elastically deform under load, which 
resu lts in an unsteady force component of the torque. The unsteady forces are 
transmitted as v ibration from the gear, through the shaft and beari ngs to the gearbox 
casi ng where it is measured. 
The static transm ission error is widely accepted as the principle source of v ibration i n  
gearboxes. Mathematical ly, th is  unsteady forc ing function due to the p in ion i s  best 
described by a complex Fourier series with fundamental frequency equal to the pin ion 
rotational rate,f, [ I  1 9] 
'" 
s(t )  = Lcn ·eJn( 2JZj, ) 1 5 .2 
11::=0 
The Fourier transform of the complex Fourier series i s  a one-sided pure l ine spectrum 
at mul ti ples of the gear rotational rate [ 1 20 ] .  
'" 
set )  = LCn ·eDu-n/; ) 5 . 3  
11::0 
We can now present a mathemat ical expression for the composite v ibration due to 
both the posit ion and the gear. Th is is accompl ished by summ ing two infin ite complex 
Fourier series. Therefore, i f  the p in ion has N teeth and the gear has M teeth, then 
equation 5.2 describes the composite v ibration due to both gears [ 1 2 1 ] . 
65 
5 .4 
11=0 m=O 
Referri n g  to equation 5 . 2, f,. is the pi nion frequency and (N/M)f, is the gear rotat ional 
freq uency. The Fourier transform of the composite v i brat ion i s  a l so a one-s i ded pure 
l i ne spectrum [ 1 22 ] .  
s(t) = I Cll ob U -III, J + I ClI/ oJ[/ - mf C�)] 11=0 111=0 
5 . 5  
The two s u m mat i o n s  share a common set o f  freq uenc ie s. I n  the second summat i on, 
wherever m equals any integer m u l tiple of M, the sum mations share the same 
frequency com ponent. Therefore, equat i on 5.3 can be fu rther decomposed as equation 
5 .4 [ 1 2 3 ] . 
<X> <X> <X> 
set) = L C, oJ u -Pllj, ) + L cll ob(/ - n/ J+ L ClI/ ob U -III, ) 
f=O n=O.II'::f:.PN m=O."r::t.fA-1 
I f  we transform back to the t i me domain, we arrive at the fo l l o w i n g  equat i on [ 1 24 ] .  
J ( 2m1j;l+a,, ) + C oe 11 
5 . 6 
5 . 7  
The first s u m mation i n  equation 5 .4 i s  com posed of v i bration components fro m  both 
the p i n ion and the gear. The first sum mat ion ' s  fu ndam enta l frequency (Nf,) i s  the gear 
mesh freq uency. We have j u st shown that the components of v i brat ion due to the gear 
mesh freq uency and its harmon ics are due to both the p i n i o n  and the gear. Th i s  is a 
fact that is negl ected in the l i terature on gear d i agnosti c s .  
66 
5.4.2 Residual Error Signals 
Mark [ 1 26] showed the component of the stat ic transm ission error that occurs at 
mu ltip les of the gear mesh ing frequency is caused by e lastic tooth deformations and 
the mesh deviations of the tooth faces from perfect involute surfaces. The remain ing 
components of the static  transmiss ion error that occur at mult iples of the gear 
rotational frequency are caused by the dynamic components of the tooth face 
dev iations. Thus, we have a concrete, physical just ification for using the static 
transm ission error for gear diagnostics. The dynam ic component of the stat ic 
transm ission error is a physical measure of any gear tooth surface deviation. Th is  
inc ludes, but is  not l im ited to, worn teeth, m issing teeth and cracked or ch ipped teeth.  
Wang and McFadden [ 1 27] described the gear motion error as the real part of the 
static transm ission error. The gear motion error is a real signal, described by an 
infin ite cosine series with fundamental period 1, . . The static transmission error was 
developed for predicting the amount of vibration produced by mesh ing gears; the gear 
motion error was developed for gearbox diagnostics. 
The decomposition of the composite gear motion error has three components; the 
harmonic error component Sey(t), the res idual error component due to the pin ion 
Ser.p(t), and the residual error component due to the gear Ser.g(t) [ 1 27] .  
se t )  = Seh ( t )  + Ser.p (t )  + Ser.� (t )  5 . 8  
Equations 5 . 1 -5 . 8  are expressed graph ica l ly  I n  figure 5 .7. The figure shows the 
spectra produced by a p in ion and gear. 
67 
Figure 5 .2 :  Frequency Domain of Graph ical Representation of Equation 5 .8  [ 1 27] 
5.5 Signal Processing 
The concept of a signal processing technique to ach ieve the d iagnosis of the gearbox 
is presented in this section. The main objective ofthe signal processing technique is to 
extract the echoing fault pulses from the m ixture, wh ich comprises the measured 
v ibration signal .  
The vibration 'y' of a gearbox can be described as a convolution between the Impu lse 
Response Function ( IRF)  of the transmission path oh'  and the combined effect of an 
anomaly caused by a localized gear fau lt (fault impu lses) 'w ' , the determin istic 
signals  'e' inherent in operating gears and the noise on' as shown in figures 5.3 and 
equation 5 .5 .  
Where 
y = Vibration of the gearbox 
h = transmission path 
w = gear fault 
e = deterministic gear excitation (inherent in gear vibration) 
68 
5 .9  
n noise 
* = conyo l ution 
e: delerminislic y,earexcilalion 
vI': .tCl1lil speclmm 
Transmission palh effect )' measured siy,nai 
11: noise 
FigUl'e 5.3: Vib.-ation of a Cea.·box 
Gears \yith a crack or a spal l  can be d i agnosed by co mparing the \ i bration 
characterist ics o f  the faults ,  F igu re 5,4 presents a proposed signal process i ng method 
for the gearbox diagnos i s  
The fi rst step o f  the s i gnal processing i s  the extraction o f  the impulse fro m the 
mixture o h i brat ion s ignals sho \\-n i n  figure 5 , 3 ,  The negat i vely i m  erted echo shown 
in figure 5 . 4  characteri/.es the effect of both the spal led and cracked teeth. ho\\'eyer. 
the t�'pe of the fault can be determined by exam i ni ng the p ropert ies of the fault s ignals 
in  the cepstrum. 
mY 
m Y  
mY 
mY 
40 
20 
0 
-20 
-40 
-50 
0 
4 
2 
0 
-2 ::-
-4 
0 
,I. I' ) \  l ,  ;' � J , ' \ I, ,\ 
I t I 1 ', I � " I,' \ , � 
I ' \  V 
200 
I� 'l (' . } \l \,! I ' ,_ _____ I 
200 
400 
400 
,1\1 \\ ' \  t, " , ... I, " , 
l I " \ '. 
'V , " ' " ' 
'I,' 
500 800 1000 1 200 
N l I l11hf'r or  �::tl11nlf'C;: 
r-' { r� 1 1 , r I. --. ) \.....1 
N I ' l11 hf'r 0 r � ::t l11nlf'C;: 
600 800 1 000 1 200 
F i g u re 5 A a: The Negati \el�' I n \erted Echo Due to the Cracked Tooth 
30.-------r-------r-------�------�------�----__.
20 
1 0  
o 
, J\ " ,1 1 I r \ I l  / I ,' I " , \ 
" ," r i " ' [' ) ' , ,' 1 ' , , . , " v '· i \ ', ,', j I ' I " '" " ,  
- 1 0 1 , '.,1 1. \ 
I " , \ . 
-20�----�------�------�-------L------�----� 
o 200 400 500 800 1 000 1 200 
2.-------.-------r-------�------�------�----__.
o 
- 1  
_2 � ______ � ______ L_ ______ L_ ______ L_ ______ L_ ____ � 
o 200 400 600 800 1 000 1 200 
F i g u re 5 A b :  The Negat i \ 'ely Im erted Echo Due to the S p aJ l  i n  a Tooth 
70 
The complex cepstrum transformation is central to the theory and appl ication of 
homomorph ic systems, that is, systems that obey certa in  general rules of 
superposition [ 1 28 ] .  
Randa l l  demonstrates i n  [ 1 29] the powerful appl ication of  the cepstrum technique i n  
mon itoring and d iagnos ing gears and ro l l ing e lement bearings. 
The harmon ics and the sidebands in the spectrum represent the concentrat ion of 
exc itation energy caused by the rotating mach ine components and they are typical ly 
monitored to detect any abnormal ity in the operating machinery .  
The advantage of using the cepstrum in machine condition mon itoring i s  that the 
combined effect of the harmonics and si debands in  the spectrum appear in the 
cepstrum as a smaller number of c learly defined rahmonic peaks: i .e. in compressed 
form, and it is therefore easier to moni tor the changes occurring in the system . It i s  
able to detect the presence and growth of  s idebands, and to  extract the spectrum 
periodicity. 
5.6 Homomorphic Theory 
Systems which the output is a superposition of the input and impulse signals by an 
operation that has the algebraic characteristics of convolution of the impuls ive and 
forc ing responses, (by exploiting the propert ies of the Fourier transform and the 
complex cepstrum)  are cal led homomorphic systems. 
The method of homomorphic fi ltering described by Oppenheim et al [ 1 33 ], Schafer 
[ 1 3 1 ], and Buhl  [ 1 30] is primar i ly  developed for the problems of echo detection and 
echo removal .  
The algorithm transforms the convolution process into an  add itive superposition of  its 
components with the result that single parts can be separated morc easi ly.  U l rych 
[ 1 32 ]  has demonstrated the appl ication of this method in se ismology for the 
separation of overlapping signals. The practical appl ication of the homomorphic fi l ter 
process in seismic reflection work is d iscussed for the first t ime by Scafer [ 1 3 1 ] , Buh l  
[ 1 30 ]  and Bryan [ 1 34] .  
A homomorphic system accepts a signal composed of two components and returns the 
signal with one of the components removed. Its processing offers a great advantage 
because no prior assumptions or knowledge of the impu lse response of the 
transm ission path is necessary; i t  has a property of bl ind deconvol ution . 
A convolved signal is shown in  equation 5 . 1 0  
7 1  
y (I) = x (I) * h (I) 
5 . 1 0  
The components x (I) and h (I) could be isolated in  order to study each individual ly .  
This research wi l l  present a gearbox with convolved s ignals from good, spa l led and 
cracked teeth and use the cepstrum technique for homomorphic b l ind deconvolution 
to separate the forc ing function from the transmission path effect, i .e. a homomorph ic 
fi lter (complex cepstrum) is appl ied to do the deconvolution of the signals. The 
procedure of homomorphic fi ltering is shown in  figure 5 .5 .  (The act of applying a 
homomorphic fi lter is cal led l iftering). 
Raw t ime 
signal Y(l) = X(I) * h(l) 
� 
FFT 
Y(f) = X(f) . H(f) 
� 
Complex cepstrum fogY (f) = fogX(f) . fogH(f) 
I 
Liftering 
1 
Inverse Y = X + H 
cepstrum 
1 
Reconstructed 
Time signal 
F igure 5 . 5 :  S ignal Processing for a Homomorphic B l ind Deconvolution 
72 
XI (t) * X2 (t) 
Figure 5 .6 :  Two Signals Deconvolved to Two Separate Signals 
Deconvolution is undoing the convolution of two signals and isolates them as shown 
in figure 5 .6.  This is  usefu l  for analysing the characteristics of the input signal and the 
impulse response when only given the output of the system.  
Homomorphic fi ltering is a determin istic process because fixed and pre-given parts of 
the complex cepstrum, wh ich are related to the undesired components, are e l im inated. 
The success of the method depends primari ly on the rate of the separat ion of the 
indiv idual components in the complex cepstrum. Therefore the successfu l  appl ication 
of the method in a gearbox diagnosis is critica l ly determ ined by the simpl ic ity and 
predictabi l ity of the ind ividual components of the gearbox cepstrum. In order to 
demonstrate the possibi l ities and difficult ies of homomorphic fi ltering, figure 5 . 7  
shows the cepstra of the gearbox with d ifferent fau l t  cases under I OONm load ing. 
5.7 Cepstrum Technique 
The Fourier transform and the inverse Fourier transform are complex domain 
processes, the cepstrum is complex if the phase information of the original t ime 
waveform is preserved. Complex cepstrum can be used for noise reduction and signal 
separation, such as echo cancel lation. Figure 5 . 5  demonstrates the procedures of the 
complex cepstrum and homomorphic fi l tering, equations 5 . 1 2  - 5 . 1 5  are its algori thm . 
This research presents an appl ication of cepstrum technique that uses homomorphic 
bl ind deconvolution to remove the effect of transm ission path transfer functions from 
external ly measured gearbox signals. For a better d iagnosis of gear fau lts, the 
cepstrum technique is used to separate source and transm ission path effects into 
d ifferent quefrency regions. The poles and zeros of the transfer functions 
73 
-2 � 
- 1 -
4 -
-') '' 
6
0 
I 
0 5  1 5  2 5  umber o f  S am p l es 
Fi gure 5 .  7a: Cepstrum o f  the gearbo:\ \\ i th cracked tooth 
� I  �---'--
-1 1 -
F O�---'O::':5:------':--�--=': ,::-- -:-----::'3 5 N u mber 0 f Samp I es 
Figure 5 . 7b :  Cepstru m of the gearbo:\ \\ i t h a spal l ed tooth 
mY o � --'-�-------� 
_ . .  
3 -
-4 -
6 -----�1 __ �I __ �I __ �I __ _ 
U .UJL 4Wl I)..W lLW IWW lMJU u mber of S am p l es 
F i gu re 5 . 7 c: Cepstrum o f  the gearbo:\ \\ i t h  undamaged teeth 
74 
from the response v ibrations are extracted from the region in the cepstrum shown in 
figures 5 . 7a, 5 .7b and 5 . 7c, by curve-fitting expressions using a homomorphic fi l ter. 
The separation of the gear mesh excitation force from the transm ission path transfer 
functions was obtained by using the cepstrum technique of homomorphic b l ind 
deconvolution without measuring the forc ing function at  the gear mesh. The poles and 
the zeros of the forc ing function were used to validate the changes in  the frequency 
response function (FRF) .  
The transformation of a signal into its cepstrum is  cal led a homomorph ic 
transformation, and the concept of the cepstrum is a fundamental part of the theory of 
homomorphic systems for processing signals that have been combined by 
convolution . 
The Cepstrum is the inverse Fourier Transform of the natural logarithm of the Fourier 
transform of a signal series. The definition of the complex cepstrum is gi ven in 
Equation 5 . 1 1 .  The spectrum of a gearbox signal consists of a number of harmonic 
fami l ies. These harmonic  fam i l ies originate from the d ifferent bal l  bear ings i n  the 
gearbox and, from the tooth mesh frequencies of the gears. These are d ifficult  to 
separate in  the spectrum .  Cepstrum is a practical tool that makes it easy to find these 
d ifferent harmon ic fami l ies, and the individual fam i l ies can be mon itored for changes 
that m ight ind icate that something is wrong. The cepstrum can be mathematica l ly  
defined as fol lows [ 1 35 ] .  
Fxx (j) is the autospectrum (power spectrum)  
Where :  
't = quefrency 
;j = fourier transform 
C = cepstrum 
5. \ I  
Cepstrum can be edited or l iftered as it i s  cal led (paraphrasing of ' filtered' )  [ 1 35] .  The 
equ iva lent spectrum, cal led the l i ftered spectrum, can be found by applying an FFT to 
the l iftered cepstrum .  T has un its of t ime, but is known as 'quefrency ' .  Harmon ical ly 
75 
re lated components in the cepstrum are known as ' rahmon ics ' .  Table 5 . 1  compares 
the terms used in the spectra and cepstral analyses. 
Table 5 . 1 :  Comparison of Terms used in Spectral and Cepstral Analysis 
Spectra Analysis Cepstral Analysis 
Spectrum Cepstrum 
Frequency (Hz) Quefrency (m i l l i seconds) 
Harmonic Rahmonics 
F i lter Lifter 
Phase Saphe 
Magnitude Gamn itude 
Frequency analysis Quefrency a lanysis 
x (I) Y (I) = x (t) * h (I) 
-----+1.1 h (I) 
. 
H (t) 
X (/) y (/) = X (t) * H (I) 
Figure 5 .8 :  Frequency Response of a System 
Figure 5 .7  describes a simple system with an input and output relationship. The output 
y(l) is equal to the convolution between the input x(l) and the impulse response h(l), 
which is mathematica l ly shown as fo l lows [ 1 2 1 , 1 29, 1 30] .  Th is is homomorph ic 
deconvolution. 
Y(I} = x(l) * h(l) 5 . 1 2  
Using the convolution algorithm, equation 5 . 1 2  wi l l  transform to equation 5 . 1 3  by 
applying the Fourier transform . 
Y(f) = X(f) . H(f) 5. 1 3  
Tak ing the logarithm of equation 5 . 1 3  wi l l  result i n  equation 5 . 1 4. 
76 
Log Y(f) = log X(f) + H(f) 5 . 1 4 
After the homomorph ic deconvolution shown in equations 5 . 1 2  - 5 . 1 4, an inverse 
transformation of equation 5 . 1 4  to the cepstral domain w i l l  produce the cepstrum in 
equation 5 . 1 5 . 
5 . 1 5  
Equation 5 . 1 5  defines the cepstrum of the signal measured, wh ich is the sum of the 
cepstra of the source and transm ission path functions. The signal from the external ly 
measured gearbox is the convolution of the path and source effects. After 
transformation to the cepstrum domain, the source and the path effects are 
deconvolved and become addit ive. Equation 5 . 1 6  shows how the structural response 
functions are treated in the Laplace domain as a ratio of polynom ials in the Laplace 
variable s. 
5 . 1 6  
Applying partial fraction expansion to equation 5 . 1 6  results i n  poles and residues for 
the indiv idual modes in equation 5 . 1 7  [ 1 ,7,8 ] .  
11 1 2  [ 
] H s = _r,_ + _r,_ ( )  L '-p, '-p, 
k= 1  
5 . 1 7  
Equation 5 . 1 8  can be obtained i n  terms of poles and zeros by fi nding the roots of the 
numerator and denominator using rational fract ion expansion [ 1 2 1 ,  1 27, 1 28] .  
n (,-=, ) 
H(s )=_',�l­
n C,-p, ) 
k == I 
The z-transform of the equation 5 . 1 8  w i l l  result in equation 5 . 1 9  [ 1 2 1 ] . 
77 
5 . 1 8  
5 . 1 9  
----------------------------------------------------
Equation 5 .20 is the cepstrum that presents the transfer function in terms of poles and 
zeros [ 1 27, 1 28 ] .  
k = 1 k = 1  
nil) Po 
= " h, " _ " ri, " � n � n 
k = 1  k = 1  
5 .20 
Qk and Ck are min imum phase and are the poles and zeros in  the un it c ircle, wh i le bk 
and dk are the poles and zeros outside the unit c i rc le [ 1 36, 1 37] .  M in imum phase 
occurs at pos itive quefrencies. The maximum phase at negative quefrencies can be 
neglected because the poles are unstable and it w i l l  not affect the detection of the 
changes in the resonances. 
5.8 Poles and Zeros Analysis 
The transfer function provides a bas is for determ in ing important system 
characteristics without so lving the complex d ifferential equation. The poles and zeros 
are the properties of the transfer function and therefore of the d ifferential equation 
describing the i nput-output system dynamics as shown in figure 5 .9 .  
x(t) ___ �� I � _______ H(._� ____ � y(t) 
Figure 5 .9 :  System with I nput-Output Re lat ionship 
Y(s) = H(s).x(s) 5 .2 1 
H(s) = Y(s)/X(s) 5 .22 
The system function is H(s), which represents the characteristics of the system. 
The poles and zeros govern the system 's  behaviour, they spec i fy the set of complex 
frequencies for which the e igenfunction response is  infin ite or zero respectively. The 
78 
n u m ber of poles in a system corresponds to the n u m ber of i n dependent state vari ables 
i n  the system. 
The p l ots are necessary because they help to eas i l y  design a fi l ter and a l so obtain its 
transfer fu nction. The n u m erator roots are the zeros of the fi lter and the denom i nator 
roots are the poles of the filter. The l ocat ion of the poles and zeros w i l l  a l l ow us to 
q u ic k l y  understand the magn itude response of the fi l ter. 
The a i m  of u s i ng a poles and zeros analysis in t h i s  chapter is to present the theory of 
how the c o m p lex or d i fferential cepstra of the path effects are c u rve fitted to extract 
poles and zeros. 
The polynom i a l  fo rm is another way that the process transfer fu nction can be 
represented as shown in equation 5 . 1 6 ; the rat i o  of polynom i a l s  i s  ca l l ed the trans fer 
fu nc t i o n .  The val ues of s that cause the numerator of the equation to equal zero are 
known as the zeros of the transfer fu nction, w h i c h are a l so the roots of the numerator 
polynom i a l .  The val ues of s that cause the denom i nator of the equation to equal zero 
are known as the poles of the process transfer fu nction, w h i c h  are the roots of the 
denom i nator polynom i a l .  
The pol e-zero form i s  another way that t h e  tran sfer fu nction can b e  represented a s  
shown i n  eq uation 5 . 2 3 .  
5 . 23 
The c o m p l ex poles or zeros m u st occ ur i n  complex conj ugate pa i rs. 
The gain-t i m e constant form i s  the one that we use most often for control system 
design. 
5 . 24 
The zeros are: { O }  
The poles are: { 1 /2, -3/4 } 
79 
Im(z) 
x 0 - X 
Re(z) 
Figure 5 . 1 0 : Poles and Zeros Plot From Transfer Function 
Once poles and zeros have been found for a given Z-transform, they can be plotted 
onto the z-plane, which is complex with an imaginary and real axis referri ng to the 
complex-val ued variable z. The plots help to easi ly design a fi lter and obtain the 
transfer function. Depend ing on the location of the poles and zeros, the magn itude 
response of the fi lter can be quickly understood. The example in figure 5 . 1 0  shows the 
locations of poles and zeros in  the z-p lane, the poles represent the mechanical natural 
frequencies and the zeros reflect the locations where the v ibration cance ls to zero. 
The next chapter is the deals with experiments using the cepstrum technique and 
homomorphic fi ltering to demonstrate their practical appl icat ion to d iagnose gearbox 
faul ts. 
80 
6. 1 I ntroduction 
Chapter 6 
Experimental Analysis 
I n  th is chapter, an experimental apparatus is described which generated the data used 
to test the cepstrum techn ique for homomorph ic b l ind deconvol ution and the resu l ts .  
V ibration signals measured on the cas ing of a gearbox are always a compound of 
source effects and transmission path effects. The gearbox is a spec ial case; where the 
tooth-mesh is  the pri ncipal source and hence signals measured wou ld d iffer primari ly 
because of the d ifferences in the transm ission path. The aim of th is  research is  to 
develop a technique to separate the forc ing function at the source, which is the gear 
mesh from the transmission path function of a measured gearbox vibration signal . 
This was achieved by col lecting vibration data from the gearbox hav ing good, spa l l  
and cracked teeth profiles under d ifferent loadings. The data was recorded in  a 
MATLAB ™ data fi le to demonstrate where the entire c hange was. The procedure was 
implemented by using the signal processing package of MA TLAB. The forc i ng 
function is concentrated in the d iscrete regions i n  the cepstrum;  the transfer function 
is located be low the first rahmonics of the forc ing function and was separated by a 
shortpass l ifter. S ince the poles and zeros occur in the complex conj ugate pairs, the 
poles and zeros of the transfer function were extracted from the response signal by 
curve fitting analytical expressions to the appropriate regions of the cepstrum .  The 
homomorphic deconvolution fi ltering was employed as a novel appl ication to a 
gearbox faul t  diagnosis, separating the resonance effect from meshing frequency. 
6.2 Gear Test Rig 
The test rig was powered hydraul ical ly as shown in figure 6. 1 .  I t  had an electric 
induction motor, which  ran the rig to its specified speed, whi le  the hydrau l ic pumps 
generated the load for the rig. The pumps operated on a c losed loop by return ing the 
flu id at the h igh-pressure outlet to the hydraul ic motor and later powered the rig. 
When the rig was runn ing at a constant speed, the purpose of the electric motor was to 
compensate for any losses in the system . 
8 1  
Some of  the components o f  the test rig in figure 6. 1 are descri bed belo\\ : 
Ind uction motor (AC)  ( 1) 
This \\ as a S . S k W. 8 poles. AC i nduction motor. which po\\ ered the rig to hm e a 
specified rotational speed. The stable  speed that the gear operated \\'as bet\\'een 2 H-t. 
and 1 4H;: of shaft speeds under a torque of 1 2 0 N m.  
W 
I 
Hydraul ic Motor ( 2 )  
Figure 0 . 1 : Gear Test Rig 
(CoUl1esy of N S W  Uni\  ersity) 
I1lerg�'n.:\ 
I Tt' sure Relll' l  
V.th l' 
This \\'as a fi"ed yol ume type. \\'hich \\ as connected in series \\ i th the electric motor 
and ran by using re-circulated pO\\ er from the pressure compensat ing pumps (loading 
devices ) .  
Variable Vol ume Pump (3 ) 
This \\'as a pressure-compensating pump that generated the l oading on the gears. 
Setti ng a slosh plate angle control led the loading on the gears and the output pressure. 
82 
V ariab l e  Vol u me Pump (4 ) 
Th i s  \\'as trunnion contro l led and also generated the l o ad i n g  on the gears. Adj ustment 
of the trunn ion on the consol e  contro l l ed the lo ad ing and adj usted the output pressure. 
Gears 
The gears are undamaged: cracked and spal l. shO\m in figu re 6.2 .  Each one has 32 
teeth. 
Gear \\i th 
spaJ l  
Flywheel (5 )  
F i gure 6 .2 :  C racked and S p aJ l  gears 
It atten uated the torsional \' i b rat ion i nd uced by load ing. 
Torque Transdu cer (6) 
Gear with a 
crack 
This \Vas connected i n  series with the i n p u t  shaft with shear p i n s  (to prevent torsi onaJ 
overload i ng) . The transd u cer \Vas capab l e  o f  measuring O \'er 200 N m  of torque. 
Control Console ( 7 )  
Thi s  cons isted o f  a speed contro l l er for the electric motor ( frequency converter) and 
seq uence \ah'es to remotely control the loadi ng appl i ed to the gears. 
Cou p l i ng 
This type of coup l i ng "'as an elastic type that al lo\\ ed only the torque to be 
trans m i tted between the shafts 
83 
6.3 I nstmmentation 
The fo 110 \\ i ng i nstruments \\ ere used in meas uring the gearbox signals :  
S ix accelerat ion s ignal s. t,,·o encoder outputs and one tachometer output \\"ere 
measured in the experiment .  Figure (,.3 sho,,·s the positions of the accelerometers and 
encoders set up for the experi ment . The tachometer is enc losed i n  the encoders. 
The s i gnaJ s measured from the accelerometers and encoders \vere processed and 
recorded b�· a Bruel & Kj aer P U L S E  system. The t\\ O encoders are con ected to the 
i nput and output shaft \\ ith specia l  precision d iaphragm coupl ings. The PO\\ er supply 
for the encoders i s  5 V .  
F igure 6.3 : Gear Test Rig 
6.4 Instrumentation for Data Collection 1 1 381  
Encoder I 
Accelero meter I 
Accelerometer 2 
Accelerometer 3 
Accelerometer 4 
Encoder 1 
• Bruel Kj aer. P U LS E  System: Front-end 3560C. Control  M odule: 75 36. 
I nput/Output Module: 3 I ()<) 
• Bruel & Kjaer. P U L S E  Soft\\ are 
• Bruel Kjaer. Accelerometers. Type 4384 
• Bruel Kjaer. Charge Ampl i fier. Type 2365 
• Heid enhain ROD .+26 Encod ers 
84 
6.5 The Structure of the Data Files: 
Four acceleration signals, two encoder signals and one tachometer pu lse were 
'I 'M measured on the test rig. These data were recorded in a MATLAB data fi le. The 
tachometer is enc losed in the encoders. The acceleration was recorded from the 
accelerometer's signals, then the signals measured from the accelerometers and 
encoders were processed and recorded by a Bruel & Kjaer PULSE system.  
Each signal was measured for five seconds with a sampl ing frequency of 65,536Hz 
and passed through a low pass fi lter. 
6.6 Blind Deconvolution 
Some mach ine components such as gearboxes produce very compl icated spectrum 
signatures, because the signal com ing from the gearbox consists of a number of 
harmonic fami l ies and sidebands, which can be d i fficult to separate in the spectrum .  
The cepstrum analysis offers a way to s impl ify the analysis o f  these signa ls and i s  a 
practical tool and a non- l i near signal processing techn ique used to find d ifferent 
harmon ic fam i l ies. The input signal to the physical system represents x(t) and the 
impu lse response of the system represents h(t) , while y(t) is the output of the system. 
The deconvolut ion methods that are su itable for gearbox d iagnosis are: 
# Cepstra Analysis 
# Homomorphic fi ltering 
In  gearbox vibrations any deviations from the exact un iformity of each tooth-mesh 
tends to show up partly as harmon ics of the shaft speed and also as sidebands around 
the toothmeshing harmonics caused by modulation of the tooth-mesh signal by the 
lower rotat ional frequenc ies. The sideband spac ing thus contains valuable information 
as to the source of the modulat ion and can be extracted using the cepstrum.  The 
cepstrum has two advantages of being able to measure it very accurate ly because it 
gives the average sideband spac ing over the whole spectrum.  
When trying to d iagnose a v ibrat ion signal i n  order to identi fy poss ible fau lts i n  the 
mach ine, the fol low ing are investigated in chapters 4 and 5 :  
# Harmonic re lations 
# Presence of sidebands 
# The re lation of energy in d i fferent sideband and harmonic fam i l ies. 
85 
Cepstrum analysis, as described in  chapter 5 :  
• Simpl ifies the analysis ofa compl icated spectrum and 
• i s  i ndependent of the signal path 
Cepstrum is an anagram of spectrum, is a non l i near signal processing techn ique used 
to identify and separate harmonic fam i l ies in the spectra of gearbox signals .  The 
calcu lation of cepstrum involves the inverse Fourier transform of the natural 
logarithm of a kind of spectrum. The fol lowing equations 6.7 to 6.9 define the 
cepstrum forms 
Complex Cepstrum 
Real Cepstrum 
Power Cepstrum 
C = --'- Jlf I [X { JU' )l JU'n d ccx 2lf -If og \e r OJ 
C =--'-Jlf 1 0g [XX' l JU'lIdOJ P 27r -Tr r 
6.7 
6 .8 
6 .9 
S ince both the Fourier transform and the inverse Fourier are complex domain 
processes, the cepstrum is complex if  the phase information of the original t ime 
waveform is preserved. The complex cepstrum can be used for noise reduction and 
signal separation, such as echo cancel lation. I f  the input of the Fourier transform is 
real (no phase i nformat ion), for example, the power spectrum or the magnitude of the 
Fourier transform of the signal ,  the cepstrum cannot be reconstructed back to the t ime 
86 
domain, we sti l l  can "I ifter" a harmonic fami ly in  the quefrency domain and obtai n  a 
l i ftered spectra. 
When the gearbox wears, the gear profi le w i l l  gradual ly change due to s l idd ing 
between two teeth in  mesh at any point except at the pitch point. This  indicates that 
changes due to wear in a gearbox wi l l  turn up at the second harmonic of the 
toothmesh frequency, and s ince the change is not sinusoidal, h igher harmonics w i l l  be 
revealed as wel l  as ind icated in a simpl ified form . 
I n  the v ibration s ignals from gears, the force at the mesh and the transfer function 
from the mesh to the measurement poi nt, largely separate in the cepstrum, in that the 
forc ing function i s  period ic and most of it concentrates at rahmonics corresponding to 
the tooth-mesh frequency and indiv idual shaft speeds. Remov ing these with a su itable 
comb l ifter al lows the remaining part of the log spectrum, domi nated by the transfer 
function to be reproduced by a forward transform . This can reveal whether resonance 
peaks have changed, and thus whether measured changes are due to changes at the 
source or in the signal transmission path. 
The output of a l inear physical system can be expressed in terms of the exc itation 
signal and transm ission path properties as a convo lution in the t ime domain (both in 
the complex and power spectra) and a summation in the logarithm ic spectrum (both i n  
the complex and power spectra). Because the Fourier transform i s  a l i near operation, 
this add it ive re lat ionsh ip i s  maintai ned in the cepstrum (both in the complex and 
power cepstra). 
Not only are the source and transm ission path effects add itive in the cepstrum, they 
are often largely separated into d ifferent regions because of thei r  characteristics w ith 
respect to frequency. 
6.7 Results 
Figures 6.4 to 6.6 i l lustrate a typical gearbox signals with undamaged, cracked and 
spa l l  teeth under 50Nm loadi ng. The two gears have 32 teeth respectively. The input 
shaft was rotat ing at a speed of 1 0Hz (600rpm).  When the gearbox was operated 
under several loads the v ibrat ion signals were acquired through the acceleration 
signals .  
87 
Orig inal  S igna l  
_5 L-__ L-__ L-__ � __ � __ � __ � __ � __ J-__ J-� 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part  
.: , 
o 1000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Disc rete Part 
:��� ��  o 1 000 2000 3000 4000 5000 6000 7000 BODO 9000 1 0000 
N umber or S amples 
Figure GA:  Und amaged Gear V i b ration S ignal 
Original Signa l  
-50 '--------'-_-'--_L...-----'-_--'--_-'----'-_-L-_-'------' 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Discrete Part 
-50 '-
-------'-_--'---_-'---------'-_--'--_-'-----'_-L-_-'------' 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Figure 6. 5 :  Cracked Tooth Vi brat ion Signal 
Original Signal  
- 1 00 '--------'-_-'--_L...-----'-_--'--_-'---'_-L-_-'------' 
o 1 000 2000 3000 4000 5000 6000 7000 BOOO 9000 1 0000 
Random Part 
�:r:���"·-, -�O '------'-_-'--_.L------'-_---'--_-'------'-_---'-_-'------' 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Discrete Part 
50��-�-��-�-��-�-��
o Nl \W\I\fIM!WNJ1:i!\,I,I��W�·�I�\W NIIW/JIMWIMM 
-50 '--------'-_--'---_-'---------'-_--'--_-'-----'_-L-_-'------'
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Number of Samples 
Figure 6 . 6 :  Spal l Tooth Vibrat ion S ignal 
R9 
Figures 0. 7 - G. 1 2  show the cepst ra for good. cracked and spall teeth. When the first 
run \\·as carried out the good gears \\"ere engaged. figures G.7 and G.S sho\\ the 
spectra. The second run i m  olved the good and the cracked gear. ,,·i th the cepstra i n  
figures o .  I) and G. 1 0 . The last run \\·as \\ hen the good gear engaged \\ ith the spal l one. 
figure 6. 1 1 and G. 1 2  demonstrates the cepstra. Each run ,,·as done u nder t\\ 0 d i fferent 
loadings SONm and I OON m respecti ,ely. 
Cepstrum - Undamaged 50Nm 
O ��------------------------------�� 
- 1  
-2 
., -,) 
-4 
-5 
_hL-------L-------L-------�------�------�----� 
- 0  2000 4000 6000 8000 1 0000 1 2000 
N umber o f  Samples 
F igure 0. 7 :  Cepstrum o f  Undamaged Teeth under SON m Load 
Cepstrum - Undamaged l00Nm 
O��--��------------------�--k-�� 
I -1 -
2 � 
-3 f-
-4 � 
-6L-----�----�------�----�------�----� 
o 2000 4000 6000 8000 1 0000 1 2000 
Figure 0 . 8 :  Cepstru m or U n d a m aged Teeth under I OO N m  Load 
O � 
-
1 r 
-2 � 
-3 
-4 -
-5 � 
-6 
0 0 5  1 5 2 2 5  3 
N u mber or S am p l es 
Figure 0.9 :  Cepstru m  or C racked Tooth under S O N  m Load 
9 1  
0 
- '1 
-2 
-3 
-4 
-5 
-6 
0 0 .5  1 .5 2 2.5 3 
Number or  Samples 
F igure 6. J 0 :  Cepstrum or  Cracked Tooth under I OONm  Load 
3.5 
X 1 04 
[I 
- 1  
-2 
-3 
-4 
-5 
-6 
0 
·1 
I 
0 
- 1  
-2  
-3 
-4 
-5 
-6 
0 
0 .5  1 .5 2 2 .5 3 
Figure 6 . 1 I :  Cepstrum of  Spal l  Tooth under 50 m Load 
0 .5  1 .5 2 2.5 3 
N umber o f  Samples 
Figure 6. 1 2 : Cepstrum of Spal l Tooth under I OONm  Load 
93 
3 .5  
X 1 04 
3.5 
X 1 04 
6.7. 1 Homomorphic Deconvolution 
The appl ication of homomorphic  fi ltering in the diagnosis of a gearbox is ach ieved by 
using cepstrum techn ique to detect those signals  that need to be suppressed and the 
actual fi ltering process which incl udes random noise reduction. 
In order to demonstrate the various possibi l ities of homomorphic fi ltering, the 
appl ication of the method is shown with three d ifferent cases, undamaged, cracked 
and spal l  gears. 
Homomorph ic bl ind deconvolution offers a considerable advantage in that no prior 
knowledge of the impulse response of the transm ission path is necessary. The 
transmission path is recovered by homomorphic deconvolution fi ltering, using the 
steps in the equations 6.4 to 6.6. 
Homomorphic  fi l tering i s  a determin istic process in the sense that fixed and pre-given 
parts of the complex cepstrum which are related to the undesired components are 
e l im inated. The success of the method depends primari ly on the rate of the separation 
of the ind iv idual components in the complex cepstrum. 
The homomorphic fi ltering was appl ied to the cepstra shown in figures 6 .7  - 6. 1 2  to 
e lucidate its possibi l i t ies and d ifficulties, the results of the fi ltering i s  shown i n  figures 
6 . 1 3  - 6. 1 5, considering on ly I OONm load ing. 
94 
'::0 
0 l .' 
. , 
-20 
-40 
-60 
0 
I ' I lA � 'I J It ( \  
1,1 '1/' v ' I 
\) \ " 
200 400 
, L 
(\ 
1 \  . l ' \  
'I . \ 1 \ I , \ I ,,\ 
t, �'l 
600 800 1 000 1 200 
4,-------,-------,-------.-------.-------,------.
-2 
_4 � ______ � ______ � ______ L_ ______ L_ ______ L_ ____ � 
o 200 400 600 800 1 000 
N umber of S amples 
F i gure 6. 1 3 :  Und amaged Gear under 1 00 m after F i l t er i n g  
95 
1 200 
40 
20 
o 
-20 
-40 
-60 
4 
2 
o 
-2 
-4 
0 
0 
1 
} 
, 
A 
f+ 
} " . I 
\ \ I "  I "� r , ) \ ' 
200 
C;; lpn l 
J\ [ \ i l 
,) 
200 
I 
, 
--
400 
""'-., 
"lI 
-
400 
B 
2 
I I 
I , I 
I I \ .. 
" I 
1 1 
t 1 600 
.. 
l , -1 I I 600 1 
Number 0 r Samples 
3 
I 
I 
, , l / 
I ,  
800 1 000 
1 � - -
\ J 
-
800 1 000 
F igure 0. 1 4 : Cracked Gear under I OONm after Fi l teri ng 
1 20 o 
1 20 o 
Step 2 
30.------.-------.------.-------r------.------� 
20 
1 0  
o 
- 1 0 
_20 L---____ L-______ L-______ � ______ � ______ � ____ � o 200 400 GOO 800 1 000 1 200 
2.-------,-------.--------.-------.--------,-------.
----- ------
o 
- 1  �- _ 
_ 2 L-______ � ______ � ______ � ______ _J ________ � ____ � 
o 200 400 GOD 800 1 000 1 200 
N umber o f  S amples 
F igure 6. 1 5 : Spal l  Gear u nder I OONm after F i l tering 
The results from the homomorphic fi l teri ng are sho\\ n i n  figures 6_ 1 3  - 6. 1 5  for 
di [ferent fault cases under I OON m load i ng 
The Res idual Motion E rrors ( RM E )  generated by the faulty gears (cracked and spal l )  
are shown i n  figures 6. 1 4  and 6. 1 5 . 
The first and second deri,-atives of  the RMEs est imate the corresponding veloci ty and 
acce lerat ion as sho\\1  6 . 1 4  ( A )  and 6 1 4  (8)  respect i vely. The sudden change i n  the 
magni tude of the R M Es appears as i nver1ed pairs of pulses in the ir  second derivat i ves. 
In a constant load env i ronment the magnitude of the T E  result ing from the gear tooth 
cracks changes l inearly ,,- i lh the st i ffness of the gear mesh. P resence o f  the crack in a 
gear tooth reduces the e ffecti ve st i ffness o f  the gear mesh as expected because o f  the 
crack i nd uced i ncrease in co mpli ance. 
The TE caused by a tooth crack results in a double stepped rectangular shape. The 
smal ler step I .  Figure 6. 1 4  is a result of  the deflection \\·hen the l o ad is carried by an 
undamaged and a damaged tooth pair and the larger step 2. Figure 6. 1 4  occurs when 
the load is carried only by the tooth pair with a crack. 
97 
The peaks in  the second derivati ve of the RME occur determ in istica l ly  at the three 
positions where the number of contact ing tooth pa irs sw itches from two to one and 
back to two. 
The second derivative of the TE from a gear mesh hav ing teeth that contain spa l l s  i s  a 
pai r  of " inverted echo pul ses". The shapes of the RMEs are determ ined by the size 
and shape of the spa l l s  and are independent of the load carr ied by the gears. 
Un l i ke the tooth cracks, the pos it ions of the pu lses appeari ng in the acceleration signal 
of the spa l l s  are not synchronized with the mesh ing cycle of the gear teeth. 
F igures 6. 1 4  and 6. 1 5  i l lustrate the d i fferences of the inverted echo pulses caused by a 
cracked tooth gear and a spa l \ '  A diagnostic method to d i fferentiate these fau lts i s  
possible by recogn izing the  two properties that affect only one of the two faul ts :  
I .  The effect of tooth crack i s  load dependent wh i le the effect of spal l  is load 
independent; thus, reducing the load should reduce the symptoms of the faul t  
i f  it i s  caused by tooth crack. 
2 .  The amount of delay between the inverted echo pai rs is d i fferent for the tooth 
crack and the spa l l .  The delay caused by the tooth crack is more pred ictable 
and correlates to the mesh ing pattern of the gears. Thus, i f  a corre lation exists 
the fault may be identified a tooth crack and if the corre lation is absent the 
fault may be identi fied as a spa l l .  
The advantage of use of the cepstrum in mach ine condi tion monitoring is that the 
combined effect of the harmonics and sidebands in  the spectrum appear in  the 
cepstrum as a smal ler number of c learly defined rahmon ic  peaks: i .e. in compressed 
form, and it is therefore easier to mon itor the changes occurring in the system. 
98 
6.7.2 Poles and Zeros Analysis 
The poles and zeros prov ide usefu l  information about the response of the fi l ter. The 
plot is a graphical representation of the transfer function which is a function in the 
complex variables, th is helps to check the system stabi l i ty. 
Poles and zeros plots is necessary because it helps to eas i ly  design a fi lter and a lso 
obtain  its transfer function . The location of the poles and zeros w i l l  al low us to 
quickly understand the magn itude response of the fi lter. 
Equation 6.6 defines the cepstrum of the measured response s ignal, which is the sum 
of the cepstra of the source and transm ission path functions. The externally-measured 
s ignal from a gearbox is the convolution of the path and source effects. A fier 
transformation to the cepstrum domain, the source and the path effects are 
deconvolved and become add it ive. Equation 6. 1 0  shows the transfer function in the 
polynom ial form . The va lues of 's ' that cause the numerator to equal to zero are 
'zeros' and the ones that cause the denominator to equal to zero or infinity are 'poles' .  
2 m 
H(s )= 
ao +als + a2s + . . .  + ams 
bO + bIS + h2s
2 + . . .  + bns
n 
6. 1 0  
Applying partial fraction expansion to equation 6. 1 0  results i n  poles and residues for 
the indiv idual modes [ 1 , 7,8] .  
n 1 2[ rk r4 ] H s - I -- +--( )
k=1  S-Pk S-Pk 
6. 1 1  
Equation 6. 1 2  can be obtained in terms of poles and zeros by fi nding the roots of the 
numerator and denominator using rat ional fract ion expansion [ 1 ,7 ,8] .  
m 
n (S-Zk ) 
H(s)=_
k 
=_
1 
__ 
n 
n (S-Pk ) 
k = 1  
The z-transform of the equation 6. 1 2  wi l l  result i n  equation 6. 1 3  [ I ] . 
99 
6. 1 2  
Equation 6 . 1 4  is the cepstrum that presents transfer function i n  terms of poles and 
zeros [ 7, 8 ] .  
6 . 1 3  
( )  mi aZ Pi cZ 6. 1 4  e n = I -+ I ­
k = 1  n k = 1  n 
mo b -n PO d,/ 
= I _k __  I -
k = 1  n k = 1 n 
ak and Ck are m in imum phase and are the poles and zeros ins ide the unit c irc le, wh i le 
bk and dk are the poles and zeros outside the un it c i rc le [ I  2 ] .  M in imum phase occurs 
at posit ive quefrenc ies. The maximum phase at negative quefrencies can be neglected 
because the poles are unstable, and it wi 11 not affect the detection of the changes in the 
resonances. 
The poles and zeros of the transm ission paths to each measurement point over 
d i fferent fau l t  cases at 50Nm loading represent the transfer function between the gear 
mesh and response measurement location for each case. Figure 6. 1 8  shows the 
transfer functions ' smoothed spectra of the good gear, gears with spa l l  and crack, that 
were separated from the source using the homomorph ic deconvolution. 
The signals due to a resonance effects are extracted for d ifferent gear fau lts; cracked 
and spa l l  gear teeth, and undamaged gear. F igure 6. 1 6  shows that the spectra are the 
same, resonance peaks have not changed, however, under each gear case, the change 
was not in the transm ission path . The poles and zeros of the FRF were extracted by 
curve fitting from the region of the cepstrum (or d ifferentia l )  as shown in figure 6 . 1 7, 
the changes between the poles and the zeros were used to evaluate the stabi l ity of the 
system .  Cepstra analysis was used to separate the source and the transm ission path, 
however, the reverse transformation was carried out to provide a smoothed spectrum .  
1 00 
This  p rocess is knO\m as homo morphic fi l tering and the result  i s  sho\\TI i n  figure 
6. 1 9 . 
Sin. JPI�d SI "/ '1 H"I ='p .. 1I =,r'-4I'1 
, , , 
�mo(l'h"f1 �rnrlnln' 
.- .a � Tu ' I  rnl'l, t 
u mber o f  Samples 
� ff " , 1  I'll !-:I''' 1'"111 " j.m "',·.1 ..... 1 ,,.. ,, 
" ' .----�-�-�---__c,________. 
4 1 
" · r 
le � 
, 
, 
,'I I t .11. I H t t -i .1  ' (n i l 1.'1.1 1 1  
N u mber o f  Samples 
Figure 6. 1 6 : S moothed S pectra for Undamaged. Spill l and Cracked gears 
] 0 1  
=;:J� A'h" :-urv fl4 
I lilrh In,-th 'tINm 
c 5r-----�------_,------,_------r_----_.------_, 
I �  1 I " 
0 5  
, 
2CO 
. 
, \ 
,-'�' .---..,,-" -'''-'..,- �-' .. J' "'-... ", 
\ 
1.00 aco Bm 1000 
H..!r l urnpdti::!U - UIIlJ�rndL1�d SUNrn 
I20C 
�", ,----------------.------�---------------,-------, 
1 ' , � 
. , " . ' 
0 5  'h]' . 
o \ : 1\ 
0 5  \ � �. 
, . � I' \: 
....... - > e' ...... I 
\ 
- - ' ·O:-------=�------4-::O-:------::60�J-----=EOO=-----I:::000':-=------,,-:'�OO-
Ff;F Compared 5["m � � rl ------,-------r------.-------r------,_----� 
�--, 
: 5
U
�-----lU
�
J
�----4�U
�
J------ul
�U-:-----���U�--�·�-----,�L� 
N umber o f  Samples 
Figure 0. 1 7 : Freq uency Response o f  System with Cracked, Spall and U nd amaged 
Teeth 
1 02 
Table 6. 1 :  The Poles and Zeros from Curve F itting Cepstra 
Crack Tooth Spa l l  Tooth Undamaged 
Output Poles Output Poles Output Poles 
0 .9927 40.2523 0.9847 40 .0371 0 .9893 1 64 .0475 
0.9835 84.8058 0.982 1 1 2 1 .7873 0 .9865 225. 1 507 
0.9838 1 22 .8589 0.97 1 5  1 54 .6904 0 .9869 249.0926 0 .9794 1 84 .493 1 0 .9858 288.6942 
0 .9743 1 72 .0098 0.9306 1 87 .09 1 7  0 .9907 331 .2494 
0.98 1 8  1 80.3605 0.9686 259. 1 794 0 .974 1 384.0393 
0.9834 2 1 6 .0 1 68 0.9768 297.862 1 0 .9754 445.4255 
0.98 1 6  290.6066 0.9793 329.467 1 0 .9843 489.00 1 0  
0 .9899 327.2236 0 .93 1 6  559.7729 0 .9778 6 1 4.5842 
0.9899 363.8738 0 .98 1 5  648.9281 
0 .9823 720.2248 
Output Zeros Output Zeros 0 .9835 825. 1 824 
0 .9838 6 1 . 8044 0.98 1 6  1 03 .2626 0 .9783 864.9938 
0 .9847 1 04.4020 0.9793 1 39 . 0656 
0 .9796 1 4 1 .787 1 0.9747 1 67.7449 0 .974 1 233.30 1 8 
0.9 1 59 1 62 .9074 0.9772 280 .2 1 42 
0.9833 1 97 .4097 0.9747 3 1 3 . 1 636 Output Zeros 
0 .9880 309.493 1 0.9777 202 .7 1 2 1  0 .9862 1 9 1 . 326 1 0 .9850 236 .5377 
0 .9904 344.9680 0 .9794 263.2265 
0 .9670 305 .0647 
0.9880 367 .8278 
0 .9728 433.6325 
0 .9764 460.2263 
0 .9871  504.7227 
0.9671 578.6067 
0 .9651  633.73 1 0  
0 .986 1 663.6466 
0 .9891  687.2795 
0 .9874 755.0808 
0 .9794 835.9365 
Table 6. 1 is generated from the FRFs in figure 6. 1 7. The figures in  the table are 
represented in  poles and zeros and their relative angles where they would stand in  a 
c i rc le .  I n  the FFT spectrum, figures 6. 1 6  and 6. 1 7  wou ld overlap, but the new 
technique separated the resonance effect shown in figure 6. 1 6  from the mesh ing 
effects in figure 6. 1 7. 
1 03 
7 . 1  I ntroduction 
Chapter 7 
Conclusion and Discussion 
As d iscussed in the earl ier chapters, the current FFT technique has its pitfa l l  of 
overlapping of frcquencies, which makes it d ifficult for vibrat ion analysis. Solving 
th is  problem has prompted the last part of this project. 
An invest igation to explore th is subject has been carried out and as a resu l t, the 
cepstrum technique using homomorph ic fi ltering was presented. I t  has been shown to 
be an effective and efficient tool in the experimental part in Chapter 6. 
Th is chapter briefly prov ides an overview of the previous chapters in this thesis, and 
presents the conc lusion and the recommendations for future work. 
Chapter I introduced what this thes is is a l l  about and the reason for the cepstrum 
techn ique. Chapter 2 presented various previous researches and the methodo logies on 
pred ictive maintenance and chapter 3 described the maintenance strategies and the 
h istory, that is, where the technology was, where i t  is  and where is going as far as 
maintenance i s  concerned. Chapter 4 introduced FFT technique and presented case 
studies using the techniques and the pitfal ls  were identi fied, which is the reason why 
cepstrum was presented. Chapter 5 explai ned the theory of cepstrum, homomorphic 
and poles and zeros representations and Chapter 6 was the experimental part that 
demonstrated the effectiveness of the cepstrum technique and homomorphic fi ltering 
to separate resonance effects from the meshing frequency. 
7.2 Discussion 
The survey on the maintenance strategies presented in th i s  thesis shows that 
preventive maintenance is not as cost effective as predictive maintenance. The 
pred ictive mai ntenance FFT technology has been extremely usefu l  in accurate ly 
d iagnosing machinery condition. The major FFT pitfal ls  are: 
• FFT can diagnose any bearing fault or a gear with broken teeth, but w i l l  not 
d iagnose the root cause. Examples of how mathemat ical approach was used in 
1 04 
addition with the FFT data to establ ish the root cause of the fai l ures are 
presented in chapter 4.  
• The overlapping of many harmon ics, sidebands, resonance effect and mesh 
frequencies that make d iagnosis of a gearbox cumbersome; th is  was the reason 
the author used cepstrum technique to diagnose gearbox fau lts under d ifferent 
load ings, which was presented in chapters 5 & 6, where resonance effect was 
separated from mesh ing frequency. 
The test resu lts demonstrated that noise generation is a complex mechan ism, and the 
cepstrum technique has successfu l ly recovered the original sources. An external ly 
measured v ibration signal is the convolution of the impu lse response and the source 
s ignals.  A fier transformation to the cepstrum domain, the source and the transm ission 
path effects are deconvolved and become add itive. Gearbox v ibration spectra 
normal ly contain sidebands due to modu lation of toothmeshing frequencies and the ir  
harmonics, and the strength of such sidebands usua l ly indicates deteriorat ing 
condition. 
The spacing of such sidebands gives valuable diagnostic information as to the ir  
source, s ince both ampl itude and frequency modulation at  the same frequency give 
sidebands w ith the same spac ing. Most faults give a combinat ion of ampl itude and 
frequency modulation at the same time, the re lative proport ions and phase 
re lationsh ips being dependent in a complex way on the response properties of the 
indiv idual machine, and so a d iv ision into the two categories is less usefu l  than a 
measure of the overal l  sideband "act iv ity" with a given spacing. 
The cepstrum is good both for detecting the presence and growth of s idebands in  
gearbox vibration spectra, and for ind icating their mean spacing over the entire 
spectrum, wh ich has proved su itable for the detection and d iagnosis of fau lts. 
Cepstrum has advantages in able to extract spectrum period icity with respect to faul t  
detection and insensitive to secondary effects l ike signal transm ission path and phase 
re lationsh i p  of amplitude and frequency modu lation . 
The cepstrum, with respect to fau lt d iagnosis, was able to measure the average 
sideband spac ing over a very wide rangc of the spectrum, thus al lowing a very 
accurate measure of the pac ing, being representat ive of the whole spectrum. The 
cepstrum has the abi l ity to concentrate the sign ificant sideband information in a very 
effic ient manner. 
1 05 
The cepstrum can be consid ered as an aid to the i nterpretation o f  the spectru m. i n  
part icular \\ i th respect to sideband fam i l i es. because i t  presents the i n format i on i n  a 
more efficient manner. 
Gear 
Condition 
Undamaged 
Cepstra after Homomorphic F i ltering 
Loadi ng: l OON m 
-20 
-40 
-60 '--------'------'-------'-o 200 400 600 
N u mber o f  Samples 
Cracked 4 
Tooth 
2 
o 
-2 - -. 
_4 �------L-------�------�------J 
Spall  Tooth 
o 
30 
20 
1 0  
o 
200 400 500 
N u mber o f  Samples 
200 400 600 
N u mber of Samples 
Figure 7. 1 :  Cepstra for Different Measurements 
l OCi 
SOD 
800 
The experimental data shows the d iagnosi s of a gearbox \vith a number o f  
measurement points o n  t h e  same gearbox \\ i t h  undamaged. cracked and spall tooth 
meshing excitat i ons. The res ults sho\\TI in figure 7. 1 are the cepstra of the three 
di fferent cases. 
Gear Smoothed Spectra after Homomorphic F i l tering 
Condition 
U nd amaged 
1 0·5 L-______ L-______ L-______ � ______ � ______ � __ 
o 2000 4000 6000 8000 1 0000 
Number or Samp les 
FigUl'e 7,2 : Cepstt-a fo.' DifTe.'ent MeasUl-ements 
A l l  machines ha\ e some p hysical characteri stics that reflect their conditions. A 
normal running leyel for that characteri stic is establ ished \\·hen the machi ne. in this 
case a gearbox is  i n  good condition. any sign i fi c ant dev iation from that level g ives 
\\ arn ing that a fault  ma\ be deyeloping and mai ntenance wi l l  be required. The three 
di fferent cases in figure 7 . 1 demonstrate a \·ari ation i n  the cepstra. \\·h ich i s  an 
i nd ication that fau lts hm·e de\ eloped. The faults are the crack and spal L \vhich \\ ould 
overlap under FFT analysis.  but  cepstru m techn i q u e  separate them. through 
homomorphic fi l teri ng. 
1 07  
Gear Smoothed Spectra after Homomorphic F i l teri ng 
Cond it i o n  
Cracked 
Tooth 1 0° 
1 0-5 
Spal l  Tooth 
1 00 
1 0- 1 
1 0-2 
1 0-3 
1 0-4 
0 2000 4000 6000 8000 
Number of Samples 
\ J 
\,� 
10000 
10-5 L--_-'---_---'-__ '----_---'---_-----'--
o 2000 4000 GOOO 8000 1 0000 
umber of Samples 
Figure 7.3: Cepstl11 fOI' DifTel'ent MeasU l'ements 
1 09 
Fi gures 7 .2  and 7. 3 are the resonance peaks. "'hich are d ue to the nature o f  the 
structure of the machine. including all i ts components l i ke the gearbox. pi ping, and 
support system. They are not sel f excited but can be \' ie\\ ed as l urki ng wi thin the 
structure of the system. ready to cause " iolent react ions \\'hen excited. They result 
functions of the mass. st iffness and damping of a structure. 
ld' Peak B 
10 . 1 
I� � �� .� I r � 1 ,? · 1,,4 �1r! m I 1 0 -
1 0,3 
I , 
1 0'4 \J 
Peak A 
1 0,5 L-__ ---' ___ --'-___ --'-___ -'-___ � 
o 2000 4000 GOOD 8000 1 0000 
N umber of Samples 
FigUl"e 7.4: E.ffect of Resonance 
When the natural freq uency of the gearbo x  \\ as excited. it ble\\ up peak B ( figure 7 , 1 )  
which res ulted i n  a l arge increase i n  the am pl i tude of \ ' ibration o f  that freq uency. Peak 
A demonstrates the effect of resonance. \\ h ich is not in peak B. The resonance effect. 
which is in the transmission path. i s  lurked together "'i th the forci ng effect to produce 
the output signal .  The F FT technique could not iden t i fy if the change \vas i n  the 
transmission path or from the forcing frequency. which the cepstrum technique has 
separated as sho\\TI in figure 7 .4 .  
Comparing the resonance peaks for the di fferent cases: undamaged. cracked and spaJ l 
gears. the peaks are the same. sho\\'ing that the change \\'as not i n  the transmi ssion 
path but from the forcing freq uency. due 10 the spal l  and the crack. 
1 09 
Figures 7 .  5 and 7 .0  sho\\ ho\\ . s imi lar to the mechanical Y i b ration case. poles and 
zeros of the freq uency response funct ions ( F R F ) o f  the gearbox cou ld be created and 
evaluated. The poles and /.eros alone suggests \\·hether the gears are undamaged or 
damaged. but the changes i n  the FRF al so con firm the c lai m that the changes are due 
to the forci ng e ffect fro m  the spal l  and crack. and not the transmi ssion path e ffect. by 
using the cepstrum technique o f  homomorphic b l ind d ecom olution. 
Gear 
Cond it ion 
Undamaged 
2 .5 
2 
1 .5 
J 
• 
J 
I 0.5 f 
o 
-0.5  
- 1  
Frequency Response F unction 
- 1 .5  L..-___ -"-___ -'-___ --'" ____ '--__ _____ o 200 400 600 800 1 000 
N umber o f  Samples 
FigUl'e 7.5: Cepstm rOl' DifTel'ent Measu l'ements 
I I ( )  
Gear 
Condition 
Cracked 
Tooth 
Spal l Tooth 
2 5  
2 
1 5 I 1 , 
0.5 , 
I � 0 • , (J: i -0 .5 : , 
- 1  , 
Frequency Response Function 
,� 
" 
1 1 
I '  , I  
1 1 
1 1 
, 
: � 1� � :: :lJr \1 V" : . :: I' I I " , \ I I i' 1 1 , I 
\ 
, 
\\ \ \ \ 
.... __ .. 
.,� - - .. 
- 1 .5 - � 
" 
11 
� � 
-2 -I 
-2 5 r 0 200 400 600 800 
umber of Samples 
2.5 
2 f\ 
I 
I 
1 .5 t , I 
\ 
, I 
1 , I  � I 0 5  J� � 1 1  , 1 1  "" ,  - � - -J�1 -- - -0 : 1 1 1  r I , , , I '  
I . , 
0 5  I , 
�. I , 
-:�� r , , I \ I I, , , I , I' , I I I I 0 200 400 600 800 
Number of  Samples 
1000 
I 
1 000 
FigUl'e 7,6: Poles and Zel'os Fl'equency Response Function (FRF) 
I 1 1  
7.3 Conclusion 
I n  conclusion, this thesis makes the fol lowing contributions: 
• The nature of maintenance practices in New Zealand major industry was the 
first contribution in  th is thesis. The maintenance practices were reactive, 
preventive and predictive. The survey showed that most of the compan ies 
operate on react ive maintenance and few on predict ive. My vis its to the power 
stat ions showed that only Genesis Power Station has on- l i ne mon itoring, the 
rest only employ the serv ices of vibration analyst to mon itor their mach ines 
once a year. Only Fonterra out of other food companies operate on predict ive 
maintenance. My visit to Griffins Food and its associated ones revealed that 
they practice preventive and reactive maintenance. New Zealand Steel out of 
other steel manufacturing companies pract ice preventive and pred ictive 
maintenance. The medium size companies mainly practice reactive 
maintenance, although some of them claim to practice preventive, but after 
invest igat ions i nto these practices, they d id not observe the routine checks that 
preventive maintenance required. 
Predictive maintenance was demonstrated in some of the companies, using 
FFT technique that was presented in  the case stud ies to identi fy mach ine 
problems, which was helpful  in schedu l ing the necessary repairs and saved the 
companies thousands of dol lars in  terms of lost production and wasted 
manpower and materials or parts. It put the manager in charge of the machine, 
instead of the machine being in charge of the manager. When the FFT 
technique identified the machine problem, it al lowed the maintenance manager 
to d i rect the correction of that problem at h is  convenience. When he d id not 
know the problem, he must react when the mach ine broke regardless of the 
day and hour. This demonstration made the companies understand the huge 
benefits in pred ictive maintenance, using FFT techn ique. The main pitfa l l  of 
the FFT techn ique is the overlapping of many harmon ics, sidebands and 
resonance effects, wh ich make the d iagnosis more cumbersome, this is  a 
problem cepstrum techn ique using homomorphic fi ltering has resolved. 
1 1 2 
• The cepstrum technique was original ly applied to analysc speech with the aim 
of detecting the harmonic structure of voiced sounds and measuring voice 
pitch, but now presented for the purpose of condition monitoring especia l ly in 
the diagnosis of a gearbox faults. 
• The cepstrum technique included homomorphic fi Itering to separate the 
gearbox cepstra, which resulted to the ident ification of the cause of the 
changes in the expected good performance of the gearbox. The fi ltering 
separated the s ignal due to the undamaged gear from the cracked and spa l l  
ones as shown in table 7 . 1 .  
• The inclusion of poles and zeros analysis in the cepstrum techn ique produced 
the frequency response function of the gearbox as shown in figures 7.5 and 
7.6. The changes in the outlook of the poles and zeros frequency response 
functions also val idate that the changes are from the meshing and not the 
transmission path. 
• Final ly, the resonance effect i n  figures 7 .2 and 7.3 also val idate that the 
changes are in the transm ission path because they are the same to the d ifferent 
cases. 
7.4 Recommendations for Future Work 
Although a significant amount of work with regard to gearbox condition mon itoring 
based on cepstrum technique was carried out, sti l l  there are lots to be done to gain a 
thorough understanding i n  th is respect. 
• This thesis has gone through series of tests. Th is technique needs to be 
extended to gearboxes with variable speed. 
• More research needs to be carried out to reduce or replace the zooming on the 
sidebands and mesh frequencies of the gearbox. 
• The work could further be extended by averaging the excitation-dominated 
parts of the original cepstra to obtain the best estimate of the exc itation 
function. This average could be subtracted from all the individual cepstra, 
1 1 3 
which could be curve-fitted in e ither the cepstrum or spectrum domain for 
est imation of the structural response functions. 
• More research needs to be carried out for further understanding of the 
relationsh ip  between the signal energy and the fau lt severity so that tables or 
charts can be produced to he lp in the gearbox condition monitoring. 
1 1 4 
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1 25 
A. 1 Transducers 
APPENDIX A 
The selection of the proper transducer can be as important as any of the steps in data 
acqu isit ion. The selection shou ld be made with some care and thought as to the types 
of defects to be detected, frequency range involved, required location of the 
transducer, etc. 
V ibrat ion data for machinery can be gathered by selecting the right transducer from 
displacement, ve loc ity or acceleration transducers. The equat ions that govern 
displacement, velocity and acceleration transducers are presented. 
A . I . I  Disp lacement Transducer 
Under this appl ication, Xi and Xm are the absolute displacements [ 1 20], whi le Xo is zero 
as weight  M acts along the x-axis, hence equation 5 .  
� = B 2�KsM 
Where 
M=  Mass 
D = I ntegrating Device 
Ks = Stiffness 
B = Damping 
Frequency response for this displacement sensor is shown i n  equation 4.6 
Xo (iw)= (iw)2 /w� Xi (iw / wn ) 2 + 2r;iw / wn + 1 
1 26 
A. I 
A .2 
Displacement transducers measure v ibratory displacement where a fixed reference for 
rel ative d isp lacement measurement is not avai lable. The transducer is dri l led i nto a 
stationary reference. Displacement transducers are cal led Eddy Current Probes. I t  i s  
has low frequency response, measures the actual d isplacement of the shaft within the 
bearing [ 1 20] .  The l imi tations are inab i l ity to measure h igh frequency, expensive to 
insta l l  and only used for low speed mach ines be low 600 cyc les per second [ 1 20] .  
t 
xi 
Motion to be 
measured 
k stiffness 
B (damper) 
F igure A. I :  Displacement Sensor 
A . I .2 Velocity Transducer 
eO = kexO 
Equation A.5 can be rewritten as shown in equation AA 
1 27 
Case 
xo 
Relative 
d i sp lacement 
transducer 
A .3  
Therefore, 
�o (ilU) X '  I 
AA 
A.S  
The configuration of  velocity transducer i s  s im i lar to figure A . I ,  but measures 
velocity Xi instead of d isplacement Xi. I t  i s  an electromagnetic  sensor, when it  
v ibrates; its magnet remains stationary due to i nertia. The magnet moves with in a coi l  
that eventua l ly  generates e lectric i ty that is  proportional to the ve loc ity of the mass. I t  
has the abi l i ty to operate under h igh temperatures and easy to use. I ts l im itat ions are 
that i s  has low s ignal to noise ratio and not su itable for low or h igh frequency 
measurements [ 1 20] . 
A. I .3 Acceleration Transducer 
The des ired i nput in th is  respect is XI equat ion S can be written as shown i n  equation 
A .6. 
�=�.O (D)= k 
D2xi xi D2 / lU� + 2�D/lUn + 1  
k =�cm /(cm / s2 ) 
wn 
A.2 Operation of Piezoelectric Accelerometer 
A.6 
The transducer selected w ith this spectrum analyzer is a piezoelectric accelerometer, 
because It has very wide range of frequency, ampl i tude and temperature. 
It is of the same configuration as figure A.2.  The mass M accelerates at Xi, the spring 
deflection Xo causes the force that w i l l  produce the acceleration, therefore, Xo is a 
measure of acceleration Xi. 
1 28 
It is the most important pickup for vibration, shock and genera l-purpose absolute 
motion measurement [ 1 20] .  
Piezoelectric came mainly i n  two types of materia l ;  q uartz and synthet ic ceramic, but 
the most used is the quartz. The piezo-electric element in  figure A .2  is squeezed 
between the mass and the base, when it experiences a force, then generates an electric 
charge between its surfaces. The force required to move seism ic mass up and down is 
proportional to the acceleration of the mass. The force on the crystal produces the 
output signal, which is  proportional to the acceleration of the transducer. The 
fol lowing should be considered whi le selecting accelerometers: 
I .  Frequency Range 
2. Dynam ic range 
lep Ampl ifier 
F igure A.2 :  The Piezoelectric Accelerometer 
A .2 . 1 Frequency Range 
Pre-Ioad ing spring 
Seism ic mass 
Piezo-e lectric crystal 
e lement 
Base 
Mounting stud 
The h igh frequency response is l im ited by the resonance of the seism ic mass coupled 
(or bolted) to the springiness of the piezo element. 
The resonance produces a very h igh peak in  the response at the natural frequency of 
the transducer, about 30kHz. 
A ru le of  thumb is that an accelerometer is usable up to about 1 /3 of its natural 
frequency. Data above this frequency wi l l  be accentuated by the resonant response. 
1 29 
Vdb 
1 Hz Fr/3 
Usable Range 
Figure A .3 :  Accelerometer Frequency Response 
Xo 
M 
Figure AA:  Construction of a Transducer 
Equation 4 . 1 1 is obtained by applying Newton's  law to the mass M 
k, xo + Bxo =MXm =M(i, -io )  
A.2.2 Dynam ic Range 
Log Frequency 
A .7  
I t  i s  the  range of variable that an  instrument is designed to measure, signal to noise 
ratio (SNR) .  The variable is the ratio of the ampl i tude of the largest signal to the 
smal lest detectable dynamic input that the instrument can accurate ly and faithfu l ly 
measure. L inear or RMS averaging can be used to reduce the noise floor and improve 
the dynamic range. Dynamic range is represented in dec ibe ls  (dB), where the dB of a 
number N is defined in equation A.8 .  
1 30 
The 96dB dynamic range of the data col lector indicates that the instrument can handle 
a range of input of 65,536 to I .  Most spectrum analysers have gone up to 1 6  bit 
analog-digital (AD) converters and c laim 96 dynam ic range. 
dB = 20 log N A.8  
A. 3 Cepstrum and  Homomorphic Filtering 
The major appl ication of the power spectrum in mach ine v ibration is  to detect and 
quant ify fam i l ies of uniform ly spaced harmon ics, such as bearing fau lts, missing 
turbine blades and gearbox faults. 
The cepstrum and auto-correlation are closely related. The main d ifference is that the 
inverse FFT is performed on the logarithm of the power spectrum itse lf. The auto­
corre lation is mainly dom inated by the h ighest values of the spectrum .  The logarithm 
used when computing the cepstrum causes it to take lower level harmon ics more into 
account than auto-correlation. The cepstrum main ly reacts to the harmonics present in  
the  auto-spectrum, but the autocorrelation is strongly influenced by the  shape of the 
time signal .  The auto spectrum of the d ifferent gear cases the author investigated are 
shown in the fol lowing figures. When we look at the auto-spectrum of the s ignal ,  
"forest" of harmonics is  c learly seen. Figure . .  i l lustrates that the  forc ing function and 
transfer function effects are separated in  the cepstrum 
Looking at the cepstra of d ifferent gear fault cases shown in the fol lowing figures, the 
advantages of using homomorphic fi lter wou ld be appreciated. Homomorphic fi ltering 
is  a determ in istic process in the sense that fixed and pre-given parts of the complex 
cepstrum which are related to the undesired components are e l im inated. The success 
of the method depends primari ly  on the rate of the separation of the indiv idual 
components in t he complex cepstrum .  The main advantage of homomorphic fi l ters for 
d i fferent deconvolution problems over other determ inistic fi l ters i s  the fact that no 
prior knowledge is  necessary, the necessary parameters can be determ ined during the 
process itse l f. 
1 3 1  
Deconvolution by homomorphic filtering is an attractive method as it reduces a 
convolution to an additive superposition of the components and the separation of the 
individual components in the complex cepstrum. 
The poles and zeros of the FRF were extracted to evaluate the stabil ity of the system. 
Poles and zeros give useful insights into a filter' s response, and could be used for 
filter design. Poles outside the unit c ircle woul d  represent instabil ities and could 
presumably be neglected. 
Zeros outside the unit circle could not be dismissed, if they were, it would sti l l  be 
possible to detect changes in the resonances (or poles) which is the primary aim in 
monitoring. The best bit transfer function could be seen in figures . . .  
Appendix A: Cepstrum Technique and Homomorphic Filtering 
Undamaged Gear - Autospectrum 
- 10r---�----.----'r----r----.-----r---�----.----' 
-20 
-30 
-40 
-50 
-60 
-70 
-80�--�----�--�----�--�----�----L---�--� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
1 32 
0 
- 1  
-2 
-3 
-4 
-5 
-6 
-7 
0 0.5 1 .5 2 2 .5  3 
Cepstrum - Undamaged 50Nm 
O ��------------------------------�� 
- 1  
-2 
-3 
-4 
-5 
J 
•• 
3 .5  
X 1 04 
-6�----�------�------�----��-----L------� o 2000 4000 6000 8000 1 0000 1 2000 
1 33 
Cepstrum - Undamaged 1 00Nm 
0 .1 
- 1 
-2 
-3 
-4 
-5 
-6 
0 2000 4000 6000 8000 1 0000 1 2000 
FRF & Phase 
1 34 
20 
0 
-20 
-40 
-60 
0 200 400 600 800 1 000 1 200 
4 
2 
0 
-2 
-4 
0 200 400 600 800 1 000 1 200 
Power Spect ra of the Sep arated Components 
0 
-- Orig 
-20 
-- Rand 
-- Disc 
-40 
-60 
CD -0 
-80 
- 1 00 
- 1 20 
- 140 '--_--'-__ .L.-_----L __ ...l.....---_--L __ ----L-_-----l'--_--'-_----' 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (H z) 
1 35 
3 
2 
, 
" h � 
r , , I 
f I 
0 , J 
- 1  
-2 
-3 
-4 
-5 
0 200 400 600 BOO 1 000 1 200 
Orig ina l  Signal  
5'---'---�----T---�----�--'---�----T---�--� 
-: 
-: 
1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
o 1 000 2000 3000 4000 5000 6000 7000 BODO 9000 1 0000 
D iscrete Part 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
1 36 
(l) � 
0 
-20 
-40 
-60 
-80 
- 1 00 
- 1 20 
- 1 40 
0 1 000 
Power Spect ra of the  Separated Components 
Undamaged 50Nm 
2000 3000 
F requency (Hz) 
4000 
Cepstrum - Undamaged 50Nm 
-- Orig 
- Rand 
Disc 
5000 6000 
o ��------------------------------�--� 
- 1  
-2 
-3 
-4 
-5 
_6 � ______ L-______ L-______ L-______ L-____ �L-____ � o 2000 4000 6000 8000 1 0000 1 2000 
1 37 
Smoothed Spectrum - Undamaged 50Nm 
1 0. 1  .----,----,----,.-- --,------:,-------=1 
1 0.6 '---___ I---___ I---___ L-___ I---___ I---__ ---' o 2000 4000 6000 8000 
Spect rum Compared  with Original 
Undamaged 50Nm 
1 0000 1 2000 
- 1 0,----,.----,,----.-----.----,,----. 
-20 
-30 
-40 
-50 
-60 
-70 
-80 
-90 
- 1 00 
- 1 1 0L-----�-------L------�----�L------L------� o 1 000 2000 3000 4000 5000 6000 
1 3 8 
FRF After Curving 
Undamaged 50Nm 
20 
1 0  A 0 
- 10  
0 200 400 600 800 1 000 1 200 
Phase - Undamaged 50Nm 
2 
o 
- 1  
_2 L-______ L-______ � ______ _L ______ _L ______ � ______ � o 200 400 600 800 1 000 1 200 
FRF Compared - Undamaged 50Nm 
2.5.------.-------.-------.------.-------.-------, 
2 
1 .5 J. : 1 
1 1 
r 1 
1 1 
1 1 
, 
I , I 
0.5 f 
o 
-0.5 
-1  
- 1 .5 L-______ L-______ L-______ L-______ L-______ L-____ -.-J o 200 400 600 800 1 000 1 200 
1 39 
FRF - 2nd Harmonic 
Undamaged 50Nm 
20.------,------�------�------�------._----__. 
10 
o 
- 10
L-
----�------�------�----�L------L------� o 200 
o 
- 1  
400 600 800 
Phase - 2nd Harmonic  
Undamaged 50Nm 
1 000 1 200 
_2 �--____ � ______ -L ______ �� ______ � ______ -L ______ � o 200 
2 
1 .5 
0.5 " � 
/ 
0 
-0.5 
- 1  
0 200 
400 600 800 
FRF Compared - 2nd  Harmonic 
... -.. 
400 
Undamaged 50Nm 
" \ j 
I 
I 
rll I I " 
� 1 I I l I I I I 
I I 
I I I \ I 
\ 
, � 
�  11  I U 11 w n 
I t  
I I 
I u It 
600 
1 40 
\ ,-� .. 
\ .' "- -' .' 
800 
1 000 1 200 
,�.  
1 000 1 200 
Power Spectra of the  Separated Components 
Undamaged 1 00Nm 
O �----�----.------.----�--�==�==� 
-- Orig 
-- Rand 
-20 -- Disc 
-40 
!g -60 
-80 
- 1 00 
- 1 20 '---__ ---'-___ -.1... ___ --'-___ -'-___ -'--__ ----' o 1 000 
0 1 
- 1  
-2  
-3 
-4 
-5 
-6 
0 2000 
2000 3000 
Frequency (Hz) 
4000 
Cepstrum - Undamaged 1 00Nm 
4000 6000 8000 
1 4 1  
5000 6000 
I. 
1 0000 1 2000 
Smoothed Spectrum - Undamaged 1 00Nm 
1 0° r------.-------.-------.------.-------.-----� 
2000 
/ fiwJv 
4000 6000 8000 
Spectrum Compared  with Original  
Undamaged 1 00Nm 
1 0000 1 2000 
- 1 0.------.-------.-------.------.-------.------. 
-20 
-30 
-40 
-50 
-60 
-70 
-80 
-90 
- 1 00�----�------�------�------�------�----� 
o 1 000 2000 3000 4000 5000 6000 
1 42 
FRF - Undamaged 1 00Nm 
20.------.------.-------.------.-------.------. 
1 0  
o 
- 1 0  
-20�----�-------L-------L------�------�----� 
o 200 400 600 800 1 000 1 200 
Phase - Undamaged 1 00Nm 
2r-------,-------�------��------�------�------_,
o 
- 1  
_2 � ____ �� ____ �L_ ____ �L_ ____ �L_ ____ � ______ � 
o 200 400 600 800 1 000 1 200 
FRF Compared - Undamaged 1 00Nm 
2 
• 
" 
1 .5 1 1  � 1 1  / / " / /  t 
1 /  / 
j� / / • / , J / / \ \ / 
0.5 / / , / 
/ " / ..... / I / .... , It I ,  r .. -.... ,.�-, 
/ ( n / "'--�'" � .. - ... - \ ' 0 1 r , I , J , / \ I J '. • J 1 -0.5 , 1 , , l 
\\l 'J - 1  , / � \,  " " t' 
- 1 .5 
0 200 400 600 800 1 000 1 200 
1 43 
FRF After  Curving - 2nd Harmonic 
Undamaged 1 00Nm 
20 �----�----��------�------�------.-------. 
10  
o 
- 1 0  
-20�----�------�-------L------�------�----� o 200 400 600 800 1 000 1 200 
Phase - 2nd  Harmonic 
Undamaged 1 00Nm 
3.-------.-------.-------.-------.-------.------.
2 
o 
-1 �------�------��------�------��------�------� o 200 400 600 800 
FRF Compared - 2nd Harmonic 
Undamaged 1 00Nm 
1 000 1 200 
2.5.-------.-------.-------.-------.-------.------. 
2 
1 .5 
0.5 
0 
-0.5 
, 
, - 1  , , 
, 
- 1 .5  ........ 
-2 
0 
.. -, • ' f 
'_J 
200 400 
�-..... -�  
'--'" 
600 800 1 000 1 200 
1 44 
Cracked 
IT) 
"U 
20 
0 
-20 
-40 
-60 
-80 
- 1 00 
- 1 20 
0 
Power Spect ra of the  Separated Components  
Crack Tooth 50Nm 
1 000 2000 3000 
Frequency (Hz) 
4000 
Cepst rum - Crack Tooth 50Nm 
-- Orig 
- Rand 
-- Disc 
5000 
0 ��1--�----______________________ �1 __ � 
- 1  
-2 
-3 
-4 
6000 
_5 � ______ L-______ L-______ L-______ L-______ L-____ � o 2000 4000 6000 8000 1 0000 1 2000 
1 45 
Smoothed Spect rum 
Crack Tooth 50Nm 
1 0° �------�------�------�-------r-------'------� 
1 0·5 L-______ L-______ � ______ _L ______ _L ______ � ______ � 
o 2000 4000 6000 
FRF After  Curving 
Crack Tooth 50Nm 
8000 1 0000 1 2000 
2.5.-------.------..-------.------..------.,------.
2 
1 .5 J 1 I I� I' 1 1 1 1 , I  1 1 1 1 t 0.5 I • � t h , I n 
o " I 1 1  l ll l: �W ,I V" -0.5  
- 1  
- 1 .5  
-2  � 
I�I I :  11 I ' I I t '" 11 I I ' I f 'I I I 1 1 i � f � I 1 1  I '  1 1  � 
: � Ij • 
-2.5 '---------'---------'---------'----------'---------'--------' o 200 400 600 800 1 000 1 200 
1 46 
FRF - Crack Tooth 50Nm 
�r------'------�-------r------.-------'------' 
20 
1 0  
o 
- 1 0  
-20
0
�-----
2
�
00
------4�0
-
0
------5�00
------8�0-0
-----1-0
�
00
----�1 200 
Phase - Crack Tooth 50Nm 
2.------.-------.-------.------.-------.------.
o 
- 1  
-2�----�-------L------�------�------�----� 
o 200 400 600 800 
Compare Or ig inal  Signal  and Spectrum 
Crack Tooth 50Nm 
1 000 1 200 
20 .-.----.-------.-------.------.-------.------, 
o 
-20 
-40 
-50 
-80 
- 100�----�-------L------�------�------�----� o 1 000 2000 3000 4000 5000 6000 
1 47 
FRF - 2nd Harmonic 
Crack Tooth 50Nm 
40�----�------�------�------�------.-------. 
20 
o 
_20 L-____ -L ______ � ______ � ____ � ______ _L ______ � o 200 400 600 800 1 000 1 200 
FRF Phase - 2nd  Harmonic 
Crack  Tooth 50Nm 
2.-------.-------.-------.--------.-------.-------.
o 
- 1  
_2 L-______ L-______ L-______ L-______ L-______ L-____ � o 200 400 600 800 
FRF  Compared - 2nd Harmonic 
Crack Tooth 50Nm 
1 000 1 200 
3�----��----��------�----��----��----� 
2 
o 
- 1  
-2  
..... 
11 
" 
• 
... _ .. 
_3 L-______ L-______ � ______ -L ______ -L ______ � ______ � o 200 400 600 800 1 000 1 200 
1 48 
Power Spectra of t he  Separated Components 
Crack Tooth 1 00Nm 
20 r-r---.-----�-----.----�--�==c===� 
-- Orig 
- Rand o 
-- Disc 
-20 
-40 
-60 
-80 
- 1 00 
- 1 20 '--__ --L ___ ---L. ___ --L-___ -L-___ -'--__ --' 
o 1 000 2000 3000 
Frequency (Hz) 
4000 
Cepstrum - Crack Tooth 1 00Nm 
5000 6000 
0.5r---�---�---�---�---�--__,
O ��I-----------------------+-I �  
-0.5 
-1 
-1 .5 
-2 
-2.5 
-3 
-3.5 
-4'----�----L----L---�---�--� o 2000 4000 6000 8000 1 0000 1 2000 
1 49 
Smoothed Spectrum - Crack Tooth 1 00Nm 
1 0° .------.-------.-------.------.-------.-----� 
1 0-4 '---____ ----' ______ ---L ______ --L ______ -'--______ -'--____ ----' 
o 2000 4000 6000 8000 
Spectrum Compared with Orig ina l  Signal  
Crack Tooth 1 00Nm 
1 0000 1 2000 
20 .-.----.-------.-------r------.-------�----_. 
o 
-20 
-40 
-60 
-80 
- 1 00 '-------�-------'--------L-----�-------L----� o 1 000 2000 3000 4000 5000 6000 
1 50 
20 
1 0  
0 
- 1 0  
-20 
0 
2 
0 
-2 
-4 
0 
3 
2 
0 
: t -1 I , 
, 10-' 
-2 
) 
-3 
0 
, I 
, 
V' 
� f 
I I I I
, J l t� 
U 
200 
200 
I� r '  :n � 
200 
FRF  After Curving 
Crack Toot h 1 00Nm 
400 600 800 1 000 1 200 
Phase - Crack Tooth 1 00Nm 
400 600 800 1 000 1 200 
FRF  Compared with Orig ina l  
Crack Tooth 1 00Nm 
, I 
n I 1 1  t I 1 \  
.. ' 
� I ....... J .. ....... ,.-' ... ,-� ... I 
'''_41"; "-' ' ... _. , 
.. 
.. 'I • I 
400 600 800 1 000 1 200 
1 5 1  
FRF  - 2nd Harmonic 
Crack Toot h 1 00Nm 
40 
20 
0 
-20 
0 200 400 600 800 1 000 1 200 
Phase - 2nd Harmonic 
Crack  Tooth 1 00Nm 
2 
o 
- 1  
-2�------�------�-------L-------L------�------� o 200 
3 
2.5 
2 
1 .5 
0.5 
0 
--�  -0.5 '---
- 1  
- 1 .5  
-2 
0 200 
400 600 800 
FRF Compared :  2nd Harmonic 
400 
Crack Tooth 1 00Nm 
I 
, 
f 
, ? , 
• 11 11 ,� 'I , 1 1  
" � 1 1 , I ' 1 
f � 1 I , IN I 1 1 1 , 1 I III ' n 
. �' , , l I 1 1  " 
U 
600 
1 52 
• l 11 
I 
, 
\ 
, \ 
, \,' / 
....... # .. 
800 
1 000 
' , ...... 
, 
I 
/ 
1 000 
1 200 
1 200 
6�----��------�------�-------r------�-------' 
4 
2 
o 
-2 
-4 
-6 
, 
I I , 
I 
4 , 
_B L---____ L-______ � ______ _L ______ _L ______ _L ______ � o 200 
0 
- 1  
-2 
-3 
-4 
-5 
-6 
0 0 .5 
400 600 
1 .5 2 
1 53 
BOO 1 000 
2 .5 3 
1 200 
3 .5 
X 1 04 
0 
- 1  
-2 
-3 
-4 
-5 
-6 
0 0.5 1 .5 2 2.5 3 3 .5 
x 1 04 
40 
20 
0 
-20 
-40 
-60 
0 200 400 600 800 1 000 1 200 
2 
0 
-2 
-4 
0 200 400 600 800 1 000 1 200 
1 54 
40.------.-------.-------.------.-------.------. 
20 
o 
-20 
-40 
-60L-----�-------L-------L------�------�----� 
o 200 400 600 800 1 000 1 200 
4.------.-------r------�------._------._----_.
2 
o 
-2 
_4 L-____ � ______ _L ______ _L ______ � ______ � ____ � 
o 200 400 600 800 1 000 1 200 
Power Spectra of the Separated Components 
40r-
--.---�--.---�---r---.--�==�==� -- Orig 
20 
-- Rand 
-- Disc  
o 
-20 
-40 
-60 
-80 
- 1 00 
- 1 20 
- 1 40 L-__ -1...... __ --..lI..-__ ---1-__ ------L ____ ---1-__ ------'-____ -L-__ ---L __ ---l 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (Hz) 
1 55 
Power Spect ra of the Sepa rat ed Components 
40r---�--'---�--�---'---'--�====c=� 
- Orig 
20 -- Rand 
-- Disc 
o 
-20 
!g -40 
-60 
-80 
- 1 00 
- 120 L-_-L.. __ L--_-I..-_ ____
 __ -I..-_ ____
 __ __l_ _ ___L_� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (Hz) 
Orig inal  S igna l  
o 
-50�-�-�-�-�--�-�-�-�--�� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
o 
-20�-�--I..--�-----I�-�---l---L-----I--L-� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Discret e Part 
50.--�-�-�-�--�-�-�-�--��
o 
_50 �_� _ __l_ _ _L _ ____I __ L-_ __l_ _ _L _ ___L __ L_� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
1 56 
Orig ina l  S igna l  
-50�--�--�--�--��--�--�--�--��--�--� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
50.---.---�--�--��--.---�---.--�----.---,
o ....  WdN __ _ 
_ 50 L-__ � __ � __ _L __ � ____ � __ � __ _L __ � ____ L_� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
40.---�--��--._--�----._--�----._--�--__. 
20 
o 
-20 
-40 
-60 
-80�--�----�--�--�L---�--�L---�--�----� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
1 57 
40�--�----�--�----�--�----�----r----.----' 
20 
o 
-20 
-40 
-60 
-80�--�----�--��--�----�----�--�----�--� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
600 800 1 000 1 200 
1 5 8 
40.---.---�----.----.----.---.----.----,----. 
20 
o 
-20 
-40 
-60 
-80�--�--�----�---L----L---�--�----�--� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
40.---�--�----�--�----�--�--�----�--_,
20 
o 
-20 
-40 
-60 
-80�--�--�----�--�----�--�--�----�--� o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
1 59 
600 800 1 000 1 200 
6r-----��------�------�------_r------�------_.
4 
2 
o 
-2 
-4 
-6 
, 
I 
I 
, I • J 
-8�------�------�------�-------L-------L------� 
o 200 400 600 800 1 000 1 200 
1 60 
0 
- 1  
-2 
-3 
-4 
-S 
-6 
0 O.S 
Cepstrum 5& 1 00Nm 
0 
- 1  
-2 
-3 
-4 
-S 
-6 
0 O.S 
1 .S 2 
1 .S 2 
1 6 1 
2.S 3 
2.S 3 
3 .S 
X 1 04 
3.S 
X 104 
40 
20 
0 
-20 
-40 
-60 
0 200 400 600 800 1 000 1 200 
2 
0 
-2 
-4 
0 200 400 600 800 1 000 1 200 
50Nm 
40 
20 
0 
-20 
-40 
-60 
0 200 400 600 800 1 000 1 200 
4 
2 
U 0 
-2 
-4 
0 200 400 600 800 1 000 1 200 
FRF l OONm 
1 62 
40 
20 
0 
-20 
-40 
CD 
� 
-60 
-80 
- 100 
- 1 20 
- 1 40 0 
Power Spectra of the  Separated Comp onents 
-- Orig 
-- Rand 
Disc 
2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (Hz) 
Power spectrum 50Nm 
Power Spectra of the Separat ed Components  
40 r-
--'---�--'--------'--�--�====�� -- Orig 
20 -- Rand 
Disc 
o 
-20 
!g -40 
-60 
-80 
- 1 00 
- 1 20 �--�----�--�----�---J----�----L----L----J 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (Hz) 
I OONm 
1 63 
Raw Signal 50Nm 
Orig ina l  S igna l  
50�--�--�--�--�--�----�--�--.----.---. 
o 
-50�--�--�--�--�--�----�--�--�--�--� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
20.---.---.----.---.---.---,.---.---.----.---.
o 
-20�--�--�--�--�--�--��--�--�--�--� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Discrete Part 
� �� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
l OONm 
Original Signal 
50 
0 
-50 
0 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
50 
-50�--�--�---L--�--�----L---�--�---L--� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
D iscrete Part 
-; o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
1 64 
Spa1l 50Nm 
Power Spect ra of the Separated Components  
Spal l 50 Nm 
40r-----.-----�-----.----�--��c===� 
-- Orig 
20 - Rand 
-- Disc 
o 
-20 
!g -40 
-60 
-80 
- 1 00 
-1 20 '-- _--'-___ -1-___ ...L-__ ---l ___ --L. __ --l o tOOO 2000 3000 
F requency (Hz) 
4000 
Cepstrum - Spal l  50 Nm 
5000 6000 
0.5 ,-- ----,-----,----r-----,----....... ----, 
O �+J--�I �------__ ��I--+I� 
-0.5 
-1 
- 1 .5 
-2 
-2.5 
-3 
-3.5 
-4 
-4.5 '-- _---'-___ --L. ___ --L ___ -L-___ -L-__ ---I o 2000 4000 6000 8000 1 0000 1 2000 
1 65 
Smoothed Spectrum - Spal l  50Nm 
1 0
° 
.-----�-------r------_r------._------._----� 
1 0-
6 � ____ -J ______ -L ______ -L ______ J-______ L-____ � 
o 2000 4000 6000 8000 
Spectrum Compared with Original 
Spal 1 50Nm 
1 0000 1 2000 
40.------.-------r------_r------._------._-----. 
20 
o 
-20 
-40 
-60 
-80 
- 1 00L-----�-------L-------L------J-------�----� 
o 1 000 2000 3000 4000 5000 6000 
1 66 
FRF Aft er Curving - Spal l  50Nm 
20 
1 0  
0 
- 1 0  
-20 
-30 
0 200 400 600 800 1 000 1 200 
Phase - Spal l  50Nm 
4 
2 
0 
-2 
0 200 400 600 800 1 000 1 200 
FRF Compared - 50Nm 
2.5 
2 � 1 
1 .5 ., t • , It , , I  1 
• \ 1 . .  (4 I t  l� l 0.5 � 1 1  , 1 1  ...... ,--I 1 1  .... ., ,. .. " I 
0 
I : M I '\ I I I � I � � , -0.5 I I I I 
, \ 
1 I 
- 1 � t , l � I 
, 
- 1 .5 I I 
-2 
11 • 
-2.5  
0 200 400 600 800 1 000 1 200 
1 67 
FRF - 2 n d  H a rm o n i c  
S p a l l 50Nm 
20.------.-------.-------.------.-------,------. 
1 0  
- 1 0  
-20�----�-------L-------L------�------�----� 
o 200 400 600 800 
P h a s e  - 2 n d  Harm o n i c  
S p a l l 50Nm 
1 000 1 200 
2.------,.------.-------.-------.-------.-------.
o 
- 1  
-2�------L-------L-------�------�------�------� 
o 200 400 600 800 
FRF C o m p a red - 2 n d  H a rm o n i c  
S p a l l 50Nm 
1 000 1 200 
2 . 5.------,.------.-------.-------.-------.-------. 
2 
1 . 5 
0.5 
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0 ....  ""-"� 
-0 . 5  �"'''  �-
� 
- 1  
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- 2  
0 200 400 600 800 1 000 1 200 
1 68 
l OONm 
Power Spectra of the Separated Components 
Spa l l 1 00Nm 
0r-----�----�----�----�--��==� 
-- Orig 
- Rand 
-20 -- Disc 
-40 
!g -60 
-80 
- 1 00 
- 1 20 
0 1 000 2000 3000 4000 5000 6000 
Frequency (Hz) 
Cepstrum - Spal l 1 00Nm 
0 1 -' J I I 
- 1  
-2 
-3 
-4 
-5 
-6 
0 2000 4000 6000 BODO 1 0000 1 2000 
1 69 
Smoothed Spectrum - Spal l 1 00Nm 
1 0° .------.-------.-------.------,,------.-----� 
1 0-5 '--____ --' ______ ---'-______ --1-______ ----1.-______ -'--____ ---' o 2000 4000 6000 8000 
Spectrum Copared with Original  
Spal l 1 00Nm 
1 0000 1 2000 
o.------,------�------�------�------�----__. 
-20 
-30 
-40 
-50 
-60 
-70 
-80 
-90 
- 1 00'--------'---------'---------1-----------1.--------'---------' o 1 000 2000 3000 4000 5000 6000 
1 70 
FRF After Curving - Spa l l  1 00Nm 
20�----�------�------�------�------.-------. 
10 
o 
- 1 0  
_20 L------J ______ -L ______ -L ______ � ______ � ____ � o 200 400 600 800 1 000 1 200 
Phase - Spa l l 1 00Nm 
2.-----_,.-----_,,_-----,�----_,,_----_,,_----_.
o 
- 1  
_2 � ______ L_ ______ � ______ -L ______ _L ______ � ______ � o 200 
2 
i 
11 
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11 I t 
1 1 , I 
1 1 
1 1 
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, I I 
, 
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FRF Compared wit h  Original 
� 
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: . I t 
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n � \ I t I \ H .J ' I t I ' 
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600 800 
1 7 1  
1 000 1 200 
I 
...... � ... 
1 000 1 200 
FRF - 2nd  Harmonic 
Spal l 1 00Nm 
20 
1 0  
0 
- 1 0  
-20 
0 200 400 600 800 1 000 1 200 
Phase - 2nd Harmonic 
Spal l 1 00Nm 
2 
o 
- 1  
_2 �------�------L-------�------L-----__ L-----� o 200 400 600 800 
FRF Compared - 2nd Harmonic 
Spal l 1 00Nm 
1 000 1 200 
2.5,-------.------,.-------.------,.------,,------. 
2 
1 .5 
0.5 
0 1 J J 
-0.5 
� ... 
- 1  
- 1 .5  
-2 
0 200 
Autospectrum 50Nm 
, Jl 1 1 . . . .  1 1 I 
400 
-...... 
600 800 
] 72 
.. -.. 
, " 
1 000 1 200 
40�--�--�----�--�----�--�--�----.---� 
20 
o 
-20 
-40 
-60 
-80�--�--�----�--�--�----�--�----�--� 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
l OONm 
Or---.----.----.----.---,.---.----.----.---� 
- 1 0  
-20 
-30 
-40 
-50 
-60 
-70 
-80�--�--�----�--�--��--�---L----L---� 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Autospectrumoriginaisignai 50Nm 
1 73 
6.-------.-------.--------.-------.-------.-------. 
4 
2 
o 
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-4 
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0 200 400 600 800 1 000 1 200 
1 00Nm 
4 
3 
, 
2 , � , l , , " , " I , \ I , 
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" 
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0 11 • I 
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0 200 400 600 800 1 000 1 200 
Cepstrurn 50 & 1 00 
1 74 
0 
- 1  
-2 
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-5 
-6 
0 0.5 1 .5 2 
1 75 
2 .5  3 3 .5 
X 1 04 
O�------I�----------------------�I----� 
-1  
-2 
-3 
-4 
-5 
-6�----�----L-----�----�----�----�----� 
o 0.5 1 .5 2 2.5 3 3.5 
X 1 04 
FRFPhase 1 00Nm 
50Nm 
�.------.------�----�------�------.-----� 
20 
1 0  
o 
- 10  
-20 L-__ ...L-__ --L-��__.L:==:::::: ::::::L==:::::::::::� __ � 
o 200 400 600 800 1 000 1 200 
2.------.------�----�------�----��----�
o 
- 1  
-2�----�------�----�------�----��----� 
o 200 400 600 800 1 000 1 200 
1 76 
40r------,------�------_r------�------._----_. 
20 
o 
-20 
-40 
-60L-----�------�-------L------�------�----� 
o 200 400 600 800 1 000 1 200 
6r-----�------�------�------�------�----_.
4 
2 
o 
-2 
1-----' 
_4 L-____ � ______ � ______ _L ______ � ______ � ____ � 
o 200 400 600 800 1 000 1 200 
Powerspectrum 50Nm 
Power Spectra of the Separated Components 
40�-
-�--�--�--�--�--�--i===�==� -- Orig 
20 -- Rand 
-- Disc 
o 
-20 
!g -40 
-60 
-80 
-1 00 
- 1 20 L----L----L----L--__ � __ � ____ � __ �L_ __ _L __ � 
I OONm 
o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
Frequency (Hz) 
1 77 
Power Spectra of the  Separated Components  
- Orig 
-- Rand 
-20 
- Disc 
-40 
-60 
-80 
- 1 00 
- 1 20 
-1 40 L....-_ ___L__--L __ .L__----L __ L...._ _ ___L__--L __ .L__--I o 2000 4000 6000 8000 1 0000 1 2000 1 4000 1 6000 1 8000 
F requency (Hz) 
Rawsigna1 50Nm 
Origina l  Signal  
1 00.--.--.--�-�-�--.--�-._-�-_, 
-100 L....-_..l..-._....l...-_ _L_---L_--l. __ L....-_.L-._....l...-_-L-_--I o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
_�r .-- -,--:� -y-t-�-�r--��-,--� --r-�-.---,�-tJ,-��+t.-•• --.-:-�---.-�-i---,' 
o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
D iscrete Part 
50r---.--.--�-�-�--.--�-.--�-_,
_50 L....-_�_....l..._ _ _L _ ___L_� __ L....__.L_ _ ___L_ _ _L_� o 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
l OONm 
1 78 
Original  Signal  
50 
0 
-50 
0 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
Random Part 
20 
0 
-20 
0 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
D iscrete Part 
20 
0 
-20 
0 1 000 2000 3000 4000 5000 6000 7000 8000 9000 1 0000 
1 79 
APPENDIX B 
Preventive Maintenance Activities 
The routine inspection carried out under preventive maintenance by varIOUS 
companies do not allow them to track equipment performance, fai lure history or any 
other data that could, and should be used to plan and schedule tasks that would 
prevent premature fai l ures, extend the useful l ife of critical plant assets and reduce 
their  l ifecyc1e cost. 
Instead, maintenance scheduling has been, and in many instances sti l l  is, determine by 
equipment fai l ures or on the perceptions of maintenance personnel who arbitrarily  
determine the type and frequency of routine maintenance. 
For example, most faci lities that employ thermography inspections have it done once 
a year or every six months. This is a purely arbitrary decision, not supported by any 
kind of factual data. 
The fol lowing schedules shown in this appendix were the results of the work done by 
the author, stripping downs machines in a biscuit manufacturing company to come up 
with a wel l  define preventive maintenance that was embedded into SAP program. 
This was based on the history of the machines, manufacturers' details and fai lure rate. 
This result was not based on a data j ust as predictive maintenance is based on a valid 
data, predictive maintenance differs from preventive maintenance by basing 
maintenance need on the actual condition of the machine rather than on some preset 
schedule. Preventive maintenance is time-based; activities such as changing lubricant 
are based on time, l ike calendar time or equipment rum time, j ust as shown in the 
author's  schedules for PM in this appendix. 
Most people change the oil  in their vehicles every 1 ,500 to 3 ,000 km travel led. This is 
effectively basing the oi l  change needs on equipment run time, without considering 
the actual condition and performance capabil ity of the oi l ;  it  is changed because of 
time, this methodology is  associated with PM task. 
1 80 
Appendix B :  Preventive Maintenance (PM) 
The PM was set up for the machines shown in this chapter for a biscuit manufacturing 
company; the information was transferred to SAP software for their implementations 
Introduction 
The term Preventive Maintenance (PM) refers to any activity that is designed to: 
• Predict the onset of component fai lure 
• Detect a fai lure before it has an impact on the asset function 
• Repair or replace asset before fai lure occurs 
PM has two features: 
• Activity to be performed 
• Frequency at which it i s  performed 
Fai lure to assess the two features wil l  result to either under-maintaining or over 
maintaining of assets, although continuous improvement wil l  identify and eliminate 
these wastes (under-maintain ing and over-maintaining of machines) . 
Under-Maintaining of Machines 
• This i s  when preventive activities are not performed at too long intervals. 
Over-Maintaining of Machines 
• Performing P M  at more frequent intervals than necessary 
• Performi ng PM activities that add no value to the output. 
1 8 1  
PM Acti�ty Costs by Frequency 
Monthly 82% 
Quarterly 5% 
Semi-Annually 8% 
Annually 4% 
Over-Annually 1 % 
SOLLICH ENROBER 
Preventive Maintenance 
1 .  CLEANING:  
82% 
4% 
1 %  
• Clean and service CHOCOLATE PUMPS every 1 2  - 24 months. 
• Clean water FILTERS in the tamperer every 3 months to ensure full 
penetration regularly. 
• ThoroughJy clean the machine weekly 
• External cleaning of the machine daily 
• Clean the blower tip weekly 
• C lean blower turbine annually. 
2.  VISUAL INSPECTION - DAIL Y  
• Visual inspection for possible damage 
1 82 
• External cleaning of the machine 
• Lubricate the sl iding bearing of the detai l ing shaft with a lubricant 
approved for foodstuff. 
• Adjust clutch for chocolate pump when starting to work with tempered 
mass, especially when the clutch slides despite being adj usted 
previously. 
3. LUBRICATION: 
• Lubricate the CHAINS FROM GEAR DRIVE monthly (Renolds 
chain tube spray recommended) . 
• Lubricate CHOCOLATE PUMP  weekJy ( if  critical, once every 3 
days) . 
• Lubricate the SPREADER DISCS of the regulatory gears weekJy. ( if 
critical, once in 3 days). 
• A l l  shafts of the machine run in  ball bearings. These are sufficiently 
greased and need lubrication after a l onger period of time, 6-1 2  
months. 
BEARINGS DETAILS 
Bearing Location Bearing Type 
Soll ich Enrober 2205 - 2 off 
6207 0 - 3 off 
6205 - 2 off 
6007 - 2 off 
Other items Size 
Oil Seals • 35 x 50 x 7 - 1 0  off 
• 25 x 40 x 7 - 2 off 
ASS 207N (NTN) 1 0  off 
F lush Back. Parallel Parallel OD. 72 OD. 35 OD 
1 83 
BEARINGS DETAILS 
Bearing Location Bearing Type 
Sollich Enrober. Flow Pans 6004 D - 2 off 
• INA Brg. Rale 20 NPP FA 1 06 
• 20mm I D  
• 42mm OD - Parallel OD. Flush 
Back 
2 off 
Other items Size 
Oil Seals 20 x 47 x 7 - 2 off 
BEARINGS DETAILS 
Bearing Location Bearing Type 
Sollich Main DrivelPump 6308 2RSR - 1 off 
2205 RSR - 1 off 
Other items Size 
Oil Seals • 68 x 90 x 8 - 2 off 
• 50 x 68 x 8 - 4 off 
• 30 x 40 x 7 - 3 off 
FAG 1 62 1 2  - Flush Back 60mm ID - 1 off 
• Greased packed bearings should be cleaned and re-greased every 6-12  months 
• Fi l l  only 113 of free volume of the bearing with grease. 
4. CHAIN TENSIONING: 
• Check CHAIN DRIVES tensioning every 3 months. 
5. WIRE BELT TENSIONING: 
• Check INFEED BELT every 3 months 
• Check ENROBER CARRIAGE BELT every 3 months 
1 84 
• Check WIRE BELT TENSION every 3 months. 
6. AIR FILTER REPLACEMENT: 
• Replace AIR FILTER every 1 2  months depending on the qual ity of 
air. 
7. DRIVE SECTION: 
• The fitted belt cleaning brush assists with the removal of build up on 
the embossed belt .  This  bui ld up is removed and ej ected on to the 
bottom stainless steel drip trays and they should be removed and 
emptied daily. 
Note: The set pressure is  recommended not to be set beyond 5 PSI as this is all that 
is required to tension the belt ful ly .  
• A l l  painted surfaces should be cleaned with a mi ld detergent and wiped 
dry daily. 
• All  stainless steel beds or drip trays should be washed daily as your 
normal practice regularly. 
• The product transfer belt (type I -GM-087) should be washed with a 
mi ld detergent raised and wiped daily. 
• Roller No. 1 and the main drive rol ler should be kept clean weekly. 
• Rollers #3 & #4 have been fitted with multiple loaded spring steel ,  
individual ly adj ustable roller scrapers, should be checked for tension 
against the rol ler every 3-4 months and reset if required. 
SOLLICH 
HEAT EXCHANGER 
Preventive Maintenance 
8. CLEANING: 
• Clean heat exchanger every 6 months. 
1 8 5 
CHECK 
1 .  In case of deposit within the tank, c lean with current solvents 
2 .  For cleaning within the pipes, use brush for pipe cleaning. 
3 .  U se new gaskets after cleaning 
.. Chocolate infeed temperature = 45°C 
.. Chocol ate output temperature = 28 .SoC 
.. Cool ing water infeed temperature = 1 2°C 
.. Cooling water output temperature = 1 8°C 
SOLLICH TUNNEL /COMPRESSOR 
9. CLEANING: 
.. Rotary knife edge at the inlet section must be cleaned daily to ensure 
trouble free tracking. 
.. Inspect evaporator section every 6 months to ensure rollers are 
rotating correctly and have no excessive powdered chocolate build up. 
.. The Chocolate crumb collecting trays have to be c leaned daily 
• The supporting armatures of the conveyor belt have to be cleaned 
from c hocolate weekly. 
• C lean the condensed water drain valve of the evaporator  weekly. 
10. LUBRICATION: 
• Check oi l  level in the compressor crank casing weekly. 
• Change oi l  after 2-3 years to prolong the l i fe of compressor. 
• Lubricate all hood seals with food grade approved s i l icone spray every 
3 months to ensure the seals sl ide together and prolong the l ife of the 
seals .  
Note: The bottom faces between the bed and the hoods have sentoprene R seals but 
require no lubrication 
1 1 . REFRIGERATION MAINTENANCE: 
• Check the efficiencies of COMPRESSORS and CONDENSER as 
per the Refrigeration Maintenance Check Lists every 2 - 3 months. 
1 86 
(see PTL manual for the check l ist, check items that apply to this 
machine) 
1 2. GEARBOX 
• Motor gearbox is an S .E .W.  type: R73 DT90 N4 0.7SKW at 1 8  rpm . 
• All  SEW gear units require minimum mai ntenance, but check oil  levels 
daily. 
• Check chain tension every 3 months 
SOLLICH TEMPERER 
• Examine water circulation systems for leaks daily 
• C lean filter in the cooling water feed pipe and filter elements in the 
pressure reducing valve weekly 
• Check transmission o i l  annually 
• C lean the cool ing water system annually 
Note: C lean surface with a dry cloth or wash in l ight soap water or water soluble 
detergent. 
• Clean the 4 water filters III the temperer weekly to ensure ful l  
penetration. 
• C lean solenoid valves of impurities from the water pipes weekly, such 
as scales of rust. 
• Retighten every 6 months the bolts between top and bottom covers. 
1 3. Temperer's Gear - Worm Gear 
• Change oi l  every 1 2- 1 8  months 
1 4. Vibration Analysis 
It i s  recommended to do vibration analysis of the machine every six months to check: 
• Alignment 
• Oil analysis (send about 0.5 l itre sample to suppl ier oi l  analyst if  it is 
alright for use) 
• Bearings outer & inner races, cage and bal ls  
1 87 
• Looseness 
• Parameters from the interoperabi l ity of machine components 
The vibration report wil l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive 
PTL ENROBER 1050 CHOCOLATE 
Serial #2739 
Preventive Maintenance 
1 5. CLEANING:  
• C lean and service CHOCOLATE PUMPS every 12  - 24 months. 
• C lean FILTERS weekly. 
• Clean ENROBER BELT CARRIAGE weekly, use long thin nozzle. 
NOTE: Never steam clean the in-feed conveyor, this may damage the electrics. 
• Clean DET AILER and INFEED plate by scrappmg off as much 
chocolate as possible daily. 
NOTE: Never steam c lean or water on any of these i tems, it may damage the 
trace heating. 
16. LUBRICATION: 
• Lubricate the ENROBING CARRIAGE CHAINS monthly. 
• Apply spray lubricant (Reno Id Chain Lubricant Recommended) on 
MAIN DRIVE CHAIN, which drives the carriage drive coupling and 
stirrer weekly. 
• Change oil  for OIL - LUBRICATED GEAR annually. 
1 .  Rossi MRV32-63B:  Enrober belt shaker gerabox 
2 .  Rossi MRCI 64 U03A 090: Enrober pump drive gearbox 
3 .  GPP 1 2525 gearbox : Enrober decorator DC drive gearbox 
Note: Lubricate bearings for every change of oil  for lubricated gear. 
1 88 
LUBRICA TE BEARINGS. GREASE NIBBLES 
• Lubricate/grease BEARING nibbles monthly. 
BEARINGS DETAILS 
Bearing Location Bearing Type 
Enrober wire belt drive housing rol ler SKF - 6005 LLU : 2 off 
bearings 
Enrober stirrer housing bearing SKF - 6 1 905 LLU : 2 off 
Enrober shaker shaft bearing unit SKF - Y AR207 - 2RF:  2 off 
Enrober wire belt drive bearing unit SKF - Y AR206 - 2RF:  1 off 
Enrober decorator l inear bearings LGW20CC : 2 off 
1 7. CHAIN TENSIONING: 
• Check ENROBING CARRIAGE CHAINS tensioning every 3 
months. 
• Check MAIN DRIVE CHAIN every 3 months. 
18. WIRE BELT TENSIONING: 
• Check IN FEED BELT every 3 months 
• Check ENROBER CARRIAGE BELT every 3 months 
• Check WIRE BELT TENSION every 3 months. Always replace the 
exact number of broken wire strips, adjust tension if replacement is 
less or more than the number of broken strips. 
NOTE: 
• Do not over-tighten; adjust equal ly either side to avoid damage to the 
wire belt. Manufacturer recommends an engineer to adjust tension. 
• The replaced wire strip must maintain the same shape after replacement. 
If twisted, it may break again. Engineers are recommended to carry out 
the replacement. 
19.  AIR FILTER REPLACEMENT:  
• Replace AIR FILTER every 1 2  months depending on  the quality of air. 
1 89 
20. GEAR MOTOR 
• Overhaul the GEAR MOTOR after 3-5 years. 
Gearbox & Motor Frame Numbers 
Description Type Qty 
Enrober belt shaker Rossi MRV32-63B 1 0: 1  1 
gearbox ratio 0 . 1 8kW 3PH motor 
Enrober Wire belt drive Rossi M RIVSO-7 1B  1 
motor 2. S4X2S 0.25 KW 3 PH 
motor 
Enrober pump dri ve Rossi M RCI 64 U03A 1 
gearbox D90 l . SkW 3PH motor 
PTL COOLING TUNNEL 
Serial #2739 
Preventive Maintenance 
2 1 .  CLEANING:  
• C lean MACHINE daily from product bui ld-up to ensure correct and 
trouble free operation. 
• C lean ALL ROLLERS weekly to prevent product bui ld-up. Dirty 
rol lers wil l  affect belt tracking and lead to belt damage. 
22. LUBRICATION: 
• Lubricate DRIVE CHAIN with chain spray monthly 
• I nspect DRIVE CHAIN for correct tension and wear every 3 months 
• Change OIL SEPARATOR (OF 303) every 1 2  months 
• Change GEAR grease (double reduction maintenance free type shown 
below) after 3/5 years operation, this wi l l  ensure a longer service l ife. 
1 .  CNHX4 1 3 S DC Cyclo:  Cooling tunnel belt drive gearbox 
2.  Qty of grease = 50% of space volume = 6Sg of grease. 
The grease recommended is AL V ANIA GREASE RA, 1 0  -50°C ambient temperature 
1 90 
Inspect the NOISE and VIBRATION of gear daily to ensure proper and continued 
optimum operation. 
LUBRICA TE BEARINGS. GREASE NIBBLES 
• Lubricate/grease BEARING nibbles monthly. 
BEARINGS DETAILS 
Bearing Location Bearing Type 
Cool ing tunnel drive shaft bearings SKF - FYTB 50 - TF: 2 off 
Cooling tunnel take up bearings S KF - YAR207 - 2RF:  2 off 
Cooling tunnel belt rol ler bearings SKF - 6307 - 2 RS 1 :  22 off 
Cooling tunnel tracking bearings S KF - 6005 - 2RS 1 :  4 off 
23. AIR LEAKAGE:  
• Check the COOLING SYSTEM for air leakages daily. 
24. REFRIGERATION MAINTENANCE:  
• Check the efficiencies of RECIPROCATING COMPRESSORS and 
CONDENSER as per the Refrigeration Maintenance Check Lists 
every 2 - 3 months. 
25. GEARBOX 
• It is pre-packed with grease and sealed and requires NO regular check 
26. FILTER REPLACEMENT 
• Replace SUCTION FILTER (Sporlan RCW 48) every 1 2  months 
27. Vibration Analysis 
I t  i s  recommended to do v ibration analysis of the machine every six months to check:  
• Alignment 
• Oil analysis (send about 0 .5  l itre sample to supplier oi l analyst if  it i s  
alright for use) 
• Bearings outer & inner races, cage and bal ls 
• Looseness 
1 9 1  
• Parameters from the interoperabi lity of machine components 
The vibration report wil l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive types. 
A: MULTI CO-EXTRUDER: UX 1 1 0 
Preventive Maintenance 
1. CLEANING: 
• Strip machine, clean and grease weekly or after a complete 
production cycle. 
2.  Lubrication :  
• Grease u p  a l l  the gears, grease nipple, chain and sprockets at the 
extruder section every month. 
• Grease up the grease nipple at the flow control ler section every month. 
Note: 
Grease Brand & Grade: Mobilux 2 (mobil), Ristan 2 (EXXON) or equivalent 
3. Checks : 
• Check chain tension every 3 months  
• Check gear teeth for wears/cracks every 6 months 
B :  HIGH SPEED ENCRUSTER: EN  3 10  
4 .  Lubrication : 
Drive Section Side View : OIL LUBRICATION 
Lubrication Frequency 
Lubricate speed reducer every 3 months 
gearbox with oi l  
Lubricate bevel gearbox with every 3 months 
oil 
Lubricate the paral lel index every 3 months 
with oil  
1 92 
Oil Grade 
Gear 632 
DTE- I OO 
OMALA 7 1  
Oil Brand 
Mobil 
Mobil 
Shell 
• C lean and change oi l  every 6 months 
Drive Section Top & Encrusting Section Side Views:  GREASE LUBRICA TION 
Lubrication Frequency Grease Grade Grease Brand 
Grease up the gears, rod ends, Monthly Mobilux 2 Ristan 2 
sprocket and chains (mobi l)  (Exxon) 
Grease up s l ide shafts, drive gears, Monthly Mobi lux 2 Ristan 2 
cam fol lower and l inear bearing (mobi l )  (Exxon) 
5. CHECKS: 
• Check weekly if the clearance between encrusting pieces and housing 
are the same. 
• Check chain tension every 3 months 
• Check gear teeth for wears/crack every 6 months. 
C: STAR WHEEL ENCRUSTER: ON 1 1 3 
& 
PRESS ROLLER: MR  2 1 0  
6 .  LUBRICATION: 
Top View 
• Grease up all gears monthly 
Front View 
• Grease up screw j ack monthly 
7. CHECKS: 
• Check wears/crack on gear teeth every 6 months 
D :  LATTICI ROLLER: OR  295 
Side View 
• Grease up pi l low b lock and worm wheel monthly 
• Check rol ler c learance regularly 
Note: Make sure that the c learance of rol lers in horizontal adjustment is the same on 
both sides (equidistant). 
1 93 
E:  UNDERNEATH CONVEYOR: 2C 3 1 6  
8. LUBRICATION: 
TOP VIEW - (Conveyor under multi co-extruder) 
• Grease up the gears, sprocket & chain monthly 
TOP VIEW - ( Row multiply unit) 
• Grease up the gears, worm and worm wheel ,  sprocket, chain, l inear 
bearings, rod-end bearing and cam monthly. 
9. CHECKS: 
• Check belt tension monthly and adj ust i f  necessary 
• Check gear teeth for wear/crack every 6 months. 
F: GUILLOTINE CUTTER: OK 774 
SIDE VIEW 
10.  LUBRICATION: 
• Grease up clevis pins, rod end, j oint pins and l inear bearings monthly 
1 1 . CHECKS & CLEANING: 
(Air Case Section) 
• Clean dirt on air fi lter & auto-drain function weekly 
Note: Clean with neutral detergent or replace if necessary 
• Check abnormal change in air pressure daily. Normal setting is 4kg/cm2 
(Solenoid Valve) 
• Check solenoid valve monthly, for unusual noise, change the valve. 
1 94 
(Air Cylinder & Cutter Section) 
• Check monthly for wear on c levis pin, bushing, knuckle j oint pin, bearing, 
pin, l inear bearing, cutter, air cyl inder and air joints. Change any worn part 
as soon as possible.  
G: EGG GRAZER 
12.  LUBRICATION: 
(SIDE VIEW) 
• Grease up the chain & sprocket monthly 
13. CHECKS: 
• Check chain tension monthly 
• Check rol ler clearance monthly .  Clearance between rol lers 1 & 2 and 
rol lers 2 & 3 should be O.2mm 
H :  CONVEYOR WITH BELT CLEANER:  1 C 358 
14. LUBRICATION: 
• Grease up the sprockets, chain & grease nipple monthly.  
1 5. Checks: 
Note: 
• Check the chain & belt tension monthly 
• Conveyor belt tension should be adj usted with tensioner bolts at both sides 
• Adj ust the dri ve tension with the tension sprocket 
1 95 
VIBRATION ANALYSIS 
It i s  recommended to do vibration analysis of the machine every six months to check: 
.. Alignment 
.. Balancing (rotor/coupling sleeves) 
.. Oi l  analysis (send about 0 .5  l itre sample to supplier/ oil  analyst if it is 
alright for use) 
- Bearings outer & inner races, cage and bal ls  
.. Looseness 
- Parameters from the interoperabil ity of machine components 
The vibration report wi l l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive types. 
OVENS 
Preventive Maintenance 
6. Cleaning: 
.. Clean big rol lers annually. 
.. C lean smal l rol lers every 3 months. 
.. Clean big rol lers "cleaning blades" monthly. 
7. Checks :  
NOTE: 
.. Check rol lers smoothness, repair as required to remove rust or product 
build up every 6 months. 
Uneven rol lers (for example, due to product build-up or rust or wear) may cause 
bearing fai lure. 
.. Check gear teeth for wears/cracks every 6 months 
.. Inspect machine daily for loose nuts and bolts resulting from machine 
vibration and tighten as required. 
.. Check driving chain and belts tension weekly and adj ust as necessary. 
1 96 
8. Lubrication : 
• Lubricate al l  bearings monthly. Grease up from the bearing nipples. 
OVEN FANS 
9. Lubrication : 
• Lubricate all bearings every monthly. Grease up from the bearing 
nipples. 
10.  Checks :  
• Check driving belt tension weekly, adj ust or change belt as required. 
• Check pul ley grooves for wear and repair as required every 6 months. 
• Check pul leys alignment weekly and adj ust as required 
VIBRATION ANALYSIS 
It  is recommended to do v ibration analysis of the machine every six months to check: 
• A ligrunent 
• Balancing (rotor/coupl ing sleeves) 
• Oil analysis (send about 0.5 litre sample to suppl ier oil  analyst if  it is 
alright for use) 
• Bearings outer & inner races, cage and bal l s  
• Looseness 
• Parameters from the interoperabi l ity of machine components 
The vibration report wil l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive types. 
RAW MATERIAL HANDLING & MIXING EQUIPMENT - Item 1. 00 
Preventive Maintenance 
1 1 .  Cleaning: 
• C lean sifting machine weekly : Dismantle and c lean 
12. Bearing: 
• Grease up through nipples monthly 
1 97 
• The bearings are sealed-type but further application of grease ejects the 
old grease and replenishes the bearing whi lst sti l l  maintaining a seal 
13. Couplings - Spider Type Coupling 
• Check every 6 months to ensure the spider is not unduly worn 
• Any undue wear wil l  be caused through misalignment of the motor and 
sifter shafts and should be carefully  checked. 
Note: Adjustments can be made by loosening off the inlet end bearing and re­
tightening correctly. 
14. Motor Bearings: 
• These are to be c leaned out and suppl ied with fresh grease every 3 
years 
15.  Sprocket Chains:  
• Clean and lubricate every 3 months 
Note: It is  recommended to mount a new chain wheel when replacing the chain, as a 
new chain running in a partly worn chain wheel wi l l  have a considerable shorter l ife. 
HYDRAULIC SYSTEM/EXTRUDER: ITEM 2.00 
• The fi lter placed on the delivery of the pump must be checked weekly 
• Drain hydraul ic oil  every 6 months and CatTY out a complete cleaning to get 
rid of any impurities accumulated at the bottom of the tank 
Note: Drain the lubrication reservoir or thoroughly fi lter oi l  reservoir every 3 months 
• C lean the worm-sleeve unit (extruder) at the end o f  one production circle or 
weekly .  
• Check worm -sleeve for wear weekly 
• Check lubrication level daily 
• Check al l  pipes for leakages daily 
• Check oi l  level daily 
• Check oi l  for contamination monthly 
• Change oi l  every 3-6 months 
1 98 
D.e. MACHINE 
• Clean external part of machine daily 
• Check tightness of connections daily 
• Main Gearbox/other Gears 
1 .  Check gears teeth every 6 months for wear or crack 
2. Rotate them at intervals to be sure they are covered in oi l  weekly 
3 .  Check temperature of main gearbox daily 
• Brushes: 
1 .  Check brushes of cooling fan motor for wear weekly. 
Note: Brushes should be set so that they are j ust clear of the screen. They must NOT 
be allowed to touch the screen. Use brushes up to 2/3 of their initial length. 
• LUBRICATION: 
• Life lubricated machine :  LSC 80, LSC 90, LSC 1 1 2, LSC 1 32 & LSC 
1 60 
• Bearings have been l ubricated by manufacturer; no l ubrication should be 
carried out. 
• Check oi l  seals weekly, replace if necessary 
• The bal l bearings of the driving drum are equipped with grease nipple 
through which the bal l  bearings should be lubricated at monthly. 
• The bal l bearings of the tension drum is lubricated through grease nipple 
in the l ink brackets monthly.  
• C heck driving chains every 3 months for tension and lubrication 
• Lubricate al l  sprocket chains every 3 months 
• All  movable l inks should be lubricated annually 
• Lubricate the guide way every 6 months 
Note: For the l ubrication of the driving chains, a thin non-corrosive, pure mineral oil 
wi l l  be preferable. 
1 99 
CONVEYOR BEFORE COOLING TUNNEL 
• Check rollers for wear every 3 months 
• Check chain belt tension every 3 months 
• Check sprocket chains every 3 months and lubricate, adj ust tension or 
change chain if necessary. 
COOLING TUNNEL 
• Check the efficiencies of RECIPROCATING COMPRESSORS and 
CONDENSER as per the Refrigeration Maintenance Check Lists 
every 2 - 3 months (see PTL manual for the check l i st, check items that 
apply to this machine) . 
• C lean al l  the venti lation apertures and vent holes weekly 
VIBRATION ANALYSIS 
This machine is designed to be vibration less; any vibration located must be 
eliminated. 
It is recommended to do vibration analysis of the machine every six months to check: 
• Alignment 
• Balancing (rotor/coupling sleeves) 
• Oil  analysis (send about 0.5 l itre sample to suppl ier oi l  analyst if it is 
alright for use) 
• Bearings outer & inner races, cage and bal ls  
• Looseness 
• Parameters from the interoperabil ity of machine components 
The vibration report wil l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive types. 
NOTE: The cleaning instructions outl ined in the "Litebread Extruder Area 
Cleaning - Daily" sheet (Ref: C LN/09/02) must be adhered 
OVERHEAD WIRECUT 
Preventive Maintenance 
200 
16.  Cleaning: 
SAFETY: 
.. The extruder should be cleaned at the end of each day 's  production. 
.. The die should be removed for cleaning daily. 
.. C lean the feed rol ls  daily : 
1 .  Use compressed air stream into the grooves of the feed rol ls  to 
remove product 
2 .  Clean the rol ls, dies and fi l ler block with hot water or steam. DO 
NOT SPRAY  WATER DIRECTLY ONTO THE FEED ROLL 
BEARINGS. 
3 .  After cleaning with water, blow dry with air. 
1 .  DANGER: The use of water, especially when sprayed from hand held hoses, 
increases the risk of an electrical shock which could cause severe inj ury or 
even loss of l ife .  Turn off electrical power source and lock-out before using 
water around the motors of electrical panels and controls .  
2 .  WARNING: Under no circumstances should any cleaning procedure be 
performed while the machine is running. A momentary distraction could result 
. . . .  
111 a senous lI1J ury. 
3 .  CAUTION: Always wear safety glasses to protect your eyes when uSll1g 
compressed air. 
1 7. Checks: 
• Inspect drive chain tension and adj ust as required daily .  
• Check gear teeth for wears/cracks every 6 months 
• Inspect machine daily for loose nuts and bolts resulting from machine 
vibration and tighten as required. 
• Check hydraul ic pipes daily for any leakage and repair as required 
• Check pneumatic pipe l ines daily for any leakage and repair or replace 
as required. 
20 1 
1 8. Lubrication:  
• Lubricate wire drop slides with food machinery lubricant weekly. 
• Lubricate drive chain and sprockets with Chevron SAE 30W oil 
(asphalt base) or equivalent lubricant weekly.  
• Lubricate the drive gears with food machinery lubricant every 2 
weeks. 
• Lubricate grease fittings in shaft ends and In frame with food 
machinery lubricant monthly 
• Lubricate swing arm shaft pivot and eccentric housing with food 
machinery lubricant monthly .  
• Lubricate al l threaded screw adj ustments with Chevron SAE 30W oil 
or equivalent monthly. 
• Lubricate all bearings with grease fittings with food machinery 
lubricant every 3 months. 
VIBRATION ANALYSIS 
It  is recommended to do vibration analysis of the machine every six months to check: 
.. Al ignment 
.. Balancing (rotor/coupling sleeves) 
.. Oi l  analysis (send about 0.5 l i tre sample to supplier o i l  analyst if it is 
alright for use) 
_ Bearings outer & inner races, cage and bal ls  
.. Looseness 
.. Parameters from the interoperabi l ity of machine components 
The vibration report wi l l  be used to optimise the settings of the machine parameters 
and move the maintenance strategy forward to both predictive and proactive types. 
202